lipid thermodynamics: new perspectives on phase …

i

GUILHERME JOSÉ MAXIMO

LIPID THERMODYNAMICS: NEW PERSPECTIVES ON PHASE STUDIES FOR

APPLICATIONS IN ENGINEERING

TERMODINÂMICA DE LIPÍDIOS: NOVAS PERSPECTIVAS EM ESTUDOS DE

FASES PARA APLICAÇÕES EM ENGENHARIA

CAMPINAS

2014

iii

UNIVERSIDADE ESTADUAL DE CAMPINAS

Faculdade de Engenharia de Alimentos

GUILHERME JOSÉ MAXIMO

LIPID THERMODYNAMICS: NEW PERSPECTIVES ON PHASE STUDIES FOR

APPLICATIONS IN ENGINEERING

TERMODINÂMICA DE LIPÍDIOS: NOVAS PERSPECTIVAS EM ESTUDOS DE

FASES PARA APLICAÇÕES EM ENGENHARIA

Thesis presented to the Faculty of Food

Engineering of the University of Campinas in

partial fulfillment of the requirements for the

degree of Doctor in Food Engineering.

Tese apresentada à Faculdade de Engenharia

de Alimentos da Universidade Estadual de

Campinas como parte dos requisitos exigidos

para a obtenção do título de Doutor em

Engenharia de Alimentos.

Supervisor/Orientador: ANTONIO JOSÉ DE ALMEIDA MEIRELLES

Co-supervisor/Co-orientador: MARIANA CONCEIÇÃO DA COSTA

Co-supervisor/Co-orientador: JOÃO ARAÚJO PEREIRA COUTINHO

ESTE EXEMPLAR CORRESPONDE À VERSÃO

FINAL DA TESE DEFENDIDA PELO ALUNO

GUILHERME JOSÉ MAXIMO E ORIENTADA

PELO PROF. DR. ANTONIO JOSÉ DE ALMEIDA

MEIRELLES

____________________________________________

CAMPINAS

2014

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v

EXAMINATION COMITTEE / BANCA EXAMINADORA

________________________________________

Prof. Dr. Antonio José de Almeida Meirelles

Supervisor / Orientador

University of Campinas, Brazil

________________________________________

Prof. Dr. Jean-Luc Daridon

Titular member / Membro Titular

University of Pau and the Adour region, France

________________________________________

Prof. Dr. Simão Pedro de Almeida Pinho


University Salvador, Brazil

________________________________________

Prof. Dr. Jérôme Pauly


University of Pau and the Adour region, France

________________________________________

Prof. Dr. José Vicente Hallak Dangelo

Titular member / Membro titular


________________________________________

Prof. Dr. Rosiane Lopes da Cunha

Substitute member / Membro suplente


________________________________________

Prof. Dr. Martin Aznar



________________________________________

Prof. Dr. Jorge Andrey Wilhelms Gut


University of São Paulo, Brazil

vii

ABSTRACT

The phase transition phenomena of lipidic systems have long since been evaluated by

several works in literature for developing chocolate, butters, dressings, spreads, cosmetic

creams, medicines or biofuels as well as for optimizing processes such as extraction,

refining, fractionation, crystallization or energy production. The aim of such works has

been to answer how the products’ composition can affect their physicochemical

characteristics especially that related to the melting processes. In fact, changes in

temperature highly impact the crystalline structure of fatty systems’ solid phase and,

consequently, in the sensorial and rheological properties of the products. These changes led

to so many thermodynamic behaviors that the determination of the solid-liquid equilibrium

of these systems can configure a particular challenge. However, the greater the complexity

of the system the lower the understanding of its behavior. In other words, despite the

number of works in literature involved in the investigation of the melting phenomena of

lipidic systems, there is still a lack of experimental data and modeling approaches for their

understanding. In this context, this work was conducted with two main goals. The first was

focused on the measurement and comprehension of the solid-liquid equilibrium phase

diagrams of lipidic binary systems of industrial interest. The second was aimed at the

development of theoretical alternatives to improve the phase diagram description based on

classical thermodynamic approaches. Thus, eleven binary systems composed by

triacylglycerols, fatty alcohols and fatty acids were evaluated. Such mixtures are potential

structuring, organogelating and energy storing agents for food, pharmaceutical and

materials industry. The solid-liquid phase diagrams of these mixtures presented distinct

behaviors depending on the formation of immiscible or miscible solid phases and the non-

viii

ideality of the system. Also, four systems built through a Brønsted acid-base reaction

between fatty acids and ethanolamines were also evaluated. In this case, the formation of

protic ionic liquid crystals with high self-assembling ability and marked non-Newtonian

behavior are promising for pharmaceutical and chemical applications. The problem

imposed by the partial miscibility of the solid phase in the construction of the phase

diagrams was overtaken by the implementation of an algorithm based on the resolution of a

non-linear equations system built by the solid-liquid equilibrium fundamental equations.

The “Crystal-T” algorithm was aimed at the determination of the temperature at which the

first and last crystal melts during the heating process. For this, the non-ideality of both

liquid and solid phases was evaluated using excess Gibbs energy equations, including the

group-contribution UNIFAC model, for the calculation of the activity coefficients. Taking

into account the growing increase of the world production and consumption of fat and oils,

this work, from industrial and academic emerging demands, contributed to overtake some

barriers on the understanding of the solid-liquid phase equilibrium of lipidic mixtures for

products and process engineering.

KEYWORDS: Solid-liquid equilibrium, Algorithm, Solid solution, Ionic liquids, Liquid

crystal.

ix

RESUMO

Para o desenvolvimento de chocolates, manteigas, molhos para salada, cremes cosméticos,

medicamentos ou biocombustíveis, assim como na otimização de processos de extração,

refino, fracionamento, cristalização e produção de energia, os fenômenos de transição de

fases dos sistemas lipídicos são temas, há muito tempo, de diversos trabalhos na literatura.

O objetivo desses trabalhos tem sido avaliar como a composição dos produtos altera as suas

propriedades físico-químicas e em especial aquelas relacionadas aos processos de fusão. De

fato, alterações na temperatura exercem um grande impacto na estrutura cristalina da fase

sólida dos sistemas graxos e, consequentemente, nas propriedades sensoriais e reológicas

dos produtos. Essas alterações produzem comportamentos termodinâmicos tão variados que

a determinação do equilíbrio de fases sólido-líquido desses sistemas representa um grande

desafio. Não obstante, quanto maior a complexidade do sistema, menor é a compreensão do

seu comportamento. Ou seja, apesar do grande número de trabalhos presentes na literatura

envolvidos na investigação dos fenômenos de fusão de sistemas lipídicos, novos dados

experimentais e abordagens teóricas para a modelagem dos diagramas são necessários para

sua compreensão. Neste contexto, este trabalho teve dois objetivos principais. O primeiro

relacionado à determinação e análise de diagramas de fases sólido-líquido de sistemas

lipídicos binários de interesse para a indústria. O segundo foi desenvolver alternativas

teóricas para aprimorar a representação dos diagramas de fases baseado em abordagens

termodinâmicas clássicas. Portanto, onze sistemas binários compostos por triacilgliceróis,

ácidos graxos e álcoois graxos foram avaliados. Esses sistemas são potenciais agentes de

estruturação, formação de organogéis, produção e armazenamento de energia na indústria

de alimentos, farmacêutica e de materiais. Os diagramas de equilíbrio sólido-líquido dessas

x

misturas apresentaram comportamentos distintos, dependentes da formação de fases sólidas

miscíveis ou imiscíveis e da não-idealidade do sistema. Além disso, foram estudados quatro

sistemas formados a partir da reação ácido-base de Brønsted entre ácidos graxos e

etanolaminas. Neste caso, a formação de líquidos iônicos próticos cristalinos com grande

habilidade para auto-organização e comportamento não-Newtoniano singular podem atuar

como auxiliares em diversas aplicações químicas e farmacêuticas. O problema imposto pela

miscibilidade da fase sólida na construção dos diagramas de fases foi superado pela

implementação de um algoritmo para a resolução de um sistema de equações não-lineares

baseado nas equações fundamentais do equilíbrio sólido-líquido. O objetivo do algoritmo

“Crystal-T” foi determinar a temperatura em que o primeiro e o último cristal se fundem

durante o aquecimento do sistema. Para isso, a não-idealidade de ambas as fases líquida e

sólida foi avaliada utilizando equações baseadas na energia de Gibbs em excesso, incluindo

o método de contribuição de grupos UNIFAC, para o cálculo dos coeficientes de atividade.

Considerando o aumento da produção mundial e do consumo de óleos e gorduras, este

trabalho, a partir de demandas emergentes da indústria e da pesquisa científica, contribuiu

na superação de alguns obstáculos relacionados à compreensão do equilíbrio de fases

sólido-líquido de sistemas lipídicos para a engenharia de produtos e processos.

PALAVRAS-CHAVE: Equilíbrio sólido-líquido, Algoritmo, Solução sólida, Líquidos

iônicos, Cristal líquido.

xi

SUMMARY

INTRODUCTION 1

OBJECTIVES 3

INTRODUÇÃO 7

OBJETIVOS 9

Chapter 1. TRENDS AND DEMANDS IN SOLID-LIQUID EQUILIBRIUM OF

LIPIDIC MIXTURES

13

1. Introduction 14

2. What do fat and oils provide? 16

3. The solid-liquid equilibrium of fatty systems 18

3.1. Evolution 19

4. Brief overview on the techniques for measuring SLE data 26

5. But, in fact, what is literature looking for? 28

6. Demands on modeling 30

7. Remarks 35

Chapter 2. SOLID-LIQUID EQUILIBRIUM OF TRIOLEIN WITH FATTY

ALCOHOLS

43

1. INTRODUCTION 44

1.1. Thermodynamic framework 46

2. MATERIALS AND METHODS 49

2.1. Differential Scanning Calorimetry (DSC) 50

2.2. Optical Microscopy 51

2.3. Modeling Procedure 51

3. RESULTS AND DISCUSSION 53

3.1. Performance of the Algorithm 53

3.2. Experimental and Predicted Solid-Liquid Equilibrium Data 53

4. CONCLUSIONS 64

Chapter 3. ON THE SOLID-LIQUID EQUILIBRIUM OF BINARY MIXTURES OF

FATTY ALCOHOLS AND FATTY ACIDS

69

1. INTRODUCTION 71

2. MATERIALS AND METHODS 72

2.1. Materials 72

2.2. Apparatus and procedure 73

2.2.1. Differential scanning calorimetry 73

2.2.2. Optical microscopy 75

2.2.3. X-ray diffraction 76

2.3. Thermodynamic modeling 76

xii


3.1. Experimental SLE data 79

3.2. Eutectic point and immiscibility assumption 86

3.3. Evaluation of the solid-phase 89

3.4. Thermodynamic modeling of SLE data 91

4. CONCLUSIONS 97

SUPPLEMENTARY DATA 101

Chapter 4. LIPIDIC PROTIC IONIC LIQUID CRYSTALS 105

1. INTRODUCTION 107

2. EXPERIMENTAL 109

2.1. Materials 109

2.2. Differential Scanning Calorimetry (DSC) 110

2.3. Light-Polarized Optical Microscopy (POM) 111

2.4. Density, Viscosity and Critical Micellar Concentration (CMC) Measurements 111

2.5. Rheological Measurements. 112


3.1. Phase Behavior 112

3.2. Self-assembling of the PILs 119

3.3. Rheological Characterization of the PILs and Their Binary Mixtures 121

4. CONCLUSIONS 130

SUPPORTING INFORMATION 137

Chapter 5. THE CRYSTAL - T ALGORITHM 143

1. INTRODUCTION 145

2. THEORY 147

2.1. Fundamentals 147

2.2. SLE algorithms 151

2.3. The Crystal-T algorithm 153

2.3.1 Adjustment of the i equations parameters 156

2.3.2. Experimental considerations 159


3.1. Experimental data analysis 161

3.2. SLE modeling using the Crystal-T algorithm 168

4. CONCLUSIONS 177

SUPPORTING INFORMATION 183

CONCLUSIONS 189

CONCLUSÃO 193

xiii

I dedicate this thesis to my family and friends

Dedico esta tese à minha família e aos meus amigos

xv

ACKOWLEDGMENTS / AGRADECIMENTOS

Agradeço ao Prof. Dr. Antonio José de Almeida Meirelles, pela orientação deste

trabalho de tese, resultado de um processo crescente de compreensão do conteúdo e de

amadurecimento acadêmico. À Prof.a Dr.

a Mariana Conceição Costa, da Faculdade de

Ciências Aplicadas/UNICAMP, pela coorientação e apoio durante todo o processo de

desenvolvimento desse trabalho. Ao Prof. Dr. João Araújo Pereira Coutinho, da

Universidade de Aveiro, pela coorientação, durante minha estadia em Portugal, e

significativa contribuição a esse trabalho de tese. À Universidade Estadual de Campinas

(UNICAMP), à Faculdade de Engenharia de Alimentos (FEA) e ao Departamento de

Engenharia de Alimentos (DEA), na qualidade de instituições-sede dessa pesquisa. Ao

CNPq pela concessão da bolsa de doutorado e à CAPES pela concessão da bolsa de

doutorado sanduíche no exterior. À Prof.a Dr.

a Rosiane Lopes da Cunha, ao Prof. Dr. Celso

Costa Lopes e ao Prof. Dr. Eduardo Augusto Caldas Batista do DEA/FEA/UNICAMP, pelo

constante apoio acadêmico. À Prof.a Dr.

a Sandra Augusta Santos do Instituto de

Matemática, Estatística e Computação Científica (IMECC)/UNICAMP, pelas sugestões na

elaboração do algoritmo. A todos os companheiros do laboratório de Extração,

Termodinâmica Aplicada e Equilíbrio (EXTRAE) do DEA/FEA/UNICAMP, pela partilha

diária de conteúdo acadêmico, sugestões e experiências. A todos do laboratório PATh, da

Universidade de Aveiro, Portugal, pela recepção, apoio e companheirismo. Agradeço à

minha família e aos meus amigos por contribuírem com o intangível.

xvii

LIST OF FIGURES

INTRODUCTION

Figure 1. Action fields of the solid-liquid equilibrium studies on the vegetable oils

processing industries.

2

INTRODUÇÃO

Figura 1. Campos de ação dos estudos do equilíbrio sólido-líquido nas indústrias de

processamento de óleos vegetais.

8


LIPIDIC MIXTURES

Figure 1. Most common phase diagrams of binary fatty mixtures with the following

nomenclature: mole fraction of the component a in the liquid (xa) and solid (za) phases,

respectively, liquid phase (l), solid phase with pure component a (Ca) or/and b (C

b), solid

phase comprising both compounds (s), solid phase with new structure formed by

peritectic transition (Cn).

20

Figure 2. Tammann plot of the eutectic reaction: enthalpy of the eutectic reaction as a

function of the concentration of the mixture (full line); mole fraction of the component a

at the eutectic point in the liquid phase xeut (dashed line), and in the solid phases (zeut) rich

in the component a (Ca) or b (C

b); represented in gray, solid solution regions rich in the

component a or b.

23

Figure 3. Sketch of the SLE phase diagram observed in mixtures of fatty acids (as

presented by Costa, et al. 37

) for some fatty acid + fatty acid binary systems. Ca

and

Cb are the solid solutions rich in one of the components of the mixture a or b; Cn is the

solid phase formed by the peritectic reaction; Cha and Ch

b are the solid phases formed

after the metatectic reaction; l is the liquid phase.

25


ALCOHOLS

Figure 1. Deviation (this work) versus deviation from the literature (data from Table 2):

(○) Carareto et al., (2011), (×) Boros (2005), (+) Huang and Chen (2000) and (Δ) Jakob

et al. (1995). Dashed line represents the straight diagonal line and the continuous line is

the curve fitted with the data (y = 1.0123x – 0.017, r2 = 0.9966). Number of observations

= 31.

55

Figure 2. Solid-liquid phase diagram (temperature in Kelvin and mole fraction) and

thermograms for the triolein (1) + 1-hexadecanol (2) system. Symbols for phase

57

xviii

diagrams: (○) experimental melting point, (■) transition near triolein melting point, (×)

solid-solid triolein beta-prime transition and data modeled by (- - -) the three-suffix

Margules equation, (—) the UNIFAC-Dortmund model and (- -) the ideal assumption.

In detail, magnification of the thermograms close to the melting temperature for x1 > 0.7

and close to the triolein alpha polymorphic form temperature transition for x1 = 1.0.

Figure 3. Solid-liquid phase diagram (temperature in Kelvin and mole fraction) and

thermograms for the triolein (1) + 1-octadecanol (2) system. Symbols for phase diagrams:

(○) experimental melting point, (■) transition near triolein melting point, (×) solid-solid

triolein beta-prime transition and data modeled by (- - -) the three-suffix Margules

equation (—), the UNIFAC-Dortmund model and (- -) the ideal assumption. In detail,

magnification of the thermograms close to the melting temperature for x1 > 0.7.

58

Figure 4. Tammann plots of (a) triolein (1) + 1-hexadecanol (2) and (b) triolein (1) + 1-

octadecanol (2). (—) Linear regression for data on (■) transition close to the triolein

melting point, (○) pure triolein transition and (- - -) hypothetical plot with a eutectic

point.

60

Figure 5. Optical micrographs of samples of triolein (1) + 1-octadecanol (2) with

magnifications of 10 ((a) to (f)) and 40 (g) at 298.15 K.

62



Figure 1. Solid-liquid phase diagram and thermograms for the system 1-tetradecanol (1)

+ dodecanoic acid (2): experimental melting temperatures (○); transition of the pure

component (); eutectic transition (■); other transitions (+), and modeled data by three-

suffix Margules equation (); UNIFAC-Dortmund model ( ) and ideal assumption

(—). Thermogram in detail shows transition at x1 = 0.0000.

80

Figure 2. Solid-liquid phase diagram and thermograms for the system 1-hexadecanol (1)

+ tetradecanoic acid (2): experimental melting temperatures (○); transition of the pure



(—). Thermograms in detail show transitions at x1 = (0.0000 and 0.6004).

81

Figure 3. Solid-liquid phase diagram and thermograms for the system 1-octadecanol (1)

+ hexadecanoic acid (2): experimental melting temperatures (○); transition of the pure



82

xix

(—). Thermogram in detail shows transition at x1 = 0.5978.

Figure 4. Effect of the thermal annealing based treatment on thermograms of 1-

hexadecanol (1) + tetradecanoic acid (2) at (A) x1 = 0.8994 and at (B) x1 = 0.3042: I,

heating curve without the thermal treatment and; II, after thermal treatment. The

metastable transition is shown by the black arrow.

85

Figure 5. Tammann plots of the eutectic transition (■) for: (A) 1-tetradecanol +

dodecanoic acid; (B) 1-hexadecanol + tetradecanoic acid and (C) 1-octadecanol +

hexadecanoic acid as well as linear regression (- - -) of the data.

87

Figure 6. Optical micrographs of samples of 1-hexadecanol (1) + tetradecanoic acid (2)

at x1 = 0.3981 and (A) 311.75 K; (B) 313.65 K; (C) 313.75 K; (D) 314.55 K and 1-

octadecanol (1) + hexadecanoic acid (2) at x1 = 0.7993 and (E) 319.15 K; (F) 321.15 K;

(G) 322.25 K; (D) 325.65 K. Some details are shown by white arrows. Magnification of

5.

88

Figure 7. Difractograms at T = 298.15 K for (A) 1-hexadecanol (1) + tetradecanoic acid

(2), from up to down: x1 = (0.0000, 0.0982, 0.1993, 0.3042, 0.5020, 0.6004, 0.7152,

0.7951, 0.8994, 1.0000) mole fraction and for (B) 1-octadecanol (1) + hexadecanoic acid

(2), from up to down: x1 = (0.0000, 0.3010, 0.4999, 0.7010, 0.8990, 0.9508, 1.0000)

mole fraction.

90

Figure 8. (A) Liquid-phase activity coefficients and (B) Mixtures’ excess free Gibbs

energy calculate by three-suffix Margules equation (in detail, magnification for x1 < 0.1)

for 1-hexadecanol (1) + tetradecanoic acid (2): 1L ( ), 2

L () and i

L (○) calculated

from experimental data by SLE equation.

93

Figure 9. Effect of the pure compounds’ standard deviations data in the modeling of the

liquidus line for 1-hexadecanol + tetradecanoic acid: experimental data (○); error bars =

0.30 K (temperature’s experimental uncertainty); ideal assumption with mean values of

the pure compounds’ melting properties () and modeling considering the standard

deviations of the pure compounds’ properties (- - -).

96

SUPPLEMENTARY DATA

Figure S1. Fractional melting curves obtained by DSC. Data were evaluated using the

analysis software from TA Instruments (New Castle).

101

Figure S2. Thermogram and fractional melting curves for 1-hexadecanol. Data were

evaluated using the analysis software from TA Instruments (New Castle).

102

Figure S3. Replicates of the DSC thermograms for 1-octadecanol (1) + hexadecanoic 104

xx

acid (2) x1 = 0.7010. In detail, magnification highlighting a solid-solid transition at T =

292.74 K.

Chapter 4. LIPIDIC PROTIC IONIC LIQUID CRYSTALS

Figure 1. Brønsted acid-base reaction between a carboxylic acid and monoethanolamine

or diethanolamine for the formation of a protic ionic liquid. R represents the alkylic

moiety of the carboxylic acid.

109

Figure 2. Solid-liquid equilibrium phase diagram of the (A) oleic acid +

monoethanolamine, (B) oleic acid + diethanolamine, (C) stearic acid +

monoethanolamine and (D) stearic acid + diethanolamine systems by () differential

scanning calorimetry and () light-polarized optical microscopy presenting solid

monoethanolamine (SMEA), solid diethanolamine (SDEA), solid fatty acid (SFA), solid protic

ionic liquid (SPIL), liquid phase (L), normal hexagonal (HI), lamellar (L), and inverted

hexagonal (HII) mesophases. Lines are guides for the eyes. Solid lines were

experimentally characterized, and dashed lines describe hypothetical phase boundaries

based on the Gibbs phase rule.

117

Figure 3. Light-polarized optical micrographs showing the mesophases textures: (A) oily

texture in the stearic acid + monoethanolamine at xfatty acid = 0.2, T = 343.15 K; (B) oily

streaks in the oleic acid + diethanolamine at xfatty acid = 0.6, T = 293.15 K; (C) maltese

crosses in an isotropic backgroup oleic acid + diethanolamine at xfatty acid = 0.5, T =

357.15 K; (D) oily streaks with inserted maltese crosses oleic acid + diethanolamine at

xfatty acid = 0.4, T = 340.15 K, (E) mosaic texture in the stearic acid + monoethanolamine

at xfatty acid = 0.4, T = 363.15 K; and fan-shaped textures in the (F) oleic acid +

diethanolamine at xfatty acid = 0.3, T = 298.15 K; (G) oleic acid + monoethanolamine at xfatty

acid = 0.7, 293.15 K and (H) oleic acid + diethanolamine at xfatty acid = 0.7, T = 298.15 K.

118

Figure 4. Conductivity ( as a function of concentration of protic ionic liquids (PIL)

aqueous solutions. Solid lines are linear fitting of the data (R2 > 0.98) for critical micellar

concentration determination (CMC).

120

Figure 5. Density data ( / g cm-3

) as a function of temperature (T / K) for the (A) oleic

acid + monoethalonamine and (B) oleic acid + diethanolamine systems at xoleic acid = 0.0

(), 0.1 (), 0.2 (), 0.3 (), 0.4 (), 0.5 (), 0.6 (), 0.7 (), 0.8 (), 0.9 () and 1.0

(). At the bottom of each plot, density data as a function of oleic acid mole fraction at T

= 298.15, 323.15, and 353.15 K. Solid and dashed lines are guide for the eyes. Gray

regions represent the liquid crystal domain.

123

xxi

Figure 6. Experimental excess mole volume data of the () oleic acid +

monoethalonamine and () oleic acid + diethanolamine systems at 298.15 K. Dashed

lines are guides for the eyes. Vertical gray line at x = 0.5 (pure PIL) depicts the “true”

system indicated at the top of the plot.

124

Figure 7. Dynamic viscosity data of (A) oleic acid + monoethanolamine and (B) oleic

acid + diethanolamine at xoleic acid = 0.0 (); 0.1 (); 0.2 (); 0.3 (); 0.4 (); 0.5 ();

0.6 (); 0.7 (); 0.8 (); 0.9 (); 1.0 (). Details at the top right of the plots show

magnifications of the data at low values. At the bottom of each plot are viscosity data

as a function of fatty acid mole fraction at 353.15 K. Vertical gray lines at x = 0.5 (pure

PIL) depict the “true” systems indicated above.

125

Figure 8. Linearization procedure of the dynamic viscosity data using the Arrhenius

like equation 1. (A) Oleic acid + monoethanolanmine and (B) oleic acid + diethanolamine

at xoleic acid = 0.0 (); 0.1 (); 0.2 (); 0.3 (); 0.4 (); 0.5 (); 0.6 (); 0.7 (); 0.8

(); 0.9 (); 1.0 (). At the right of each plot are linear fittings of the data (R2 > 0.99)

at some concentrations. Gray regions represent the liquid crystal domain.

126

Figure 9. Shear stress () versus shear rate ( ) curves of (A) monoethanolammonium

oleate and (B) diethanolammonium oleate at 293.15 (), 298.15 (), 308.15 (), 323.15

(), 328.15 (), 348.15 (), 353.15 (+), and 363.15 () K. Solid lines are fitted curves.

Labels N, ST, V, BP, and HB stand for Newtonian, shear-thinning, Vocadlo, Bingham

plastic, and Herschel-Bulkley models, respectively.

129

SUPPORTING INFORMATION

Figure S1. Tammann plots of the eutectic transitions Heut in the ethanolamine-rich

region (x = 0.0 to 0.5 fatty acid molar fraction) and in the fatty acid-rich region (x = 0.5 to

1.0 fatty acid molar fraction) of the (+) oleic acid + monoethanolamine, () oleic acid +

diethanolamine, () stearic acid + monoethanolamine and () stearic acid +

diethanolamine systems. Solid lines are linear fitting of the data (R2 > 0.95 considering

that y = 0.0 at the pure compounds concentration). Dashed lines are supposed plots close

to pure component concentration. () Diethanolamine and () monoethanolamine

melting enthalpy for analysis purpose.

137

Chapter 5. THE CRYSTAL - T ALGORITHM

Figure 1. Thermodynamic cycle comprising the heating, melting and cooling processes

of the system, from T to Tfus, from a solid to a subcooled liquid state taking into account

148

xxii

the polimorphysm phenomena at Ttr.

Figure 2. Solid-liquid equilibrium phase diagram of a discontinuous binary solid solution

case.

151

Figure 3. Block diagram for the Crystal-T algorithm 156

Figure 4. Nested structure for the SLE modeling using the Crystal-T algorithm 159

Figure 5. Experimental ( by DSC and by microscopy) and modeled (solid lines) phase

diagrams using the 3-suffix Margules equation for the triacylglycerol + fatty alcohols

mixtures. AijS, Bij

S are the parameters for the i

S equation and Aij

L, Bij

L for the i

L equation

(kJmol-1

). A) trilaurin (1) + 1-hexadecanol (2), B) trilaurin (1) + 1-octadecanol (2), C)

trimyristin (1) + 1-hexadecanol (2), D) trimyristin (1) + 1-octadecanol (2), E) tripalmitin (1) +

1-hexadecanol (2), F) tripalmitin (1) + 1-octadecanol (2).

162

Figure 6. Thermograms for the mixture trimyristin (1) + 1-hexadecanol (2).

Magnification of the thermogram for x1 = 0.778 mole fraction, in detail, showing the

eutectic transition.

163

Figure 7. Tammann plot of the enthalpy of the eutectic transition for the trimyristin (1) +

1-hexadecanol (2) mixture. Dashed lines are linear regression.

163

Figure 8. Melting transition at the eutectic temperature (Teut = 319.46 K) for the

trimyristin (1) +1-hexadecanol (2) system at x1 = 0.694 molar fraction. A) 319.15 K, B)

319.65, C) 320.15 K. White arrows highlight details during the melting process.

164

Figure 9. Heating and melting processes of trimyristin (1) + 1-hexadecanol (2) system at

x1 = 0.8937 molar fraction at T = A) 313.15 K, B) 322.15 K, C) 323.35 K, D) 323.55 K,

E) 323.95 K, F) 324.35 K, G) 327.65 K and H) 329.05 K. White arrows highlight details

during the heating process.

166

Figure 10. Micrographies and thermogram of the system tripalmitin (1) + 1-octadecanol

(2) at x1 = 0.697 molar fraction. Pictures are at a temperature before (A. 293.15 K) and

after (B. 320.15 K) the solid-solid transition at 318.75 K. Black arrows in the thermogram

highlight the transitions. Eutectic transition in detail (T = 329.20 K).

168

Figure 11. SLE phase diagram of the tripalmitin (1) + 1-octadecanol (2) mixture using 2-

suffix Margules as iS equation and considering that i

L = 1.0 (simple solid line) (Aij

S =

6.93 kJmol-1

) or using the original UNIFAC model (bold line) (AijS = 6.23 kJmol

-1) and

the UNIFAC-Dortmund model (dashed line) (AijS = 7.63 kJmol

-1) as i

L equation. DSC

() and microscopy () data.

171

Figure 12. Deviations (Equation 14) from experimental data for the system tripalmitin 173

xxiii

+ octadecanol using the 2-suffix Margules equation as iL and i

S models. Aij

S and Aij

L are

the iS and i

L parameters (kJmol

-1), respectively. In detail, phase diagrams using

different parameters sets.

Figure 13. Deviations (Equation 14) from experimental data for the system tripalmitin

+ 1-octadecanol using original UNIFAC as iL model and 3-suffix Margules equation as

iS model with Aij

S and Bij

S as parameters. In detail, phase diagrams using different

parameters sets.

174

Figure 14. Deviations (Equation 14) from experimental data for the system tripalmitin

+ 1-octadecanol using 3-suffix Margules equation as both iL and i

S models. Aij

S and Bij

S

are parameters for iS

and AijL and Bij

L are parameters for i

L. In detail, phase diagrams

using different parameter sets.

176


Figure S1. Tammann plots of the experimental eutectic transition enthalpy eutH () and

linear regression (dashed lines) for the systems A) trilaurin (1) + 1-hexadecanol (2), B)

trilaurin (1) + 1-octadecanol (2), C) trimyristin (1) + 1-hexadecanol (2), D) trimyristin (1)

+ 1-octadecanol (2), E) tripalmitin (1) + 1-hexadecanol (2), F) tripalmitin (1) + 1-

octadecanol (2).

186

xxv

LIST OF TABLES


LIPIDIC MIXTURES

Table 1. Fatty acid mass composition of vegetable oils. 18

Table 2. Solid-liquid phase diagrams of binary mixtures of fatty compounds reported in

literature.

21


ALCOHOLS

Table 1: Deviation data from the literature (lit.) and from the algorithm proposed in this

work

54

Table 2: Experimental solid-liquid equilibrium data for triolein (1) + 1-hexadecanol (2). 57

Table 3: Experimental solid-liquid equilibrium data for triolein (1) + 1-octadecanol (2). 58

Table 4: Estimated parameters (A and B) and mean absolute deviations of the

predicted data from the experimental data (in Kelvin).

60

Table 5: Pure fatty components properties from the literature (lit.) and in this work 63



Table 1. Fatty compounds used in this work, supplier, purification method, molar

fraction purity and method used to confirm the purity.

73

Table 2. Experimental melting temperatures Tfus, solid-solid transitions Ttr and total

melting enthalpies fusH of the pure components obtained in this work and from literature.

75

Table 3. Experimental solid-liquid equilibrium data for 1-tetradecanol (1) + dodecanoic

acid (2) for molar fraction x, temperature T and pressure p = 94.6 kPa.

80

Table 4. Experimental solid-liquid equilibrium data for 1-hexadecanol (1) +

tetradecanoic acid (2) for molar fraction x, temperature T and pressure p = 94.6 kPa.

81

Table 5. Experimental solid-liquid equilibrium data for 1-octadecanol (1) + hexadecanoic

acid (2) for molar fraction x, temperature T and pressure p = 94.6 kPa.

82

Table 6. Estimated parameters, A and B, and mean absolute deviations a between

predicted and experimental data.

92

SUPPLEMMENTARY DATA

Table S1. Solid-liquid and solid-solid transitions temperatures obtained in replicates for 8

binary mixtures.

103

Chapter 4. LIPIDIC PROTIC IONIC LIQUID CRYSTALS

xxvi


Table S1. Experimental solid-liquid equilibrium data for oleic acid + ethanolamine

systems for mole fraction x, temperature T †

and pressure p = 102.0 kPa.

138

Table S2. Experimental solid-liquid equilibrium data for stearic acid + ethanolamine

systems for mole fraction x, temperature T †

and pressure p = 102.0 kPa.

139

Table S3. Density data ( / g cm-3

) of the oleic acid-based binary mixtures. 140

Table S4. Dinamic viscosity ( / mPas) data of the oleic acid-based binary mixtures. 141

Table S5. Rheological models’ parameters related to shear stress / shear rate curves fitted

to flow experimental data for the PILs.

142

Chapter 5. THE CRYSTAL - T ALGORITHM


Table S1. Melting temperatures (Tfus / K) and enthalpies (fusH / kJmol-1

) and solid-solid

temperatures (Ttr / K) and enthalpies (trH / kJmol-1

) of the pure compounds used in the

modeling procedure and obtained in this work or from literature.

184

Table S2. Experimental solid-liquid equilibrium data for the triacylglycerols + fatty

alcohols systems for mole fraction x and temperature T for solidus and liquidus line.

185

xxvii

NOMENCLATURE

SLE solid-liquid equilibrium

xi mole fraction of compound i in the liquid phase

zi mole fraction of compound i in the solid phase

iL activity coefficient of the compound i in the liquid phase

iS activity coefficient of the compound i in the liquid phase

Tfus melting temperature of pure compound

fusH melting enthalpy of pure compound

R ideal gas constant

T melting temperature of the system

fusCp melting heat capacity of pure compound

Ttr temperature of the solid-solid transition of pure compound

trH enthalpy of the solid-solid transition of pure compound

xeut mole fraction of the compound in the liquid phase and at the eutectic point

zeut mole fraction of the compound in the solid phase and at the eutectic point

Teut temperature of the eutectic transition of the system

Heut enthalpy of the eutectic transition of the system

Aij , Bij binary interaction parameters of 2- and 3-suffix Margules equations

Rk, Qk UNIFAC structural parameters for groups

amn UNIFAC group-interaction parameters

UNIFAC UNIQUAC Functional-group Activity Coefficient

Fobj objective function

niL number of moles of compound i in the liquid phase

niS number of moles of compound i in the solid phase

G variation of the Gibbs energy

TAG triacylglycerol

VLE vapor-liquid equilibrium

ARD average relative deviations

RMSD root mean square deviation

xxviii

1

INTRODUCTION

The world production and consumption of vegetable oils overtook 150 millions of

tons in 2012 (F.A.O., 2013) and this reveals the relevance of the fats and oils industry in the

world economy. This scenario has been stimulating the construction of biorefinaries,

especially in emerging economies that attend for more than 70% of this amount, and

indicates the important role that the oilchemistry may play in the future bioeconomy.

Through the biorefinary concept, new demands for fats and oils rise as well as favorable

prospects for the development of processes and products based on derivatives of fatty

components (H. Clark et al., 2009; Octave e Thomas, 2009). In this context, an accurate

understanding of the most relevant thermodynamic mechanisms that rules the

physicochemical, sensorial and rheological phenomena involving such substances and their

mixtures is fundamental. One aspect of such an understanding is achieved by the

knowledge of the phase equilibrium behavior of fatty systems, and in particular their solid-

liquid transitions (Figure 1).

The melting process of lipidic compounds is highly complex when compared with

other phase changes. This complexity is especially due to the inherent ability of the fatty

crystals to self-assembling into stable and metastable structures in their multiple solid

phases. Also, in a mixture, fatty components can also present mutual miscibility or even

total immiscibility in the solid phase. Consequently, apart from the fact that such

phenomena largely affect microstructural changes and, therefore, the set of industrial

quality requirements of products, numerous operational and economical reasons emphasize

the importance of a critical thermodynamic evaluation of the fatty systems for process

design and optimization.

2

Figure 1. Action fields of the solid-liquid equilibrium studies on the vegetable oils processing

industries.

Experimental and modeled solid-liquid equilibrium (SLE) phase diagrams have

been long since evaluated by several authors (Wesdorp, 1990; Coutinho et al., 1995;

Domanska e Gonzalez, 1996; Inoue et al., 2004; Costa et al., 2012). Despite the great

number of experimental data on fatty systems, works in literature very frequently fails in

the complete description of their melting behavior. The reason is that, because the

complexity of the solid phase, the well established thermodynamic theory is usually

simplified, either by the lack of pure compounds experimental properties or by neglecting

3

the presence of other phenomena. Concerning to the optimization of extraction, refining,

crystallization or fractionation processes as well as the development of chocolate, butters,

dressings, spreads, cosmetic creams, medicines or biofuels, the determination of the SLE of

fatty systems as well as the improvement of modeling tools is more than an demand, but an

imperative.

OBJECTIVES

This work is aimed at deepening the understanding of solid-liquid equilibrium of

fatty systems by the evaluation of mixtures of interest in the industry, not yet available in

the literature, as well as improving the approaches for modeling the SLE of fatty systems,

by implementation of an alternative algorithm that includes both liquid and solid phases

non-ideality for the description of the phase diagram. This thesis is divided in five works

whose complexity increases as the comprehension of the systems increases. The specific

objectives, and a short summary of each work are related below:

The first work comprises a review on the current understanding of the SLE

behavior of fatty systems and on the approaches used in literature for their

modeling, taking into account that, despite the amount of available

experimental data, a deepest knowledge on SLE of fatty compounds is still

required.

The second work reports experimental data and the corresponding modeling

results for the solid-liquid equilibrium phase diagrams of binary systems

composed by triolein + 1-hexadecanol and triolein + 1-octadecanol. Triolein is

4

a representative triacylglycerol of a set of vegetable oils and fatty alcohols are

well known surfactant agents. The phase diagrams showed a eutectic profile

with immiscibility in the solid phase and eutectic point very close to pure

triolein. Modeling could accurately describe the non-ideality of the liquidus line

by using adjustable excess Gibbs equations and group contribution UNIFAC

models.

The third work determines the experimental data and reports the corresponding

equilibrium results for systems composed of 1-tetradecanol + dodecanoic acid,

1-hexadecanol + tetradecanoic acid and 1-octadecanol + hexadecanoic acid.

Mixtures of fatty acids and alcohols are structuring agents for the production of

organogels as well as suitable energy storing materials. Such mixtures

presented a small solid solution region and the liquid phase showed a particular

non-ideal profile, varying from positive to negative deviations due to the

particular interactions between acids and alcohols.

The forth work evaluates the SLE behavior of systems composed of fatty acids

and ethanolamines. Through a Brønsted acid-base reaction, such mixtures led to

the formation lipidic protic ionic liquids. The phase diagrams of these systems

depicted a congruent melting behavior. The high self-assembling ability of such

ionic liquids led to the formation of liquid crystals, highly promising for

numerous pharmaceutical applications.

The fifth work presents an algorithm for the calculation of SLE phase diagrams.

The Crystal-T algorithm considers the formation of solid solutions and

5

calculates both liquidus and solidus lines. The procedure was based in the

classical Bubble-T algorithm for calculation of vapor-liquid equilibrium. The

activity coefficients were determined by excess Gibbs energy based equations,

including the UNIFAC model. The effectiveness of the routine was evaluated

by the description of 6 experimentally evaluated discontinuous solid solution

systems of triacylglycerols + fatty alcohols.

7

INTRODUÇÃO

A produção e o consumo mundiais de óleos vegetais ultrapassaram 150 milhões de

toneladas em 2012 (F.A.O., 2013), relevando a importância da indústria de óleos e gorduras

na economia mundial. Este cenário tem estimulado a construção de biorefinarias,

especialmente nas economias emergentes, responsáveis por 70% deste total, e indica o

papel fundamental que a óleo-química pode exercer, em um futuro próximo, na

bioeconomia. O conceito da biorefinaria incentiva o surgimento de novas demandas no

processamento de óleos e gorduras, além de perspectivas favoráveis para o

desenvolvimento de novos processos e produtos baseados em derivados de compostos

graxos (H. Clark et al., 2009; Octave e Thomas, 2009). Neste contexto, uma compreensão

cuidadosa dos mecanismos termodinâmicos mais relevantes que determinam os fenômenos

físico-químicos, sensoriais e reológicos que envolvem essas substâncias, e suas misturas, é

fundamental. Um aspecto de tal compreensão pode ser obtido através do estudo do

equilíbrio de fases, em particular as transições sólido-líquido (Figura 1).

O processo de fusão dos compostos lipídicos é particularmente complexo quando

comparado a outras mudanças de fase. Esta complexidade é devida a inerente habilidade

dos cristais de compostos graxos de se auto-organizarem em estruturas estáveis e meta-

estáveis em suas múltiplas fases sólidas. Além disso, em uma mistura, os compostos graxos

também podem apresentar miscibilidade parcial ou até mesmo imiscibilidade total na fase

sólida. Esses fenômenos produzem importantes mudanças microestruturais nos sistemas,

que influenciam uma série de requisitos de qualidade industriais. Deste modo, inúmeras

razões operacionais e econômicas enfatizam a importância de uma avaliação

8

termodinâmica crítica dos sistemas graxos para a otimização e projeto de processos e

produtos.

Figura 1. Campos de ação dos estudos do equilíbrio sólido-líquido nas indústrias de processamento

de óleos vegetais.

Os diagramas de fases do equilíbrio sólido-líquido (ESL) têm sido avaliados por

diversos autores na literatura (Wesdorp, 1990; Coutinho et al., 1995; Domanska e

Gonzalez, 1996; Inoue et al., 2004; Costa et al., 2012). Porém, apesar do grande número de

dados experimentais de sistemas graxos, os trabalhos na literatura frequentemente falham

na completa descrição do seu comportamento de fusão. Isso porque, devido à complexidade

9

da fase sólida, a teoria termodinâmica do equilíbrio sólido-líquido é comumente

simplificada, seja pela falta de dados experimentais relativos às propriedades dos

compostos puros ou por negligenciar a presença de outros fenômenos. Considerando a

otimização de processos de extração, refino, cristalização ou processos de fracionamento

assim como o desenvolvimento de chocolates, manteigas, molhos para salada, cremes

cosméticos, medicamentos ou biocombustíveis, a determinação do equilíbrio sólido-líquido

de sistemas graxos, assim como o melhoramento de ferramentas para sua modelagem, além

de uma demanda, é um imperativo.

OBJETIVOS

Este trabalho tem o objetivo de aprofundar a compreensão do equilíbrio sólido-

líquido de sistemas graxos pela avaliação de misturas de interesse na indústria, ainda não

avaliados pela literatura, e aprimorar as abordagens para a modelagem do ESL de sistemas

graxos através da implementação de um algoritmo alternativo que inclui a não-idealidade

de ambas as fases sólidas e líquidas para a descrição dos diagramas de fase. Esta tese é

dividida em cinco trabalhos. Os objetivos específicos e um breve resumo dos trabalhos

estão descritos abaixo.

O primeiro trabalho é uma revisão bibliográfica sobre a compreensão atual do

ESL de sistemas lipídicos e as abordagens utilizadas pelos trabalhos na

literatura para a sua modelagem, levando em consideração que, apesar da

quantidade de trabalhos sobre o tema na literatura, um conhecimento mais

profundo sobre o ESL de sistemas graxos é ainda necessário.

10

O segundo trabalho reporta dados experimentais e modelados para o diagrama

do ESL de sistemas binários compostos por trioleína + 1-hexadecanol e

trioleína + 1-octadecanol. A trioleína é um triacilglicerol representativo de uma

classe de óleos vegetais e os alcoóis graxos são agentes surfactantes muito

conhecidos. Os diagramas de fases descreveram um comportamento eutético

com imiscibilidade na fase sólida e ponto eutético muito próximo à

concentração da trioleína pura. A modelagem pôde descrever com precisão a

não-idealidade da linha liquidus através da utilização de equações ajustáveis de

energia de Gibbs em excesso e do modelo de contribuição de grupos UNIFAC.

O terceiro trabalho determina dados experimentais e modelados do ESL de

sistemas compostos por 1-tetradecanol + ácido dodecanóico, 1-hexadecanol +

ácido tetradecanóico e 1-octadecanol + ácido hexadecanóico. Misturas de

ácidos e álcoois graxos são agentes estruturantes para a produção de organogels

e materiais para armazenamento de energia. Tais misturas apresentaram uma

pequena região de solução sólida e fase líquida com um perfil de não idealidade

variando entre desvios positivos e negativos devido às interações ácido/álcool.

O quarto trabalho avalia o ESL de sistemas formados por ácido graxos e

etanolaminas. Através de uma reação ácido-base de Brønsted, essas misturas

levaram à formação de líquidos iônicos próticos. Os diagramas de fases desses

sistemas apresentaram um perfil de fusão congruente. A habilidade de auto-

organização dos líquidos iônicos foi determinante para a formação de cristais

líquidos, promissores em inúmeras aplicações farmacêuticas.

11

O quinto trabalho apresenta um algoritmo para o cálculo do diagrama de fases

do ESL de sistemas graxos. O algoritmo Crystal-T considera a formação de

soluções sólidas e calcula a não-idealidade de ambas as fases líquida e sólida. O

procedimento foi baseado no algoritmo clássico Bubble-T utilizado no cálculo

do equilíbrio líquido-vapor. Os coeficientes de atividade foram determinados

através de equações de energia de Gibbs em excesso, incluindo o modelo

UNIFAC. A efetividade da rotina pôde ser avaliada através do ajuste de 6

sistemas com solução sólida descontínua compostos por triacilgliceróis +

alcoóis graxos, determinados experimentalmente.

12

REFERENCES / REFERÊNCIAS

COSTA, M. C. et al. Phase diagrams of mixtures of ethyl palmitate with fatty acid ethyl esters.

Fuel, v. 91, n. 1, p. 177-181, 2012.

COUTINHO, J. A. P.; ANDERSEN, S. I.; STENBY, E. H. Evaluation of activity coefficient

models in prediction of alkane solid-liquid equilibria. Fluid Phase Equilibria, v. 103, n. 1, p. 23-

39, 1995.

DOMANSKA, U.; GONZALEZ, J. A. Solid-liquid equilibria for systems containing long-chain 1-

alkanols .2. Experimental data for 1-dodecanol, 1-tetradecanol, 1-hexadecanol, 1-octadecanol or 1-

eicosanol plus CCl4 or plus cyclohexane mixtures. Characterization in terms of DISQUAC. Fluid

Phase Equilibria, v. 123, n. 1-2, p. 167-187, 1996.

F.A.O. OECD-FAO Agricultural Outlook 2013 (2013). Available in www.fao.org. Acessed in

09/01/2013.

H. CLARK, J.; E. I. DESWARTE, F.; J. FARMER, T. The integration of green chemistry into

future biorefineries. Biofuels, Bioproducts and Biorefining, v. 3, n. 1, p. 72-90, 2009.

INOUE, T. et al. Solid-liquid phase behavior of binary fatty acid mixtures 2. Mixtures of oleic acid

with lauric acid, myristic acid, and palmitic acid. Chemistry and Physics of Lipids, v. 127, n. 2, p.

161-173, 2004.

OCTAVE, S.; THOMAS, D. Biorefinery: Toward an industrial metabolism. Biochimie, v. 91, n. 6,

p. 659-664, 2009.

WESDORP, L. H. Liquid-multiple solid phase equilibria in fats, theory and experiments. 1990.

Delft University of Technology, Delft.

13

TRENDS AND DEMANDS IN SOLID-LIQUID EQUILIBRIUM OF

LIPIDIC MIXTURES

(submitted to RSC Advances)

Guilherme J. Maximo, a Mariana C. Costa,

b João A. P. Coutinho,

c and Antonio J. A.

Meirelles a

a Food Engineering Department, University of Campinas, R. Monteiro Lobato 80, 13083-

862, Campinas, São Paulo, Brazil. b

School of Applied Sciences, University of Campinas,

R. Pedro Zaccaria, 1300, 13484-350, Limeira, São Paulo, Brazil. c CICECO, Chemistry

Department, University of Aveiro, 3810-193, Aveiro, Portugal.

Chapter 1

14

ABSTRACT

The production of fats and oils presents a remarkable impact in the economy, in particular

in developing countries. Academic research aims at forecast and prepare to attend

forthcoming demands. In this context, the study solid-liquid equilibrium of fats and oils is

highly relevant as it may support the development of new processes and products as well as

improve those already existent. However, the task is daunting because lipidic compounds

present multiple solid phases leading to behaviors that deserve special attention. The high

complexity of these systems requires a particular effort for the experimental study and

theoretical description of their phase behavior. This work is addressed at perspectives to

better understand and overcome some of these issues.

KEYWORDS: Solid-liquid phase diagrams, Modeling, Triacylglycerols, Fatty alcohols,

Fatty acids, Fatty esters.

1. Introduction

The study of the solid-liquid equilibrium (SLE) of lipidic mixtures is a fundamental

tool for the development and optimization of the processing of fatty based products. Fats

and oils are remarkable suppliers of food, materials, chemicals and also energy. In this

context, vegetable oils represented more than 150 milions of tons 1 of produced and

consumed material in 2012. This information reveals the importance that fats and oils

should have in the RD&I policy agenda especially in the context of developing countries,

that attend for more than 70% of this amount. Finding alternatives for adding value to a

15

long list of products and byproducts extracted from crops, fruits or seeds, as proposed in the

biorefinary concept, is a task that is gaining a growing attention. A fats and oils biorefinary

involves all the manufacturing steps concerning the extraction of the oil from the feedstock

and production of any derived fatty based biochemical 2, 3

. It means that numerous

separation and purification processes such as extraction, refining, crystallization or

fractionation as well as products such as chocolate, butters, dressings, spreads, cosmetic

creams, medicines or biofuels with specific physicochemical properties shall be then

correctly designed and this can only be attended by a reliable evaluation of the phase

transition phenomena involving the compounds presents in fats and oils and their

derivatives.

This review is aimed at providing an overview on the current understanding of the

solid-liquid equilibrium behavior of fatty systems and on the approaches used in the

literature for their modeling, taking into account that a deepest knowledge on solid-liquid

equilibrium of fatty compounds is still required. The complex nature of fats and oils

suggests that the discussion on their phase equilibrium is best tackled starting with the

simplest systems. As the complexity of the system increases, the efforts for obtaining a

better understanding of the systems behavior also increases. Knowing that fatty systems

comprises a large class of compounds, this review addresses mixtures comprising these

components directly found in vegetable oils, namely acylglycerols (mono-, di- and

triacylglycerols) and fatty acids, as well as those directly produced from these sources,

namely fatty alcohols and esters.

16

2. What do fats and oils provide?

Fats and oils are composed of at least 90% of triacylglycerols plus a set of

minoritary components but a lot of further information can be added to this very simplified

view. First of all, triacylglycerols are esters built by a glycerol moiety and three long-chain

organic acids. Such fatty acids carbon-chains mostly range from 8 to 20 carbons comprising

both saturated and unsaturated compounds. Table 1 shows the mostly frequently found fatty

acids in the triacylglycerols present in vegetable oils. Thus, taking also into account that

such set of organic chains varies into 3 positions in the glycerol moiety structure, those

90% of triacylglycerols constitute, in fact, a very large variety of molecules. Therefore,

assuming that the carbon-chain length and the number of unsaturations in the molecule

have a significant effect on the feedstock’s physicochemical properties, the knowledge of

the composition of the oil is crucial.

Considering a predominant fraction composed by triacylglycerols, but neglecting

the other minority set of compounds is a mistake. Crude oils comprise a group of fatty

acids originated from the hydrolysis of the triacylglycerol molecule and consequently,

mono-, diacylglycerols and glycerols molecules are also present. Additionally, a small

fraction of phospholipids, sterols, carotenes, triterpene alcohols, chlorophylls, tocopherols

and tocotrienols are commonly found, as well as several other non-lipidic compounds,

minerals, metal ions and proteins 4-9

. Most of them are usually removed or reduced during

the refining processes, whilst a set of them still remain on the refined final product. From

the industrial point of view, the presence of some of them highly affects the

physicochemical, sensorial and rheological profile of the final product, despite their low

concentrations. Moreover, they may produce undesirable effects for the quality

17

requirements, such as changes in the crystallization kinetics, stimulating or retardating the

nucleation or growth of the crystals, solidification at low temperatures, changing the strain,

stress and the yield force during the flow or emulsification of the system, preventing the

effectiveness of separation processes, etc. 8, 10-12

Although such compounds are usually removed, they may be also deliberately

added to the fat and oils or other derived products in order to play significant roles in the

final profile of the product. In fact, even some triacylglycerols not present in the original

crude oil are sometimes added to the product in order to obtain the desired effects.

Additionally, they are also used for the production of other additives in the industry, such

as fatty alcohols and fatty esters. Fatty alcohols are produced from fatty acids or even from

triacylglycerols by different routes of esterification and hydrogenation 13

, but are also found

in small amounts in vegetable waxes such as those from sugar cane, sunflower or peanuts

14. Fatty esters are produced by transesterification of triacylglycerols using alcohols. Both

are widely used for the production of several other additives, especially surfactants, for

food and cosmetic products 15-17

. Furthermore, several works have long since been

evaluating the use of fatty acid esters mixtures as an alternative fuel for the replacement of

fossil fuels. The transesterification process for the biodiesel production is mainly based on

the utilization of methanol, but also ethanol, in convergence to the larger production of

sugar-cane, especially provided by several emerging countries 18-20

.

18

Table 1. Fatty acid mass composition of vegetable oils

Source <

C12

C12:0

Lauric

C14:0

Myristic

C16:0

Palmitic

C16:1

Palmitoleic

C18:0

Stearic

C18:1

Oleic

C18:2

Linoleic

C18:3

Linolenic

>

C18

Rice brain 21

- - 0.96 18.17 0.61 1.54 38.50 35.61 2.67 1.92

Palm oil 22

0.17 1.15 1.24 40.68 0.15 4.72 41.78 8.84 0.18 0.68

Macadamia nut oil 23

- - 0.98 9.38 19.28 3.40 59.76 2.03 0.14 5.02

Brazil nut oil 23

- - - 15.86 - 11.34 30.68 42.12 - -

Cottonseed oil 24

- - 0.32 15.53 0.12 3.40 21.23 54.07 4.59 0.72

Jatropha curcas oil 25

- - 0.06 13.34 0.89 6.30 41.68 37.00 0.21 0.34

Canola oil 22

- - 0.07 4.72 0.25 2.55 62.56 20.13 7.08 9.62

Soybean oil 22

- - 0.09 11.18 0.09 4.13 25.62 50.88 4.97 1.49

Coconut oil 26

13.10 51.00 23.0 6.10 6.10 - - - - -

Crambe oil 27

- - - 2.07 - 1.03 19.38 8.33 4.53 64.66

Fooder radish oil 27

- - - 5.11 - 2.36 39.47 16.69 12.19 24.18

Macauba oil 27

- - - 21.8 4.08 2.76 58.97 11.64 0.75 -

Cuphea oil 9 - 76.40 7.80 2.40 - 0.70 5.90 6.90 0.10 -

Olive oil 9 - - - 11.00 0.80 2.20 72.50 7.90 0.60 -

Grapeseed oil 28

- 0.03 0.11 8.14 0.16 4.05 15.12 71.20 0.57 0.52

Cocoa butter 9 - 0.10 25.40 0.20 33.20 32.6 2.80 0.10 - -

Palm kernel oil 9 54.20 16.40 8.10 - 2.80 11.4 1.60 - - -

Buriti fruit oil 5 - 0.03 0.08 16.78 0.32 1.77 74.06 4.94 1.04 0.83

Tucum oil 29

3.60 50.60 23.70 5.30 - 2.50 9.30 3.60 0.1 0.1

Sunflower oil 30

- 0.04 0.10 6.80 0.08 4.16 22.75 63.83 0.82 1.42

3. The solid-liquid equilibrium of fatty systems

The nature of the solid-liquid equilibrium of fatty mixtures is complex. Comprising

multiple solid phases at the same temperature and pressure condition, literature very

frequently fails to correctly describing the phase behavior of these mixtures and this

becomes worst as more complex behaviors are observed. What makes the SLE of fatty

mixtures so particular is their inherent ability to polymorphism phenomena 31-34

. It means

that the long-hydrocarbon chains of the fatty compounds and consequently their crystal

lattice can be configured into numerous micro- and macromolecular arrangements, directly

related to the thermal treatment to which the mixture is submitted. Triacylglycerols,

particularly, present three classical and well known polymorphic forms: α, β’ and β, not

19

accounting for additional sub modifications that also appear during thermal processes. The

first structure is formed into fast cooling. When submitted to a slow heating, such

arrangement melts and is recrystallized into a more stable structure, the ’ form, and

sequentially into the β form. Since different crystal lattices are observed in these cases,

namely hexagonal, orthorhombic and triclinic, different transition temperatures and

enthalpies are also observed. Crystalline structure of fatty acids, alcohols and esters can

also pack into different polymorphic forms, usually in temperatures very close to the most

stable form 31, 35-37

. Knowing that the polymorphism phenomena can be managed by

particular thermal treatments, the parameters of the processes to which mixtures are

submitted, time and temperature, can define the profile of the final product.

3.1. Evolution

The first studies on SLE of fatty mixtures published in the literature presented only

the melting temperature behavior, also known as the liquidus line 38-41

and most of them

only in a restricted concentration range, such that phase diagrams could not be completely

represented. On the other hand, the interest on the solid-liquid transitions of these systems

as well as the capacity of a better characterization of their solid phases has grown

significantly in the last decades. Table 2 shows the set of binary fatty mixtures that have

already been reported in the open literature. Efforts to better characterize these systems

have been growing, but increasing also the complexity of their description. In this context,

four principal types of phase diagrams could be identified for binary mixtures, as sketched

in Figure 1.

20

Figure 1. Most common phase diagrams of binary fatty mixtures with the following

nomenclature: mole fraction of the component a in the liquid (xa) and solid (za) phases,

respectively, liquid phase (l), solid phase with pure or rich in component a (Ca) or b (C

b),

solid phase comprising both compounds (s), solid phase with new structure formed by

peritectic transition (Cn).

326

0 1

Tem

per

atu

re

xa, z a

312

0 1

Tem

per

atu

re

xa, z a

Teut

Ca

l

Cb

Cb + lCa + l

l

Ca + Cb

327

0 1

Tem

per

atu

re

xa, z a

Teut300

335

0 1

Tem

per

atu

re

xa, z a

Teut

l

SS

SS

Cb + Cn

Ca + Cn

Ca + l

Cn + l

Cb + l

s + ls + l

Ca + Cb

l

s + l

s

T

x z

l

(B)(A)

(C) (D)

T

x z

21

Table 2. Solid-liquid phase diagrams of binary mixtures of fatty compounds reported in literature.

System Phase

Diagram

Ref. System Phase

Diagram

Ref.

Fatty ester + fatty ester

Fatty acids + fatty acids Ethyl caprylate + ethyl palmitate E 42

Caprilic acid + capric acid ESS/P/M 36

Ethyl caprylate + ethyl stearate E 43

Caprilic acid + lauric acid ESS/P/M 37

Ethyl caprate + ethyl palmitate E 42

Caprilic acid + myristic acid ESS/P/M 44

Ethyl caprate + ethyl stearate E 43

Caprilic acid + oleic acid ESS 45

Ethyl laurate + ethyl palmitate E 42

Capric acid + lauric acid ESS/P/M 36, 46

Ethyl laurate + ethyl stearate E 43

Capric acid + myristic acid ESS/P/M 37, 46

Ethyl myristate + ethyl palmitate E 42

Capric acid + palmitic acid ESS/P/M 44, 46

Ethyl myristate + ethyl stearate E 43

Capric acid + stearic acid E 46

Ethyl palmitate + ethyl stearate E 43, 47, 48

Capric acid + oleic acid ESS 45, 49

Ethyl palmitate + ethyl oleate E 42

Lauric acid + myristic acid ESS/P/M 36, 46

Ethyl palmitate + ethyl linoleate E 42

Lauric acid + palmitic acid ESS/P/M 37, 46

Ethyl stearate + ethyl oleate E 43

Lauric acid + stearic acid ESS/P/M 44, 46

Ethyl stearate + ethyl linoleate E 43

Lauric acid + oleic acid E 50

Methyl laurate + methyl palmitate E 51

Myristic acid + palmitic acid ESS/P/M 36

Methyl myristate + methyl palmitate ESS/P/M 35, 51, 52

Myristic acid + stearic acid ESS/P/M 37

Methyl myristate + methyl stearate ESS/P/M 35

Myristic acid + oleic acid E 50

Methyl palmitate + methyl stearate ESS/P/M 35, 47, 51

Palmitic acid + stearic acid ESS/P/M 36

Methyl palmitate + methyl oleate E 51

Palmitic acid + oleic acid E 53

Mehtyl palmitate + methyl linoleate E 51

Palmitic acid + linoleic acid E 53

Methyl stearate + methyl oleate E 51

Oleic acid + stearic acid E 49, 54

Methyl stearate + methyl linoleate E 51

Oleic acid + linoleic acid E 49

Methyl oleate + methyl linoleate E 51

Triacylglycerol + triacylglycerol

Fatty alcohols + fatty alcohols Tricaprylin + tristearin ESS 34

1-octanol + 1-decanol ESS/P/M 55

Trilaurin + tripalmitin ESS 34

1-decanol + 1-dodecanol ESS/P/M 55

Trilaurin + tristearin ESS 34

1-dodecanol + 1-tetradecanol Ɏ 55

Trimyristin + tripalmitin ESS 34

1-dodecanol + 1-hexadecanol ESS/P/M 55

Tripalmitin + tristearin ESS 56

1-dodecanol + 1-octadecanol ESS 57

Tripalmitin + triolein ESS 34, 53, 56

1-tetradecanol + 1-hexadecanol Ɏ

55 Tripalmitin + trilinolein ESS

53

1-tetradecanol + 1-octadecanol ESS/P/M 55

Tristearin + triolein E 34

1-hexadecanol + 1-octadecanol SS 48, 58

Triacylglycerol + fatty acid

Tricaprylin + myristic acid E 59

Fatty acid + fatty alcohol Tripalmitin + oleic acid ESS 49, 53

Capric acid + 1-dodecanol ESS/P 60

Tripalmitic + linoleic acid ESS 53

Lauric acid + 1-dodecanol P 60

Tristearin + palmitic acid ESS 56

Lauric acid + 1-tetradecanol ESS 61

Tristearin + linoleic acid ESS 56

Myristic acid + 1-dodecanol P 60

Triolein + palmitic acid E 53, 59

Myristic acid + 1-tetradecanol P 60

Trilinolein + palmitic acid E 53

Myristic acid + 1-hexadecanol E 61

Trilinolenin + stearic acid E 59

Palmitic acid + 1-dodecanol P 60

Palmitic acid + 1-tetradecanol E 60, 62

Triacylglycerol + fatty alcohol

Palmitic acid + 1-hexadecanol P 60

Trilaurin + 1-hexadecanol ESS 63

Palmitic acid + 1-octadecanol ESS 61

Trilaurin + 1-octadecanol E 63

Stearic acid + 1-dodecanol E 60

Trimyristin + 1-hexadecanol ESS 63

Stearic acid + 1-tetradecanol E 60

Trimyristin + 1-octadecanol ESS 63

Stearic acid + 1-hexadecanol P 60

Tripalmitin + 1-hexadecanol ESS 63

Stearic acid + 1-octadecanol P 60, 64

Tripalmitin + 1-octadecanol ESS 63

Triolein + 1-hexadecanol E 65

Triolein + 1-octadecanol E 65

E = Simple eutectic, P = Peritect, M = Metatectic, ESS = Eutectic with partial miscibility in the solid phase,

SS = Continuous solid solution, Ɏ

= not defined.

22

The first and simplest phase diagram is the so-called eutectic (Figure 1 A). Some

binary mixtures of fatty acids, mixtures of fatty esters or systems composed by fatty acids

and fatty alcohols present this behavior. Simple-eutectic mixtures are such that during the

cooling process, their compounds crystallize independently. The eutectic point establishes

the concentration at which the system melts at a single, well defined, and minimum

temperature. In a simple eutectic system there are 4 domains: one homogeneous liquid

phase (l); two biphasic solid-liquid domains (regions Ca + l and C

b + l); and one biphasic

solid-solid domain (region Ca + C

b). In such a system when a solid mixture is heated it

starts to melt always at the same temperature (eutectic temperature) and the composition of

the liquid phase changes along one of the branches of the liquidus line according to the

initial concentration of the solid mixture.

The second case (Figure 1 B) shows the phase diagram of a mixture with solid

solution in the extremes of the phase diagram. Depending on concentration of the mixture,

the molecules of a compound are incorporated into the lattice of another crystal 66

during

crystallization. It means that within this concentration range, in general close to one of the

pure components, the compounds do not crystallize independently. In case of lipidic

systems, solid solutions are particularly interesting because they can be intentionally

developed such that physicochemical properties could be adjusted to specific requirements

67-69. Several fatty binary mixtures present solid solution formation at some concentrations,

especially those composed of triacylglycerols or fatty alcohols 34, 56, 57, 61

. The phase

diagrams of such mixtures comprise 6 domains as shown in Figure 1 B. The domains are

explicitly circumscribed by two boundaries: the liquidus line, in which the last crystal of

the mixture melts, and the solidus line indicates the limits of the melt of the first crystal.

The eutectic point in this case establishes a triphasic equilibrium in which the liquid phase

23

is in equilibrium with two solid solutions with distinct compositions. The evaluation of the

eutectic point and the solubility region of the solid phase is usually carried out using the

Tammann plot (Figure 2) 45, 56, 65, 70

. This diagram relates the enthalpy of the eutectic

reaction as a function of the mixture concentration in which the enthalpy rises up to the

eutectic point when it begins to decrease. The concentration at which the solid solution is

formed is obtained when enthalpy of such reaction Heut = 0.

Figure 2. Tammann plot of the eutectic reaction: enthalpy of the eutectic reaction as a function of

the concentration of the mixture (full line); mole fraction of the component a at the eutectic point in

the liquid phase xeut (dashed line), and in the solid phases (zeut) rich in the component a (Ca) or b

(Cb); represented in gray, solid solution regions rich in the component a or b.

A behavior not so common occurs when the components of the liquid phase

crystallize as a solid solution throughout the entire concentration range. It means that only 3

domains are observed (Figure 1 C): the liquid region, the solid domain and the region of

coexistence of both liquid and solid phases. Many mixtures of triacylglycerols with similar

molecular sizes, such as PPS (Glycerol 1,2-palmitate,3-stearate) + PPP (tripalmitin) or SOS

24

(Glycerol 1,3-stearate,2-oleate) + POS (Glycerol 1-palmitate,2-oleate,3-stearate) 34

are able

to form solid solutions. In this case, systems are continuous solid solutions.

Frequently, in the crystallization processes of lipidic compounds, associative

phenomena can occur during the building of the crystal lattice. Such associative behavior

may lead to the appearance of a new crystalline structure that acts as a new compound. This

is the so-called peritectic reaction. This reaction is defined as an isothermal and reversible

process between a liquid and a solid phase resulting, during the cooling of a system, in new

solid phases 66

. It is possible to understand such phenomena taking into account the

inherent polymorphic ability of fatty compounds. Some works suggest to interpret such

phenomenon as a chemical reaction so that the original components form a product

according to a specified stoichiometry. If the new compound crystallizes independently of

the mixture’s compounds the phase diagram behavior is that presented in Figure 1 D. This

means that there are two biphasic solid regions, each with two immiscible crystalline

structures, the new compound Cn and one of the pure components of the original mixture Cb

or Ca , Furthermore, there are 3 solid-liquid domains involving one of the pure components

in the crystalline form and the liquid phase or the new compound and the liquid phase. Note

that the new compound exists only in the solid phase, and disappears during the system’s

melting. Works in literature report the appearance of peritectic profiles in binary mixtures

of fatty acids and some systems composed by methyl esters 35-37, 44

.

Despite the classification of many fatty mixtures into the typical four phase

diagrams shown in Figure 1, the understanding of the phase behavior of the fatty systems is

still far from complete. It is not uncommon that the solid phase presents further transitions

that remain to be clarified 71

. Metatectic transitions have also been identified on these

systems. In this case, the mixture can recrystallize during the melting process, i.e on heating

25

above the solidus line 36

. It means that the crystalline profile of the solid phase clearly

changes and probably a corresponding set of other particular properties. Recent studies 36,

37, 44 describe fatty systems with up to 15 different domains (Figure 3). In these mixtures all

the phenomena previously discussed are present in a single phase diagram, depending on

concentration and temperature: eutectic, peritectic and metatectic transitions as well as

partial miscibility of the solid phases.

Figure 3. Sketch of the SLE phase diagram observed in mixtures of fatty acids (as presented by

Costa, et al. 37

) for some fatty acid + fatty acid binary systems. Ca and

C

b are the solid solutions rich

in one of the components of the mixture a or b; Cn is the solid phase formed by the peritectic

reaction; Cha and Ch

b are the solid phases formed after the metatectic reaction; l is the liquid phase.

In fact, a large set of fatty binary mixtures were not evaluated yet: mixtures of

triacylglycerols; systems composed of triacylglycerols and fatty acids, alcohols or esters;

systems comprising methylic and ethylic fatty esters; mixtures of fatty esters and fatty acids

or alcohols; not to mention a long list of mono- and diacilglycerols mixtures. Moreover,

26

beyond these binary fatty systems, many works in literature, aiming at the design of

products and processes, have been evaluating the SLE of binary systems of these fatty

compounds with other organic solvents such as cyclohexane and ethanol 72

, alkanes 73

,

aromatic compounds 74

and drugs 75

. Additionally, the SLE of many lipid-derivative based

mixtures composed of surfactants 76

, phospholipids 70

, glycolipids 77

or lipidic-based ionic

liquids 78

have also been reported. These systems display a set of liquid crystalline states or

mesophases. Such mesophases are called as the “forth state of matter” since their

physicochemical properties are similar than those of a liquid state but the oriented nature of

the molecules confers particular properties of a solid state 79

. The presence of these

mesophases highly increases the complexity of the system equilibrium.

In summary, all these works reveals the diversity of the solid-liquid equilibrium

behavior of lipidic mixtures but also that several experimental studies are still required for a

detailed characterization and understanding of these systems.

4. Brief overview on the techniques for measuring SLE data

The temperatures and enthalpies of the transitions of both solid-liquid and solid-

solid phenomena, including those due to the polymorphic transitions, can be obtained by

differential scanning calorimetry (DSC). Such a technique is classically used for the

description of solid-liquid phase diagrams of fatty systems. However, owing to the

polymorphism of the solid phase, multiple crystalline structures can be present in a mixture.

Thus, some authors in literature 46

propose that samples should be submitted to a thermal

treatment before the measurement of the melting properties. First, with complete melting of

the mixture, the previously organized crystalline structures, that literature calls thermal

27

history, are deleted. Knowing that the polymorphic forms are highly dependent on the

temperature and the heating/cooling rates, specific procedures are required in order to

assess the temperatures and enthalpies of such different crystal structures. This can be

reached by melting the sample above the highest melting point of the components, cooling

at low rates, followed by an isothermal treatment at a very low temperature and a slow

heating run up to the melting of the component or mixture of compounds. In fact, the DSC

method is not a classical static method for the determination of equilibrium data. However,

slow rates allow to assess a quasi-equilibrium state in which crystal structures can be

rearranged such that temperatures and enthalpies of the transitions are measured. Moreover,

this technique is also able to detect endo- and exothermic events; it means that it detects not

only melting transitions but recrystallization phenomena of the solid phase, such as

polymorphic or metatectic transitions.

Besides DSC, a set of other analytical tecniques, such as X-ray diffraction and

microscopy, are frequently required in order to characterize in more detail the phase

behavior of the system and are often used in the literature for the evaluation of fatty

mixtures 10, 12, 37, 68, 80

. Single-crystal and powder X-ray diffraction tecniques allow assess

information on the crystal structure of the pure compounds and their mixtures. On the

molecular point of view, through the knowledge of the molecular structure of the

compounds, enthalpic and entropic molecular interactions can be inferred and the

ideal/non-ideal thermodynamic behavior of the mixture explained. Controlled-temperature

microscopy allows the visual observation of the beggining and the end of the melting,

crystallization and recrystallization phenomena, and the evalution of the growth and

disapearance of the crystals. Information obtained by these techniques can clarify the

28

transitions observed by DSC, such as polymorphic transitions, formation of solid solutions,

solid phase immiscibility, peritectic and metatectic reactions.

5. But, in fact, what is literature looking for?

Although several transitions or even complete behaviors have been clarified in the

literature, the solid-liquid phase diagrams of various fatty mixtures are still unknown or

were published with limited information concerning various aspects of their real behavior.

The knowledge of the SLE behavior of fatty systems open borders for new applications or

to the understanding of unclear industrial or biochemical phenomena involving such

substances. In fact, the phase equilibrium study really creates an additive design concept. It

means that if one aims to change the nutritional, sensorial or physicochemical profile of a

fatty product by the introduction or removal of components, increasing or decreasing the

melting point, the evaluation of the phase change profile is essential. In this context, a SLE

phase diagram is a powerful tool.

The solid-liquid equilibrium of fatty systems had been long evaluated to obtain an

assessment on the description of numerous processes or development of products 10, 11, 32, 69,

81. Some examples can be easily mentioned. a) Optimization of fractionation processes in

which the material are separated into fractions depending on the melting point by a set of

crystallization procedures 82

; b) Optimization of interesterification processes in which fatty

acids moieties are added or removed from the triacylglycerols in order to obtain lower or

higher melting points materials. This process is a classical alternative for the replacement of

the hydrogenation procedure which promotes the formation of saturated or trans-

unsaturated fatty compounds related as precursors of cardiovascular diseases 8; c)

29

Development of structured lipids for the improvement of the nutritional or physicochemical

characteristics of the product. This process involves chemical or enzymatic pathways and

is aimed at the modification of the triacylglycerols’ fatty acid profile 33

; d) Control of

crystallization phenomena in lubricants or oils for frying processes, in which solid particles

or even compounds that could promote crystallization are undesirable or in butters, creams

and analogous products, in which the crystalline structure is responsible for the desired

texture 10, 11, 69, 81

Other special cases take into account the production of new materials for the

applications in food, pharmaceutical, materials or energy industries. Mixtures of fatty acids

and fatty alcohols, for example, had been evaluated for the formulation of organogels 83, 84

and phase change materials 85-87

. Moreover, mixtures of fatty esters have long been used as

biofuels where the crystallization of saturated esters is a major challenge limiting their

operation at low temperatures 19, 20, 35, 88, 89

.

Organogels are structured materials formed by self-assembling of the components

through noncovalent interactions. They can become an alternative for structuring fat-based

systems making possible to replace traditional industrial processes as hydrogenation,

fractionation and interesterification. Fatty acids and alcohols are compounds 15, 16

that can

replace saturated fats by acting as gelator agents and promoting the formation of

organogels. Thus, the rheological properties of these products can be controlled by

formation of structured networks with different packing arrangements and particular shear

strain and stress profiles 90

.

Phase change materials are materials for energy storage. Concerning a phase-change

heat storage system, energy could be stored and released by reversible solid-solid or solid-

liquid phase changes. Fatty acids, alcohols and esters have relative low melting point, low

30

vapor pressure, low toxicity and high latent heats, being suitable for thermal storage

processes. 85, 91

Such materials play an important role as an environmentally friend way of

accumulating and saving energy, replacing traditional storage fluids such as those used in

refrigeration systems and contributing for the reduction of the emission of greenhouse-

gases.

Biodiesel is a mixture of the mono-alkyl esters obtained as derivatives of fat and oils

and thus, it is a renewable energy source. Consequently, they are environmentally

attractive, promoting the reduction of the emission of pollutant gases in replacement of

fossil fuels. Because of this, nowadays, biodiesel is mandatorily added to petrodiesel in

several countries. However, the biofuel industry is still looking for alternatives to overtake

several technical problems associated to biodiesel production, storage and use. The

solidification at low temperatures is one of them. The presence of fatty esters with high

melting temperature, such as methyl stearate and methyl palmitate is a factor that makes

difficult the use of this biofuel at low temperatures. Moreover, other minor components

such as monoacylglycerols of saturated fatty acids can also be present and can precipitate in

the storage tanks at low temperatures leading to the clogging of tubes and filters of the

vehicles. In all these cases a deeper knowledge of the solid-liquid equilibrium of fatty

mixtures can help optimizing industrial processes and improving the formulation of

products with desirable properties.

6. Demands on modeling

This growing number of new experimental data has not been followed by

proportional efforts to better model these complex phase diagrams. The greater the interest

31

in new systems or applications, the higher the demand to improve reliable modeling

approaches. The modeling of the melting profile of lipidic systems is best tackled by

depicting the melting temperature T as a function of the composition of the mixture or, in

other words, by depicting the phase diagram. This problem is solved by evaluating the well

known thermodynamic equilibrium condition. The thermodynamic equilibrium is

established when at the same temperature and pressure, the chemical potential of a

compound in every phase is also the same, in the present case, a liquid and a solid phase.

Theoretically, this problem is usually described by Equation 1 that relates the mole fraction

of the component i in the liquid phase xi and the melting temperature Tfus and enthalpy

fusH of the pure compound, so that the melting temperature of the mixture T can be

calculated 92

.

fusi

fus

1 1ln

Hx

R T T

(1)

where R is the gas constant. However, this equation is far from being adequate to accurately

depict the real state of the system. The SLE can be fully considered, and so better

described, by Equation 2 92, 93

.

Lfus tri i

fu

fus fus fus

s tri i 1

1 1 1 1ln 1ln

tr

pn

S

H Hx

R T T R

C T

T T R

T

T Tz

(2)

where zi is the mole fraction of component i in the solid phase, iL and i

S are the activity

coefficients of component i in the liquid and solid phases, respectively, Ttr and trH are

thermal transitions temperatures and enthalpies of the n solid-solid transitions (polymorphic

forms) of the component i and fusCp is the difference between the heat capacity of the pure

component i of the liquid and solid phases. If both equations are compared, it is observed

that Equation 1 was built under three main considerations. Firstly, it does not consider the

32

non-ideality of the phases by means of the calculation of the activity coefficients of

component i in both phases liquid iL and, if it is the case, solid i

S. Moreover, it assumes

that the solid phase is composed of immiscible pure components such that zi i

S = 1.0. Also,

it neglects the presence of polymorphic transitions and so the effects of the thermal

transitions temperatures Ttr and enthalpies trH that are present in the heating profile of the

components of the mixture.

Through Equation 2, the non-ideality of both phases is fully considered. Also, it

presents additionally two terms: The first term takes into account the effects of the

polymorphic forms of the mixture components on the melting profile. The second one is

related to the specific heat capacity fusCp that is usually neglected due to a clear lack of

reliable experimental data and because the magnitude of this property supposedly does not

affect the solid-liquid equilibrium calculation. Moreover, Equation 2 reveals that, the

modeling of fatty mixtures’ phase diagrams is based on a fundamental problem: the

miscibility of the solid phase or the presence of solid solutions, so that zi i

S 1.0. This is

related to the calculation of the solidus line. The solidus line depicts the behavior of the

melting temperature T as a function of the solid phase composition zi.

Despite the fact that solid solutions are more common than usually admitted, most

authors have adopted the modeling approach based on the solid phase immiscibility. In the

works that take into account a more comprehensive approach and consider the formation of

such solid solutions 33, 34, 89

two main focuses can be identified. From the academic focus,

the solid-liquid equilibrium theory is formulated for complete description of the solid-liquid

phase diagram of a system of interest, this means for calculating the liquidus and the

solidus lines. From the industrial focus, the knowledge of the solid content behavior of a

33

vegetable oil or a mixture of triacylglycerols has a particular interest for the formulation of

products. This behavior is best assessed by the construction of a diagram that represents the

solidified fraction of the system as a function of temperature. The aim is the manipulation

of the melting point of the mixture by the right choice of its composition. It is known that,

for instance, many sensorial aspects, such as crispness, spreadability, aroma and oiliness are

largely affected by the solid/liquid ratio in lipidic products, such as cocoa and peanut

butters, but also in case of cosmetic creams 10, 81

. Analogously, the melting behavior of a

biodiesel mixture is largely dependent on the original fat or oil composition as well as the

alcohol used in the transesterification reaction 19

. It means that blends with high

concentration of long carbon saturated fatty esters are more susceptible to high solid

content at low temperatures, worsening their flow properties 20, 51

. Other example for the

construction of solid fat content diagrams is the development of the so-called structured

lipids. By changing the fatty acid composition of triacylglycerols it is possible to improve

specific properties 33

. High amounts of saturated or trans-unsaturated fatty acids can, for

instance, bring negative effects concerning the nutricional claim of the product and,

additionally, can increase its melting point. Thus, by the adequate right choice of fatty acids

the desired solid content profile of a mixture can then be designed avoiding, for instance,

the presence of trans-unsaturated fatty acids.

In order to assess the SLE described by Equation 2, works in literature apply mainly

two well known algorithms: the minimization of the Gibbs energy and the isoenthalpic

flash calculation 34

. The first is based on the stability criteria in which a mixture at

equilibrium condition present the minimum Gibbs energy. The second one, in analogy with

the vapor-liquid equilibrium, considers the feeding of a mixture in an isothermic and

isobaric vessel and the equilibrium condition is then calculated through the analysis of the

34

mass balance and the fundamental SLE equations. Both approaches are robust in obtaining

the equilibrium state of the mixture but sensitive to initial concentrations estimates.

For the description of the non-ideality of the system, these optimization procedures

calculate the activity coefficients of the liquid and solid phases. The activity coefficients of

the components in the liquid phase iL are usually calculated using equations for the excess

Gibbs energy 92

such as Margules or UNIQUAC equations 94

or the group-contribution

UNIFAC model 95, 96

. Equation 3 shows the 2-suffix Margules equation, commonly used in

the SLE modeling of binary systems, comprising one adjustable parameter A12, related to

the interaction between the compounds of the binary.

L 2

1 12 2 ln( )RT A x (3)

where x is the composition of the component in the liquid phase, T is the melting

temperature of the mixture and R is the ideal gas constant. Despite the slight non-linearity

of this model, what is favorable in case of optimization procedures, its disadvantage is the

calculation of symmetric non-ideal behaviors. It means that the compounds should present

positive or negative deviations but not both behaviors depending on the concentration. The

UNIFAC equation is a predictive method commonly used in case of liquid-liquid and

vapor-liquid equilibrium and that can be also applied for the calculation of the iL in case of

SLE studies 96

. This model is based on the group-contribution concept so that the activity

coefficient of the component is calculated by a sum of terms related to enthalpic and

entropic interactions. It is well applied for the description of the liquid phase in the SLE of

fatty systems presenting slight deviations from ideality. However, the model can fail in the

prediction of strong non-ideal behaviors such those observed in cases where the compounds

are very different in size.

35

Two approaches were up to now used for the calculation of activity coefficients of

the components in the solid phase of fatty systems: the two-suffix Margules equations 34

for

the description of the solid phase of mixtures of triacylglycerols and a predictive version of

the UNIQUAC model 89, 97

for the description of mixtures of fatty esters. Applying

Margules equation, Equation 3 is used but evaluating the composition of the compound in

the solid phase zi. In the predictive version of the UNIQUAC model, the binary interactions

parameters are calculated by using the physicochemical properties of the pure compound,

as described by the authors.

Apart from discussions on the effectiveness these approaches, taking into account

the description of the lipidic systems listed in Table 2 that present different kind of

behaviors as well as numerous mixtures that were not evaluated yet, the SLE modeling of

fatty systems is a field yet to be explored.

7. Remarks

In this large and opened context, several demands are clearly evident. The first and

most obvious is the enlargement of the number of reliable experimental data of binary,

ternaries and even more complex mixtures of fatty systems. Additionally, pure compound

experimental data, melting temperatures and enthalpies as well as solid-solid transitions

properties and specific heat capacity of the phases are highly demanded, since all of these

parameters are required in the modeling procedure. The second demand is the improvement

of the description of the non-ideality of the solid phase by using reliable equations or

predictive models as a tool for the design of mixtures with specific behaviors. The third is

the evaluation of the modeling of systems comprising the peritectic reaction whose efforts

36

are too incipient in the literature. The forth is deepening the understanding of the solid

phases, with experimental and modeling tools in order to describe its behavior according to

the well known thermodynamic theories. The better the description of the SLE behavior of

fatty systems the easiest the development or the optimization of fatty-based products and

processes will be. New alternatives can be thus found to overcome industrial problems,

opening pathways for new academic studies.

ACKNOWLEDGEMENTS

The authors are grateful to the national funding agencies FAPESP (2012/05027-1,

2008/56258-8), CNPq (304495/2010-7, 483340/2012-0, 140718/2010-9, 479533/2013-0)

and CAPES (BEX-13716/12-3) for the financial support.

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43

SOLID-LIQUID EQUILIBRIUM OF TRIOLEIN WITH FATTY

ALCOHOLS

(published in Brazilian Journal of Chemical Engineering v. 30, n. 1, p. 33-43, 2013)

Guilherme J. Maximo1, Mariana C. Costa

2 and Antonio J. A. Meirelles

1*

1 Laboratory of Extraction, Applied Thermodynamics and Equilibrium, Department of Food

Engineering, School of Food Engineering, Phone: + (55) (19) 3521 4037, Fax: + (55) (19)

3521 4027, University of Campinas, Av. Monteiro Lobato 80, 13083-862, Campinas - SP,

Brazil. E-mail: [email protected] 2

School of Applied Sciences, University of

Campinas, R. Pedro Zaccaria 1300, 13484-350, Limeira - SP, Brazil.

Chapter 2

mailto:[email protected]

44

ABSTRACT

Triacylglycerols and fatty alcohols are used in the formulation of cosmetic, pharmaceutical

and food products. Although information about the phase transitions of these compounds,

and their mixtures, is frequently required for design and optimization of processes, and

product formulation, these data are still scarce in the literature. In the present study, the

solid-liquid phase diagrams of two binary systems composed of triolein + 1-hexadecanol

and triolein + 1-octadecanol were evaluated by differential scanning calorimetry (DSC) and

optical microscopy. The experimental data were compared with predicted data by solving

the phase equilibrium equations using an algorithm implemented in MATLAB. The liquid-

phase activity coefficients were calculated using the Margules equation (two- and three-

suffix) and the UNIFAC model (original and modified Dortmund model). The approaches

used for calculating the equilibrium condition allowed gave accurate predictions of the

liquidus line, with deviations from the experimental data lower than 0.57 K.

KEYWORDS: Triolein; Fatty alcohol; Solid-liquid equilibrium; Differential scanning

calorimetry; Modeling; UNIFAC.

1. INTRODUCTION

Fats and oils are multicomponent systems composed of a mixture of triacylglycerols

(TAGs) and minor components, such as free fatty acids and nutraceuticals. Under thermal

treatment, triacylglycerols are responsible for the formation of a crystalline network and,

consequently, particular microstructures that influence the sensorial, rheological and

45

thermodynamic profiles of food and chemical products (Bruin, 1999; O’Brien, 2004).

Within the food and chemical industry, there is a clear trend towards the development of

new ways of structuring these systems, such as the utilization of surfactants and co-

surfactants. In particular, fatty alcohols have been evaluated as gelling and surfactant agents

in food, chemical and pharmaceutical oil-based products (Egan et al., 1984; Kreutzer, 1984;

Daniel and Rajasekharan, 2003). Therefore, the study of the phase equilibrium of these

compounds is a powerful tool for process and product design.

The differential scanning calorimetry technique (DSC) is often used for the

experimental determination of solid-liquid equilibrium (SLE). Some data on solid-liquid

transitions of fatty mixtures, phase diagrams and pure component properties using this

technique, including TAGs, fatty acids, esters and alcohols, can be found in the literature

(Wesdorp, 1990; Costa et al., 2007, 2009, 2010a, 2010b, 2011; Carareto et al., 2011). The

phase transition behavior can be modeled by solving a system of equations based on the

conditions of thermodynamic equilibrium (Wesdorp, 1990; Dos Santos et al., 2011).

Several approaches for this procedure can be found in the literature; the majority is based

on evaluation of the activity coefficients of the compounds in the equilibrium phases

(Wesdorp, 1990; Slaugther and Doherty, 1995; Coutinho et al., 1998). The activity

coefficients in the solid-liquid equilibrium can be estimated with adjustable models such as

the Margules equation, or with predictive methods such as the group-contribution UNIFAC

model (Fredenslund et al., 1975; Gmehling et al., 1978; Chiavone Filho and Rasmussen,

2000; Coutinho et al., 2001), both based on the calculation of excess Gibbs free energy.

Binary solid-liquid equilibrium data on systems composed of mixtures of

triacylglycerols, mixtures of fatty alcohols or mixtures of these components with other fatty

compounds are available in the literature, but data on systems composed of triacylglycerols

46

+ fatty alcohols are still scarce. In the present work, solid-liquid equilibrium data on two

fatty mixtures, triolein + 1-octadecanol and triolein + 1-hexadecanol, were measured by

differential scanning calorimetry (DSC), evaluated with optical microscopy and modeled

by resolution of the thermodynamic equilibrium equations using the two- and three-suffix

Margules equations, the original UNIFAC (Fredenslund et al., 1975) and the modified

UNIFAC-Dortmund model (Gmehling et al., 1993) for calculation of the liquid-phase

activity coefficient. An optimization algorithm was implemented in MATLAB for

prediction of the melting point.

1.1. Thermodynamic framework

The solid-liquid equilibrium of component i in a binary or two-phase system is

represented by Equation (1), as discussed by Prausnitz et al. (1986).

L Lfusi i

S Sfusi i

1 1exp

Hx

R T Tx

(1)

where Lix and S

ix are the mole fractions of component i in the liquid (L) and solid (S)

phases, Li and S

i are the activity coefficients of component i in the same phases, fusH is

the melting enthalpy, and fusT is the melting temperature of pure component i, T is the

temperature of the system, and R is the ideal-gas constant (8.314 Jmol-1K

-1). The Margules

equation and the group-contribution UNIFAC model are often used for calculation of i

Using the two-suffix Margules equation for a binary mixture, the of component 1 is

given by Equations (2) and (3). Using the three-suffix Margules equation, the of the

47

components in a binary mixture are calculated using Equations (4) and (5) (Reid et al.,

1987).

21 2R lnT Ax (2)

22 1R lnT Ax (3)

2 31 2 2R ln ( 3 ) 4T A B x Ax (4)

2 32 1 1R ln ( 3 ) 4T A B x Ax (5)

where A and B are adjustable parameters. According to the UNIFAC model (Equations (6)

to (17)) (Fredenslund et al., 1975), the activity coefficient can be written as the sum of a

combinatorial contribution Ci , which accounts for the effects of size and shape, and a

residual contribution Ri , which accounts for interactions among groups.

C Ri i iln ln ln (6)

i i i

i i i

Ci i i j j jln ln 5 ln

x xq l x l

(7)

(i) (i)Ri k kk kln (ln ln ) (8)

i i i i5( ) ( 1)l r q r (9)

i ii

j j j

r x

x r

(10)

i ii

j j j

q x

x q

(11)

(i)i k kkr R (12)

(i)i k kkq Q (13)

48

m km

n nmk k m m mk m n

ln 1 ln( )Q

(14)

m mm

n n n

Q X

Q X

(15)

( j)j m j

m ( j)j n n j

xX

x

(16)

nmnm exp

a

T

(17)

where i is the volume fraction of molecule i, i is the area fraction of molecule i, ri is the

molecular volume parameter, qi is the surface area parameter, ik is the number of k-type

groups in molecule i, k is the activity coefficient of group k in the mixture composition,

(i)k is the activity coefficient of group k for a group composition corresponding to pure

component i, i is the surface area fraction of component i in the mixture, mX is the group

mole fraction of group m, nm is the Boltzmann factor, Rk and Qk are the structural

parameters for the groups and anm is the temperature-dependent group-interaction

parameter (Reid et al., 1987). In this work, in addition to the original UNIFAC model, the

modified UNIFAC-Dortmund model (Gmehling et al., 1993) was also used. In this model,

the combinatorial term Ci (Equation (18)) was empirically changed to make it possible to

deal with compounds that are very different in size. Also, the Boltzmann factor nm

(Equation (20)) of the residual term is temperature-dependent, with three new group-

interaction parameters, anm, bnm and cnm.

C i i i ii i

i i i i

ln 1 ln 5 1 lnqx x

(18)

49

3/4i i

i 3/4j j j

x r

x r

(19)

2nm nm nm

nm expa b T c T

T

(20)

For systems that show only a eutectic transition and whose components are

immiscible in the solid phase, it is possible to assume that the solid phase is composed of a

pure component, so Equation (21) becomes valid.

S Si i 1x (21)

With these considerations, a system of equations can be constructed for prediction

of the melting point using: i) the equation expressing the equilibrium condition for each

component (Equation (1)), ii) a model for calculation of the activity coefficients of the

liquid phase (Equations (2) to (20)) and iii) the global molar balance of the system.

2. MATERIALS AND METHODS

Triolein (C57H104O6), 1-octadecanol (C18H38O) and 1-hexadecanol (C16H34O) with

purity higher than 99% by mass were supplied by Sigma-Aldrich (USA). Samples (1 g) of

triolein + 1-octadecanol and triolein + 1-hexadecanol were prepared gravimetrically in

amber flasks using an analytical balance (Precisa Gravimetrics AG, Dietkon) with a

precision of 2×10-4

g and a mole fraction of component 1 from 0.0 to 1.0. The samples were

pretreated on Thermoprep (Metrohm, Herisau) by heating in a nitrogen atmosphere to 15 K

above the highest melting point of the components. The mixtures were sealed under inert

50

atmosphere, allowed to cool to room temperature, and kept in a freezer at 273.15 K until

DSC analysis.

2.1. Differential Scanning Calorimetry (DSC)

SLE of pure triolein, fatty alcohols and their mixtures were characterized by DSC

using a DSC8500 calorimeter (PerkinElmer, Waltham) that was equipped with a

refrigerated cooling system, which in this work operated between 223 and 343 K using

nitrogen as a purge gas. Indium (certificated by PerkinElmer, Waltham) and cyclohexane

(C6H12) (Merk, USA), both with 0.99 mass fraction purity, had previously been used as

primary standards to calibrate the melting temperature and heat flow at a heating rate of 1

Kmin−1

. Samples (2-5 mg) of each mixture, triolein + 1-hexadecanol and triolein+1-

octadecanol, were weighed in a microanalytical balance AD6 (PerkinElmer, Waltham) with

a precision of 2×10−6

g and put in sealed aluminum pans. In order to erase previous thermal

histories related to the effects of polymorphism, a pretreatment was carried out based on the

methodology described by Costa et al. (2007). For this purpose, each sample was kept at a

temperature of 15 K above the highest melting point of the components. After 20 min at

this temperature, the samples were cooled to 40 K below the lowest melting point of the

components at a cooling rate of 1 Kmin−1

and allowed to remain at this temperature for 20

min. After this pretreatment, each sample was analyzed in a heating run at a heating rate of

1 Kmin−1

. Measurements were evaluated using PerkinElmer (Waltham) analysis software.

The temperatures of the thermal transitions were the peak top temperatures and the

enthalpies were calculated from the area of the corresponding peaks.

51

2.2. Optical Microscopy

In order to evaluate the behavior of the solid:liquid fraction of the systems as a

function of the concentration of the components, as well as the assumption of solid phase

immiscibility, both systems were analyzed at 298.15 K by optical microscopy using a Carl

Zeiss model Scope A1 microscope (Zeiss, Germany). Samples of each mixture of both

systems were heated from storage temperature (above 273.15 K) to 298.15 K on a

Thermoprep (Metrohm, Herisau). The images obtained were taken with magnifications of

10 and 40.

2.3. Modeling Procedure

SLE modeling was carried out according thermodynamic approach previously

discussed. The binary parameters A and B of the Margules equations were numerically

adjusted by an algorithm implemented in MATLAB 7.0, and based on the calculation of the

melting temperatures by Equation (1), rewritten as a function of T, and by Equations (2) to

(5) as the Li model. The one-variable optimization problem (using the two-suffix Margules

equation) was implemented using a parabolic interpolation method (MATLAB function

fminbnd). The two-variable optimization problem (using the three-suffix Margules

equation) was carried out using a sequential quadratic programming method (MATLAB

function fmincon). In both cases, the objective function was the root mean square deviation

(RMSD) (Equation (22)) between the experimental (Texp) and calculated temperatures

(Tcalc).

52

2i 1 exp calc i2

( )RMSD

n T T

n

(22)

where n is the number of observations. In the case of the UNIFAC or the UNIFAC-

Dortmund model for calculation of Li , equilibrium Equation (1) cannot be rewritten as a

function of T, and thus an optimization algorithm was implemented in MATLAB 7.0 using

sequential quadratic programming (MATLAB function fmincon) for the calculation of the

melting temperature of the mixtures. In this case, the objective function was the square of

the absolute deviation between the experimental temperature (Texp) and the calculated one

(Tcalc) (Equations (23) and (24)) for a composition Lix . The routine was repeated for 0 < L

ix

< 1 and the first iteration started with a melting temperature sufficiently close to that of the

optimal solution, taken as the melting point of pure component 1 or 2.

2obj exp calc iF ( )T T (23)

fus fuscalc L L

fus fus i iR ln

H TT

H T x

(24)

For modeling, the pure component properties (temperature and enthalpy of fusion)

were taken from the experimental data measured in this work. Also, data from the literature

(Wesdorp, 1990; Ventolà et al., 2004; Nichols et al., 2006) was used for evaluation of the

significance of these properties for modeling accuracy. Accounting for the immiscibility in

the solid phase, the procedure described above was applied along the entire composition

range for calculating the mixtures’ melting points, assuming that either the light or the

heavy component represents the pure solid phase. Therefore, two temperatures were

obtained, with the equilibrium temperature (liquidus line) being the higher. This is the usual

procedure for estimating equilibrium temperatures in a simple eutectic mixture, so the left-

53

hand curve corresponds to a solid phase composed of the pure heavy component and the

right-hand curve to a solid phase of the pure light component and the predicted eutectic

mixture occurs exactly at their intersection.

3. RESULTS AND DISCUSSION

3.1. Performance of the Algorithm

To evaluate the performance of the algorithm, solid-liquid equilibrium experimental

data on fatty mixtures, and other organic binaries, from the literature were calculated by the

aforementioned modeling procedure. The deviations obtained were compared with

deviations obtained by the literature works’ modeling procedure (Table 1) and plotted for

evaluation (Figure 1). The agreement between the data from the literature and the data in

this study was good since the fitted curve (continuous line in Figure 1) determined by linear

regression shows only a slight deviation from the straight diagonal line. Apart from

differences in numerical procedures, the observed deviations are probably due to

differences in pure component properties, which have an important effect on the results of

the equilibrium estimation, as will be discussed below.

3.2. Experimental and Predicted Solid-Liquid Equilibrium Data

The reproducibility of the data was checked by performing three repeat runs for the

calibration standard (indium) and for the pure components (triolein, 1-hexadecanol and 1-

octadecanol). The standard deviation of the melting point data obtained was 0.13 K. This

54

deviation was assumed to be the uncertainty of all of the melting points measured in this

work. Also, these experimental data were compared with experimental data obtained from

the literature (Ferguson and Lutton, 1947; Kolp and Lutton, 1951; Wesdorp, 1990;

Rolemberg, 2002; Ventolà et al., 2004; Carareto et al., 2011; National Bureau of Standards,

2011). The average relative deviations (ARDs) (%) of the melting data measured in this

work (Twork

) in relation to data found in the literature (Tlit

) were calculated according to

Equation (25), where n is the number of observations. The agreement between both sets of

data was good, since the ARD was 0.14 %.

lit worki in

i liti

100 1ARD (%)

n

T T

T

(25)

Table 1. Deviationa data from the literature (lit.) and from the algorithm proposed in this work

System

Margules

two-suffix

Margules

three-suffix UNIFAC

UNIFAC -

Dortmund Ideal

lit. this

work lit.

this

work lit.

this

work lit.

this

work lit.

this

work

palmitic acid + tristearinb 0.36 0.34 0.16 0.14 - - 0.46 0.46 - -

trilinolein + stearic acidb 1.07 1.06 1.02 0.94 - - 5.20 5.92 - -

capric acid + palmitic acidb 0.86 0.84 0.56 0.57 - - 2.89 2.89 - -

capric acid + stearic acidb 0.78 0.76 0.67 0.67 - - 1.68 1.68 - -

triolein + tripalmitinb 0.40 0.39 0.10 0.10 - - 0.57 0.57 - -

1-octanol + 1-dodecanolc 2.00 1.90 1.80 1.85 - - 2.60 2.58 2.60 2.46

1-dodecanol + 1-octadecanolc 1.00 1.04 0.40 0.40 - - 4.30 3.94 4.30 4.05

1-decanol + 1-hexadecanolc 1.10 1.15 0.80 0.70 - - 7.30 7.31 7.30 7.53

2-aminobenzoic acid + benzoic acidd - - - - 6.95 7.10 - - - -

tetrachloromethane + 2-dodecanonee - - - - 2.75 2.94 - - - -

tetrachloromethane + 2-undecanonee - - - - 1.04 1.09 - - - -

indane + dodecanee - - - - 0.50 0.74 - - - -

a RMSD (Equation (22)) data from

bBoros (2005),

cCarareto et al. (2011),

dHuang and Chen (2000)

and average of the absolute deviations ni calc exp i

nT T from eJakob et al. (1995).

55

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

Dev

iati

on

fro

m t

his

wo

rk

Deviation from literature

Figure 1: Deviation (this work) versus deviation from the literature (data from Table 2): (○)

Carareto et al., (2011), (×) Boros (2005), (+) Huang and Chen (2000) and (Δ) Jakob et al. (1995).

Dashed line represents the straight diagonal line and the continuous line is the curve fitted with the

data (y = 1.0123x – 0.017, r2 = 0.9966). Number of observations = 31.

The thermograms obtained with DSC runs and the phase diagrams of the two binary

systems evaluated, (1) triolein + (2) 1-hexadecanol and (1) triolein + (2) 1-octadecanol, are

presented in Figures 2 and 3. Figures 2 and 3 also show modeling results with the ideal

assumption, using the adjustable three-suffix Margules equation and the predictive

UNIFAC-Dortmund model for Li calculation. In addition, the experimental data related to

the thermogram analysis are presented in Tables 2 and 3.

For pure 1-hexadecanol and 1-octadecanol two overlapping peaks could be seen in

the region very close to the melting temperature, as observed by other authors (Ventolà et

al., 2004; Carareto et al., 2011). In fact, fatty alcohols have rotator forms during

crystallization processes (TFA rotator form, Tables 2 and 3) that are structurally different but

with very similar thermodynamic properties (Ventolà et al., 2004). Despite the fact that the

melting temperatures of these rotator forms could easily be found on the thermograms, the

56

proximity of their values makes determination of the enthalpy of each of these pure

component forms difficult.

For pure triolein two well-defined peaks and a third mild peak at a lower

temperature were observed. In fact, TAGs usually have three polymorphic forms, known as

alpha, beta-prime and beta, with differences in the crystal lattice packing, temperatures and

heats of fusion (Wesdorp, 1990; Rolemberg, 2002; Costa, 2008). According to Fergusson

and Lutton (1947), triolein also has these three polymorphic forms, melting at 241.15 K,

260.15 K and 278.65 K, respectively, and these values are very similar to the temperatures

found in this work (Tables 2 and 3).

The thermograms of the mixtures of triolein and 1-hexadecanol or 1-octadecanol

clearly showed three well-defined peaks, which were also observed by other authors for

fatty mixtures with triacylglycerols (Costa et al., 2010a, 2010b, 2011). The thermal

transition at the highest temperature is related to the solid-liquid equilibrium temperature of

the mixture. The transition at the lowest temperature is close to the solid-solid transition of

the triolein beta-prime polymorphic form, and thus is probably related to this transition.

The last one (Ttr, Tables 2 and 3) is a transition temperature close to the triolein melting

point, which will be discussed below. The transition related to the alpha polymorphic form

of triolein, the polymorphic form with the lowest transition temperature, was not well

identified in the thermograms of the mixtures and is not shown in Figures 2 and 3.

57

Table 2. Experimental solid-liquid equilibrium data (K) for triolein (1) + 1-hexadecanol (2).

xtriolein Tfus TFA rotator form Ttr T’melting T melting

0.0000 322.34 321.62

0.1018 320.40 277.18 259.74

0.1975 319.07 277.41 260.12

0.3000 317.92 277.80 260.44

0.4017 316.48 278.10 260.56

0.5014 314.51 278.15 260.62

0.5963 312.42 278.28 260.78

0.7006 307.58 277.78 260.20

0.7840 304.03 278.29 260.47

0.8833 296.43 278.00 260.47

0.9463 287.33 277.82 259.74

1.0000 278.16 259.31 241.34

240

260

280

300

320

340

0.0 0.2 0.4 0.6 0.8 1.0

Tem

per

atu

re /

K

x1

x1 = 0.0

x1 = 1.0

Heat Flow / u.a.

x1 = 0.80

x1 = 0.90

x1 = 0.95

Temperature / K280 295

286 300

290 315

Hea

t F

low

/ u

.a.

Temperature / K

Hea

t F

low

x1 = 1.0

248233

Figure 2: Solid-liquid phase diagram (temperature in Kelvin and mole fraction) and thermograms

for the triolein (1) + 1-hexadecanol (2) system. Symbols for phase diagrams: (○) experimental

melting point, (■) transition near triolein melting point, solid-solid triolein () alpha and (×) beta-

prime transitions and data modeled by (- - -) the three-suffix Margules equation, (—) the UNIFAC-

Dortmund model and (- -) the ideal assumption. In detail, magnifications of the thermograms close

to the melting temperature for x1 > 0.7 and close to the triolein alpha polymorphic form temperature

transition for x1 = 1.0.

58

Table 3. Experimental solid-liquid equilibrium data (K) for triolein (1) + 1-octadecanol (2).

xtriolein Tfus TFA rotator form Ttr T’melting T melting

0.0000 331.04 330.35

0.1048 329.93 277.65 258.87

0.2030 328.66 277.87 259.80

0.3097 326.50 277.51 260.53

0.4046 325.23 277.52 260.69

0.5004 323.49 277.61 259.73

0.5910 321.13 278.19 261.29

0.6993 317.70 278.24 260.77

0.7996 313.58 278.03 260.72

0.8975 305.38 278.00 260.13

0.9467 296.60 278.72 259.74

1.0000 278.16 259.31 241.34

240

260

280

300

320

340

0.0 0.2 0.4 0.6 0.8 1.0

Tem

per

atu

re /

K

x1

x1 = 0.0

x1 = 1.0

Heat Flow / u.a.

x1 = 0.80

Temperature / K

295.5 298

290 314

300 325

Hea

t fl

ow

/ u

.a.

x1 = 0.90

x1 = 0.95

Figure 3: Solid-liquid phase diagram (temperature in Kelvin and mole fraction) and thermograms

for the triolein (1) + 1-octadecanol (2) system. Symbols for phase diagrams: (○) experimental

melting point, (■) transition near triolein melting point solid-solid triolein () alpha and (×) beta-

prime transitions and data modeled by (- - -) the three-suffix Margules equation (—), the UNIFAC-

Dortmund model and (- -) the ideal assumption. In detail, magnification of the thermograms close

to the melting temperature for x1 > 0.7.

59

Figure 4 contains the Tammann plots of the mixtures, showing the enthalpy

variation of the observed invariant transitions as a function of triolein molar concentration.

In general, the polymorphic transitions and the eutectic reaction, which separates the solid-

liquid region from the solid-solid, are the most common invariant thermal events of

mixtures of triacylglycerols and fatty compounds. The Tammann plot allows a better

determination of the eutectic point, since enthalpy increases as the mixture concentration

approximates the eutectic composition, where the enthalpy should begin to decrease. In

several cases, the increase in the difference between melting temperatures of pure

components increases the proximity of the eutectic point to the melting temperature of the

pure lighter component (Levine, 2002). The linear regression (with r2 > 0.99) of the

Tammann curves for the transition close to the triolein melting point (Figure 4) shows that,

for x = 1, the enthalpy variation is very close to the corresponding value for pure triolein.

This means that this invariant thermal event may correspond to a eutectic reaction with a

composition very close to that of pure triolein, making it virtually impossible to

differentiate the eutectic composition from pure triolein. In agreement with this

observation, triolein + 1-octadecanol and triolein + 1-hexadecanol modeled phase diagrams

had eutectic points higher than 0.99 and 0.98 triolein mole fraction, respectively, for all

Li models.

60

y = 117.69x 0.76

r² = 0.99990.0

20.0

40.0

60.0

80.0

100.0

120.0

0.0 0.2 0.4 0.6 0.8 1.0

H

( k

Jm

ol-1

)

x1

y = 115.05x + 0.14r² = 0.9998

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.0 0.2 0.4 0.6 0.8 1.0

H

( k

Jm

ol-1

)

x1

(a) (b)

Figure 4: Tammann plots of (a) triolein (1) + 1-hexadecanol (2) and (b) triolein (1) + 1-octadecanol

(2). (—) Linear regression for data on (■) transition close to the triolein melting point, (○) pure

triolein transition and (- - -) hypothetical plot with a eutectic point.

Table 4. Estimated parameters (A and B) and mean absolute deviationsa of the predicted data

from the experimental data (in Kelvin).

Model triolein +

1-hexadecanol

triolein +

1-octadecanol Average

Two-suffix Margules A 1065.77 855.15

0.53 0.60 0.56

Three-suffix Margules A 1186.79 1026.36

B 396.02 507.89

0.32 0.34 0.33

UNIFAC 0.45 0.42 0.43

UNIFACDortmund 0.68 0.47 0.57

Ideal 2.31 1.78 2.04

a

exp predni i i

n

T T

The binary parameters (Jmol-1

) for both Margules equations and the deviations

between calculated and experimental data for each modeling approach are shown in Table

4. It can easily be observed that the liquidus line was well described by all models, since

61

the average absolute deviation was always less than 0.57 K. The Margules parameter values

obtained were very similar to those found in the literature for binary fatty mixtures with

TAGs and for systems with fatty alcohols (Costa et al., 2010a, 2011; Carareto et al., 2011).

The ideal assumption shows the highest deviations, indicating that the systems of triolein +

1-hexadecanol and triolein + 1-octadecanol are slightly non-ideal. In fact, the activity

coefficients calculated by all the models were higher than 1 for both systems and the

highest values were obtained for the most accurate model, the three-suffix Margules

equation. In this case the Li values were close to 2 when L

ix was close to 0.

Solid phase immiscibility is usually assumed for the purpose of modeling fatty

systems (Wesdorp, 1990; Rolemberg, 2002; Costa et al., 2007). Nevertheless, several fatty

mixtures have regions of solid solution close to the pure component composition on the

phase diagram (Costa et al., 2009, 2011; Carareto et al., 2011). In order to check the

immiscibility assumption and thus comprehend the behavior of the solid:liquid fraction in

the solid-liquid biphasic region (under the liquidus line), optical micrographs of both

systems were taken at 298.15 K. Some of the images of the binary mixture of triolein (1) +

1-octadecanol (2) are shown in Figure 5. Firstly, it was clearly observed that increasing the

concentration of triolein decreased the solid fraction, in agreement with the lever rule

(Figures 5(a) to 5(f)). Since the melting points of the pure saturated fatty alcohols 1-

hexadecanol and 1-octadecanol are higher than that of triolein, in this region of the phase

diagram the solid fraction of the system is probably composed only of pure fatty alcohol.

Secondly, the micrograph of the system with a triolein mole fraction of 0.1 at a

magnification of 40 (Figure 5(g)) clearly shows that there is a liquid fraction even at this

relatively low concentration. Thus, there is probably no solid solution at the concentration

62

close to the pure heavy component (x1 = 0.0). Tammann plots of both systems also

corroborate this probability, since enthalpy values tend to zero at x1 = 0.0. Both

observations validate our modeling approach.

(a)

(b)

(c)

x1 = 0.3

10

x1 = 0.1

10

x1 = 0.0

10

x1 = 0.1

40

x1 = 0.7

10

x1 = 0.9

10

x1 = 1.0

10

(d)

(f)

(e)

(g)

Figure 5. Optical micrographs of samples of triolein (1) + 1-octadecanol (2) with magnifications of

10 ((a) to (f)) and 40 (g) at 298.15 K.

Finally, the influence of pure component properties on the accuracy of the modeling

approach was investigated. Component properties taken from the literature (Wesdorp,

1990; Ventolà et al., 2004; Nichols et al., 2006) as well as the values obtained in this work

are presented in Table 5. The values from the literature were also used with the modeling

63

procedure presented above. In the case of the pure component properties taken from the

literature, the global average absolute deviation between the calculated and the

experimental results, including the ideal solution assumption, was 0.90 K, while for the

pure component properties obtained in this work the deviation was 0.79 K. Firstly, the

differences in the pure compounds’ experimental values observed in Table 5 can probably

be attributed to differences between the experimental method used in the literature and in

this work (different heating and cooling rates and isothermal conditions). In addition, the

effects of polymorphism could produce peaks that overlap or are too close, which disrupts the

determination of enthalpy, especially for fatty alcohols, as discussed previously. In case of the

interactions parameters and the corresponding liquid phase activity coefficients obtained by using

literature’s pure compounds properties, an increasing of the positive deviations was observed, when

Li values were compared with that obtained in this work, as previously discussed. Literature data

presented Li values slightly higher than 2 when L

ix was close to 0 for three-suffix Margules

equation, also the most accurate model in this case. This highlights the fact that pure component

properties are important for a reliable modeling approach, being significant for the solid-liquid

equilibrium calculation.

Table 5. Pure fatty components properties from the literature (lit.) and in this work.

Component Temperature (K) Enthalpy (kJmol

-1)

lit. this work lit. this work

Triolein 277.95 a 278.15 100.000

a 115.560

1hexadecanol 321.60 b 322.34 58.400

c 56.591

1octadecanol 330.30 b

331.04 69.600 c

65.642

a Wesdorp (1990),

b Ventolà et al. (2004),

c Nichols et al. (2006).

64

4. CONCLUSIONS

In the present work the solid-liquid phase diagrams for the binary mixtures of

triolein + 1-hexadecanol and triolein + 1-octadecanol were measured using differential

scanning calorimetry. Both diagrams exhibited three well-defined transitions: the mixture

melting temperature, the solid-liquid transition related to the melting of triolein or of a

triolein-rich eutectic mixture and a solid-solid transition related to the triolein beta-prime

polymorph. The two- and three-suffix Margules equations and the group-contribution

UNIFAC and UNIFAC-Dortmund models were accurate for estimating the activity

coefficients of the liquid phase and provided a melting point of the fatty mixtures evaluated

with a global mean absolute deviation of 0.47 K. Micrographs showed that the assumption

of solid phase immiscibility was valid for the systems investigated. The present work also

showed that pure component properties are very important for developing a reliable

modeling approach.

ACKNOWLEDGMENTS

The authors are grateful to FAPESP (2008/56258-8 and 2009/54137-1) and CNPq

(304495/2010-7, 480992/20009-6 and 140718/2010-9) for the financial support.

REFERENCES

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Bruin, S., Phase equilibria for food products and process design. Fluid Phase Equilibria, 158, 657

(1999).

Carareto, N. D. D., Costa, M. C., Rolemberg, M. P., Krähenbühl, M. A. and Meirelles, A. J. A., The

solid-liquid phase diagrams of binary mixtures of even saturated fatty alcohols. Fluid Phase

Equilibria, 303, No. 2, 191 (2011).

Chiavone Filho, O. and Rasmussen, P., Modeling of salt solubilities in mixed solvents. Brazilian

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69

ON THE SOLID-LIQUID EQUILIBRIUM OF BINARY MIXTURES

OF FATTY ALCOHOLS AND FATTY ACIDS

(published in Fluid Phase Equilibria, v. 366, p. 88-98, 2014)

Guilherme J. Maximo a, Natália D. D. Carareto

a, Mariana C. Costa

b, Adenilson O. dos

Santos c, Lisandro P. Cardoso

d, Maria A. Krähenbühl

e, Antonio J. A. Meirelles

a*

a Laboratory of Extraction, Applied Thermodynamics and Equilibrium, School of Food

Engineering, University of Campinas (UNICAMP), R. Monteiro Lobato 80, 13083-862, Campinas,

São Paulo, Brazil. b School of Applied Sciences, University of Campinas, R. Pedro Zaccaria, 1300,

13484-350, Limeira, São Paulo, Brazil. c Social Sciences, Health and Technology Center, University

of Maranhão, 65900-410, Imperatriz, Maranhão, Brazil. d Institute of Physics Gleb Wataghin

(IFGW), University of Campinas, 13083-859, Campinas, São Paulo, Brazil. e DDPP - School of

Chemical Engineering, University of Campinas, 13083-970, Campinas, São Paulo, Brazil.

GRAPHICAL ABSTRACT

SLE phase diagrams of three fatty alcohol + fatty acid systems. Experimental measurements by

DSC and thermodynamic modeling for iL calculation. Liquid phase activity coefficients’

evaluation. Micrographs of the solid-liquid transition and X-ray diffraction of the solid-phase.

Chapter 3

70

ABSTRACT

Fatty alcohols and fatty acids are used in the cosmetic, pharmaceutical and food industries

as surfactants. They are also considered phase change materials for thermal storage

processes. Information on their thermal properties is required for optimizing production

processes as well as for improving their industrial and home use. In the present study, the

solid-liquid phase diagrams of three binary systems of 1-tetradecanol + dodecanoic acid, 1-

hexadecanol + tetradecanoic acid and 1-octadecanol + hexadecanoic acid were determined

by differential scanning calorimetry. The phase-transition phenomena were further

investigated by optical micrographs and X-ray diffraction patterns. The experimental data

showed that the systems present eutectic transitions and some exhibit also partial solid

phase miscibility. The liquid phase activity coefficients were calculated by Margules 2 and

3-suffix and by UNIFAC and UNIFAC-Dortmund methods. The modeling approach

resulted in an accurate prediction, with average absolute deviations from experimental data

lower than 1.16 K. The values of excess Gibbs energy present an unusual behavior, with

positive deviations at very low alcohol concentrations and negative ones at high

concentrations of this component. This occurs due to changes in the H-bonding interactions

along the concentration range of the mixture.

KEYWORDS: Solid-Liquid Equilibrium; Differential Scanning Calorimetry; Fatty

alcohols; Fatty acids; X-ray diffraction; Thermodynamic modeling.

71

1. INTRODUCTION

Fatty alcohols and fatty acids are biocompounds found in fats and oils, extracted

from them by separation processes or produced by specific routes from triacylglycerols.

They are widely used in the cosmetic, pharmaceutical and food industries as surfactant and

co-surfactant structuring agents for emulsification, gellation and coating [1-3]. Moreover,

different authors evaluated them as suitable phase change materials for thermal storage

processes, as required in solar energy application, cooling or heating systems and industrial

heat recovery [4, 5]. Under specific thermal conditions, fatty acids and alcohols exhibit

particular crystalline microstructures that influence the rheological and physical chemical

patterns of products involving such substances [6, 7]. Thus, taking into account design and

optimization of such applications, information about phase transitions of these compounds

and their mixtures is required. Nevertheless, these data are yet scarce in the literature.

Differential scanning calorimetry (DSC) and other techniques, such as optical

microscopy or X-ray diffraction, were frequently used for determination and analysis of

solid-liquid transitions of several pure substances and their mixtures, including fatty

compounds [8-19]. These techniques allow the evaluation of the phase diagrams,

particularly solid-liquid transitions or crystal formation behavior. In fact, recent studies

have shown that phase diagrams of binary systems of fatty acids are more complex than

they were usually presented by literature [11-13], suggesting a similar complexity for

systems of fatty acid + fatty alcohols.

In the present study, solid-liquid equilibrium data of three fatty mixtures, 1-

tetradecanol + dodecanoic acid, 1-hexadecanol + tetradecanoic acid and 1-octadecanol +

hexadecanoic acid, were measured by differential scanning calorimetry. Also, some thermal

72

transitions were evaluated with the aid of optical microscopy at controlled temperatures and

Xray diffraction analysis. The systems were modeled by solving the thermodynamic

equilibrium equations with an algorithm implemented in MATLAB. The liquid phase

activity coefficients were calculated using the two and three-suffix Margules equations

[20], the original UNIFAC [21] or the modified UNIFAC-Dortmund methods [22].

2. MATERIALS AND METHODS

2.1. Materials

Fatty compounds used in this work, supplier, mass fraction purity and method used

to confirm the purity are indicated in Table 1. Samples (1 g) of 1-tetradecanol + dodecanoic

acid, 1-hexadecanol + tetradecanoic acid and 1-octadecanol + hexadecanoic acid systems

were prepared gravimetrically on amber flasks in the whole composition range using an

analytical balance (Precisa Gravimetrics AG, Dietkon) with precision of 1×10-4

g. The

samples were pre-treated on Thermoprep (Metrohm, Herisau) by heating under a nitrogen

atmosphere until 15 K above the higher melting point of the components. The mixtures

were sealed at inert atmosphere, allowed to cool down to room temperature, and kept in a

freezer (below 273.15 K) until DSC analysis. The uncertainty of the compositions x1,

obtained by error propagation from the values of the weighed masses, was estimated as not

higher than 5×10−4

(in mole fractions).

73

Table 1. Fatty compounds used in this work, supplier, purification method, mole fraction purity and

method used to confirm the purity.

Chemical name Source

Mass

fraction purity

as received a

Purification

method b

Purity

analysis

method

Mole

fraction

purity

1-tetradecanol

Sigma-Aldrich

> 0.990 -

DSC c

0.995

1-hexadecanol > 0.990 - 0.994

1-octadecanol > 0.990 - 0.992

Dodecanoic acid > 0.990 - 0.991

Tetradecanoic acid > 0.990 - 0.994

Hexadecanoic acid > 0.990 - 0.995

a as reported by the supplier.

b no further purification method was required.

c using

the analysis

software from TA Instruments (New Castle). Fractional melting curves in Supplementary data.

2.2. Apparatus and procedure

2.2.1. Differential scanning calorimetry

The SLE data of the mixtures were characterized by DSC at local ambient pressure

p = 94.6 0.1 kPa, using a MDSC 2920 calorimeter (TA Instruments, New Castle)

equipped with a refrigerated cooling system which, in this work, operated between 250 K

and 350 K, using nitrogen as a purge gas. The melting temperature and heat flow were

previously calibrated with primary calibration standards, indium (certificated by

PerkinElmer, Waltham), naphthalene and cyclohexane (Merck, Whitehouse Station), with

purity greater than 0.99 mass fraction, at a heating rate of 1 K min−1

(such as that used in

the methodology described below). Samples of each mixture (2–5 mg) were weighed in a

microanalytical balance AD6 (PerkinElmer, Waltham) with precision of 1×10−6

g and put

in sealed aluminum pans. The methodology, as described by Costa et al. [10], is based on a

pre-treatment in order to erase previous thermal histories due to the fatty compounds

74

polymorphism effects. Thus, each sample was isothermally kept at 15 K above the highest

melting point of the components for 30 min. After this the samples were cooled to 40 K

below the lowest melting point of the components at a cooling rate of 1 Kmin−1

, and

allowed to stay at this temperature for 30 min. Finally, the samples were analyzed in a 1

Kmin−1

heating run. The temperatures of the thermal transitions were taken as the peak top

temperatures and the enthalpies were calculated from the area of the corresponding peaks.

The data were evaluated using the analysis software from TA Instruments (New Castle).

The uncertainties were calculated by performing up to five repeated DSC runs for

the pure compounds studied, and 2 – 4 repeated runs for eight binary mixtures selected

among the samples of the systems evaluated (replicates for the binary mixtures are reported

in Supplementary data). Table 2 shows the experimental pure components’ properties and

their standard deviations. The mean standard deviations of temperature values, including

the results obtained for the binary mixtures with 3 – 4 replicates, were not higher than 0.30 K

and this value was taken as the temperature experimental uncertainty. Moreover, the

experimental pure components’ properties were compared with data obtained from

literature [12, 18, 23-36]. The root-mean-square deviations were 0.63 K and 2.02 kJmol-1

for melting temperatures and enthalpy values, respectively, and the absolute deviations

obtained were close to the experimental errors.

75

Table 2. Experimental melting temperatures Tfus, solid-solid transitions Ttr and total melting

enthalpies fusH of the pure components obtained in this work and from literature.

Tfus / K Ttr / K fusH / ( kJ mol

-1 )

Component this work a literature this work

a literature this work

a literature

1-tetradecanol 311.39 0.08 311.2 [24] 310.45 0.10 310.8 [24] 47.6 1.0 48.4 [28]

311.2 [29] 310.8 [29]

47.0 [24]

311.2 [18] 310.1 [18]

49.5 [29]

312.0 [30]

47.3 [30]

1-hexadecanol 323.17 0.10 322.3 [29] 322.27 0.09 322.2 [24] 56.4 1.5 58.4 [29]

322.3 [24] 322.2 [29]

58.4 [24]

322.9 [23]

57.7 [27]

323.3 [18]

58.4 [28]

322.2 [27]

1-octadecanol 331.82 0.17 331.8 [23] 330.97 0.08 330.6 [32] 65.4 1.8 69.6 [28]

331.6 [18] 330.0 [36]

66.6 [33]

331.2 [32] 329.5 [33]

66.7 [32]

331.2 [25]

Dodecanoic acid 318.29 0.19 317.5 [26] 317.90 0.24 317.6 [12] 35.6 0.6 36.3 [26]

318.1 [12]

38.7 [12]

318.0 [34]

36.7 [24]

37.2 [35]

Tetradecanoic acid 328.13 0.16 327.5 [26] 327.65 0.16 328.2 [12] 43.8 0.8 45.2 [26]

328.9 [12]

44.0 [12]

327.3 [24]

45.2 [24]

328.0 [34]

49.5 [29]

Hexadecanoic acid 336.34 0.26 335.8 [26] - 53.3 1.1 52.3 [26]

335.4 [12]

55.9 [12]

335.7 [24]

54.9 [24]

337.5 [31]

52.0 [35]

336.4 [35]

53.4 [31]

337.7 [30]

51.4 [30]

a Experimental data obtained in this work and standard deviations of the values. Uncertainty for

melting temperature and solid-solid transitions temperature is 0.30 K and for melting enthalpy,

evaluated from the standard deviation.

2.2.2. Optical microscopy

The behavior of the solid-liquid transition of some mixtures among the evaluated

systems was additionally analyzed by temperature controlled optical microscopy using a

76

microscope Leica DM LM (Leica Microsystems, Wetzlar). The images were obtained by

putting a sample on a cover-slip in a hot stage FP82H, connected to a Mettler Toledo FP 90

(Mettler-Toledo, Columbus) central processor unit programmed to heat the sample at a

heating rate of 0.1 Kmin−1

until the melting of the sample. The images were acquired at

each 0.5 K with a magnification of 5.

2.2.3. X-ray diffraction

The solid phase of the systems was also evaluated by X-ray diffraction technique.

Diffractograms of the samples (0.2 - 0.4 g) were obtained using a Philips X’Pert

diffractometer (Philips Analytical, Almelo) operating in the reflection mode with an anode

of Cu–K (= 1.5406 Å) and diffracted-beam graphite monochromator. Diffraction data

were collected from 4° to 50° with a Bragg-Brentano geometry (:2) with steps of 0.02° at

each 2s. The procedure used anti–scatter slits for incident and diffracted beams of 1° and

receiving slit of 0.1 mm.

2.3. Thermodynamic modeling

Phase diagram modeling was carried out using the solid-liquid equilibrium equation

for each component of the mixture (Equation 1) as presented elsewhere [37, 38]

L Lfus tr fus fusi i

Sfu

fus

s tri i 1

1 1 1 1e ln 1xp

n

S

p

tr

H Hx

R T T R T T

C

R

T

T Tx

T

(1)

77

where xiL and xi

S are the mole fractions of the component i in the liquid (L) and solid (S)

phases, iL and i

S are the activity coefficients of the component i in the same phases, fusH

and Tfus are the melting enthalpy and temperature of the pure component i , T is the melting

temperature of the mixture, trH and Ttr are the solid-solid transitions enthalpies and

temperatures of the pure component i and fusCp is the heat capacity change of the pure

component i at melting temperature.

The modeling procedure was applied considering only the occurrence of a eutectic

reaction, based on the methodology described by Maximo et al. [19]. As a consequence, the

immiscibility in the solid phase was assumed, so that this phase is composed of pure fatty

acid or pure fatty alcohol (xiSi

S = 1). Moreover, the term related to fusCp can be neglected

as explained elsewhere [20, 37-39]. Also, as will be discussed later, fatty acids and alcohols

show polymorphism phenomena during the melting process with transition temperature

very close to melting temperature, i.e Ttr Tfus. In this case, the solid-solid transition

enthalpy trH can be embodied in the total melting enthalpy fusH. Thus, the SLE equation

1 can be simplified as presented in equation 2.

L L fusi i

fus

1 1exp

Hx

R T T

(2)

The iL values were calculated using the two and three-suffix Margules equations or

the group-contribution UNIFAC and modified UNIFAC-Dortmund models. Furthermore,

the systems were also modeled assuming the liquid phase as an ideal solution (iL

= 1).

Since the liquidus line was calculated for a simple eutectic mixture, the left-hand curve

corresponded to the equilibrium with a solid phase composed of pure fatty acid and the

78

right-hand curve corresponded to the equilibrium with a solid phase composed of pure fatty

alcohol, being the eutectic point their intersection.

In this procedure, the binaries parameters of Margules equations were numerically

estimated by an algorithm implemented in MATLAB 7.0. The algorithm was based on the

calculation of the melting temperatures by equation 2, rewritten as a function of T. The

adjustment of the two-suffix Margules equation’s parameter was a one-variable

minimization problem and implemented using a parabolic interpolation method (MATLAB

function fminbnd). Using the three-suffix Margules equation, a two-variable minimization

problem was carried out using a sequential quadratic programming method (MATLAB

function fmincon). In this case, the objective function was the summation of the square of

the absolute deviation ibetween experimental temperature Texp and the calculated one Tcalc

(Equations 3 and 4) for each composition xiL. When UNIFAC or UNIFACDortmund were

used as iL model, the algorithm was based on the sequential quadratic programming

(MATLAB function fmincon) for the calculation of the melting temperature of the mixtures

by minimization of the objective function (Equation 3). In this case, the routine was

repeated for 0 < xiL < 1 and the first iteration started with a melting temperature value

sufficiently close to the optimal solution. Moreover, the pure components’ melting

temperatures and enthalpy values, Tfus and fusH, used in equation 2, were taken from

experimental data measured in this work (Table 2).

2i exp calc i( ) T T (3)

fus fuscalc L L

fus fus i iln

H TT

H R T x

(4)

79


3.1. Experimental SLE data

Figures 1 to 3 show the solid-liquid phase diagrams and the thermograms of the

pure components and mixtures evaluated in the temperature range close to the biphasic

region: 1-tetradecanol + dodecanoic acid (Figure 1), 1-hexadecanol + tetradecanoic acid

(Figure 2) and 1-octadecanol + hexadecanoic acid (Figure 3). The experimental melting

temperatures obtained from DSC thermograms are presented in Tables 3 to 5. Since some

transitions presented in Tables 3 to 5 are not apparent in the phase diagrams of Figures 1 to

3 due to magnification effects, some details are presented in such figures in order to clearly

show some of these transitions (see inserts in Figures 2 and 3). For each one of the pure

alcohols, 1-tetradecanol, 1-hexadecanol and 1-octadecanol, two overlapped peaks were

observed in the region very close to melting temperature, probably related to rotator forms

(Ttrans,pure, Tables 3 to 5) that appear during melting and crystallization processes [18, 19,

40]. These rotator forms are structurally different but present very similar thermodynamic

properties what explains the overlapping of the peaks. The melting profiles of pure

dodecanoic and tetradecanoic acids also showed more than one and overlapped transitions

(see inserts in Figures 1 and 2, highlighted by black arrows) in agreement with literature

[12], indicating that probably there are also polymorphic transitions during the melting

processes of these fatty acids. With the occurrence of a marked overlap phenomenon in all

these cases, the determination of the enthalpy of the transition htr by means of peak area

measurement does not lead to accurate and reliable values.

80

Table 3. Experimental solid-liquid equilibrium data for 1-tetradecanol (1) + dodecanoic acid (2) for

mole fraction x, temperature T and pressure p = 94.6 kPa

a.

a Uncertainties for mole fraction, temperature and pressure are 0.0005, 0.30 K and 0.1 kPa,

respectively. b pure dodecanoic acid (2).

c pure 1-tetradecanol (1).

Figure 1. Solid-liquid phase diagram and thermograms for the system 1-tetradecanol (1) +

dodecanoic acid (2): experimental melting temperatures (○); transition of the pure component ();

eutectic transition (■); other transitions (+), and modeled data by three-suffix Margules equation

(); UNIFAC-Dortmund model ( ) and ideal assumption (—). Thermogram in detail shows

transition at x1 = 0.0000.

295.0

300.0

305.0

310.0

315.0

320.0

0.0 0.2 0.4 0.6 0.8 1.0

T/ K

x1-tetradecanol

Heat Flow

-15

-10

-505

Heat Flow (W/g)

-15

-10-505

Heat Flow (W/g)

27

52

80

28

52

90

29

53

00

30

53

10

31

53

20

Te

mpe

ratu

re (

K)

Exo

Up

Univ

ersa

l V4.5

A T

A I

nst

rum

ents

315

320

0.0

00

0

0.1

03

1

0.2

00

5

0.2

99

0

0.4

00

7

0.4

99

6

0.5

48

4

0.6

01

8

0.6

27

3

0.6

49

90

.69

96

0.7

99

0

0.9

00

2

x1 = 0.0000

x1

1.0

000

x1 Tfus / K T trans,pure / K Teutectic / K Ttrans1 / K Ttrans2 / K Ttrans3 / K Solid phase

0.0000 318.29 317.90 2b

0.1031 314.98 299.48 279.19 2

0.2005 312.70 300.20 278.40 2

0.2990 309.26 299.91 276.07 2

0.4007 306.95 299.73 278.92 2

0.4996 303.79 299.71 275.70 2

0.5484 301.61 299.03 2

0.6018 299.52 298.56 278.30 1c

0.6273 301.12 299.53 298.54 279.95 1

0.6499 301.41 299.51 298.21 281.48 1

0.6996 303.77 300.01 298.85 284.77 1

0.7990 306.44 299.92 298.40 289.24 285.62 1

0.9002 308.99 299.16 288.03 1

1.0000 311.39 310.45 1

81

Table 4. Experimental solid-liquid equilibrium data for 1-hexadecanol (1) + tetradecanoic acid (2)

for mole fraction x, temperature T and pressure p = 94.6 kPa

a.

x1 Tfus / K Ttrans,pure / K Teutectic / K Ttrans1 / K Ttrans2 / K Ttrans3 / K Ttrans4 / K Ttrans5 / K Solid phase

0.0000 328.13 327.65 2b

0.0982 325.88 312.44 2

0.1993 323.76 312.39 2

0.3042 321.80 312.57 306.71 2

0.3981 318.78 312.63 306.88 288.13 2

0.5020 315.20 312.66 311.82 307.43 287.39 2

0.5497 312.06 311.04 307.48 284.47 1c

0.6004 313.56 312.52 311.39 306.73 288.21 1

0.6506 314.21 312.06 310.85 307.53 291.21 284.10 1

0.7152 316.32 312.81 311.65 306.52 293.61 290.80 1

0.7951 319.19 312.81 311.53 305.97 299.30 294.47 1

0.8994 320.91 312.16 298.98 1

1.0000 323.17 322.27 1


respectively; b pure tetradecanoic acid (2);

c pure 1-hexadecanol (1).

Figure 2. Solid-liquid phase diagram and thermograms for the system 1-hexadecanol (1) +

tetradecanoic acid (2): experimental melting temperatures (○); transition of the pure component ();


(); UNIFAC-Dortmund model ( ) and ideal assumption (—). Thermograms in detail show

transitions at x1 = (0.0000 and 0.6004).

305.0

310.0

315.0

320.0

325.0

330.0

335.0

0.0 0.2 0.4 0.6 0.8 1.0

T/ K

x1-hexadecanol

Heat Flow

-50510

Heat Flow (W/g)

-5-3-113579

Heat Flow (W/g)

28

52

90

29

53

00

30

53

10

31

53

20

32

53

30

33

5

Tem

pera

ture

(K

)E

xo U

pU

nive

rsal

V4.

5A T

A I

nstr

umen

ts

325

330

305

307

0.0

000

0.0

98

2

0.1

993

0.3

042

0.3

98

1

0.5

02

0

0.5

497

0.6

004

0.6

50

6

0.7

15

2

0.7

951

0.8

994

1.0

00

0

x1

x1 = 0.6004

x1 = 0.0000

82

Table 5. Experimental solid-liquid equilibrium data for 1-octadecanol (1) + hexadecanoic acid (2)

for mole fraction x, temperature T and pressure p = 94.6 kPa

a.

x1 Tfus / K T trans,pure / K Teutectic / K Ttrans1 / K Ttrans2 / K Ttrans3 / K Ttrans4 / K Solid phase

0.0000 336.34 2b

0.0965 334.09 321.95 293.93 2

0.1981 332.36 322.05 294.23 2

0.3010 330.39 322.42 293.52 2

0.3992 327.63 322.34 290.86 2

0.4506 325.29 321.60 294.05 2

0.4999 322.80 312.48 292.58 2

0.5534 322.15 316.01 293.62 1c

0.5978 323.64 322.13 314.59 293.10 1

0.7010 326.00 321.82 315.67 303.69 292.74 1

0.7993 327.82 322.69 314.86 307.70 304.76 1

0.8990 329.93 321.67 319.88 307.58 1

0.9508 330.65 1 + 2 d

1.0000 331.82 330.97 1


respectively; b pure hexadecanoic acid (2);

c pure 1-octadecanol (1);

d solid solution composed by 1-

octadecanol (1) and hexadecanoic acid (2).

Figure 3. Solid-liquid phase diagram and thermograms for the system 1-octadecanol (1) +

hexadecanoic acid (2): experimental melting temperatures (○); transition of the pure component ();


(); UNIFAC-Dortmund model ( ) and ideal assumption (—). Thermogram in detail shows

transition at x1 = 0.5978.

310.0

315.0

320.0

325.0

330.0

335.0

340.0

0.0 0.2 0.4 0.6 0.8 1.0

T/ K

x1-octadecanol

Heat Flow

-12

-10

-8-6-4-202

Heat Flow (W/g)

-15

-10-505

Heat Flow (W/g)

29

03

10

33

0

Te

mpe

ratu

re (

K)

Exo

Up

Univ

ersa

l V4.5

A T

A I

nst

rum

ents

311

316

0.0

00

0

0.0

965

0.1

98

1

0.3

01

0

0.3

99

2

0.4

506

0.4

999

0.5

53

4

0.5

97

8

0.7

010

0.7

993

0.8

99

0

1.0

000

x1

0.9

508

x1 = 0.5978

83

The thermal analysis of the mixtures showed at least two well-defined endothermic

peaks. The thermal transition at the higher temperature is related to the melting temperature

of the mixture (Tfus, Tables 3 to 5). The second transition is the eutectic reaction

(Teutectic,Tables 3 to 5). For the systems with 1-tetradecanol and 1-octadecanol the intensity

of the eutectic thermal transition decreased when the concentration was close to pure fatty

alcohol and at x1-octadecanol 0.95 mole fraction no thermal transition at the eutectic

temperature was observed, showing that the compounds involved in these mixtures may

probably be partially miscible, close to this concentration range. However, since the

observation of no eutectic peaks could be also related to weak transitions due to the

proximity to the pure compound concentration, this aspect will be further investigated by

Tammann plots evaluation, powder X-Ray diffractometry and later discussed.

The thermograms of the mixtures also presented endothermic peaks below the

eutectic reaction temperature. In some cases, these peaks, which are related to solid-solid

thermal transitions, are overlapped, indicating the existence of a complex phase diagram

probably due to the fatty compounds’ polymorphism. The solid-solid transitions

temperatures (Ttrans1 to Ttrans5) are also presented in Tables 3 to 5. Moreover, it was observed

that some thermograms of the mixtures presented thermal transitions inside the biphasic

region (above eutectic temperature and below liquidus line). These transitions could be

probably related to metastable molecular conformations of the fatty compounds but

eventually to peritectic or metatectic reactions [11, 13]. In order to check this supposition,

some of these samples were submitted to a heating-cooling cycle treatment during which

the sample was cooled down from 15 K above the highest melting point of the components

to 40 K below the lowest melting point of the components at a cooling rate of 5 Kmin−1

84

and allowed to stay at this temperature for 30 min. Then, the sample was heated to the onset

temperature at which it was observed the supposed metastable transition and kept there for

60 min. The final cycle followed the aforementioned methodology by which the sample

was cooled down to the lower temperature, kept isothermally for 30 min and heated again

at the same rate of 1 Kmin-1

until sample melting. Figure 4 shows the results of the thermal

annealing for mixtures of 1-hexadecanol (1) + tetradecanoic acid (2) at x1 = (0.3042 and

0.8994) mole fractions whose related transitions are indicated by the black arrows. The

thermograms obtained before the thermal treatment (Figure 4, curves I) show two peaks in

the region of solid-liquid transition related to melting and eutectic reaction, and a very

small one comprised between the melting and eutectic peaks. As can be seen, after thermal

treatment (Figure 4, curves II) the very small peak was clearly not observed, indicating that,

in fact, it is related to a metastable transition. According to literature [26, 41] the crystals

network structure of the fatty compounds presents, during thermal processes, transitions

through hexagonal and metastable chain packings to orthorhombic and more stable states.

When submitted to a thermal annealing based treatment, which consisted in an isothermal

condition in a specific temperature followed by a cooling process at a low rate, the structure

of the material is supposedly converted. Considering that after the thermal treatment such

transitions were no longer observed, one can suppose that they were related to a residual

solid-phase in hexagonal chain packing that was converted to the orthorhombic and more

stable form. In fact, as previously observed, the thermograms of the fatty acids and fatty

alcohols presented polymorphic forms with different chain packing and stability which

probably induced the appearance of these metastable transitions observed in the

calorimetric measurements. Therefore, since it was confirmed that these transitions are

metastable phenomena that can be eliminated by a proper thermal treatment of the sample,

85

they were not presented in Tables 3 – 5. Note that solid-solid transitions below eutectic

reaction are reported in data Tables 3 – 5 but further analyses are still required.

Figure 4. Effect of the thermal annealing based treatment on thermograms of 1-hexadecanol (1) +

tetradecanoic acid (2) at (A) x1 = 0.8994 and at (B) x1 = 0.3042: I, heating curve without the thermal

treatment and; II, after thermal treatment. The metastable transition is shown by the black arrow.

The phase diagrams of the systems were very similar to each other. In all cases, the

liquidus lines showed just one inflexion point in the temperature of the invariant thermal

transition temperature observed in the thermograms, namely the eutectic transition. The

phase diagrams presented at least four well-defined regions, with the first one related to a

liquid phase above liquidus line, two biphasic regions between the melting temperature and

the eutectic transition and a solid phase below eutectic temperature. At the left side of the

diagram, the biphasic region corresponds to a liquid mixture in equilibrium with pure fatty

acid in the solid phase. At the right side the biphasic region corresponds to a liquid mixture

in equilibrium with pure fatty alcohol or, as it will be discussed later, a fatty alcohol-rich

solid phase. In this last case a fifth region occurs in the right side of the diagram. This

behavior is very similar to the so-called eutectic system that is commonly found in the

295 305 315 325 335

Hea

t fl

ow

T / K

295 305 315 325 335

T / K-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

He

at

Flo

w (

W/g

)

295 305 315 325 335

Temperature (K)Exo Up Universal V4.5A TA Instruments

-2

0

He

at

Flo

w (

W/g

)

295 305 315 325 335


-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

He

at

Flo

w (

W/g

)

295 305 315 325 335


II

I

(B)(A)

II

I

86

literature in case of fatty mixtures [10, 17], for which small regions of miscibility may

occur in the solid phase, usually close to the extremes of the phase diagram. Tables 3 to 5

present the compound in the solid phase that is in equilibrium with the liquid phase, being a

pure compound or a solid solution, in case of miscibility of the solid phase, according the

evaluation of the Tammann plots, discussed as follows.

3.2. Eutectic point and immiscibility assumption

Figure 5 exhibits the behavior of the enthalpy variation of the systems’ invariant

transitions as a function of the concentration. This diagram is the so-called Tammann plot

and allowed the characterization of the eutectic point, since the corresponding enthalpy

increases as the mixture concentration comes close to the eutectic composition and should

begin to decrease after this transition [17, 42]. Experimental data were submitted to linear

regression and equations were presented in Figure 5. In the hypothesis of immiscibility of

solid phase, it was assumed that heutetic = 0 for x1 = 1 or 0. Since R2 > 0.98 for all cases,

the assumption is, most probably, valid. Fitted data allowed the determination of the

experimental eutectic points, xalcohol, eutetic = (0.5750, 0.5490 and 0.5100) mole fraction for the

systems 1-tetradecanol + dodecanoic acid, 1-hexadecanol + tetradecanoic acid and 1-

octadecanol + hexadecanoic acid, respectively.

87

Figure 5. Tammann plots of the eutectic transition (■) for: (A) 1-tetradecanol + dodecanoic acid;

(B) 1-hexadecanol + tetradecanoic acid and (C) 1-octadecanol + hexadecanoic acid as well as linear

regression (- - -) of the data.

The experimental behavior around the eutectic temperature could also be observed

by optical micrographs. Figure 6 shows results for the 1-hexadecanol + tetradecanoic acid

system at x1-hexadecanol = 0.3981 mole fraction (micrographs A to D) and for the 1-

octadecanol + hexadecanoic acid system at x1-octadecanol = 0.7993 mole fraction (micrographs

E to H). For the first system, at T = 311.75 K (Figure 6 A) both components were in the

solid phase. As the temperature was raised to T = 313.65 K (Figure 6 B) a fraction of the

solid crystals started to melt and this phenomenon is indicated in the Figure 6 B by white

arrows. A slight increase of the temperature from T = 313.65 K to T = 313.75 K (Figure 6

C) was sufficient to induce the increase of the amount of melted mixture in the sample, as

could be clearly observed in the border of the crystals. With the continuous increase in

temperature inside biphasic region the fraction of the liquid phase also increased (Figure 6

D), as expected and in agreement with the lever rule. The optical micrographs of the system

1-octadecanol + hexadecanoic acid (Figures 6 E to H) presented a similar behavior, since

the liquid phase fraction increased as temperature increased with the beginning of melting

y = 63.632xR² = 0.9898

y = -103.45x + 96.03R² = 0.9817

0.0

10.0

20.0

30.0

40.0

50.0

h

eu

teti

c/

kJm

ol-1

x1-tetradecanol

y = 54.04xR² = 0.9836

y = -65.73x + 65.73R² = 0.9822

x1-hexadecanol

y = 81.769xR² = 0.9909

y = -105.36x + 95.222R² = 0.9552

x1-octadecanol

(A) (B) (C)

0.0 1.0 0.0 0.01.0 1.00.50.50.5

88

transition at the eutectic temperature. In this case, some of the melting phenomena observed

are indicated by white arrows. Moreover, some images of these mixtures at other

compositions were taken at temperatures below the eutectic point and, as expected, it was

observed no liquid fraction, in agreement with experimental DSC results.

Figure 6. Optical micrographs of samples of 1-hexadecanol (1) + tetradecanoic acid (2) at x1 =

0.3981 and (A) 311.75 K; (B) 313.65 K; (C) 313.75 K; (D) 314.55 K and 1-octadecanol (1) +

hexadecanoic acid (2) at x1 = 0.7993 and (E) 319.15 K; (F) 321.15 K; (G) 322.25 K; (D) 325.65 K.

Some details are shown by white arrows. Magnification of 5.

The Tammann curves also allowed to determinate the regions of miscibility in the

phase diagrams. If complete immiscibility of the solid phase occurs, the enthalpy values of

the eutectic reaction tend to zero when mixture concentration tends to the pure components.

However, the Tammann plots of the mixtures of 1-tetradecanol + dodecanoic acid and 1-

octadecanol + hexadecanoic acid showed that the solid components of these binaries in the

right side of the phase diagram are partially miscible because the enthalpy variation value

200 mm

200 mm

200 mm 200 mm 200 mm

200 mm 200 mm 200 mm

A B C D

HGFE

89

tended to zero at x1-tetradecanol = 0.9283 mole fraction and at x1-octadecanol = 0.9038 mole

fraction.

3.3. Evaluation of the solid-phase

In order to evaluate some aspects of the behavior of the solid phase of the systems,

diffraction patterns at T = 298.15 K and at different compositions of the 1-hexadecanol (1)

+ tetradecanoic acid (2) and 1-octadecanol (1) + hexadecanoic acid (2) systems were

carried out at 15.0° < 2 < 27.5°, which is the diffraction angle range in which it was

observed the most meaningful diffraction profiles (see Figure 7). According to the

system’s phase diagram (Figures 1 to 3) at T = 298.15 K both components in all systems

are in the solid state. Figure 7 A, that presents the 1-hexadecanol (1) + tetradecanoic acid

(2) system, shows that pure tetradecanoic acid (x1 = 0.0000 mole fraction) presents some

overlapped diffraction peaks at the regions close to 2θ (19°, 21.5° and 24°) and pure 1-

hexadecanol (x1 = 1.0000 mole fraction) exhibits two intense diffraction peaks at 2θ 21.5°

and 2θ 24.5° and a mild peak at 2θ 20.5°. For this system, the diffraction patterns of the

mixtures shows that pure components’ diffraction peaks could be observed throughout the

concentration range, except for x1 = 0.8994 mole fraction. At this concentration, the

behavior differed from the pure component pattern suggesting that the crystalline structure

of the mixture was changed. In fact, according to Table 4, at x1 = 0.8994 mole fraction the

DSC measurements showed that at T = 298.98 K a solid transition was observed (Ttrans 4,

Table 4).

90

Figure 7. Difractograms at T = 298.15 K for (A) 1-hexadecanol (1) + tetradecanoic acid (2), from

up to down: x1 = (0.0000, 0.0982, 0.1993, 0.3042, 0.5020, 0.6004, 0.7152, 0.7951, 0.8994, 1.0000)

mole fraction and for (B) 1-octadecanol (1) + hexadecanoic acid (2), from up to down: x1 =

(0.0000, 0.3010, 0.4999, 0.7010, 0.8990, 0.9508, 1.0000) mole fraction.

Furthermore, the overall evaluation of the diffractograms suggested that both pure

components coexist in the solid phase and they were independently crystallized, in

agreement with the previous evaluation of the immiscibility assumption that was took into

account in the modeling approach and observed by the DSC data and the Tammann plots

(Figure 5 B). Figure 7 B, that presents the 1-octadecanol (1) + hexadecanoic acid (2)

system, shows that pure hexadecanoic acid (x1 = 0.0000 mole fraction) presents two intense

diffraction peaks at 2θ 21.0° and 2θ 24.5° and a mild peak at 2θ 20.5° and pure 1-

octadecanol (x1 = 1.0000 mole fraction) exhibits also two intense diffraction peaks at the

same diffraction angles and two other mild peaks at 2θ 20.5° and 2θ 22.5°. In this case,

the diffraction patterns of the mixtures shows that both pure 1-octadecanol and

hexadecanoic acid coexist in the solid phase in a concentration range up to x1 = 0.8990

mole fraction, because the pure components’ diffraction peaks could be clearly observed up

15.0 17.5 20.0 22.5 25.0 27.5

Inte

nsi

ty (

u.a

.)

2

(B)

15.0 17.5 20.0 22.5 25.0 27.5

Inte

nsi

ty (

u.a

.)

2

(A)

91

to this concentration. However, the mixture at x1 = 0.9508 mole fraction presented a

diffraction pattern equal to that of pure 1-octadecanol. In fact, according to the evaluation

of the Tammann plots this system presented partial miscibility at x1 > 0.9038 mole fraction.

Thus, at this concentration, both components were not independently crystallized and

because this solid solution is a 1-octadecanol-rich mixture, its diffraction pattern is similar

to that one observed for pure 1-octadecanol.

3.4. Thermodynamic modeling of SLE data

Table 6 shows the deviations between calculated and experimental data for each

modeling approach as well as the binary parameters (Jmol-1

) for both Margules equations.

First of all, since it was observed a very small solubility of the solid phase for two systems

and a complete insolubility for one of them, the modeling assumed that the mixtures

behaves as a simple eutectic system. It was observed that liquidus line was well described

by all models since the average absolute deviations were less than 1.2 K for all, including

the ideal assumption. The modeling approach using the three-suffix Margules equation as

iL model allowed a better description of the systems’ behavior.

The values of the liquid phase activity coefficients indicated that these systems are

slightly non-ideal. This could be observed by the modeled data in the SLE phase diagrams

(Figures 1 to 3) by which for the 1-tetradecanol + dodecanoic acid and 1-hexadecanol +

tetradecanoic acid systems, the deviations of the ideal liquidus lines were positive at low

concentrations of fatty alcohols and negative at high concentrations of this compound.

Moreover, for the 1-octadecanol + hexadecanoic acid system, the deviation of the ideal

92

liquidus line was negative throughout the phase diagram. These observations are in

agreement with literature’s liquid phase activity coefficients at infinite dilution for

analogous fatty mixtures or other acid-alcohol mixtures [43-45].

Table 6. Estimated parameters, A and B, and mean absolute deviations a between

predicted and experimental data.

Model 1-tetradecanol +

dodecanoic acid

1-hexadecanol +

tetradecanoic acid

1-octadecanol +

hexadecanoic acid

Two-suffix Margules A / J mol-1

-496.86 -501.24 -938.79

/ K 0.92 0.71 0.36

Three-suffix Margules A / J mol-1

-912.33 -1027.24 -1168.16

B / J mol-1

-1351.78 -1199.45 -440.745

/ K 0.50 0.28 0.28

UNIFAC / K 1.07 0.88 0.44

UNIFAC-Dortmund / K 1.16 0.92 0.68

Ideal / K 1.11 0.93 0.63

aexp predn

i i i

n

T T

Figure 8 shows the liquid phase activity coefficients for the system 1-hexadecanol +

tetradecanoic acid (Figure 8 A) as well as the behavior of the corresponding excess Gibbs

free energy (GE) (Figure 8 B), calculated using the three-suffix Margules equation, the most

accurate model. It is worth noting that this system exhibits a simple eutectic behavior, with

total immiscibility in the solid phase. In this case, the modeling approach based on equation

2 requires absolutely no approximation, increasing the reliability of the liquid phase activity

coefficients estimated using the three-suffix Margules model.

93

Figure 8. (A) Liquid-phase activity coefficients and (B) Mixtures’ excess free Gibbs energy

calculate by three-suffix Margules equation (in detail, magnification for x1 < 0.1) for 1-hexadecanol

(1) + tetradecanoic acid (2): 1L ( ), 2

L () and i

L (○) calculated from experimental data by

SLE equation.

It could be observed that when alcohol is added to pure fatty acid, the acid activity

coefficient increases until reaching a maximum value, when it begins to decrease with the

increasing of alcohol concentration. On the other hand, when acid is added to pure fatty

alcohol, the alcohol activity coefficient tends to decrease until reaching a minimum value,

when it begins to increase. In addition, GE values presented negative deviations throughout

the concentration range, except for slightly positive deviations at the region of low

concentration of fatty alcohol.

This behavior can be probably explained on the basis of two main factors, namely

intermolecular H-bonding interactions and changes observed in these interactions along the

entire concentration range of the mixture. Mixtures containing fatty acids and/or alcohols

exhibit van der Waals interactions between their carbon chains and H-bonding interactions

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0.0 0.2 0.4 0.6 0.8 1.0

i

x1-hexadecanol

-350

-250

-150

-50

50

0.0 0.2 0.4 0.6 0.8 1.0

GE

n-1

/ Jm

ol-1

x1-hexadecanol

-5

0

5

0.0 0.1

(A) (B)

94

between their polar groups. It is well known that the energy of H-bonding interactions

between carboxyl moieties is greater than that observed between the hydroxyl groups

belonging to alcohol molecules, because the adjacent hydroxyl and carbonyl groups of the

carboxyl moiety makes this moiety even more strongly polarized [46, 47]. Furthermore, H-

bonding interactions between carboxylic acid molecules are responsible for their trend to

self associate and form dimers.

Considering the addition of alcohol molecules to the pure organic acid, some of the

H-bonding interactions between two carboxylic acids are broken and replaced by the

relatively weaker H-bonding interactions between hydroxyl and carboxyl groups, which

explains the positive deviations of the fatty acid activity coefficients as well as the positive

deviations of the GE

values and so the lower stability of the mixture than the corresponding

ideal one at low alcohol concentrations. On the other hand, the H-bonding interactions

between hydroxyl and carboxyl groups may engage a large number of molecules, so that

this kind of H-bonding can build a network of interacting molecules, compensating its

relative weakness in comparison to H-bonding involving only carboxyl moieties by the

pervasiveness of its effect along the mixture. Such behavior probably predominates as the

alcohol concentration raises, since this increases the likelihood that carboxyl moieties

interact by H-bonding with hydroxyl groups of the alcohol molecules. It also favors the

stabilization of the system (GE < 0) and explains the negative deviations of the fatty acid

activity coefficients.

Considering the addition of acid molecules to pure fatty alcohol, some of the H-

bonding interactions between two alcohol molecules are broken and replaced, in the present

case, by the relatively stronger H-bonding interactions between hydroxyl and carboxyl

groups. This justifies the observed negative deviations of the alcohol activity coefficients.

95

On the other hand, the continuous increase of the concentration of fatty acid raises the

likelihood of the energetically more favorable H-bonding interactions between two

carboxyl moieties. This means that, after some concentration value of fatty acid, the H-

bonding interactions between acid molecules tend to predominate, causing an inversion in

the trend of decreasing alcohol activity coefficients. Furthermore, the alcohol activity

coefficient assumes values above 1.0 in the diluted alcohol solutions, probably because the

alcohol molecules, in this range of concentrations, are surrounded by organic acids

interacting strongly with one another, i.e. they are in fact surrounded mainly by organic

acid dimers.

Moreover, Figure 8 A shows the experimental activity coefficients of the liquid

phase calculated from the SLE model (Equation 2). This estimation took into account the

standard deviations of the experimental pure compounds properties fusH and Tfus from

Table 1, so that the iL-errors are also shown in Figure 8 A. As it can be seen, the

experimental values are in good agreement with those calculated using the three-suffix

Margules equation. It is important to note that, as immiscibility assumption was taken into

account, the experimental iL were calculated only in the concentration range that the

species were in both phases, i.e., compound 2 before eutectic concentration and compound

1 after this.

Additional information on the non-ideal behavior of the systems could be obtained

if the experimental errors of the pure compounds’ properties (Table 2) are taken into

account in the estimation of the ideal melting temperatures. Figure 9 shows the description

of the SLE diagram of the system 1-tetradecanol + dodecanoic acid with such assumptions.

It could be observed that there is no significant difference between most of experimental

96

melting point data and the calculated liquidus line below the eutectic concentration. Similar

results were obtained for the other two systems. As mentioned before, at this concentration

range, the most accurate model, three-suffix Margules equation, provided slightly positive

deviations and this observation is in reasonable agreement to literature review.

Nevertheless, modeled melting temperatures are within the uncertainty range of values

around the ideal behavior, so that these mixtures may be approximated by ideal systems in

case of fatty alcohol concentrations lower than the eutectic point. Moreover, after this

concentration, the system presents a significant non-ideal behavior with negative deviations

from ideality, confirming the above discussion.

Figure 9. Effect of the pure compounds’ standard deviations data in the modeling of the liquidus

line for 1-hexadecanol + tetradecanoic acid: experimental data (○); error bars = 0.30 K

(temperature’s experimental uncertainty); ideal assumption with mean values of the pure

compounds’ melting properties () and modeling considering the standard deviations of the pure

compounds’ properties (- - -).

310.0

314.0

318.0

322.0

326.0

330.0

0.0 0.2 0.4 0.6 0.8 1.0

T/

K

x1-hexadecanol

97

4. CONCLUSIONS

Solid-liquid equilibrium for the binary mixtures of 1tetradecanol + dodecanoic

acid, 1hexadecanol + tetradecanoic acid and 1-octadecanol + hexadecanoic acid were

measured using differential scanning calorimetry. Phase diagrams exhibited two well-

defined transitions that were the mixture melting temperature and the eutectic reaction.

Systems also presented many thermal transitions below eutectic temperature and other

metastable transitions above eutectic temperature. Micrographs allowed the observation of

the melting behavior around the eutectic temperature and the results were in agreement

with the lever rule. According to the DSC data, Tammann plots and X-ray diffraction

analysis, the mixtures of 1tetradecanol + dodecanoic acid and 1-octadecanol +

hexadecanoic presented partial miscibility in the solid phase within the concentration range

close to the pure fatty alcohol, unlike the 1-hexadecanol + tetradecanoic acid system for

which the pure compounds were independently crystallized along the entire concentration

range. The two-suffix Margules equations, the group-contribution UNIFAC and UNIFAC-

Dortmund methods were accurate for describing the melting point of the evaluated fatty

mixtures, since the mean absolute deviations were less than 1.16 K. The approach based on

the three-suffix Margules equation gave the best results with mean absolute deviation less

than 0.36 K.

98

ACKNOWLEDGEMENTS

The authors are grateful to FAPESP (2008/56258-8, 2009/54137-1 and 2012/05027-

1) and CNPq (304495/2010-7, 483340/2012-0 and 140718/2010-9) for the financial

support.

REFERENCES

[1] R.R. Egan, G.W. Earl, J. Ackerman, J. Am. Oil Chem. Soc., 61 (1984) 324-329.

[2] J. Daniel, R. Rajasekharan, J. Am. Oil Chem. Soc., 80 (2003) 417-421.

[3] H.M. Schaink, K.F. van Malssen, S. Morgado-Alves, D. Kalnin, E. van der Linden, Food Res.

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101

SUPPLEMENTARY DATA

Purity analysis of the pure compounds

Figure S1 depicts the fractional melting curves for the pure compounds used in this

work and the fitted curves by linear regression. Note that, except for hexadecanoic acid,

polymorphic phenomena were observed in all pure compounds. However, temperature of

the polymorphic form is very close to the melting temperature of the compound, being the

difference between both temperatures of up to 1.0 K approximately. Thus, even with the

changes in the fractional melting curve profile generated by this phenomenon, purity mole

fractions are higher than 0.990 for all cases. Figure S2 show the thermogram for pure 1-

hexadecanol that present a polymorphic form, as well as fractional melting curves,

depicting this fact. Data were evaluated using the analysis software from TA Instruments

(New Castle).

Figure S1. Fractional melting curves obtained by DSC. Data were evaluated using

the analysis

software from TA Instruments (New Castle).

y = - 0.128 x + 317.540R² = 0.994

y = - 0.102 x + 327.640R² = 0.997

y = - 0.149 x + 335.940R² = 0.994

y = - 0.357 x + 311.000R² = 0.985

y = - 0.265 x + 322.920R² = 0.983

y = - 0.174 x + 331.210R² = 0.984

305

310

315

320

325

330

335

340

0 4 8 12

Tem

pera

ture / K

Total area / partial area

DtotalH /DpartialH

(with area correction)

Dodecanoic acid

Tetradecanoic acid

Hexadecanoic acid

1-Tetradecanol

1-Hexadecanol

1-Octadecanol

102

Figure S2. Thermogram and fractional melting curves for 1-hexadecanol. Data were evaluated

using the analysis software from TA Instruments (New Castle).

103

Table S1. Solid-liquid and solid-solid transitions temperatures obtained in replicates for 8 binary

mixtures a.

System x1 replic. Tfus / K Teut / K Ttrans / K

1-tetradecanol (1) + dodecanoic acid (2)

0.6018 1 299.52 298.56 278.30

2 300.73 298.53 277.72

1-hexadecanol (1) + tetradecanoic acid (2) 0.3042 1 321.80 312.57 306.71

2 321.40 312.31 305.86

3 321.58 312.46 305.82

1-hexadecanol (1) + tetradecanoic acid (2)

0.6004 1 313.56 312.39 311.39 306.73 288.21

2 313.98 312.83 311.75 306.37 288.30

1-hexadecanol (1) + tetradecanoic acid (2) 0.8994 1 320.91 312.16 298.98

2 320.69 311.87 299.04

3 320.69 311.60 298.91

4 320.85 312.02 298.98

1-octadecanol (1) + hexadecanoic acid (2)

0.4999 1 322.80 312.48 292.58

2 322.42 313.10 293.33

1-octadecanol (1) + hexadecanoic acid (2) 0.7010 b 1 326.00 321.82 315.67 303.69 292.74

2 325.99 322.27 315.56 303.69 292.70

3 326.02 322.46 315.93 302.82 293.20

1-octadecanol (1) + hexadecanoic acid (2) 0.7993 1 327.82 322.69 314.86 307.70 304.76

2 327.80 321.91 314.51 307.83 304.31

3 327.71 321.94 314.93 308.03 304.84

a the mean standard deviation taking into account Tfus, Teut and Ttrans and related to the results

obtained for the systems with 3-4 replicates is 0.24 K. b

Results for this composition were depicted

in Figure S3.

104

Figure S3. Replicates of the DSC thermograms for 1-octadecanol (1) + hexadecanoic acid (2) x1 =

0.7010. In detail, magnification highlighting a solid-solid transition at T = 292.74 K.

290 300 310 320 330

Hea

t fl

ow

Temperature / K

3rd replicate

2nd replicate

1st replicate

290 300 310

105

LIPIDIC PROTIC IONIC LIQUID CRYSTALS

(published in ACS Sustainable Chemistry & Engineering, 2014, in press)

Guilherme J. Maximo, †‡

Ricardo J. B. N. Santos, ‡ José A. Lopes-da-Silva,

§ Mariana C.

Costa, ║

Antonio J. A. Meirelles † and João A. P. Coutinho*

‡

† Laboratory of Extraction, Applied Thermodynamics and Equilibrium, School of Food

Engineering, University of Campinas, Campinas, São Paulo, Brazil. ‡ CICECO, Chemistry

Department, University of Aveiro, 3810-193, Aveiro, Portugal. § QOPNA, Chemistry Department,

University of Aveiro, 3810-193, Aveiro, Portugal. ║

School of Applied Sciences, University of

Campinas, 13484-350, Limeira, São Paulo, Brazil.

GRAPHICAL ABSTRACT

Mixtures of fatty acids and ethanolamines show a complex multiphase diagram resulting in

the formation of protic ionic liquid crystals with non-Newtonian behavior.

Chapter 4

106

ABSTRACT

Protic ionic liquids (PILs) based on lipidic compounds have a range of industrial

applications, revealing the potential of oil chemistry as a sustainable basis for the synthesis

of ionic liquids. PILs of fatty acids with ethanolamines are here disclosed to form ionic

liquid crystals, and their mixtures with the parent fatty acids and ethanolamines display a

lyotropic behavior. Aiming at characterizing their rheologic and phase behavior, four

ethanolamine carboxylates and the mixtures used for their synthesis through a Brønsted

acid-base reaction are investigated. Their phase diagrams present a complex multiphase

profile, exhibiting lyotropic mesophases as well as solid-liquid biphasic domains with a

congruent melting behavior. These PILs present a high self-assembling ability and a non-

Newtonian behavior with yield stress in the liquid crystal mesophase. The appearance of

lamellar and hexagonal structures, with probably normal and inverted configurations in the

mixtures, due to the formation of the PIL is responsible for the high viscoelasticity and

notable nonideality that is mainly ruled by hydrophobic / hydrophilic interactions.

Considering their renewable origin, the formation of liquid crystalline structures, in

addition to the non-Newtonian behavior and ionic liquids properties, and the mixtures here

evaluated possess a great potential, and numerous applications may be foreseen.

KEYWORDS: Ionic liquids, Solid-liquid Equilibrium, Fatty acid, Ethanolamine, Liquid

crystal, Rheology.

107

1. INTRODUCTION

More than a remarkable presence in the open literature during the past decade, ionic

liquids and mesotherm (i.e. low melting point) salts have long since been embodied in a

large range of detergents, personal care cosmetic, pharmaceuticals and chemical marketed

products. The interest for ionic liquids, salts with melting temperatures below 100°C, was

driven by their peculiar properties: negligible vapor-pressure, wide liquid phase range, no

or limited flammability and a tunability that offers freedom for the design and optimization

of chemical processes and product formulation. Such flexibility makes them also

environmentally friendly by reducing the amount of byproducts in the industry 1-3

. A wide

range of mesotherm salts based on fatty acids and their derivatives have been used long

since as surfactants, and for many other purposes, without actually being recognized as

ionic liquids. Protic ionic liquids (PILs) are produced through a Brønsted acid-base reaction

(Figure 1) and therefore, are capable of particular chemical interactions, including proton

acceptance and proton donation. Because they are easily prepared, often from low-cost or

even renewable reactants, PILs may be used in several industrial applications besides their

use as surfactants, such as the design of electrolyte fuel cells, biocatalytic reactions,

separation, and self-assembly processes 4-6

.

Addressing the claims of sustainable chemistry, the search for natural sources for

the synthesis of ionic liquids with low environmental impacts seems to be more than a

forthcoming trend; it seems to be an imperative demand 7-9

. In this way, taking into account

the renewable aspects and relevance of several industrial sectors in the actual worldwide

economic scenario, oil chemistry shows great potential to serve as a sustainable supplier of

green-chemicals. In fact, nowadays, the world production and consumption of vegetable

108

oils is larger than 150 millions of tons 10

. Considering not only the refining process, but

also several other steps of the oil production chain, the fatty acids emerge as a widely

relevant byproduct. Being edible, chemically attractive, due to the particular properties of

their long carbon chain, and having low toxicity, they are widely used by the industry as the

anion for the production of salts, and potentially of PILs, with properties tailored by choice

of an appropriate proton acceptor 11-15

. Alkanolamines, such as mono-, di- or tri-

ethanolamine, are compounds naturally found in phospholipid biological membranes. They

are often taken as the cation of the acid-base reaction with fatty acids to produce soaps,

which are actually PILs, used in the formulation of industrial and hand-cleaners, cosmetic

creams, aerosol shave foams, and industrial lubricants due to their excellent emulsifying,

thickening and detergent ability in oil-in-water emulsions 16-19

. In particular, the

monoethanolamine oleate is long been embodied in the pharmaceutical industry. Approved

by U.S. Food and Drug Administration (FDA), it acts as sclerosant agent when a diluted

solution is administrated intravenously in the treatment of leg veins, bleeding esophageal

varices, mucosal varicosities, and other similar surgical procedures 20-23

. This is quite

curious taking into account that ILs’ research is looking for effective pharmaceutical

applications, up to now with limited success 24

.

These ionic liquids with long alkyl chains and their mixtures, as happens to other

surfactant compounds, present thermotropic and lyotropic liquid crystalline stable

mesophases 25-31

respectively, associated to complex rheologic behaviors, often

characterized by non-Newtonian flows and specific viscoelasticities 32-34

that are

characteristics that are so far poorly exploited. Because of their amphiphilic and

asymmetric nature such PILs can organize themselves in oriented crystalline matrices

above the melting temperature, despite presenting liquid flow properties, and are thus able

109

to be used as supporting media for chemical reactions, development of self-assembling

drug delivery systems, materials for membrane separation processes, or electrical

conducting media 35-36

.

This work aims at the characterization of the rheological and thermotropic behavior

of four protic ionic liquid and the solid-liquid equilibrium of the binary mixtures of their

precursors: oleic acid + monoethanolamine, oleic acid + diethanolamine, stearic acid +

monoethanolamine, and stearic acid + diethanolamine. These compounds were chosen

because of the sustainable character of fatty acids, and despite the use of ethanolamine

soaps in commercial products, these systems have not been previously investigated in the

literature. This choice of systems allows the characterization of the effects of molecular

structure, alkyl chain length, and presence of unsaturation in the thermodynamic and

rheological behavior of these systems and the protic ionic liquids that they originate.

Figure 1. Brønsted acid-base reaction between a carboxylic acid and monoethanolamine or

diethanolamine for the formation of a protic ionic liquid. R represents the alkylic moiety of the

carboxylic acid.

2. EXPERIMENTAL SECTION

2.1. Materials

R

O

OH

+OH

H2NOH

+NH3

carboxylic acid monoethanolamine monoethanolammonium carboxylate

diethanolammonium carboxylatediethanolamine

R

O

OH

carboxylic acid

HO

HN

OH

R

O

O

R

O

O HO

H2N

OH

+

110

Oleic acid, stearic acid, monoethanolamine, and diethanolamine were supplied by

Sigma-Aldrich (St. Louis, MO) with mass purities higher than 99%. Samples of

approximately 1.0 g of oleic acid + monoethanolamine, oleic acid + diethanolamine, stearic

acid + monoethanolamine, and stearic acid + diethanolamine systems were prepared

gravimetrically on flasks using an analytical balance (Mettler Toledo, Inc., Columbus, OH)

with a precision of ± 1×10−4

g and concentration of component 1 varying from x1 = (0.0 to

1.0) mole fractions for the complete description of the phase diagrams. The mixtures were

stirred at 10 K above the mesophases domain of the samples in an oil bath and under

injection of nitrogen to avoid oxidation of the compounds. The uncertainty x of the

compositions x1, obtained by error propagation from the values of the weighed masses, was

estimated as x = 5×10−4

(mole fraction).

2.2. Differential Scanning Calorimetry (DSC)

The solid-liquid equilibrium (SLE) data of the mixtures were characterized using a

DSC8500 calorimeter (PerkinElmer, Waltham, MA) previously calibrated with indium

(PerkinElmer, Waltham), naphthalene and cyclohexane (Merck, Whitehouse Station, NJ) at

ambient pressure p = (102.0 ± 0.5) kPa . The samples were submitted to a cooling-heating

cycle at 1 K min-1

based on a methodology established for measuring of the SLE of fatty

systems 37-38

. The temperatures of the thermal transitions were then analyzed in the last

heating run and taken as the peak top temperatures. The uncertainty of the temperature

wasT 0.40 K and this value was obtained by the average of the standard deviation

111

obtained by triplicates of melting temperature values of the pure compounds and mixtures

of them.

2.3. Light-Polarized Optical Microscopy (POM)

The melting profile of the liquid crystalline mesophases of the mixtures were

evaluated using a BX51 Olympus polarized optical microscope (Olympus Co., Tokyo,

Japan) equipped with a LTS120 Linkam temperature controlled stage (Linkam Scientific

Instruments, Ltd., Tadworth, U.K.) that in this study operated between 243.15 and 393.15

K. Samples (2 mg, approximately) were put in concave slides with coverslips, cooled to

243.15 K, and allowed to stay at this temperature for 30 min. After this, the samples were

observed in a 0.1 K min-1

heating run. The uncertainty of the temperature obtained from

POM measurements was taken as not higher thanPOM 1.0 K. The value was estimated

by the mean standard deviation obtained by triplicate evaluation of some of the binary

mixtures.

2.4. Density, Viscosity and Critical Micellar Concentration (CMC)

Measurements

Density and dynamic viscosity measurements of the mixtures were performed

between 288.15 and 373.15 K using an automated SVM 3000 Anton Paar rotational

Stabinger viscometer-densimeter (Anton Paar, Graz, Austria) as described elsewhere 39

.

The relative uncertainty for the dynamic viscosity was 0.35%, and absolute uncertainty for

density was 5×10−4

g cm−3

. CMC measurements of the protic ionic liquids were performed

112

by conductivity using a Mettler-Toledo SevenMulti pHmeter/Conductivimeter (Mettler

Toledo Inc., Columbus, OH) with a precision of ± 0.01 S cm-1

. Aqueous mixtures of

approximately 103

M of each protic ionic liquid were prepared with Milli-Q water and kept

at 298.15 0.1 K with a thermostatic water bath. Other concentrations were obtained by

successive dilution. The values of the CMC were taken as the interceptions of two

successive linear behaviors in the conductivity versus concentration plot.

2.5. Rheological Measurements

The stress-strain flow behavior of the protic ionic liquids was determined using a

Kinexus-pro stress controlled rotational rheometer (Malvern Instruments Ltd.,

Worcestershire, U.K.). The curves were obtained with a shear rate ranging from 0 to 100

s−1

at 298.15 – 388.15 K using a stainless steel cone and plate geometry with a diameter of

40 mm, angle of 4º, and gap set to 50 m. The temperature was controlled ( 0.1 K) by a

Peltier system built in the lower fixed flat plate.


3.1. Phase behavior

The solid-liquid equilibrium (SLE) phase diagrams of the fatty acid + ethanolamine

systems exhibit a complex multiphasic profile sketched in Figure 2. Experimental SLE data

for these systems are reported in Supporting Information (SI). In all the binary mixtures

113

under study, there is the formation of a protic ionic liquid, i.e., the ethanolammonium salt

of a fatty acid, according to the proton transfer reaction sketched in Figure 1, as shown by

Alvarez et al. 12

. In fact, at the equimolar composition (x1 = 0.5 mole fraction), the

thermogram shows no thermal transitions below the melting temperature, unlike what was

observed for the other mixtures, as reported in the experimental data tables in SI. At this

concentration, the system comprises only the pure PIL. Considering the formation of such

an intermediate compound, the phase diagrams should be read taking into account two

well-defined regions. The left-hand side of the diagram, or the region at x = 0.0 to 0.5 fatty

acid mole fraction, describes the equilibrium between the ethanolamine and the protic ionic

liquid. The right-hand side of the diagram, or the region at x = 0.5 to 1.0 fatty acid mole

fraction, describes the equilibrium between the protic ionic liquid and the fatty acid. It

means that the four solid-liquid phase diagrams here reported display an intermediate

compound with a congruent melting profile and thus represent, indeed, eight equilibrium

profiles, namely, monoethanolammonium oleate + monoethanolamine, oleic acid +

monoethanolammonium oleate, diethanolammonium oleate + diethanolamine, oleic acid +

diethanolammonium oleate, monoethanolammonium stearate + monoethanolamine, stearic

acid + monoethanolammonium stearate, diethanolammonium stearate + diethanolamine,

and stearic acid + diethanolammonium stearate.

These systems present several thermal invariant transitions. In each phase diagram,

two of them are related to the eutectic reaction that bounds the solid phase and the other

biphasic domains. The first eutectic is observed in the ethanolamine-rich composition

region of the diagram and the second in the fatty acid-rich composition region. They are

thus related to the minimum point of the liquidus line, i.e., the curve that describes the

behavior of the melting temperature of the system. The Tammann plots of these invariant

114

transitions are reported in the SI. Their behavior is typically observed for eutectic

transitions, with the corresponding enthalpy increasing to the eutectic composition and then

decreasing after this transition 40

. These plots suggest that the systems present a full

immiscibility in the solid phase because enthalpy is close to zero at pure compound

concentration. For stearic acid-based mixtures, the extrapolation of the trend is very close

to the pure ethanolamine melting enthalpy value meaning that the eutectic point in such a

region is probably very close to pure ethanolamine concentration. The large difference

between the pure stearic ionic liquid and pure ethanolamine melting temperatures supports

such an evaluation.

Figure 3 presents the principal textures of the lyotropic and thermotropic

mesophases (in the case of mixtures or pure PIL at x1=0.5, respectively) above the liquidus

line. Five types of profiles were characterized, those described as oily textures (Figure 3A),

oily streaks (Figure 3B), oily streaks with inserted maltese crosses (Figure 3C), maltese

crosses in an isotropic background (Figure 3D), and mosaic textures (Figure 3E), related to

the appearance of a lamellar mesophase and those with well-defined fan-shaped textures

(Figures 3F-H) related to the presence of hexagonal mesophases. These structures are

typical of the liquid crystalline state 26-28,41-42

. Well-defined lamellar mesophases were

observed in all systems at a particular composition range. Hexagonal mesophases could be

clearly observed in the oleic acid-based systems at the extremes of the liquid crystal

domain, and this is in agreement with the self-assembly behavior of surfactant molecules.

In fact, in aqueous surfactant solutions, hexagonal ensembles are structured at high water

concentration, while lamellar matrices appear at intermediate concentrations26-28

. Thus,

considering that the solute, in this case, is the ethanolamine or the fatty acid, the appearance

of hexagonal mesophases before lamellar ones is expected. Moreover, when the ionic liquid

115

is in solution with the ethanolamine, the solvent is hydrophilic. Otherwise, with the fatty

acid, the solvent is hydrophobic. Thus, in the ethanolamine-rich region, the hexagonal

mesophase observed probably assumes a normal structure, unlike in the fatty acid-rich

region, where it probably assumes inverted ones. Normal and inverted hexagonal

mesophases are known in the literature as type I and II, respectively. It means that, in

normal type I hexagonal mesophases, the hydrophilic moiety of the surfactant interacts with

the medium, while the hydrophobic moiety is inside of the ensemble. On the other hand, in

inverted type II hexagonal mesophases, the opposite structure is observed. Moreover, as

previously mentioned, hexagonal mesophases were not observed in the stearic acid-based

mixtures. This probably happens because the linear structure of the fatty acid carbon-chain

prefers to self-assemble in layers instead of cylindrical shapes 43

. This will be further

discussed.

Because liquid crystals were not observed in the pure ethanolamines and fatty acids,

such structures could be related to the formation of the protic ionic liquids. In fact, oily

textures and maltese crosses were clearly observed throughout the liquid crystal phase

temperature range at x = 0.5 fatty acid mole fraction, i.e., the pure protic ionic liquid. The

same textures were reported in the literature for similar compounds 44-48

. They occur due to

the amphiphilic nature of the ethanolammonium soap and the complex lyotropic behavior

of some of these mixtures, resulting from the different packaging profiles that depend on

the polarity of the coexistent compound, either the polar ethanolamine in the ethanolamine-

rich composition region or the non-polar fatty acid in the fatty acid-rich composition

region.

Taking into account the existence of these mesophases, it is possible to characterize

the other thermal invariant transitions that are observed in the biphasic domain. Oleic acid-

116

based mixtures (Figure 2A and B) present, at the left-hand side of the diagram, two

invariant transitions. The first, at a higher temperature, is related to the formation of the

hexagonal mesophase and the second is related to the formation of the lamellar mesophase.

In the right-hand side of the diagrams, the ionic liquid-rich region shows one invariant

transition related to the lamellar mesophase formation and the fatty acid-rich region

presents one transition, probably related to the formation of the inverted hexagonal

mesophase. On the other hand, because stearic acid-based mixtures (Figure 2C and D)

showed only lamellar mesophases, the invariant thermal transitions in the biphasic region

are related to the formation of such structure.

The profile of the phase diagrams, including the solid-liquid equilibrium and the

mesophases, could be sketched in Figure 2A-D, considering the experimental observations

and the Gibbs phase rule imposing that at a constant pressure and temperature, at most three

phases can coexist in a binary mixture 40,49-51

. Taking into account the coexistent phases and

mesophases, namely, solid ethanolamine (SEA), solid fatty acid (SFA), solid protic ionic

liquid (SPIL), isotropic liquid (L), normal hexagonal (HI), lamellar (L), and inverted

hexagonal (HII), it is possible to summarize all biphasic domains that are present in the

phase diagrams. In the oleic acid + monoethanolamine (Figure 2A) and oleic acid +

diethanolamine (Figure 2B) systems, we have SEA + SPIL, SEA + L, SEA + HI, SEA + L, SPIL

+ SFA, SPIL + L, SPIL + HII, SFA + HII, and SFA + L. In the stearic acid + monoethanolamine

system (Figure 2C) we have SEA + SPIL, SEA + L, SEA + L, SPIL + SFA, SPIL + L, SPIL + L,

and SFA + L. In the stearic acid + diethanolamine system (Figure 2D), we have SEA + SPIL,

SEA + L, SPIL+ L, SPIL + SFA, SPIL + L, SFA + L, and SFA + L.

117

Figure 2. Solid-liquid equilibrium phase diagram of the (A) oleic acid + monoethanolamine, (B) oleic

acid + diethanolamine, (C) stearic acid + monoethanolamine and (D) stearic acid + diethanolamine

systems by () differential scanning calorimetry and () light-polarized optical microscopy presenting

solid monoethanolamine (SMEA), solid diethanolamine (SDEA), solid fatty acid (SFA), solid protic ionic

liquid (SPIL), liquid phase (L), normal hexagonal (HI), lamellar (L), and inverted hexagonal (HII)

mesophases. Lines are guides for the eyes. Solid lines were experimentally characterized, and dashed

lines describe hypothetical phase boundaries based on the Gibbs phase rule.

260

270

280

290

300

310

320

330

340

350

360

370

380

390T

/ K

SMEA + SPILSFA + SPIL

L

L

SPIL + L

SPIL + LHII

HI

SMEA + L

SFA + L

SFA+ HIISPIL+ HII

L

L

277

281

0.00 0.12

SMEA+ L

SMEA+ HI

HI

SMEA+ L

270

280

290

300

310

320

330

340

350

360

370

380

390

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

T/

K

xfatty acid

SFA + SPIL

SPIL + L

SFA + SPIL

SPIL + L

SMEA + L

SMEA + L

L

L

SPIL + L

SFA + L

LL

L

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

xfatty acid

L L

LL

SFA + L

SFA + L

SFA + SPIL

SDEA + SPIL

SPIL + L

SMEA + L

SPIL + L

SPIL + L

L

HII

HI

L

SDEA + SPIL

SFA + L

SFA + SPIL

SDEA + L

SDEA + HI

SFA + HII

SDEA + L

SPIL + HII

SPIL + LSPIL + L

L

L

(A) (B)

(D)(C)

118

Figure 3. Light-polarized optical micrographs showing the mesophases textures: (A) oily texture in

the stearic acid + monoethanolamine at xfatty acid = 0.2, T = 343.15 K; (B) oily streaks in the oleic

acid + diethanolamine at xfatty acid = 0.6, T = 293.15 K; (C) maltese crosses in an isotropic backgroup

oleic acid + diethanolamine at xfatty acid = 0.5, T = 357.15 K; (D) oily streaks with inserted maltese

crosses oleic acid + diethanolamine at xfatty acid = 0.4, T = 340.15 K, (E) mosaic texture in the stearic

acid + monoethanolamine at xfatty acid = 0.4, T = 363.15 K; and fan-shaped textures in the (F) oleic

acid + diethanolamine at xfatty acid = 0.3, T = 298.15 K; (G) oleic acid + monoethanolamine at xfatty acid

= 0.7, 293.15 K and (H) oleic acid + diethanolamine at xfatty acid = 0.7, T = 298.15 K.

119

3.2. Self-Assembling of the PILs

It was mentioned before that the appearance of the liquid crystal mesophases is due

to the formation of the protic ionic liquid. In fact, it presents an amphiphilic and

asymmetric molecular structure, containing a hydrophilic (ethanolammonium cation) and

hydrophobic moiety (fatty acid anion). Such profile characterizes a mesogen, i.e., a

compound that under suitable temperature and pressure conditions can build liquid crystal

matrices 36,42

. For the understanding of the self-organizing behavior of the protic ionic

liquids formed by reaction of the fatty acids with ethanolamines mixtures the critical

micellar concentration of these compounds in water was measured by conductivity.

Figure 4 shows the conductivities of the diluted aqueous solutions of the four protic

ionic liquids here studied. As the conductivity increases with the concentration of the ionic

liquids in solution, the slope changes defining essentially three different linear regions.

Thus, considering that the different dependence of conductivity upon PIL concentration is

due to differences in the self-assembly of the mesogens, two CMC values were obtained (as

shown in Figure 4). Literature shows that with an increase in the surfactant concentration in

aqueous solutions, spherical micelles, cylindrical micelles, or bilayers are formed from the

monomers52

. After the first CMC value, the protic ionic liquid is probably self-assembled in

spherical micelles. In fact, taking into account the molecular geometry (local) constraints,

the critical packing parameter53

in all cases assumed values lower than 1/3. This value is

related to the formation of spherical micelles with the polar headgroup (ethanolammonium

cation) interacting with the aqueous medium (as depicted in Figure 4). Moreover,

considering the global constraints imposed by an increase in the concentration of the

mixture and intermolecular interactions, the second CMC value could be probably related

120

to the formation of more complex structures, according to similar observations in the

literature54-56

. The formation of such structures is more evident in the oleate ionic liquids

because they present a more pronounced shift in the slope and lower CMC2 values.

Assuming, in this case, both global and local constraints, the presence of the unsaturation in

the carbon-chain of the oleic ionic liquids might probably favor the formation of cylindrical

self-assembling. On the other hand, the geometry of the saturated alkyl chain of the stearic

ionic liquids probably led to the formation of bilayer structures. This observation

corroborates with the fact that stearic acid based mixtures did not present hexagonal

crystals, unlike oleic acid ones, as previously discussed.

Figure 4. Conductivity ( as a function of concentration of protic ionic liquids (PIL) aqueous

solutions. Solid lines are linear fitting of the data (R2 > 0.98) for critical micellar concentration

determination (CMC).

0

5

10

15

20

25

30

35

0.0 0.2 0.4 0.6 0.8 1.0

/

S

cm-1

PIL / mM

PIL CMC1 CMC2

[MEA][Oleic] 0.159 0.714

[DEA][Oleic] 0.184 0.632

[MEA][Stearic] 0.159 0.721

[DEA][Stearic] 0.092 0.744

more complex

structures

121

3.3. Rheological Characterization of the PILs and Binary Mixtures

Taking into account the organized nature of a liquid crystal microstructure, its

properties should present a particular behavior, or even a different profile, when compared

with an isotropic media. In fact, visually, some mixtures close to x = 0.5 fatty acid mole

fraction, including the equimolar concentration, presented a very viscous gel-like behavior.

The phase diagrams of the mixtures here studied show that above the liquidus line, there is

a very large liquid crystalline domain in a broad concentration range and with maximum

temperature values close to 390 K. Thus, density and viscosity measurements were

determined in order to characterize these fluids, fostering the understanding of the

interactions between the compounds in the mixture because in this work the compounds

react to form a new substance (density and viscosity data are reported in SI). Unfortunately,

due to their high melting points, the mixtures of stearic acid could not be studied. Figure 5

presents the densities of the oleic acid + monoethanolamine and oleic acid +

diethanolamine binary systems from 288.15 to 373.15 K because such mixtures are liquid

above 288.15 K. As a first observation, the results seem to be quite trivial with density

values at fixed concentrations decreasing linearly (R2 0.99) with increasing temperature,

ranging from = 1.10 to 0.85 g cm-3

, i.e., from pure ethanolamine to pure oleic acid density

values. However, if the density results are seen on their composition dependency at a fixed

temperature, the values also decrease with an increase in oleic acid concentration, but a

more complex behavior is revealed. Three different regions are now apparent: (1) one in the

ethanolamine rich region before the liquid crystal formation, (2) one delimited by the liquid

crystal domain (dashed lines of the Figure 5), and (3) one in the fatty acid rich region where

122

no liquid crystal is observed. These differences in the density result from the peculiar

packing profiles that liquid crystals present, which induce changes in the densities of the

mixtures. The excess molar volume VEX

/ cm3 mol

-1 data calculated from the experimental

density data (Figure 6) are in agreement with the observed nonlinear density dependency

and provide further significant details on the molecular interactions. It is important to note

that the excess molar volume was calculated considering that at x = 0.0 to 0.5 oleic acid

mole fraction the mixture is the ethanolamine + ionic liquid binary system and at x = 0.5 to

1.0 oleic acid mole fraction the system is the fatty acid + ionic liquid mixture. The results

clearly show that, at a fixed temperature, the excess molar volumes of the ethanolamine +

protic ionic liquid mixtures present a significant negative deviation from ideal behavior. On

the other hand, the excess molar volumes of the oleic acid + protic ionic liquid mixtures

present significant positive deviations. Because negative deviations were observed in the

first part of the diagram, one can infer that from the point of view of excess molar volumes

the interactions between ethanolamine and the ionic liquid are more favorable than the

interactions between fatty acid and the ionic liquid. In fact, ethanolamines and fatty acid

have quite different size, shape, and polarities. In the ethanolamine + ionic liquid mixture,

due to the polar behavior of the ethanolamine, the interactions with the hydrophilic moiety

of the ionic liquid are preferred. The large size differences may also favor the packing of

the ensemble. On the opposite, in the fatty acid + ionic liquid systems, the interactions with

the hydrophobic moiety of the ionic liquid are preferred due to the apolar behavior of the

organic acid. Thus, the rigid structure of the liquid crystal formed and the large size of the

long carbon chain probably do not allow much possibilities of packing leading to positive

deviations from ideal behavior.

123

Figure 5. Density data ( / g cm-3

) as a function of temperature (T / K) for the (A) oleic acid +

monoethalonamine and (B) oleic acid + diethanolamine systems at xoleic acid = 0.0 (), 0.1 (), 0.2

(), 0.3 (), 0.4 (), 0.5 (), 0.6 (), 0.7 (), 0.8 (), 0.9 () and 1.0 (). At the bottom of

each plot, density data as a function of oleic acid mole fraction at T = 298.15, 323.15, and 353.15 K.

Solid and dashed lines are guide for the eyes. Gray regions represent the liquid crystal domain.

124

Figure 6. Experimental excess mole volume data of the () oleic acid + monoethalonamine and

() oleic acid + diethanolamine systems at 298.15 K. Dashed lines are guides for the eyes. Vertical

gray line at x = 0.5 (pure PIL) depicts the “true” system indicated at the top of the plot.

Figure 7 shows the measured dynamic viscosity data for the same systems from

288.15 to 358.15 K except at and close to the equimolar composition for the oleic acid +

monoethanolamine system due to its high viscosity with a gel-like behavior. In the case of

pure PILs, shear rate-dependent rheological measurements were conducted and will be later

discussed. An exponential decay of the viscosity with temperature was observed, being

more pronounced close to the pure ionic liquid. This is clearly visible considering the

isothermal behavior at 353.15 K of the viscosity with the fatty acid concentration at the

bottom of Figure 7. The viscosity values increased with the concentration from pure

ethanolamine composition to the protic ionic liquid, and then they start to decrease again to

the value of pure oleic acid. Another singular behavior from the viscosity measurements

can be highlighted if the data is fitted to an Arrhenius-like exponential equation (Eq. 1)

AEln( ) ln(A)

RT (1)

-6.0

-4.0

-2.0

0.0

2.0

4.0

0.0 0.2 0.4 0.6 0.8 1.0

VE

/ cm

3

mo

l-1

xoleic acid

PIL + ethanolamine oleic acid + PIL

125

where is the dynamic viscosity (Pa s), EA is the activation energy (J mol-1

), R is the ideal

gas constant (8.314 J mol-1

K-1

), T is the absolute temperature (K), and A is the pre-

exponential factor (Pa s). Thence, Figure 8 shows the logarithm of the viscosity data, ln

(), as a function of T-1

. The fitting procedure, which is presented at the right side of Figure

8, shows that the trend presents a shift with a significant change in the activation energy EA

at a temperature (Tinters in Figure 8) close to the melting of the mesophases. Considering the

meaning of the coefficients of the Arrhenius equation, the results reveal that the activation

energy of the liquid crystalline state is higher than that in the isotropic liquid phase. The

crystalline mesophase needs, thus, more energy to flow than the isotropic liquid 57

.

Figure 7. Dynamic viscosity data of (A) oleic acid + monoethanolamine and (B) oleic acid +

diethanolamine at xoleic acid = 0.0 (); 0.1 (); 0.2 (); 0.3 (); 0.4 (); 0.5 (); 0.6 (); 0.7 ();

0.8 (); 0.9 (); 1.0 (). Details at the top right of the plots show magnifications of the data at

low values. At the bottom of each plot are viscosity data as a function of fatty acid mole fraction

at 353.15 K. Vertical gray lines at x = 0.5 (pure PIL) depict the “true” systems indicated above.

0

500

1000

1500

2000

2500

3000

3500

285 300 315 330 345 360 375

/ m

Pa

s

T / K

(A)

285 300 315 330 345 360 375

T / K

(B)

0

70

140

0.0 0.2 0.4 0.6 0.8 1.0

/ m

Pa

s

xoleic acid

353.15 K

0.0 0.2 0.4 0.6 0.8 1.0xoleic acid

353.15 K

0

250

500

285 300

0

250

500

290 300 310

PIL + ethanolamine oleic acid + PIL PIL + ethanolamine oleic acid + PIL

126

Figure 8. Linearization procedure of the dynamic viscosity data using the Arrhenius like equation

1. (A) Oleic acid + monoethanolanmine and (B) oleic acid + diethanolamine at xoleic acid = 0.0 ();

0.1 (); 0.2 (); 0.3 (); 0.4 (); 0.5 (); 0.6 (); 0.7 (); 0.8 (); 0.9 (); 1.0 (). At the

right of each plot are linear fittings of the data (R2 > 0.99) at some concentrations. Gray regions

represent the liquid crystal domain.

Figure 9 shows some of the flow curves of the oleate-based PILs (x = 0.5 oleic acid

mole fraction) from 293.15 to 363.15 K, describing the shear rate-dependence of the

samples’ shear stress. For the monoethanolammonium oleate sample at T > 348.15 K, the

y = 41.55x - 2.57

y = 51.44x - 5.64

9

13

Tinters. = 324 K

7.50

8.75

10.00

11.25

12.50

13.75

15.00

ln (/

Pas)

(A)

y = 54.20x - 4.27

y = 64.73x - 7.54

11

14

Tinters. = 322 K

y = 47.02x - 2.89

y = 57.47x - 6.29

10

14

0.28 0.3510-2 T-1

Tinters. = 307 K

y = 55.49x - 4.22

y = 67.19x - 7.99

11

15

Tinters. = 310 K

y = 41.55x - 2.57

y = 53.84x - 5.16

10

14

Tinters. = 307 K

y = 60.93x - 6.15

y = 72.75x - 9.94

11

15

Tinters. = 312 K

7.50

8.75

10.00

11.25

12.50

13.75

15.00

0.27 0.29 0.31 0.33 0.35

ln (/

Pa

s)

10-2T-1

(B)

127

shear rate is directly proportional to the shear stress, with no evidence of yield stress (0),

characterizing a clear Newtonian behavior (Eq. 2). The same result is observed for

diethanolammonium oleate samples at T > 323.15 K. Below such temperature values, for

both PILs, the increase in shear rates leads to a nonlinear increase in shear stress. At 298.15

T 348.15 K, the monoethanolammonium oleate sample presented a significant yield

stress (outlined by the dashed circles in Figure 9), whose values increase with a decrease in

temperature from 0 = 10 to 70 Pa. At this range, the shear rate/shear stress dependence

changes gradually to a marked nonlinear behavior that could be adjusted by the Vocadlo

model 58-59

(Eq. 3) up to T > 293.15 K. At this low temperature, the yield stress increases to

0 > 200 Pa with a linear dependence between shear rate and shear stress such that the flow

curve is well-characterized by the Bingham plastic model (Eq. 4, R2 > 0.99).

Comparatively, the non-Newtonian temperature domain of the diethanolammonium oleate

samples did not present yield stress up to 308.15 K, where the flow curve is well adjusted

(R2 > 0.99) by a shear-thinning profile (Eq. 5). However, with the temperature decreasing

(T < 308.15 K) the flow curve presents a yield stress and the Herschel-Bulkley model (Eq.

6) could be accurately adjusted (R2 > 0.95). The model’s parameters fitted to flow

experimental data are in SI. The flow models adopted here 60

can be described as follows

(2)

Vv

n1 n

0V VK

/ (3)

0 ' (4)

n K (5)

Hn

0H H K (6)

128

where is the shear stress (Pa), is the viscosity (Pa s), is the shear rate (s-1

), 00V

0Hare the yield stresses (Pa) related to each model, K, KV and KH are the consistency

indexes related to each model, ’ is the Bingham plastic viscosity, n, nV and nH are flow

behavior indexes related to each model, and the subscripts v and H make reference to the

Vocadlo and Herschel-Bulkley models, respectively. The non-Newtonian behavior

displayed by these PILs is thus a unique characteristic of these compounds, and the flow

phenomena here observed play a key role in numerous industry applications 32-36,57

. The

self-assembly ability of the PILs and formation of thermotropic mesophases with bilayered

lamellar-oriented structures above the melting point are the main reason for the non-

Newtonian rheological behavior here described. Moreover, the chemical interactions

among the molecules appear to be strong enough for the requirement of a critical shear

stress. The increasing temperatures lead to a decrease in the apparent viscosity. This, for

practical purposes, says there is an attenuation of the non-Newtonian behavior followed by

the appearance of a Newtonian profile at sufficiently high temperatures. The temperature

increase induces the breaking of the interactions that support the liquid crystalline

microstructure. The concentration of the isotropic phase increases with depletion of the

mesophase, as observed in the phase diagrams (Figure 1) and in the polarized optical

micrographs (Figure 2A, typical lamellar texture at low temperatures; Figure 2C, textures at

high temperatures). It was also observed that the non-Newtonian behavior of

monoethanolammonium oleate is more evident than for the diethanolammonium oleate in

special at low temperatures where such a PIL follows a Bingham plastic profile, presenting

very high yield stresses. So, regarding the size of the cation in the surfactant molecule

structure, one might suppose that the bilayers constructed by the monoethanolammonium

129

oleate are more packed with stronger intermolecular hydrogen bonding networks than the

diethanolammonium oleate structure, whose larger cation decreases the self-assembly

ability. In fact, complex structures are more easily formed by monoethanolammonium

oleate due to its lower CMC2 value. The non-Newtonian behavior exhibited by the

ethanolammonium oleates is quite interesting concerning their use in the formulation of

products and considering the particular physicochemical properties of the protic ionic

liquids for specific applications 4-6,12,15-17,35-36

.

Figure 9. Shear stress () versus shear rate ( ) curves of (A) monoethanolammonium oleate and

(B) diethanolammonium oleate at 293.15 (), 298.15 (), 308.15 (), 323.15 (), 328.15 (),

348.15 (), 353.15 (+), and 363.15 () K. Solid lines are fitted curves. Labels N, ST, V, BP, and HB

stand for Newtonian, shear-thinning, Vocadlo, Bingham plastic, and Herschel-Bulkley models,

respectively.

0 20 40 60 80 100

/ s-1

(B)

.

0

100

200

300

400

500

600

700

0 20 40 60 80 100

/ P

a

/ s-1

(A)

.

0

15

30

0 50 100

0

5

10

15

20

25

30

0 50 100

N

V

BP

N

ST

HB

V

V

V

ST

N

HB

130

4. CONCLUSIONS

Four PILs based on oleic and stearic acids, with mono- and di-ethanolamines as

cations, and the binary mixtures used for their preparation were here investigated. The

protic ionic liquids are shown to display an interesting thermotropic behavior with the

formation of lamellar mesophases. The SLE phase diagrams of the mixtures of their

precursors display a congruent melting behavior with lamellar and hexagonal lyotropic

mesophases. Moreover, the oleic acid based systems also present a non-Newtonian

behavior clearly observed in the flow curves obtained by the stress-controlled rheological

assays. Although many ethanolammonium carboxylates have a range of industrial

applications known, considering their renewable origin, the novel characteristics here

reported, such as the formation of liquid crystalline structures in addition to the non-

Newtonian behavior and the unique properties resulting from their ionic liquid character,

confer to the compounds here investigated a great potential. On the basis of these results,

numerous applications may be foreseen for these compounds, besides those currently in

use, which should be the object of future studies.


Tables with experimental solid-liquid equilibrium data, Tammann plots of eutectic

transitions, conductivity data for aqueous solutions of PILs, density, and viscosity data for

the binary mixtures, shear stress, and shear rate data of PILs at different temperatures, and

rheological models’ parameters fitted to experimental flow curves. This material is

available free of charge via the Internet at http://pubs.acs.org.

131

ACKNOWLEDGEMENTS

The authors are grateful to the national funding agencies FAPESP (2012/05027-1,

2008/56258-8), CNPq (304495/2010-7, 483340/2012-0, 140718/2010-9, 479533/2013-0)

and CAPES (BEX-13716/12-3) from Brazil, and FCT (Pest-C/CTM/LA0011/2013) from

Portugal for the financial support. The authors declare no competing financial interest.

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137


Figure S1. Tammann plots of the eutectic transitions Heut in the ethanolamine-rich region (x = 0.0

to 0.5 fatty acid mole fraction) and in the fatty acid-rich region (x = 0.5 to 1.0 fatty acid mole

fraction) of the (+) oleic acid + monoethanolamine, () oleic acid + diethanolamine, () stearic

acid + monoethanolamine and () stearic acid + diethanolamine systems. Solid lines are linear

fitting of the data (R2 > 0.95 considering that y = 0.0 at the pure compounds concentration). Dashed

lines are supposed plots close to pure component concentration. () Diethanolamine and ()

monoethanolamine melting enthalpy for analysis purpose.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0.0 0.2 0.4 0.6 0.8 1.0

H

eu

t/ k

Jm

ol-1

xfatty acid

138

Table S1. Experimental solid-liquid equilibrium data for oleic acid + ethanolamine systems for

mole fraction x, temperature T †

and pressure p = 102.0 kPa

‡.

oleic acid (1) + monoethanolamine (2) oleic acid (1) + diethanolamine (2)

x1 Teut / K T1 / K Tm / K TLCm / K x1 Teut / K T1 / K T2 / K Tm / K TLCm / K

0.0000 280.01 0.0000

300.75

0.1008 328.15 0.1033 272.81 275.22 282.53 296.43

0.1025 271.80 277.97 279.24 0.1993 275.25 277.38 280.74 293.00

0.1964 373.15 0.2986

308.15

0.2058 272.65 276.31 0.3206 275.69 278.15

281.98

0.2504 274.58 275.90 0.4089

353.15

0.2953 272.44 277.40 0.4097 274.48

279.89

0.2999 382.15 0.4445 273.76

283.07

0.3381 273.65 278.59 0.5000

283.60 360.95

0.3972 271.67 281.54 0.5383 262.72 271.29

283.65

0.4001 376.45 0.6200

323.15

0.4259 272.35 284.22 0.6184 262.83 271.35

275.00

0.5000 288.08 358.15 0.6880

304.35

0.5626 276.89 281.96 284.79 0.6940

265.37

0.6020 324.35 0.7984 265.80

271.40 279.97

0.6042 277.15 280.92 284.23 0.9019 267.06

270.48 285.08

0.7000 298.05 1.0000

287.11

0.7200 278.82

0.7762 279.19 281.53

0.8991 278.48 282.26 285.43

1.0000 287.16

† Teut is the temperature of the eutectic transition, T1 and T2 are the temperatures of the other

invariant transitions, Tm is the melting temperature (liquidus line) and TLCm is the melting of the

liquid crystal. ‡ Uncertainties for mole fraction and pressure are 0.0005 and 0.5 kPa, respectively. Uncertainty

for temperatures Teut, T1, T2, Tm is 0.4 K and for temperature TLCm is 1.0 K.

139

Table S2. Experimental solid-liquid equilibrium data for stearic acid + ethanolamine systems for

mole fraction x, temperature T †

and pressure p = 102.0 kPa

‡.

stearic acid (1) + monoethanolamine (2) stearic acid (1) + diethanolamine (2)

x1 Teut / K Tm / K TLCm / K x1 Teut / K T1 / K Tm / K TLCm / K

0.0000

280.01

0.0000

300.80

0.0230

348.45 0.0987 298.68

324.24

0.0996 277.12 339.08

0.2009 298.05

327.38

0.1000

375.00 0.2983 297.99 328.88 331.78 353.15

0.1971 274.93 344.16

0.3957

373.15

0.2004

388.15 0.4103 298.08 328.97 336.36

0.2973 277.18 346.75

0.5000

339.48 380.15

0.3960

388.15 0.5521 330.43

333.28

0.3996 276.49 350.58

0.5940

355.15

0.5000

351.65 373.15 0.6088

330.55

0.5455 344.15 351.15

0.6698 331.16

332.98

0.5495

365.15 0.6700

334.00

0.6061 344.06 350.65

0.8053 332.18 334.55 337.84

0.6600

351.15

0.8944 331.90 334.65 341.53

0.7078 340.60 350.40

1.0000

343.57

0.7936 341.35 347.34

0.9003

342.06

1.0000

343.57

† Teut is the temperature of the eutectic transition, T1 is the temperature of the other invariant

transitions, Tm is the melting temperature (liquidus line) and TLCm is the melting of the liquid crystal. ‡ Uncertainties for mole fraction and pressure are 0.0005 and 0.5 kPa, respectively. Uncertainty

for temperatures Teut, T1, T2, Tm is 0.4 K and for temperature TLCm is 1.0 K.

140

Table S3. Density data ( / g cm-3

) of the oleic acid-based binary mixtures.

oleic acid (1) + monoethanolamine (2)

x1

T / K 0.0000 0.1008 0.1964 0.2999 0.4001 0.5000 0.6020 0.6700 0.7900 0.8991 1.0000

288.15 1.021 0.989 0.971 - - - - 0.927 0.914 0.905 0.896

293.15 1.017 0.985 0.968 - - 0.944 0.931 0.924 0.911 0.901 0.892

298.15 1.013 0.981 0.965 - - 0.940 0.928 0.920 0.907 0.898 0.889

303.15 1.009 0.978 0.961 - - 0.937 0.925 0.917 0.904 0.894 0.885

308.15 1.005 0.974 0.958 - - 0.934 0.921 0.913 0.901 0.891 0.882

313.15 1.001 0.971 0.955 - - 0.931 0.918 0.910 0.898 0.887 0.879

318.15 0.997 0.967 0.952 - - 0.928 0.915 0.906 0.894 0.884 0.875

323.15 0.993 0.964 0.949 - - 0.925 0.912 0.903 0.891 0.881 0.872

328.15 0.989 0.961 0.945 - - 0.922 0.908 0.900 0.888 0.877 0.868

333.15 0.985 0.958 0.942 - - 0.919 0.905 0.896 0.884 0.874 0.865

338.15 0.981 0.954 0.939 - - 0.916 0.902 0.893 0.881 0.871 0.861

343.15 0.977 0.951 0.935 - - 0.913 0.899 0.890 0.878 0.867 0.858

348.15 0.973 0.947 0.932 - - 0.910 0.895 0.886 0.875 0.864 0.855

353.15 0.969 0.943 0.929 - - 0.906 0.892 0.883 0.871 0.861 0.851

oleic acid (1) + diethanolamine (2)

x1

T / K 0.000 0.1033 0.1993 0.3010 0.4089 0.5000 0.6000 0.6940 0.8050 0.9019 1.000

293.15 1.098 1.054 1.025 1.000 - - - 0.931 0.916 0.902 0.892

298.15 1.094 1.051 1.022 0.996 - 0.960 0.944 0.928 0.913 0.899 0.889

303.15 1.091 1.048 1.018 0.993 - 0.958 0.941 0.925 0.909 0.896 0.885

308.15 1.088 1.044 1.015 0.990 - 0.955 0.937 0.921 0.906 0.892 0.882

313.15 1.084 1.041 1.012 0.987 - 0.953 0.934 0.918 0.903 0.889 0.879

318.15 1.081 1.038 1.009 0.984 - 0.950 0.931 0.915 0.899 0.885 0.875

323.15 1.078 1.035 1.006 0.981 - 0.947 0.928 0.912 0.896 0.882 0.872

328.15 1.075 1.032 1.003 0.978 - 0.944 0.925 0.909 0.893 0.879 0.868

333.15 1.071 1.029 0.999 0.975 - 0.941 0.922 0.905 0.889 0.875 0.865

338.15 1.068 1.025 0.997 0.972 - 0.938 0.919 0.902 0.886 0.872 0.861

343.15 1.065 1.022 0.993 0.969 - 0.935 0.915 0.899 0.883 0.869 0.858

348.15 1.061 1.019 0.990 0.966 - 0.932 0.912 0.896 0.880 0.865 0.855

353.15 1.058 1.016 0.987 0.963 - 0.929 0.909 0.893 0.876 0.862 0.851

141

Table S4. Dinamic viscosity ( / mPas) data of the oleic acid-based binary mixtures.

oleic acid (1) + monoethanolamine (2)

x1

T / K 0.0000 0.1008 0.1964 0.2999 0.4001 0.5000 0.6020 0.6700 0.7900 0.8991 1.0000

288.15 31.30 204.61 634.31 - - - - 744.92 210.56 81.52 42.47

293.15 24.14 148.95 441.61 - - - 3070.60 543.59 161.51 64.42 34.22

298.15 18.94 109.37 310.11 - - - 2069.50 398.04 124.75 51.81 28.30

303.15 15.11 82.03 224.88 - - - 1441.80 299.60 98.36 42.18 23.55

308.15 12.22 62.55 166.37 - - - 1028.80 229.27 78.66 34.76 19.81

313.15 10.02 48.52 126.06 - - - 749.08 179.05 63.86 28.94 16.76

318.15 8.31 38.08 96.30 - - - 556.01 140.33 52.18 24.39 14.42

323.15 6.97 30.31 75.12 - - - 419.19 111.94 43.19 20.72 12.46

328.15 5.90 24.45 59.38 - 369.41 - 320.92 90.35 36.09 17.75 10.85

333.15 5.05 20.00 47.74 - 301.39 - 249.20 73.88 30.53 15.34 9.49

338.15 4.35 16.48 38.66 - 236.87 - 195.50 60.70 25.90 13.33 8.39

343.15 3.78 13.75 31.77 - 182.26 - 155.19 50.43 22.20 11.67 7.45

348.15 3.31 11.59 26.36 - 142.32 - 124.15 42.23 19.16 10.27 6.65

353.15 2.91 9.87 22.14 - 112.36 - 100.17 35.62 16.67 9.10 5.94

358.15 - - - - 89.73 - - - - - -

363.15 - - - - 72.22 - - - - - -

368.15 - - - - 58.63 - - - - - -

358.15 - - - - 89.73 - - - - - -

oleic acid (1) + diethanolamine (2)

x1

T / K 0.000 0.1033 0.1993 0.3010 0.4089 0.5000 0.6000 0.6940 0.8050 0.9019 1.000

293.15 859.75 1483.70 2123.60 2890.50 - - - 604.10 160.54 60.43 34.22

298.15 565.34 973.89 1391.60 1893.20 - - - 434.85 123.88 48.73 28.30

303.15 383.69 659.35 944.52 1274.90 - - 1007.10 322.16 97.57 39.75 23.55

308.15 266.73 456.87 655.31 878.11 - - 697.98 242.99 77.81 32.81 19.81

313.15 190.57 325.42 465.64 619.97 - - 501.73 187.33 62.89 27.33 16.76

318.15 137.49 233.45 334.96 443.22 - - 367.53 144.99 51.13 23.06 14.42

323.15 101.53 171.54 245.99 323.76 - - 275.12 114.38 42.15 19.60 12.46

328.15 75.82 128.30 183.67 240.44 - - 209.10 91.41 35.11 16.80 10.85

333.15 58.00 97.69 139.44 181.85 - - 161.66 74.07 29.62 14.52 9.49

338.15 44.83 75.16 106.96 139.50 - - 126.43 60.26 25.09 12.64 8.39

343.15 35.25 58.76 83.50 108.56 - - 100.18 49.70 21.48 11.07 7.45

348.15 28.08 46.45 66.00 85.54 - - 80.26 41.36 18.51 9.75 6.65

353.15 22.68 37.24 52.77 68.18 84.94 88.12 64.94 34.74 16.10 8.64 5.94

358.15 - - - - - 70.20 - - - - -

363.15 - - - - 54.48 56.68 - - - - -

368.15 - - - - 44.39 46.10 - - - - -

373.15 - - - - 36.56 37.97 - - - - -

378.15 - - - - 30.32 31.35 - - - - -

142

Table S5. Rheological models’ parameters related to shear stress / shear rate curves fitted to flow

experimental data for the PILs.

monoethanolammonium oleate diethanolammonium oleate

T / K 0 / Pa K † n

‡ R

2 model 0 / Pa K

† n

‡ R

2 model

293.15 217.78 4.600 1.000 0.9908 Bingham plastic 20.79 30.438 0.589 0.9634 H-B

298.15 74.22 2.260 106 0.307 0.9706 Vocadlo 14.34 10.822 0.873 0.9520 H-B

303.15 62.58 5.803 105 0.316 0.9586 Vocadlo 2.09 1.740 0.870 0.9908 H-B

308.15 39.69 1.010 106 0.298 0.9556 Vocadlo 0.00 1.706 0.813 0.9908 Shear thinning




328.15 25.17 1.060 105 0.298 0.9585 Vocadlo 0.00 0.251 1.000 0.9999 Newtonian

333.15 15.97 2.249 104 0.318 0.9517 Vocadlo 0.00 0.188 1.000 0.9999 Newtonian

338.15 14.10 1907.900 0.364 0.9862 Vocadlo 0.00 0.144 1.000 0.9999 Newtonian



353.15 0.00 0.072 1.000 0.9999 Newtonian 0.00 0.069 1.000 0.9999 Newtonian



† KV for Vocadlo model, ’ for Bingham plastic model, KH for H-B model and for Newtonian

model. ‡ nV for Vocadlo model, n for shear-thinning model and nH for H-B model.

143

THE CRYSTAL-T ALGORITHM

(submitted to Physical Chemistry Chemical Physics)

Guilherme J. Maximo a, Mariana C. Costa

b, and Antonio J. A. Meirelles

a*

a Food Engineering Department, University of Campinas, R. Monteiro Lobato 80, 13083-862,

Campinas, São Paulo, Brazil. b School of Applied Sciences, University of Campinas, R. Pedro

Zaccaria, 1300, 13484-350, Limeira, São Paulo, Brazil.

GRAPHICAL ABSTRACT

The Crystal-T algorithm accurately depicts the SLE phase diagrams of lipidic mixtures

presenting solid solution, measured in this work, by using liquid and solid phase models.

Chapter 5

144

ABSTRACT

The thermodynamic modeling procedures sometimes fail in the correct description of the

phase behavior and their inability increases with the complexity of the system. Lipidic

mixtures present a particular phase change profile highly affected by their unique

crystalline structure. Consequently, marked deviations from ideality do not allow

reasonable accuracy by using the classical solid-liquid equilibrium (SLE) modeling

approach according to which the solid phase is assumed to be a pure component.

Considering the non-ideality of both liquid and solid phases, this study describes the

Crystal-T algorithm for the calculation of the SLE of binary mixtures. The algorithm is

aimed at the determination of the temperature in which the first and last crystal of the

mixture melts. The evaluation is focused on experimental data measured and reported in

this work for systems composed by triacylglycerols and fatty alcohols. The effectiveness of

the description of the liquidus and solidus lines of discontinuous solid solutions were tested

by using excess Gibbs energy based equations, and the group contribution UNIFAC model

for the calculation of the activity coefficients. Very low deviations between theoretical and

experimental data evidenced the strength of the algorithm, contributing to the enlargement

of the scope of the SLE modeling.

KEYWORDS: Solid-liquid equilibrium, Modeling, Solid solution, Non-ideality,

Triacylglycerols, Fatty alcohols.

145

1. INTRODUCTION

Several works in literature have long since been engaged in the understanding of the

melting and crystallization phenomena of systems formulated by lipidic compounds as well

as the modeling of their solid-liquid equilibrium (SLE) behavior1, 2

. Notwithstanding the

success of this task is inversely proportional to the complexity of the system. Fats and oils

mixtures are remarkably known by presenting a particular crystalline structure highly

dependent on the processes conditions to which the mixtures are submitted. A special and

common phenomenon in this context is the formation of solid solutions, in which crystals

of a compound are fitted into the lattice of another crystal3. Lipid-based products

commonly present this phenomenon, highly affecting the rheological and physicochemical

profile of the system4, 5

. Mixtures of triacylglycerols and fatty alcohols, here evaluated, are

an example. Fatty alcohols are used as surfactant structuring agents in lipidic-based systems

in replacement of hydrogenated vegetable oils or saturated TAGs. Moreover, TAGs and

fatty alcohols are used in microbiostatic coating for foods, formulation of organogels or

controlled release medicines6-12

.

In fact, world production and consumption of vegetable oils actually overtake 150

millions of tons per year13

. Being one of the most important items of the human diet as well

as a distinguished flavor and texture builder, fats and oils becomes also an important

renewable energy source, increasing the worldwide economic impact of the oilchemistry in

industrial and academic fields. Paradoxically, in some cases, they can act as promoters of

serious cardiovascular diseases, drawing attention of international policy and academic

research towards finding effective solutions. Taking into account these demands, the phase

equilibrium modeling is the ideal first step for the optimization and design of industrial

146

operations as well as the formulation of products with the desired properties. However,

literature presents a set of approaches that fails in describing the SLE behavior of lipidic

mixtures either by the lack of pure compounds experimental properties or by describing

them as simple eutectic systems and consequently neglecting the presence of solid

solutions. In fact, few works in literature went beyond the limitation of the simple eutectic

behavior in order to evaluate the SLE of fatty systems2, 14, 15

. For this reason, this work was

aimed at describing the SLE phase diagrams of lipid-based mixtures presenting solid

solutions by using an algorithm, namely Crystal-T. The evaluation was focused on binary

systems of triacylglycerols (TAGs) and fatty alcohols experimentally determined by

differential scanning calorimetry and microscopy.

The “Crystal-T” algorithm was developed with the aim of improving the modeling

of the SLE of lipidic based mixtures presenting solid solutions. The procedure was based in

the classical “Bubble-T” algorithm16-19

used for the determination of the bubble point in the

classical vapor-liquid equilibrium (VLE) calculation. The routine considers the non-ideality

of both liquid and solid phases and uses the classical isofugacity equilibrium

thermodynamic criteria and activity coefficient models in order to calculate the liquidus and

solidus lines of the phase diagrams. The calculation was anchored to the experimental data

obtained in the evaluation of the Tammann plots of the eutectic transition. The set of non-

linear equations was solved by an optimization routine that identified the temperature and

the composition in which the first and last crystal melts.

147

2. THEORY

2.1. Fundamentals

Considering an isobaric system, the classical thermodynamic establishes a well

defined theory for the description of the solid-liquid equilibrium (SLE) relating 3

fundamental variables: the mole fraction of the compound i in the liquid phase xi, in the

solid phase, zi and temperature T. The equation that relates these variables is built through

the isofugacity criteria17-19

. Taking into account the relation between the fugacities of the

compounds in both phases, the SLE is described by the calculation of the Gibbs energy of a

defined heating-colling process, depicted in Figure 1. Further details are in Supporting

Information. The SLE is so given by Equation 1.

Lfus tri i

fu

fus fus fus

s tri i 1

1 1 1 1ln 1ln

tr

pn

S

H Hx

R T T R

C T

T T R

T

T Tz

(1)

where iL and i

S are the activity coefficients of the component i in the liquid and solid

phases, respectively, T is the melting temperature (K) of the mixture, R is the ideal gas

constant (8.314 J·mol-1

·K-1

), Tfus and fusH are the melting temperature (K) and enthalpy

(J·mol-1

) of the component i, Ttr and trH are thermal transitions temperatures (K) and

enthalpies (J·mol-1

) of the n solid-solid transition (polymorphic forms) of the component i

and fusCp is the difference between the heat capacity (Jmol-1

K-1

) of the pure component i

of the liquid and solid phases.

148

Figure 1. Thermodynamic cycle comprising the heating, melting and cooling processes of the

system, from T to Tfus, from a solid to a subcooled liquid state taking into account the polimorphysm

phenomena at Ttr.

In order to describe the SLE of a mixture, the calculation of T, xi and zi must be

considered by using Equation 1 and the adjustment of the i equations. This is classically

obtained by a numerical optimization procedure. However, considering the high non-

linearity of Equation 1, some theoretical approximations, well applied for simplest cases,

are frequently found in literature. The general suppositions are that i) the specific heat

capacity of the pure compounds can be neglected when compared with the magnitude of the

fusH; ii) the compounds in the solid phase are immiscible such that the term related to the

non-ideality of the component i in the solid phase are zi i

S = 1.0; and iii) the liquid phase

behaves as in an ideal system, being the liquid phase activity coefficient iL

= 1.0. Also,

pure compounds’ solid-solid (polymorphic) transitions are often neglected although, when

compared to the fusH values, the magnitude of the trH can significantly impact in the

modeling results. Despite the eventual non reliability of one or other of these hypotheses,

the intrinsic nature of the adjustment procedure can generate good results. Consequently, all

those assumptions must be carefully evaluated.

A marked feature of fatty mixtures’ SLE is the appearance of solid solutions. From

the SLE point of view, solid solutions are so that zi iS 1.0. Therefore, the activity

Tfus

T Solid Subcooled

Liquid

Melting

Ttr

149

coefficients of the component i in both liquid iL and solid phases i

S should

necessarily be

taken into account. In this work, the well-known Margules equation, was used for the

calculation of both iL

and iS

models as well as the group contribution UNIFAC equation

for the description of iL. The Margules equation is a function relating T, xi or zi that is able

to accurately model systems comprising chemicals with similar molar volumes17

. In case of

binary mixtures, this equation can be written using one or two adjustable parameters,

namely the 2- or 3-suffix Margules equations, respectively Equations 2 and 3, considering

the utilization of up to quadratic or cubic terms17

as follows:

2

ij j

iexp

R

A z

T

(2)

2 3 2 3

ij ij j ij j ij ij i ij i

i j

3 4 3 4exp exp

R R;

A B z B z A B z B z

T T

(3)

where i, j = components 1, 2 and Aij and Bij (kJmol-1

) are empirical parameters related to

the thermodynamic interactions between the two compounds in the mixture. The UNIFAC

(UNIQUAC Functional-group Activity Coefficient) model is a predictive model based on

the group-contribution concept20, 21

in which the activity coefficient can be found by means

of a sum of both enthalpic and entropic contributions of the chemical groups in the mixture.

Some modifications of this model consider the temperature-dependence of the enthalpic

contribution or changes in the entropic contribution22

. Details concerning the UNIFAC

model are described elsewhere20-22

. Thus, in this work, the following approaches were used

for calculating the activity coefficients: i) original UNIFAC or UNIFAC-Dortmund models

for iL and 2-suffix Margules equation for i

S; ii) original UNIFAC model for i

L and 3-

suffix Margules equation for iS; iii) 2-suffix Margules equation for both i

L and i

S; and iv)

150

3-suffix Margules equation for both iL and i

S. In case of UNIFAC models, the parameters

where taken from literature22, 23

.

Considering the non-ideality of the solid phase (ziiS 1.0), the system can present

either continuous or discontinuous solid solutions. In this work, the mixtures evaluated

presents discontinuous solid solutions, in which the compounds are miscible in the solid

phase in a restrained concentration range. This case is analogous to the VLE of azeotropy-

heterogeneous mixtures. The classical shape of this phase diagram is sketched in Figure 2.

The curves that circumscribe the biphasic region are called liquidus and solidus lines and

describe, respectively, the melting temperature T of the mixture as a function of xi and zi. At

T = Teut, the behavior of both curves presents a discontinuity. This is due to the formation of

an additional solid phase, establishing a solid-solid-liquid equilibrium state. According to

the isofugacity criteria, this triphasic point is such that

0 0 0L L S S S S

i i i i i i i iI II

ix f z f z f (4)

where 0L

if and

0S

if are the standard state fugacities of the compound i in the liquid phase

and in both solid phases I and II. This point is the so-called eutectic point, in which the

mixture at a composition xi, ziI, zi

II melts in a minimum and single temperature Teut. From

the industrial point of view, the correct determination of the eutectic point is of utmost

importance if one is interested in the formulation of mixtures with low melting point, for

instance in order to avoid the solidification by low temperatures, as in case of biodiesel

mixtures24-26

, lubricants or controlled melting mixtures27, 28

.

151

Figure 2. Solid-liquid equilibrium phase diagram of a discontinuous binary solid solution case.

2.2. SLE algorithms

The equilibrium thermodynamic theory is long since well established for the

resolution of the vapor-liquid and liquid-liquid equilibria. On the other hand, the SLE

problems have been developed by analogies, using for instance, the same models for the

description of the non-ideality of the phases. Two algorithms had been already presented in

the literature for the description of the SLE: the stability test based on the Gibbs energy

minimization and the isoenthalpic flash calculation. Both are detailed explained elsewhere2,

14, 15, 29. In the first case, the algorithm considers that for a given temperature or composition

a system in equilibrium has the minimum Gibbs energy G. The function that represents G is

written by relating the activity coefficients of the phases iL and i

S, as described in

Equation 5.

326

0 1

Tem

per

atu

re

x1, z 1

Tfus 2

Tfus 1

Teut

xeut zeut IIzeut I

Solid Solution

Solid + Liquid

S+L

Liquid phase

Solid phase

liquidus line

solidus line

Teut x z0 1

152

nc

L L S S L L L

i

f

i i

us fu

1

S fus tri

1 1fu

s fu

tr

s

s

R ln

1 1 1 1 R

ln

i

nc n

i tr

p

G n g n g g n T x x

H Hn T z

R T T R

C T T

T

T

T

TR

S

i iln1 z

(5)

where nL , n

S , g

L and g

S are, respectively, the number of moles n and the mole Gibbs

energy g of both liquid L and solid S phases. Mathematically, the minimum of Equation 4 is

obtained by an optimization procedure in which given a defined mixture at a fixed

temperature T the composition of the system in the equilibrium condition is obtained.

Considering a binary mixture this problem becomes a bidimensional problem and the

independent variables could be for instance, the number of moles of the liquid phase niL.

The number of moles of the solid phase niS is so calculated through the mass balance of the

system.

In case of the isoenthalpic flash calculation, the algorithm considers that a system

with a known composition feeds a vessel at a fixed temperature T and pressure P where the

equilibrium condition must be attended. The final composition is calculated by equations

relating the mass balances as well as the SLE equilibrium equation (Equation 1). The

solution is based on the minimization of an objective function written by this set of

equations, being that the most known is the Rachford and Rice equation (Equation 6), as

presented elsewhere16, 30

.

2 2 2i i

i i

i=1 i 1 i 1 i

10

1 1

K nx z

K

(6)

153

where Ki is the xi / zi ratio, from Equation 1, ni is the number of moles of the compound i in

the feeding and is the ratio between the liquid phase amount L and the total feed mixture

F.

In this work, in order to evaluate the effectiveness of the proposed Crystal-T

algorithm, the Gibbs and flash algorithms were implemented for the description of the SLE

phase diagrams of the binary fatty systems. The minimization of the free Gibbs energy was

written using a procedure based on a multidirectional optimization problem. In this case, a

Sequential Quadratic Problem (SQP) algorithm was used, given by the MATLAB function

fmincon. The isoenthalpic flash calculation algorithm was implemented using an

optimization routine written in LINGO (Lindo Systems) for the minimization of the

Rachford and Rice equation (Equation 5). For this, a Generalized Reduced Gradient (GRG)

method for non-linear problems was considered. Markedly, both algorithm are highly

dependent on the initial estimate, since it must be within the biphasic domain for the

complete description of the liquidus and solidus lines of the SLE diagram. Once the

biphasic domain is unknown, the introduction of additional algorithms to test the initial

estimate or the number of phases in the equilibrium state becomes necessary.

2.3. The Crystal-T algorithm

The Crystal-T algorithm is aimed at the construction of the liquidus and solidus

lines of the SLE phase diagram, as sketched in Figure 1, which means to represent the

temperature T as a function of xi and zi. It was applied for depicting the thermodynamic

behavior of binary mixtures. For this, a routine was formulated in which the mole fraction

of the compound i in the solid phase zi and the melting temperature T are calculated in order

154

to attend the equilibrium criteria (Equation 1) for a given mole fraction of the compound i

in the liquid phase xi. The procedure was based in finding the root of the function F,

defined as the mole balance of the solid phase (Equation 7).

2

i1

i

F z (7)

where,

nLfus tri i

if

fus fus

us t

u

ri r

f s

t 1

ln1

11 1 1

exp lnp

S

H Hxz

R T T R T T

C T T

T TR

(8)

iL = f ( xi, T, parameters of the equation ) (9)

iS = f ( zi, T, parameters of the equation) (10)

0.0 < xi, zi < 1.0 ( xi, zi ; i = 1, 2 ) (11)

T > 0.0 ( T ) (12)

Figure 3 sketches the block diagram of the routine. 1) The algorithm starts for a

given composition xi, a set of phase transition properties Tfus, fusH, Ttr, trH, fusCp and

parameters for the i equations. The parameters are Aij (Jmol-1

) in case of 2-suffix Margules

equation, Aij and Bij (Jmol-1

) in case of 3-suffix-Margules equation and, for the UNIFAC

model, the structural parameters for each group k, Rk and Qk, and the group-interaction

parameters amn between the groups m and n in the mixture. A melting temperature T is

firstly assumed and iS taken as 1.00. 2) In the first interaction, zi is calculated (Equation 8),

the solid phase mole fractions are normalized and the iS calculated considering the

estimated T and the new zi values. 3) In the following step, zi is newly calculated

(Equation 8) and compared with the previously one, with a tolerance level lower than 110-

4. Once such comparison is attended, 4) the mole balance of the solid phase is then tested

155

with the same tolerance level. The values for T and z are then obtained if such criterion is

established. If the criterion is not attended, 5) a new estimate for T (T*) is done through a

modified quasi-Newton method in which only the first derivative of the function F is

considered (Equation 13). The numerical derivative of the function F’ was calculated by an

infinitesimal range of = 510-3

. The convergence is established at a tolerance level lower

than 110-5

. The new T* value is then used in the next iteration.

FT T

F '* (13)

Since the eutectic transition establishes a minimum point in the liquidus and solidus

lines, in the domain restrained by Tfus < T < Teut, being Tfus the lower melting temperature

between both pure compounds, there are two composition pairs (xi, zi) attending the

equilibrium criteria for one single temperature T. Thus, a well approximated estimate for T

in the procedure is essential. For this reason, the algorithm is calculated for 0.0 < xi < 1.0

and sequentially for 1.0 < xi < 0.0. The first calculation starts at T = Tfus,2 and the second

one at T = Tfus,1. At each iteration, the initial estimate for T is given by the melting

temperature of the previous iteration and the composition step xi 0.01. This procedure

led to the appearance of two profiles T, xi, zi as depicted in Figure 2, being the interception

of the curves the solid-solid-liquid equilibrium state (Equation 4), corresponding to the

eutectic point. The supposed extension of the melting behavior of each profile is depicted

by dashed lines in Figure 2. They are metastable melting transitions possibly present in the

heating process of the mixture. It is remarkable that in case of no discontinuity in the

behavior of the functions, the algorithm naturally attend the continuous solid solution case

with no further procedures, comprising or not minimum/maximum points.

156

Figure 3. Block diagram for the Crystal-T algorithm.

2.3.1. Adjustment of the i equation parameters

Once the algorithm for the calculation of the SLE was established, the parameters of

the 2- and 3-suffix Margules equations were adjusted using an optimization routine that

embodies the Crystal-T algorithm. Considering the calculation of iL and i

S, one, two or

four parameters were fitted depending on the approach used. In this work, the adjustment of

one parameter, in case of using UNIFAC model and 2-suffix Margules equation for iL and

iS calculation, respectively, was implemented using an algorithm based on the Nelder-

.T.

.F..T.

.F.

.T.

.F.|[zi]I

[zi]II|< 10-4

START

|1[zi]n|< 10-4

xi

Aij, Bij, Rk, Qk, amn

T = Tfus

iS = [1.0, 1.0]

END

F = 1 zi

T’ = T + 0.0005

F’ = 1 z’i

T * = T ‒ F / F’T = T *

| F | < 10-5

[zi] Izi = zi / zi

iS

[zi] II

157

Mead Simplex direct search (MATLAB function fminsearch). The objective function used

in this procedure was built as proposed by literature31

, taking into account the ratio between

the square absolute deviations between calculated and experimental (exp.) data and the

experimental uncertainties 2, as follows:

exp exp exp exp expeut euti eut eutI II

2 22 2 2 exp expexp exp exp

eut eut eut euti i eut eut eut eut I II

2 2 2 2 2

n

i T xT z z

z z z zT T T T x x

(14)

where Ti are the mixture melting temperature and (T, xi, ziI, zi

II)eut represents the eutectic

point i.e. the solid-solid-liquid equilibrium SSLE point with two solid phases I and II. The

experimental eutectic point was calculated using the well known Tammann plot, through

the evaluation of the behavior of the eutectic enthalpies as a function of the concentration,

as explained elsewhere32-34

. The uncertainties were obtained experimentally, as will be

discussed later.

In the adjustment of two parameters, in case of using UNIFAC model and 3-suffix

Margules equation for iL and i

S calculation, respectively, or using 2-suffix Margules

equation for the calculation of both iL and i

S and in the adjustment of four parameters, by

using the 3-suffix Margules equation for both phases, the numerical optimization fails in

find a unique solution. It means that there is not a single set of adjustable parameters that

answer an optimization routine. This problem is well known in the literature17, 31

concerning the calculation of non-linear thermodynamic problems. By determining both

liquidus and solidus lines, the number of independent variables increases, when compared

with description of only the liquidus line, as well as the number of adjustable parameters.

Considering that the number of experimental data points is the same, the degrees of

freedom of the problem also increase. This prevents obtaining a unique solution. For this

158

reason, a heuristic method was adopted. The problem is finding the set of parameters Aij

and Bij of the 2- and/or 3-suffix Margules equation (Equations 2 and 3) that minimizes the

deviation between calculated and experimental data (Equation 13). Considering n number

of parameters to adjust, depending on the case, n vectors with m elements were built. The m

elements were possible solutions for the problem. Thus, n m sets of calculated data were

found and the deviation (Equation 13) was calculated for each set. A multi-dimensional

surface relating the n m sets of parameters and the deviation were then found. The surface

presented a minimum region that circumscribed the set of parameters and answered the

problem.

The modeling procedure can be summarized by Figure 4. The routine is represented

by a three level nested structured: 1) the first one is the Crystal-T algorithm, where the

equilibrium point (T, xi, zi) is calculated; 2) the second one comprises the execution of the

first level for 0.0 < xi < 1.0 and sequentially for 1.0 < xi < 0.0 in order to depict the SLE

phase diagram; 3) the third one is the adjustment of the i parameters by a numerical or a

heuristic optimization procedure in which the first and the second levels are executed until

convergence is established.

159

Figure 4. Nested structure for the SLE modeling using the Crystal-T algorithm.

2.3.2. Experimental considerations

The Crystal-T algorithm was used in the modeling of SLE experimental data of the

following triacylglycerols + fatty alcohols mixtures: trilaurin + 1-hexadecanol, trilaurin +

1-octadecanol, trimyristin + 1-hexadecanol, trimyristin + 1-octadecanol, tripalmitin + 1-

hexadecanol and tripalmitin + 1-octadecanol. As previously specified, the SLE problem

takes into account the knowledge of pure compounds transitions properties. In this work,

specific heat capacity fusCp, solid-solid transitions temperature Ttr and enthalpy trH were

taken from literature2, 35-38

. Melting temperatures Tfus and enthalpies fusH of the pure

triacylglycerols and fatty alcohols (Sigma-Aldrich, 99% mass fraction) were obtained by

six-replicates using differential scanning calorimetry with a DSC8500 calorimeter

(PerkinElmer, Waltham) at ambient pressure following a specific methodology developed

for fatty systems, as described elsewhere32, 34

. Melting temperatures and enthalpies of pure

compounds were compared with literature values2, 35, 36, 38-44

and low mean relative

Numerical or heuristicoptimization procedure for the adjustment of the i equations

Evaluation of the Crystal-T algorithm for 0.0 < xi < 1.0

and for 1.0 < xi < 0.0.

Crystal - T algorithm(T, xi,zi)

1st Level

2nd Level

3rd Level

160

deviations of 1.1% and 5.5%, respectively, were observed. The triacylglycerol + fatty

alcohol mixtures were prepared gravimetrically and their melting properties were obtained

following the same methodology.

Because the beginning of the melting process (solidus line), in case of solid solution

formation is difficult to identify by using the DSC data, being often overestimated, the

mixtures were evaluated by temperature controlled microscopy using a BX51 Olympus

optical microscope (Olympus Co., Tokyo) coupled to a LTS120 Linkam temperature-

controller apparatus (Linkam Scientific Instruments Ltd., Tadworth). Samples were

observed in a 0.1 K min-1

heating run. Melting temperatures of the pure compounds and

some of their mixtures were evaluated by microscopy and results compared with the DSC

data. Deviations between experimental data obtained by DSC and by microscopy were

estimated to be not higher than 1.0 K.

The uncertainty of the mixture’ melting temperature was obtained by the evaluation

of at least three-replicates of the pure compounds and some of the binary mixtures. The

uncertainty of the eutectic point was calculated by error propagation method, considering

the equations obtained in the fitting procedure of the Tammann plot. The xi experimental

errors were also calculated by error propagation from the values of the weighted masses.

Uncertainties for melting temperatures and mole fractions as well as for the eutectic

temperature and mole fraction were estimated as not higher than 0.38 K, 0.001, 0.58

K and 0.005, respectively.

Since the evaluation of the SLE experimental data is fundamental for the accuracy

of the modeling procedure, their results will be detailed explained.

161


3.1. Experimental data analysis

Figure 5 depicts the solid-liquid transitions experimental data of the binary mixtures

as well as the modeled liquidus and solidus lines. Tables with experimental data are

reported in the Supporting Information. The DSC technique was able to clearly show the

melting temperature behavior of the mixtures, i.e the liquidus line and the eutectic reaction,

when it exists. Figure 6 sketches the melting behavior observed by the DSC thermograms

obtained for the trimyristin (1) + 1-hexadecanol (2) mixture. In all cases, the liquidus line

shows a minimum and an invariant transition is observed at the same temperature of this

inflexion point. This behavior is typically observed in case of systems presenting eutectic

transitions.

The eutectic transition and the formation of solid solution were investigated using

Tammann plots and temperature-controlled microscopy. Figure 7 presents the Tammann

plots of the trimyristin (1) + 1-hexadecanol (2) mixture for the invariant transition observed

and Figure 8 the optical micrographs for the melting process of the same mixture at x1 =

0.694 mole fraction. At this concentration, DSC data show the presence of an invariant

transition at T = 319.46 K. Micrographies taken at temperatures before and after T = 319.46

K show that at this temperature the mixture clearly starts to melt, delimiting the biphasic

region. In fact, the well-described triangle-shape of the Tammann plot of the invariant

transition, considering the linear regressions of the data (R2 > 0.98), was able to show the

typical profile of a eutectic transition. It means that the enthalpy of the transition increases

up to the eutectic point (x1 = 0.124 0.005 mole fraction) when it begins to decrease.

162

Figure 5. Experimental ( by DSC and by microscopy) and modeled (solid lines) phase diagrams

using the 3-suffix Margules equation for the triacylglycerol + fatty alcohols mixtures. AijS, Bij

S are the

parameters for the iS equation and Aij

L, Bij

L for the i

L equation (kJmol

-1). A) trilaurin (1) + 1-

hexadecanol (2), B) trilaurin (1) + 1-octadecanol (2), C) trimyristin (1) + 1-hexadecanol (2), D)

trimyristin (1) + 1-octadecanol (2), E) tripalmitin (1) + 1-hexadecanol (2), F) tripalmitin (1) + 1-

octadecanol (2).

312

316

320

324

328

332

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z trilaurin

312

316

320

324

328

332

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z trilaurin

(A) (B)

315

319

323

327

331

335

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z trimyristin

315

319

323

327

331

335

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z trimyristin

315

320

325

330

335

340

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z tripalmitin

320

325

330

335

340

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z tripalmitin

(C) (D)

(E) (F)

(Aij, Bij) L = (10.0, -2.0)

(Aij, Bij) S = (1.6, -0.5)

(Aij, Bij) L = (2.2, 0.5)

(Aij, Bij) L = (9.0, -5.0)

(Aij, Bij) S = (-0.1, 0.1)

(Aij, Bij) L = (12.0, -3.0)

(Aij, Bij) S = (0.5, -1.5)

(Aij, Bij) L = (5.9, -4.3)

(Aij, Bij) S = (-0.5, 0.1)

(Aij, Bij) L = (5.0, -5.0)

(Aij, Bij) S = (-0.5, 0.5)

163

Figure 6. Thermograms for the mixture trimyristin (1) + 1-hexadecanol (2). Magnification of the

thermogram for x1 = 0.778 mole fraction, in detail, showing the eutectic transition.

Figure 7. Tammann plot of the enthalpy of the eutectic transition for the trimyristin (1) + 1-

hexadecanol (2) mixture. Dashed lines are linear regressions.

315

319

323

327

331

335

0.0 0.2 0.4 0.6 0.8 1.0

T /

K

x, z trimyristin

H = 93.042x + 72.158

R² = 0.98

H = 489.09 x

R² = 0.99

0

10

20

30

40

50

60

70

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH/ k

Jm

ol-1

xtrimyristin

(A) (B)

164

Figure 8. Melting transition at the eutectic temperature (Teut = 319.46 K) for the trimyristin (1) +1-

hexadecanol (2) system at x1 = 0.694 mole fraction. A) 319.15 K, B) 319.65, C) 320.15 K. White

arrows highlight details during the melting process.

Note that the enthalpy associated to the eutectic transition disappears at x1 = 0.0

mole fraction in the left-hand side of the Tammann plot and at x1 = (0.775 0.005) mole

fraction in the right-hand side. It means that, in case of the trimyristin (1) + 1-hexadecanol

(2) mixture, at the left-hand side of the phase diagram, the solid phase in the biphasic

region is composed by pure fatty alcohol or, considering the experimental uncertainty, a

solid solution with a composition very close to pure fatty alcohol. However, in the right-

hand side of the diagram, the system is a mixture with both compounds in the solid-phase

as a solid solution (x1 0.775 mole fraction). For the other mixtures, solid phase miscibility

was also observed at the triacylglycerol-side of the diagram. The Tammann plots for all

systems are in the Supporting Information. In summary, trilaurin (1) + 1-hexadecanol (2)

presents a eutectic at (x1, z1I, z1

II) (0.552, 0.000, 0.949) mole fraction, trimyristin (1) + 1-

octadecanol (2) at (x1, z1I, z1

II) (0.521, 0.000, 0.937) mole fraction, tripalmitin (1) + 1-

hexadecanol (2) at (x1, z1I, z1

II) (0.025, 0.000, 0.743) mole fraction and tripalmitin (1) + 1-

octadecanol (2) at (x1, z1I, z1

II) (0.112, 0.000, 0.682) mole fraction. Thus, at x1 > xeut, the

solid phase of the mixture is composed by both compounds at the biphasic domain. On the

other hand, at x1 < xeut experimentally is virtually impossible to know if the solid phase of

the system is really immiscible or if there is a small miscibility gap very close to pure fatty

165

alcohol, i.e. z2 1.00. Tammann plot for trilaurin (1) + 1-octadecanol (2) shows an almost

simple eutectic behavior with solid phase immiscibility through the entire concentration

range. In this case, the eutectic point is at (x1, z1I, z1

II) (0.802, 0.000, 1.000) mole fraction.

In summary, solid solutions are clearly evidenced in almost all cases and always at the

right-hand side of the diagram, indicating that they are triacylglycerol-rich solutions. Also,

the higher the difference between the pure compounds’ melting temperatures or the higher

the triacylglycerol carbon chain, the larger the solid solution region.

When the compounds in solid phase are miscible such that a solid solution is

formed, the transition for the description of the solidus line, i.e when the first crystal melts,

was difficult to be observed by the DSC measurements (see highlights in Figure 6). Thus,

in order to verify firstly the previous supposition on the existence of solid solution and to

indentify the temperature of the solidus line, the samples were also submitted to thermal-

controlled microscopy at this defined region. Figure 9 shows the melting process of the

trimyristin (1) + 1-hexadecanol (2) system at x1 = 0.894 mole fraction beginning from a

temperature T < Teut. White arrows were used to highlight the appearance of the liquid

phase at T = 323.55 K (Figure 9 D). A slight enlargement of the crystal is observed with the

rounding of the angulated boundaries of the solid particle. Consequently, the amount of the

liquid phase starts to increase with the entrance in the biphasic region. This means that the

melting starts at a temperature higher than that previously evaluated as being the eutectic

transition (T = 319.46 K). Thus, at a temperature lower than T = 323.55 K there is only a

solid solution.

166

Figure 9. Heating and melting processes of trimyristin (1) + 1-hexadecanol (2) system at x1 = 0.894

mole fraction at T = A) 313.15 K, B) 322.15 K, C) 323.35 K, D) 323.55 K, E) 323.95 K, F) 324.35

K, G) 327.65 K and H) 329.05 K. White arrows highlight details during the heating process.

As previously mentioned, fatty compounds generally present some thermal

transitions in the solid phase and this is the case of both fatty alcohols and triacylglycerols.

This phenomenon is very known by literature and the compounds evaluated in this work

have already been reported by presenting polymorphic forms during the heating process of

the solid phase2, 32, 35, 44, 45

. All of the triacylglycerols used in this work, trilaurin, trimyristin

and tripalmitin present three principal polymorphic forms, namely , ’ and , with

different crystal packing, respectively hexagonal, orthorhombic and triclinic and with

increasing thermal stability and transition properties, temperatures and enthalpies. Apart

from these principal polymorphic forms, some sub modifications in the crystal structure

167

could happen during the heating process, implying in additional rearrangements of the

long-carbon chains. Thus, a single thermogram may present several solid-solid transitions,

related to these numerous conformational rearrangements of the compound’s crystal lattice.

Fatty alcohols, specifically 1-hexadecanol and 1-octadecanol, investigated in this work,

also present one characteristic polymorphic form whose transition temperature is very close

to the melting temperature35, 36

. All these transitions are clearly evident in the thermograms

of the pure compounds but are also present in case of mixtures. The pure components

melting properties and the solid-solid transitions are presented in Supporting Information.

Micrographs before and after the solid-solid transition evidenced at T = 318.75 K for the

system tripalmitin (1) + 1-octadecanol (2) at x1 = 0.697 mole fraction are shown in Figure

10. Changes in the crystalline structure of the mixture and so in the refraction properties of

the solid particle is clearly observed. This transition is probably related to one of the

polymorphic forms of the tripalmitin since, at the same temperature, the pure compound

present a solid-solid transition that, according to literature2, is related to the form (Ttr =

317.85 K). This thermal event is also identified by the thermogram of the mixture, as

shown in Figure 10. The thermogram clearly shows an endothermic transition followed by

an exothermic one. This fact configures a resolidification phenomenon probably related to a

rearrangement into the ’ polymorphic form. The identification of the pure compounds’

solid-solid transitions is important because for transition temperatures higher than the

eutectic point, the solid-liquid equilibrium behavior of the mixture is influenced by these

transitions. This is described by the Equation 1. Details about the SLE equation are

presented in Supporting Information.

168

Figure 10. Micrographies and thermogram of the system tripalmitin (1) + 1-octadecanol (2) at x1 =

0.697 mole fraction. Pictures are at a temperature before (A. 293.15 K) and after (B. 320.15 K) the

solid-solid transition at 318.75 K. Black arrows in the thermogram highlight the transitions. Eutectic

transition in detail (T = 329.20 K).

3.2. SLE modeling using the Crystal-T algorithm

Taking into account the comprehension of the experimental melting behavior of the

systems, the modeling of the SLE phase diagrams was carried out. Firstly, some remarks

can be done considering the performance of the procedure. At the first level routine of the

nested structure of the modeling procedure (Figure 4) the Crystal-T algorithm was executed

and the equilibrium point (T, xi, zi) of a mixture for a given liquid phase composition was

calculated. Since the given liquid phase composition xi lay on the liquidus line the

equilibrium point could be directly determined and no additional routine to test the number

of phases was required. On the other hand, by using the Gibbs energy minimization, and the

isoenthalpic flash algorithms, the calculation of the SLE was very sensitive to the initial

100 mm 100 mm

BA

307.0 313.5 320.0 326.5 333.0 339.5 346.0

Hea

t fl

ow

T / K

327 331

169

estimate. If the composition was inside the biphasic region, the mixture is separated in two

phases and the answer is the phase change point (T, xi, zi). However, out of this domain, the

mixture has only one phase and the liquidus and solidus lines are not described, requiring a

routine to test the number of phases. Considering that the description of the entire SLE

phase diagram implies in the evaluation of a relatively large set of points that would be

additionally followed by an adjustment procedure for the i models’ parameters, the

numerical efforts increases exponentially. Apart from discussions on the performance of the

procedures, the results obtained by using the Crystal-T, the Gibbs or flash algorithms were

(and should be) exactly the same because they use the same thermodynamic theory

expressed by Equation 1.

At the second level of the modeling, the Crystal-T algorithm was executed

considering each one of the pure compounds as initial estimate and generating two profiles,

being the interception of both profiles the solid-solid-liquid equilibrium point (Figure 2).

This procedure avoided additional phase test routines and problems with the discontinuity

of the profile, as already mentioned.

At the third level of the procedure the parameters of the liquid and solid i equations

were estimated. The results obtained were here exemplified through the system tripalmitin

(1) + 1-octadecanol (2) because this case presented the larger solid solution region. For the

estimation procedure, this work considered that both liquid and solid phases are non-ideal

and thus equations for depicting iL and i

S were used. Two kinds of i equations were

evaluated. The UNIFAC model20, 22

is absolutely predictive and this is a great advantage for

the design of a phase change based unitary operation if one does not know any

experimental information about the mixture. On the other hand, the Margules equation is a

170

function with adjustable parameters. Although such model is not predictive, the function

presents a lower non-linearity, reducing the numerical efforts, but presenting a good

agreement with the experimental data as it has been already reported in the literature34, 46, 47

.

Figure 11 depicts the SLE diagram of the system tripalmitin (1) + 1-octadecanol (2)

using the original or modified UNIFAC models to calculate the iL

and the 2-suffix

Margules equation to calculate the iS. Additionally, the liquid phase were also taken as

ideal (iL

= 1.0). In these cases, the optimization procedure is unidirectional, taking into

account the adjustment of the Aij parameter of 2-suffix Margules equation. These

approaches fail in the prediction of the liquidus line as well as the SSLE (eutectic)

temperature and composition. The iL values obtained from both UNIFAC models did not

deviate significantly from the ideality. However, in case of original UNIFAC model, the

solid phase positive deviation calculated by 2-suffix Margules equation was slightly

decreased when compared with the other approaches. The lower the positive deviation from

ideality, the lower the tendency to phase separation. Consequently, when liquid phase was

calculated by original UNIFAC, the 2-suffix Margules could described a solidus line with a

solid solution domain larger than that described by the approach using the modified

UNIFAC version. These observations show that probably neither the ideal assumption nor

the UNIFAC models can accurately depict the liquid phase behavior or 2-suffix Margules

equation are not able to describe the solid phase non-ideality. Furthermore, original and

modified UNIFAC sketch different SLE profiles. If original and modified UNIFAC models

are compared, different combinatorial and residual terms are observed 20, 22

. This means

that, considering the same system, both models can predict different molecular interactions

and entropic effects. In fact, in some previous works 32, 48

original UNIFAC model were

171

slightly more accurate in depicting the liquid phase behavior in the SLE of fatty systems

than the modified version, despite modifications to improve the non-ideality calculation.

Also, some works show that fatty compounds molecules can be better represented using a

different way of counting groups, such as the ester group in TAG molecules, or using new

or readjusted UNIFAC interaction parameters 49, 50

. These considerations allied to the fact

that UNIFAC’s parameters were adjusted by VLE experimental data 20

, show that the

utilization of the UNIFAC model for accurate description of SLE are probably restrict to

simple cases, such as that considering solid phase immiscibility. However, in this work, the

use of UNIFAC model in more complex approaches is additionally investigated. For this,

and based on the aforementioned comments, the original version was chosen.

Figure 11. SLE phase diagram of the tripalmitin (1) + 1-octadecanol (2) mixture using 2-suffix

Margules as iS equation and considering that i

L = 1.0 (simple solid line) (Aij

S = 6.93 kJmol

-1) or

using the original UNIFAC model (bold line) (AijS = 6.23 kJmol

-1) and the UNIFAC-Dortmund

model (dashed line) (AijS = 7.63 kJmol

-1) as i

L equation. DSC () and microscopy () data.

326

328

330

332

334

336

338

340

0 0.2 0.4 0.6 0.8 1

T /

K

x, z tripalmitin

172

Using the 2-suffix Margules equation for the calculation of both phases’ activity

coefficients or the 3-suffix Margules equation and the original UNIFAC model for the

calculation of iS and i

L, respectively, the optimization procedure is bidirectional. Owing to

the set of experimental data points with an inherent experimental uncertainty as well as the

number of parameters to fit the data, the problem could not be answered by numerical

procedures and was solved by a heuristic method. For this, tridimensional surfaces were

built relating the parameters used for the iL and i

S calculation and the deviation (Equation

14) generated by them. Figures 12 and 13 show the contour plots of the surfaces generated

by these approaches and sketch the changes in the calculated SLE phase diagrams

according to the different sets of parameters used to represent the behaviors. The phase

diagram with the lowest deviation in each case is represented in the bottom right of the

figure.

Both approaches improved the accuracy of the theoretical liquidus line and,

consequently, the description of the solidus line when compared to the previous one-

variable problem. The minimum deviations observed (Equation 14) were described by

valleys and were not single points. However, the valleys were as small as the accuracy of

the model to represent the activity coefficients or the quality and quantity of experimental

data increased. In the first case, sketched in Figure 12, an adjustable equation was

introduced for the calculation of both phases’ activity coefficients. In the second case,

sketched in Figure 13, an equation with two parameters was used for calculating solid

phase activity coefficients but keeping the predictive character of the liquid phase activity

coefficients. In general, the second approach, i.e using 3-suffix Margules as iS equation

and original UNIFAC as iL equation, described more precisely the phase diagrams. The

173

mean deviation decreased from = (18.10 to 3.0), approximately, especially due to a better

characterization of the solidus line. In fact, the calculation of the non-ideality of the

compounds by using 2-suffix Margules equation is such that the behavior is strictly

symmetrical reflecting the specific feature of this model (Equation 2). Symmetrical activity

coefficient values say that the compounds have similar mutual interactions. However, such

assumption is not probably the best in present cases. In fact, by using the non-symmetrical

3-suffix Margules equation the activity coefficients values assume very distinguished

behaviors.

Figure 12. Deviations (Equation 14) from experimental data for the system tripalmitin +

octadecanol using the 2-suffix Margules equation as iL and i

S models. Aij

S and Aij

L are the i

S and

iL parameters (kJmol

-1), respectively. In detail, phase diagrams using different parameters sets.

328

332

336

340

0 0.5 1T

/ K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

7.2 7.6 8.0 8.4 8.8 9.2 9.6 10.00.2

0.4

0.6

0.8

1.0

1.2

1.4

B i

j (k

J.m

ol-1

)

A ij (kJ.mol

-1)

18.5

20.0

22.0

24.0

28.0

30.0

32.0

328

332

336

340

0 0.5 1

T/

K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

AijS= 12.0

AijL = 4.0

AijS = 12.0

AijL = - 1.0

AijS = 7.9

AijL = 0.7

AijS = 4.0

AijL = 4.0

AijS = 4.0

AijL = - 1.0

AijS (kJ mol-1)

Aij

L (k

J m

ol-1

)

= 18.1= 100.0

= 503.6

= 78.0

= 27.62

174

Figure 13. Deviations (Equation 14) from experimental data for the system tripalmitin + 1-

octadecanol using original UNIFAC as iL model and 3-suffix Margules equation as i

S model with

AijS and Bij

S as parameters. In detail, phase diagrams using different parameters sets.

Figure 14 sketches the results obtained by applying the 3-suffix Margules equation

for the description of both liquid and solid phases non-ideality. The optimization method

considered so a four-directional search. In this case, similarly to the previous cases, a cross-

evaluation of two matrices AijS Bij

S (parameters for i

S equation) and Aij

L Bij

L

(parameters for iL equation) were performed and the region with the lowest deviations was

depicted. The first contour plot AijS Bij

S presents the results at a fixed set of i

L parameters

(AijL, Bij

L) and the second one Aij

L Bij

L at a fixed set of i

S parameters (Aij

S, Bij

S). The fixed

328

332

336

340

0 0.5 1

T/

K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

328

332

336

340

0 0.5 1

T/

K

x1, z1

AijS = 10.0

BijS = 1.0

AijS = 10.0

BijS = -7.0

AijS = 6.5

BijS = -4.0

AijS = 4.0

BijS = 1.0

AijS = 4.0

BijS = -7.0

4.5 5.0 5.5 6.0 6.5 7.0-5.0

-4.5

-4.0

-3.5

-3.0B

ij (

kJ.

mo

l-1)

A ij (kJ.mol

-1)

3.03.13.33.54.07.010.015.020.0

AijS (kJ mol-1)

Bij

S (k

J m

ol-

1)

= 3.0

= 9.6

= 42.3 = 171.1

= 65.7

175

parameters were inside the best fitting region found. The adjustment was considerably

improved with deviations (Equation 14) lower than = 1.6. With this improvement one

could suppose that the behavior of the activity coefficients was more precisely assessed. In

the last cases, the liquid phase activity coefficients were very close to the ideality

presenting positive or negative deviations not higher than 10%. However, by this approach,

the deviation from ideality of the liquid phase presented marked negative deviations of up

to 25% and in fact, Figure 11 showed that by considering the liquid phase as ideal the

liquidus line presented a slight negative deviation. Likewise, the positive non-ideality of the

solid phase was slightly decreased when compared with the last cases. It means that the

improvement of the description of the liquid phase non-ideality, and consequently the

liquidus line, improved the non-ideal profile of the solid phase. Thus, the solidus line was

also more precisely assessed.

Figures 12 to 14 also show, in detail, the evolution of the behavior of the phase

diagrams shape by using different parameters sets. This is interesting since the parameters

of the i equations were directly related to the non-ideality of the system. In general, when

parameters of both liquid and solid phases i equations were low, the higher the trend to an

ideal behavior (i 1) and consequently the trend to show a continuous solid solution

SLE phase diagram. Increasing the values of the solid phase i equations parameters led to

the increase of the positive deviation from ideality and consequently to the solid-solid

phase separation. The behavior of the liquidus and solidus lines thus showed a

discontinuity, corresponding to the eutectic point. The higher the positive deviation in iS

values the smaller the solid solution region until the compounds were completely

immiscible in the solid phase.

176

Figure 14. Deviations (Equation 14) from experimental data for the system tripalmitin + 1-

octadecanol using 3-suffix Margules equation as both iL and i

S models. Aij

S and Bij

S are parameters

for iS

and AijL and Bij

L are parameters for i

L. In detail, phase diagrams using different parameter

sets.

As mentioned before, by using the heuristic method the optimized answer was a

region and not a single set of parameters. It means that into the minimum deviation region,

the set of parameters float around a small range of values. This means that once liquidus

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2-0.1

0.0

0.1

0.2

0.3

0.4

D i

j (k

J.m

ol-1

)

C ij (kJ.mol

-1)

1.60

1.70

1.80

1.90

2.00

3.00

326

330

334

338

342

0.0 0.2 0.4 0.6 0.8 1.0

T/ K

x1, z1

AijS, Bij

S = 5.9, -4.3 AijL, Bij

L = - 0.5, 0.1

5.8 5.9 6.0 6.1 6.2 6.3 6.4-4.8

-4.7

-4.6

-4.5

-4.4

-4.3

-4.2

B i

j (k

J.m

ol-1

)

A ij (kJ.mol

-1)

1.60

1.65

1.70

1.80

1.90

2.00

AijS, Bij

S = 5.90, -4.40AijL, Bij

L = - 0.50, 0.10

328

332

336

340

0.0 0.5 1.0

T/

K

x1, z1

AijS, Bij

S = 1.0, -1.0

AijL, Bij

L = 0.5, 0.1

AijS (kJ mol-1)

328

332

336

340

0.0 0.5 1.0

T/

K

x1, z1

AijS, Bij

S = 5.9, -4.3

AijL, Bij

L = 5.0, 5.0

328

332

336

340

0.0 0.5 1.0

T/

K

x1, z1

AijS,Bij

S = 5.9, -4.3

AijL, Bij

L = -3.0, -5.0

Bij

S(k

J m

ol-1

)

= 1.60

= 391.80

328

332

336

340

0.0 0.5 1.0

T/

K

x1, z1

AijS, Bij

S = 15.0, -2.0

AijL, Bij

L = 0.5, 0.1

= 2.60

AijL (kJ mol-1)

Bij

L(k

J m

ol-1

)

= 614.2

= 173.5

177

line is accurately predicted by a defined set of parameters, the modeling can fail in the

description of the solidus line. Likewise, when a set of parameters are used for the accurate

description of the solidus line, the behavior of the liquidus line is slightly altered. Thus, the

minimum region assumes so a rough surface-type shape which prevented the utilization of

optimization procedure based on a classical numerical method.

The modeling results for all binary mixtures experimentally evaluated in this work

are depicted in Figure 5 and, as indicated, 3-suffix Margules equation was considered for

the calculation of both liquid and solid phases non-ideality. Quantitatively, this approach

provided the best description of the SLE behavior, with the lowest deviations between

calculated and experimental data. In fact, when compared with the other approaches, the

increase of the accuracy was in this case obtained by means of the increase of the number

of adjustable parameters. However, this implied in the decrease of the predictive ability of

the model. Qualitatively, the utilization of the UNIFAC model as iL equation and the 3-

suffix Margules equation for the solid phase also presented reasonable results. Even with

slightly higher deviations, this approach presented a higher predictive ability and was also

able to represent the overall thermodynamic behavior of the mixtures.

4. CONCLUSIONS

The non-ideality of the solid phase could be embodied in the SLE modeling by an

effective procedure, here called as Crystal-T algorithm. In contrast with prior works in

literature that usually consider lipidic mixtures as exhibiting a solid phase with compounds

independently crystallized, triacylglycerol + fatty alcohol systems presented a

discontinuous solid solution behavior. The solid solution region could be accurately defined

178

by the Tammann plots of the eutectic transition and the results obtained by such evaluation

anchored to the modeling procedure. The algorithm was not sensitive to initial estimate and

thus, very robust and effective. This because it calculates the SLE from a given liquid phase

xi, that is a composition of the the liquidus line, from x1 = 0 to 1 and from x1 = 1 to 0.

Consequently, the algorithm avoids the problem with the discontinuity of the function in

the eutectic point, and additional routines to test the number of phases, used in Gibbs and

flash SLE algorithms. The most accurate results were obtained by using the 3-suffix

Margules equation for both liquidus and solidus lines description, due to the increasing of

the number of adjustable parameters. However, considering the future evaluation of a large

set of binary mixtures, and consequently, the construction of a parameters databank, the

SLE of more complex systems could be effectively described. Otherwise, considering a

reasonable qualitative overall description, the utilization of original UNIFAC model as iL

associated with 3-suffix Margules equation as iS

should also be applied.

This work contributed for the expansion of the boundaries of the classical SLE

modeling comprising not trivial mixtures as in case of food, oilchemistry and

pharmaceutical fields.


Description of the SLE equations, Tables with pure components melting properties

and mixtures’ experimental equilibrium data and Tammann plots of the eutectic transitions.

179

ACKNOWLEDGEMENTS

The authors are grateful to the brazilian funding agencies FAPESP (2008/56258-8,

2012/05027-1), CNPq (304495/2010-7, 483340/2012-0, 140718/2010-9) and CAPES

(BEX-13716/12-3) for the financial support. The authors are also grateful to Professor Dr.

Sandra Augusta Santos from IMECC/UNICAMP for the suggestions.

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183


Deduction of the SLE equations considering polymorphism phenomena

The isofugacity criteria establish that, in case of solid-liquid equilibrium (SLE), the

fugacity of the compound fi in both solid (S) and liquid (L) phases are equal.

S L

i if f S1

Equation S1 can be written in terms of the standard fugacity of the compounds fi0 in

each phase as follows:

0

0 0

0

L SL L S i i i

i i i i i i Li i i

S

S

x fx f z f

z f

S2

where xi and zi are mole fractions of the compound i in both liquid and solid phases,

respectively, and iL and i

S are the activity coefficients of both liquid and solid phases,

respectively. It means that the temperature T of the system must be the same in both solid

and liquid phases. This is attended considering a subcooled liquid state. The L S

i i i ix z

ratio can be calculated by the variation of the Gibbs energy G as follows,

0

0

S

i

L

i

R lnf

G Tf

S3

of the following process: heating the system from T to the melting temperature Tfus,

followed by the complete melting and then cooling to the temperature T. The G of such a

process is calculated by Equation S4, knowing the variation of the enthalpy H (Equation

S5) and entropy S (Equation S6) of the process, and considering the n solid-solid

transitions.

184

G H T S S4

tr fus

fus tr

n nS S L L

i tr i fus i i

tr=1 tr=1

d d + d d

T T T T

T T T T

H Cp T H Cp T H Cp T Cp T

S5

tr fus

fus tr

S S L Ln ntr fusi i i i

tr=1 tr=1tr fus

d d d dT

T T T T

T T T T

H HCp Cp Cp CpS T T T T

T T T T T

S6

where fusH and Tfus are the melting enthalpy and temperature of the compound i, and trH

and Ttr are the solid-solid transitions enthalpy and temperature of the compound i. Knowing

that the behavior of the heat capacity of the compound i in both liquid CpiL

and solid CpiS

phases as a function of the temperature is small1-3

(in the range evaluated), CpiL

and Cpi

S

can be considered as constants as well as the variation of the heat capacity fusCp = CpL

CpS. Thus, the SLE can be determined by Equation S7 from Ttr < T < Tfus, by Equation S8

for T < Ttr , and analogously, in case of more than one solid-solid transition.

Lfusi i

fusi i

fus fus fus1 1ln 1ln

S

pC T T

T

H

R T

x

T T Rz

S7

Lfus tri i

f

fus fus f

i

us

us tri

1 1 1 1ln 1ln

S

pH Hx

R T T R T

C T T

Tz TR T

S8

Table S1. Melting temperatures (Tfus / K) and enthalpies (fusH / kJmol-1

) and solid-solid

temperatures (Ttr / K) and enthalpies (trH / kJmol-1

) of the pure compounds used in the

modeling procedure and obtained in this work or from literature.

Compound Tfus ref. fusH ref. Ttr1 ref. tr1H lit. Ttr2 ref. tr2H ref.

Trilaurin 319.39

this work

116.45

this work

308.25 4 86.00

4 288.75

4 69.80

4

Trimyristin 330.90 141.97 319.05 4 106.00

4 305.75

4 81.90

4

Tripalmitin 338.98 165.88 328.85 4 126.50

4 317.85

4 95.80

4

1-hexadecanol 322.61 33.60 5 321.89

this work 23.70

5 - -

1-octadecanol 331.42 40.10 6 330.55 26.50

6 - -

185

Table S2. Experimental solid-liquid equilibrium data for the triacylglycerols + fatty alcohols

systems for mole fraction x and temperature T for solidus and liquidus line.†

trilaurin (1) +

1-hexadecanol (2)

trilaurin (1) +

1-octadecanol (2)

trimyristin (1) +

1-hexadecanol (2)

x1 Solidus

/ K

Liquidus

/ K

x1 Solidus

/ K

Liquidus

/ K

x1 Solidus

/ K

Liquidus

/ K

0.000 322.61 0.000 331.42 0.000 322.61

0.097 315.39 321.13 0.101 317.31 330.00 0.042 320.35 321.68

0.197 315.44 319.48 0.197 317.42 328.56 0.100 319.98

0.295 315.55 318.38 0.294 317.50 327.25 0.137 320.82

0.402 315.96 317.30 0.395 317.67 325.84 0.192 320.11 322.05

0.503 315.86 0.501 317.56 323.71 0.246 319.89 322.98

0.592 315.85 316.28 0.597 318.01 321.73 0.394 319.11 324.71

0.703 315.18 316.79 0.701 317.76 319.85 0.498 319.30 326.30

0.781 315.06 317.15 0.790 317.76 318.67 0.594 318.99 326.78

0.863 315.00 318.58 0.884 317.70 318.77 0.694 318.80 327.59

1.000 319.39 1.000 319.39 0.778 319.10 328.24

0.894 323.55 ‡ 329.24

1.000 330.90

trimyristin (1) +

1-hexadecanol (2)

tripalmitin (1) +

1-hexadecanol (2)

tripalmitin (1) +

1-octadecanol (2)

x1 Solidus

/ K

Liquidus

/ K

x1 Solidus

/ K

Liquidus

/ K

x1 Solidus

/ K

Liquidus

/ K

0.000 331.42 0.000 322.61 0.000 331.42

0.100 325.99 329.88 0.050 322.60 0.058 329.20 330.27

0.199 326.26 328.60 0.101 322.90 328.69 0.099 328.90 329.80

0.300 326.01 327.28 0.201 321.90 331.98 0.151 329.56

0.393 325.90 0.299 321.93 333.62 0.200 328.95 331.40

0.493 325.88 0.408 321.68 334.75 0.300 328.80 333.40

0.592 325.77 326.73 0.501 321.90 335.93 0.401 329.50 334.79

0.691 325.65 327.67 0.597 322.00 336.61 0.502 328.80 335.63

0.793 325.48 328.90 0.701 321.82 337.35 0.595 329.00 336.63

0.878 325.61 329.52 0.800 330.45 ‡ 338.32 0.697 329.20 337.35

1.000 330.90 0.894 336.05 ‡ 338.85 0.797 332.05 ‡ 338.16

1.000 338.98 0.906 335.85 ‡ 338.82

1.000 338.98

† Uncertainties for molar fraction and liquidus line temperature are 0.001 and 0.38 K.

Uncertainty for solidus line temperature measured by DSC and by microscopy ‡ is 0.58 K.

186

Figure S1. Tammann plots of the experimental eutectic transition enthalpy eutH () and linear

regression (dashed lines) for the systems A) trilaurin (1) + 1-hexadecanol (2), B) trilaurin (1) + 1-

octadecanol (2), C) trimyristin (1) + 1-hexadecanol (2), D) trimyristin (1) + 1-octadecanol (2), E)

tripalmitin (1) + 1-hexadecanol (2), F) tripalmitin (1) + 1-octadecanol (2).

y = -93.04 x + 72.16

R² = 0.981

y = 506.01 x - 1.40

R² = 0.993

0

10

20

30

40

50

60

70

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH/ k

Jm

ol-1

xtrimyristin

y = 255.42 x - 0.45

R² = 0.9998

y = -319.09 x + 298.97R² = 0.994

0

20

40

60

80

100

120

140

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH /

kJm

ol-1

xtrimyristin

y = 140.53 x - 0.11R² = 0.996

y = -566.99x + 566.99R² = 0.999

0

20

40

60

80

100

120

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH/ k

Jm

ol-1

xtrilaurin

(B)

(D)

y = 194.20 x - 1.02

R² = 0.998

y = -267.63x + 253.93

R² = 0.987

0

20

40

60

80

100

120

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH/ k

Jm

ol-1

xtrilaurin

y = -36.42 x + 27.17R² = 0.990

0

10

20

30

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH/ k

Jm

ol-1

xtripalmitin

Supposed plot

y = -92.08 x + 62.807R² = 0.985

y = 510.34x - 3.749R² = 0.999

0

10

20

30

40

50

60

0.0 0.2 0.4 0.6 0.8 1.0

eu

tH/ k

Jm

ol-1

xtripalmitin

(A)

(E) (F)

(C)

187

REFERENCES

1. G. Charbonnet and W. S. Singleton, J. Am. Oil Chem. Soc., 1947, 24, 140.

2. R. Ceriani, R. Gani and A. J. A. Meirelles, Fluid Phase Equilibr., 2009, 283, 49.

3. J. Xing, Z. C. Tan, Q. Shi, B. Tong, S. X. Wang and Y. S. Li, J. Therm. Anal. Calorim., 2008,

92, 375.



5. C. Mosselman, J. Mourik and H. Dekker, J. Chem. Thermodyn., 1974, 6, 477.



189

CONCLUSIONS

Concerning the use of natural renewable resources and the valuation of

biocompounds extracted from vegetable oils, this work was addressed at the study of the

phase transition behavior of several lipidic mixtures, especially those related to melting

phenomena as a tool for the design of products and processes.

Among the binary systems composed of triacylglycerols, fatty acids and fatty

alcohols, whose solid-liquid equilibrium (SLE) phase diagrams were experimentally

characterized in this work by differential scanning calorimetry, the formation of eutectic

mixtures with partial miscibility in the solid phase was observed. It means that solid

solutions can be formed during the crystallization process of these mixtures. The formation

of solid solutions could be evaluated through X-Ray diffraction and optical microscopy.

The concentration of the mixture at which solid solution is obtained could be calculated

through the Tammann plot of the eutectic reaction. Also, in some systems, compounds

presented both positive and negative deviations from ideality in the liquid phase depending

on the compound in excess. Due to this behavior, the Margules equation with two

adjustable parameters should be used for the calculation of the activity coefficient. In

addition to binary mixtures composed by two lipidic components, the SLE of systems

composed by fatty acids and ethanolamines was also evaluated. These mixtures led to the

formation of ethanolamine carboxylates. These compounds are protic ionic liquids formed

during the proton transfer reaction between the reagents of the mixture. Due to the

formation of this new compound, the SLE diagrams of these mixtures presented a

congruent melting profile. Moreover, the formation of lamellar and hexagonal mesophases

190

(liquid crystals) could be identified by using light polarized optical microscopy. Such ionic

liquid crystals showed a great structuring ability and a special non-Newtonian behavior.

Based on the thermodynamic complexity observed, one may conclude that the

theoretical description of the lipidic systems’ phase diagrams could not be carried out with

the simplification of the SLE theory, which is in fact a usual procedure in literature. The

formation of solid solutions suggested that the non-ideality of both liquid and solid phases

could play an important role on the description of the phase diagram. Thus, the calculation

of the SLE diagrams of lipidic mixtures with partial miscibility in the solid phase could be

effectively carried out by the algorithm “Crystal-T”, developed in this work. The

calculation of the activity coefficient of the liquid and solid phases using the Margules

equation with 2 adjustable parameters, the consideration of the polymorphic phenomena

and the solid phase solubility information obtained by the Tammann plots were

fundamental for the accuracy of the modeling. The solid phase of the mixtures could be

quantified and characterized by the description of the solidus line of the phase diagram.

Consequently, the description of the liquidus line was also improved.

From the experimental point of view, the results suggested that, for future works,

the determination of a larger number of fatty compounds’ physicochemical properties, such

as melting and solid phase transitions temperatures, enthalpies and heat capacities is

fundamental, since they can play a significant role for the description of the SLE phase

diagrams. Likewise, the results highlighted that, future works on the determination of the

SLE of binary and multicomponent fatty systems of industrial and academic interest are

still required in order to improve the understanding of the thermodynamic behavior of such

mixtures. From the theoretical point of view, this work converges to the improvement of

the approaches for the calculation the SLE diagrams of fatty systems presenting more

191

complex thermodynamic behaviors. Thus, it is necessary to develop works related to the

design of algorithms that takes into account mixtures presenting congruent melting profiles,

peritectic reactions, compounds with strong deviation from ideality, unusual non-ideal

behaviors, and the utilization of different activity coefficient models for both liquid and

solid phases.

The diversity of the lipidic mixtures’ solid-liquid equilibrium behaviors observed in

this work through the formation of eutectic mixtures with miscible or immiscible solid

phases, congruent melting profiles or liquid crystal mesophases is the key for the

development of several applications for the food, pharmaceutical and material industry. The

SLE phase diagram can be a useful tool for the formulation of lipidic-based products such

as cosmetic creams, pharmaceuticals and biofuels, for the manipulation of specific

physicochemical properties and for the development of industrial processes such as

crystallization, purification, flowing, and energy generation. In general, the use of fatty

compounds extracted or produced from vegetable oils, in the context of the “green

chemistry”, can promote the decrease of environmental and health negative impacts.

193

CONCLUSÕES

Considerando o reaproveitamento de recursos renováveis naturais e o aumento do

valor agregado dos biocompostos extraídos de óleos vegetais, este trabalho contribuiu para

o estudo experimental e teórico do comportamento das transições de fases de diversas

misturas lipídicas, em especial aquelas relacionadas aos fenômenos de fusão, como

ferramenta para o desenvolvimento de produtos e processos.

Entre os sistemas binários formados por triacilgliceróis, ácidos graxos e alcoóis

graxos, cujos digramas de fases do equilíbrio sólid-líquido (ESL) foram caracterizados

experimentalmente neste trabalho por calorimetria diferencial exploratória, foi observada a

formação de misturas eutéticas com miscibilidade parcial na fase sólida. Ou seja, soluções

sólidas podem ser formadas durante o processo de cristalização dessas misturas. A

formação de soluções sólidas pôde ser avaliada através de difração de raio-X e microscopia

ótica. A concentração da mistura em que a solução sólida foi formada pôde ser obtida a

partir do diagrama de Tammann da reação eutética. Além disso, em alguns sistemas, os

compostos apresentaram desvios da idealidade positivos e negativos na fase líquida,

dependendo do composto em excesso. Devido a este comportamento, a equação de

Margules com 2 parâmetros ajustáveis foi utilizada para o cálculo do coeficiente de

atividade. Além de misturas binárias formadas por dois compostos lipídicos, sistemas

formados por ácidos graxos e etanolaminas foram também avaliados. Essas misturas

levaram a formação de carboxilatos de etanolamina. Esses compostos são líquidos iônicos

próticos formados durante a reação de transferência de prótons entre os reagentes da

mistura. Pela formação desses novos compostos, os diagramas de ESL dessas misturas

apresentaram um perfil de fusão congruente. Além disso, a formação de mesofases

194

lamelares e hexagonais (cristais líquidos) pode ser identificada através de microscopia de

luz polarizada. Tais líquidos iônicos cristalinos mostraram grande habilidade estruturante e

comportamento não-Newtoniano singular.

Com base na complexidade termodinâmica observada, conclui-se que a descrição

teórica dos diagramas de fase dos sistemas lipídicos não pode ser realizada através da

simplificação da teoria do ESL, o que é um procedimento usual encontrado na literatura. A

formação de soluções sólidas sugeriu que a não-idealidade de ambas as fases líquidas e

sólidas teve um papel importante na descrição do diagrama de fases. Portanto, o cálculo dos

diagramas de ESL de misturas graxas com miscibilidade parcial na fase sólida pôde ser

efetivamente realizado através do algoritmo “Crystal-T” desenvolvido neste trabalho. O

cálculo do coeficiente de atividade das fases líquidas e sólidas utilizando a equação de

Margules com 2 parâmetros ajustáveis, a consideração dos fenômenos polimórficos e das

informações experimentais sobre a solubilidade da fase sólida obtidas pelo diagrama de

Tammann da reação eutética foram fundamentais para a precisão da modelagem. A fase

sólida das misturas puderam ser quantificadas e caracterizadas a partir da descrição da linha

solidus do diagrama de fases. Consequentemente, a descrição da linha liquidus foi, da

mesma forma, melhorada.

Do ponto de vista experimental, os resultados apresentados sugerem que, como

trabalho futuro, é fundamental a determinação das propriedades físico-químicas

(temperatura, entalpia e capacidade calorífica da fusão dos compostos puros e das

transições da fase sólida) de um maior número de compostos graxos, como os

triacilgliceróis, acilgliceróis parciais, alcoóis, ácidos e ésteres graxos. Essas propriedades

podem influenciar na descrição dos diagramas de fases sólido-líquido. Os resultados ainda

destacam que, trabalhos futuros envolvidos na determinação do ESL de sistemas lipídicos

195

binários e multicomponentes de interesse industrial ou acadêmico são necessários para

ampliar a compreensão do comportamento termodinâmico dessas misturas. Do ponto de

vista teórico, os resultados convergem para o aperfeiçoamento das abordagens para o

cálculo dos diagramas de ESL de sistemas graxos que possuam comportamentos

termodinâmicos mais complexos. Para isso, é necessária o desenvolvimento de trabalhos

relacionados à elaboração de algoritmos que considerem casos de misturas que apresentam

fusões congruentes, reações peritéticas, compostos com fortes desvios da idealidade,

comportamentos não-ideais incomuns, e a utilização outros modelos para o cálculo do

coeficiente de atividade das fases.

A diversidade do comportamento termodinâmico de sistemas binários de compostos

lipídicos observada neste trabalho através da formação de misturas eutéticas com fases

sólidas miscíveis ou imiscíveis, fusão congruente ou formação de líquidos cristalinos é a

chave para o desenvolvimento de novas aplicações para a indústria de alimentos,

farmacêutica e de materiais. O ESL pode ser ferramenta útil na formulação de produtos

com base lipídica, como cremes cosméticos, fármacos e biocombustíveis, na manipulação

de propriedades físico-químicas e no desenvolvimento ou otimização de processos

industriais como a cristalização, purificação de compostos, escoamento ou geração de

energia. De modo geral, a utilização de compostos graxos extraídos ou produzidos a partir

de óleos vegetais, no contexto da “química verde”, pode promover a diminuição de

impactos negativos no ambiente e na saúde humana.

lipid thermodynamics: new perspectives on phase …

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