lysozyme partitioning in novel aqueous-two phase systems ... · lysozyme partitioning in novel...

Lysozyme Partitioning in Novel Aqueous-two PhaseSystems based on Hyperbranched Polymers

Beatriz Noriega Fernandes

Thesis to obtain the Master of Science Degree in

Biological Engineering

Supervisors: Prof. Tim ZeinerProf. Ana Margarida Nunes da Mata Pires de Azevedo

Examination Committee

Chairperson: Prof. Gabriel Antonio Amaro MonteiroSupervisor: Prof. Maria Raquel Murias dos Santos Aires Barros

Member of the Committee: Prof. Ana Margarida Nunes da Mata Pires de Azevedo

September 2015

Anyone who has never made a mistake has never tried anything new.Albert Einstein

Abstract

Aqueous two-phase systems (ATPS) constitute a promising process technology for the separation

and purification of biomolecules. Despite scalability and mild extraction conditions, commercial appli-

cation is scarce due to multiplicity of process variables, which lead to significant experimental efforts

towards the design of ATPS processes.

The aim of this work is to study and model the partitioning of lysozyme in ATPSs with linear and

hyperbranched polymers (HBP) as phase forming components. Dextran T40 and polyethylene glycol

(PEG) polymers with a molar mass of 6000 and 8000 were chosen as linear polymers. The used HBP

were hyperbranched polyester with a PEG core and 2,2-bis(methylol)propionic acid branching units.

The Lattice Cluster Theory (LCT) in combination with the Wertheim Association Theory was used

to model the studied ATPSs and the lysozyme partitioning.

The goal was partially achieved as the partitioning in the HBPs based ATPS could not be mea-

sured. Although, the ternary systems polymer – polymer – water were successfully modelled as well

as the lysozyme partitioning coefficients in the linear polymers’ based systems.

Keywords

Aqueous Two-Phase Systems (ATPS), Lysozyme, Lattice Cluster Theory (LCT), Whertheim The-

ory, Partition.

iii

Resumo

Os sistemas de duas fases aquosas (ATPS – aqueous two phase systems) constituem uma tec-

nologia promissora para a separacao e purificacao de biomoleculas. Apesar da possibilidade de au-

mento de escala e das condicoes de extraccao nao serem extremas para as proteınas, a aplicacao

comercial e ainda escassa devido a multiplicidade de variaveis de processo, o que tem levado ao au-

mento dos esforcos experimentais direccionados para o desenvolvimento de processos de ATPS. O

objectivo deste trabalho e estudar e modelar a particao da proteına lisozima em ATPS com polımeros

lineares e hiper-ramificados como componentes de formacao de fase. Os polımeros lineares escol-

hidos foram Dextrano T40 e dois tipos de polietileno glicol (PEG) com massas molares de 6000 e

8000. Os polımeros hiper-ramificados usados foram de poliester hiper-ramificado com um nucleo de

PEG e unidades ramificadas de acido 2,2-bis(metilol)propionico.

A Lattice Cluster Theory (LCT) em conjuncao com a Teoria de Associacao de Wertheim foi usada

para modelar os ATPS estudados e a particao da lisozima.

O objectivo foi so parcialmente atingido, uma vez que nao foi possıvel medir a particao nos ATPS

baseados em polımeros hiper-ramificados. Contudo, os sistemas ternarios polımero – polımero –

agua foram modelados com sucesso, assim como os coeficientes de particao da lisozima nos sis-

temas baseados em polımeros lineares.

Palavras Chave

Sistema de duas fases aquosas, Lisozima, Lattice Cluster Theory, Teoria de Wertheim, Particao.

v

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 State of the Art 5

2.1 Aqueous Two Phase System (ATPS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Hyperbranched polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Protein partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Fundamental Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Modelling of ATPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5.1 Empirical Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5.2 Osmotic viral equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5.3 Equations of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5.4 Activity coefficient models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5.4.A Flory-Huggins Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Experimental Setup 19

3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.1 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.2 Lysozyme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.3 Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Determination of the binodal curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Introduction to High Performance Liquid Chromatography . . . . . . . . . . . . . . . . . 22

3.4 HPLC method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5 Calibration of the polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.6 Determination of Tie Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.7 Partitioning of the Lysozyme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Model 37

4.1 Lattice Cluster Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Wertheim theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

vii

5 Results and Discussion 42

5.1 Liquid-liquid equilibria for the lysozyme-water system . . . . . . . . . . . . . . . . . . . . 43

5.2 Liquid-liquid equilibria for ternary systems . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.1 Calibration for tie-line determination . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.2 Tie-line modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3 Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3.1 Calibration for lysozyme quantification . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6 Conclusions and Future Work 63

Bibliography 67

Appendix A Lattice Cluster Theory (LCT) correction terms A-1

Appendix B Experimental data B-1

B.0.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

B.0.4 Systems without lysozyme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2

B.0.5 Systems with Lysozyme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5

B.0.6 Partitioning data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-6

viii

List of Figures

2.1 Schematic ternary diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Number of publications containing ”Aqueous Two Phase Systems” and ”Protein” from

1970 to 2014. Date: 26th March 2015, sourse: www.scopus.com . . . . . . . . . . . . . 8

2.3 Schematic description of dendritic polymers. . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Equilibrium between two phases for a pure component. . . . . . . . . . . . . . . . . . . 12

2.5 Illustration of the distribution of chains of polymers and a solvent in a lattice. . . . . . . . 15

3.1 Idealized structure of PFLDHB-G2-PEG6k-OH (G2). . . . . . . . . . . . . . . . . . . . . 20

3.2 Idealized structure of PFLDHB-G3-PEG6k-OH (G3). . . . . . . . . . . . . . . . . . . . . 21

3.3 Flow Sheet of High-performance Liquid Chromatography (HPLC). . . . . . . . . . . . . 22

3.4 Example of a typical chromatography diagram. . . . . . . . . . . . . . . . . . . . . . . . 23

3.5 Chromatogram obtained from a PEG 6000 – Dextran aqueous solution at 80°C with a

flow rate of 0,2 ml/min. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.7 Dextran influence in the lysozyme Ultraviolet (UV) spectrum. . . . . . . . . . . . . . . . 32

3.8 Absorbance of lysozyme at 220 and 280 nm. . . . . . . . . . . . . . . . . . . . . . . . . 33

3.9 Influence of dextran concentration in the measurement of lysozyme concentration. . . . 33

4.1 United atom group models for monomers of poly(ethylene) (PE), poly(propylene) (PP),

poly(thylene propylene) (PEP) and poly(isobutylene). Circles represent CHn groups,

solid lines designate C - C bonds inside the monomer, and dotted lines indicate C - C

bonds linking the monomer to its neighbours along the chain. . . . . . . . . . . . . . . . 38

5.1 Lysozyme structure illustration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Liquid-liquid equilibrium of aqueous lysozyme solution. . . . . . . . . . . . . . . . . . . . 44

5.3 Calibration Diagram for the linear polymers. . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.4 Calibration Diagram for the Hyperbranched Polymers (HBP). . . . . . . . . . . . . . . . 45

5.5 Experimental and LCT+Wertheim modelled points of ATPS consisting of linear polymers. 47

5.6 Experimental and LCT+Wertheim modelled points of ATPS consisting of HBP polymers. 50

5.7 Comparison can be made between the linear and the hyperbranched systems. . . . . . 51

5.8 Calibration diagram for the lysozyme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.9 Calibration diagram for G2 spectrometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.10 Experimental tie-lines of ATPS consisting of PEG 6000 – dextran 40 – water – lysozyme. 56

ix

5.11 Experimental tie-lines of ATPS consisting of PEG 8000 – dextran 40 – water – lysozyme. 56

5.12 Experimental tie-lines of ATPS consisting of HBP – dextran 40 – water – lysozyme. . . . 57

5.13 Lysozyme partition coefficient in PEG 6000 – Dextran and PEG 8000 – Dextran Aque-

ous Two Phase Systems (ATPS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.14 Lysozyme partition coefficient in PEG 6000 – Dextran – water and PEG 6000 – Dextran

– water, experimental and calculated results. . . . . . . . . . . . . . . . . . . . . . . . . 59

5.15 Lysozyme partition coefficient in PEG 6000 – Dextran – water and PEG 6000 – Dextran

– water, experimental and calculated results. . . . . . . . . . . . . . . . . . . . . . . . . 60

x

List of Tables

3.1 Characteristics of the used polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 My caption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Retention time differences between PEG 6000 and dextran for different flow rates at 80

°C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Summary of the methods and measurement times. . . . . . . . . . . . . . . . . . . . . . 27

3.5 Prepared bulk solutions for calibration of the polymers. . . . . . . . . . . . . . . . . . . . 27

3.7 Prepared PEG 8000 Samples for Calibration. . . . . . . . . . . . . . . . . . . . . . . . . 28

3.6 Prepared PEG 6000 Samples for Calibration. . . . . . . . . . . . . . . . . . . . . . . . . 28

3.8 Prepared Dextran Samples for Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.9 Prepared G2 Samples for Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.10 Prepared G3 Samples for Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.11 Composition and measured values of the components of the systems used to obtain

the tie lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.12 Information about apparatus and Software in spectrophotometry. . . . . . . . . . . . . . 31

3.13 Composition of the solutions analysed in Figure 3.7. . . . . . . . . . . . . . . . . . . . . 32

3.14 Prepared G2 samples for calibration in spectrophotometer. . . . . . . . . . . . . . . . . 34

3.15 Prepared solutions to test the lysozyme measurement method in samples containing

G2. BS stands for bulk solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.16 Composition of prepared systems with lysozyme and linear polymers. . . . . . . . . . . 35

3.17 Composition of prepared systems with lysozyme and HBP. . . . . . . . . . . . . . . . . 35

3.18 Prepared lysozyme samples for calibration in spectrophotometer. . . . . . . . . . . . . . 36

5.1 Binary interaction, association and LCT parameters for the aqueous lysozyme solution. 44

5.2 Association parameters of water and linear polymers. . . . . . . . . . . . . . . . . . . . 46

5.3 Interaction parameters of LCT+Wertheim for systems with linear polymers. . . . . . . . 47

5.4 Summary of LCT and Wertheim Association parameter set for linear polymers. . . . . . 48

5.5 Summary of LCT and Wertheim Association parameter set for the HBP. . . . . . . . . . 52

5.6 Prepared and calculated concentrations, measured and calculated absorbances, and

error fo the solutions used on the explained test. . . . . . . . . . . . . . . . . . . . . . . 54

5.7 Average mixing point of the partitioning experiments. . . . . . . . . . . . . . . . . . . . . 55

xi

5.8 Absorbance and lysozyme concentration on the top and bottom phases of ATPS con-

taining G2. The A correspond to systems with 0,3 wt % of lysozyme and the B to

systems with 1 wt %. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

B.1 Calibration data for the linear polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

B.2 Calibration data for the HBP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2

B.3 Calibration data for lysozyme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2

B.4 Calibration diagram for G2 spectrometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2

B.5 Experimental data of ATPS system PEG6000 – dextran – water, for tie-line 1. . . . . . . B-2






B.11 Experimental data of ATPS system G2 – dextran – water, for tie-line 1. . . . . . . . . . . B-4





B.16 Experimental data of ATPS system PEG6000 – dextran – water with 0,3 wt% lysozyme,

for tie-line 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5


for tie-line 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5

B.18 Experimental data of ATPS system PEG6000 – dextran – water with 1 wt% lysozyme,

for tie-line 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5


for tie-line 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5


for tie-line 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5


for tie-line 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-6


for tie-line 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-6


for tie-line 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-6

B.24 Experimental lysozyme concentration used to calculate the partition coefficients for

systems with PEG 6000 - first measurement. . . . . . . . . . . . . . . . . . . . . . . . . B-6


systems with PEG 6000 - second measurement. . . . . . . . . . . . . . . . . . . . . . . B-6

xii


systems with PEG 8000 - first measurement. . . . . . . . . . . . . . . . . . . . . . . . . B-7


systems with PEG 8000 - second measurement. . . . . . . . . . . . . . . . . . . . . . . B-7

B.28 Experimental partition coefficients and deviation for the ATPS formed by linear polymers.B-7

xiii

Abbreviations

ATPS Aqueous Two Phase Systems

bis-MPA 2,2-bis(methylol)propionic acid

EOS Equation of State

FH Flory-Huggins

G2 PFLDHB-G2-PEG6k-OH

G3 PFLDHB-G3-PEG6k-OH

HBP Hyperbranched Polymers

HPLC High-performance Liquid Chromatography

LCT Lattice Cluster Theory

LLE Liquid-Liquid Equilibrium

NRTL Non Random Two Liquids

PC-SAFT Perturbed-chain Statistical Associating Fluid Theory

PEG Polyethylene Glycol

PFC Phase Forming Components

RID Refractive Index Detector

SAFT Statistical Association Fluid Theory

SEC Size Exclusion Chromatography

TL Tie Line

TLL Tie Line Length

UNIQUAC Universal Quasichemical

UV Ultraviolet

VERS Viral Equation Relative Surface

VLE Vapour-Liquid Equilibrium

xv

Nomenclature

Latin Letters

Acalc Calculated absorbanceAest Estimated absorbanceAmeas Calculated absorbanceb3,i Number of branching points of three of component

ib4,i Number of branching points of four of component i

∆E1 Energy contribution of the first order∆E2 Energy contribution of the second order

∆mixG Gibbs free energy of mixtureG Total Gibbs free energyg Gibbs energy per segmentGE Excess Gibbs free energykB Boltzmann constantKP Partition coefficientKassoij Association volume defined by Eq. (4.8)

MM i Molar mass of the component iNi Number of molecules of the component ini Amount of substance of component iNL Number of lattice sitesP PressureR Ideal gas constantS Combinatorial entropy of a mixtureMi Number of segments of the component iT TemperatureA AbsorbanceT Transmittance

XSi X

εi X

ε2

i coefficients defined by eqs. (A.1) to (A.5),eqs. (A.6) to (A.11), eqs. (A.12) to (A.18)

xi Mole fraction of the component iz Coordination number

Greek Letters

∆ij association strength between molecule i andmolecule j defined by Eq. (4.7)

∆εij Interaction energy defined by (2.11)εassoij Association energy between segments of molecule

i and molecule j.Φi Segment fraction of component iµ Chemical PotentialΩ Number of possible configurations on a lattice

xvii

1Introduction

Contents1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1

1.1 Motivation

Over the last 20 years a great productivity increase took place in the biomanufacturing industry.

Titers of recombinant proteins in fermentation broths were boosted from a scale of milligrams to

grams per litre [1]. This development was especially motivated by the increasing market value of

biopharmaceutical products, particularly antibodies and proteins [2]. Simultaneously, downstream

processing did not keep up with the productivity improvement, despite still being the main responsible

for the production cost of biopharmaceuticals (between 45% and 92% [3]), thus creating a bottleneck

in the biotechnological industry [4].

Notably, therapeutic proteins require high purification values (<0,1% impurities [5]). Proteins de-

rive their functions from a complex three-dimensional structure that can easily be lost when subjected

to pH and temperature values far from moderate. Moreover, structural damage can be irreversible,

leading to biomolecules without functionality, and therefore, value. Chromatography is a simple pro-

cess with a high resolving power that embodies the right conditions for the purification of biomolecules.

For that reason it becomes indispensable as a unit operation. However, it has low capacity and is dif-

ficult to scale up, hence being one of the reasons for the high costs of downstream processing [6].

In an attempt to either replace chromatography or reduce the load of impurities in the feedstream so

that one or more chromatography stages can be eliminated, alternative separation processes have

been proposed. Aqueous Two Phase Systems (ATPS) show potential to overcome the limitations of

chromatography.

ATPS are formed by mixing two hydrophilic, incompatible components, such as a salt and a poly-

mer, a salt and an alcohol, two hydrophilic polymers or two surfactants in water above a critical con-

centration [7]. These systems can be used effectively for the separation and purification of proteins

given that both phases consist mainly of water, and have a low interfacial tension resulting in a low

mechanical stress on the proteins during the extraction process. The practical application of ATPS

has been demonstrated on a large number of cases with excellent levels of purity and yield [8].

Separation processes based on ATPS overcome chromatography limitations: it is possible to run

them continuously [9] and they can easily be scaled-up [10]. Consequently, ATPS have been the

object of extensive studies regarding the purification of therapeutic proteins and others of industrial

interest [11], although industrial applications are still rare.

Nonetheless, these systems present some disadvantages. The polymer-salt systems are not opti-

mal due to the low solubility of amphiphilic molecules in the salt phase - high tendency of aggregation

[12] - and the shielding of proteins by the salt, which prevents an easy adsorption in further necessary

separation steps [13]. Furthermore, salt-polymer systems are generated with a high amount of salt,

and thus require a large consumption of phase-forming chemicals [14], which gives rise to environ-

mental and economical problems. On the other hand, polymer-polymer systems do not present the

listed problems, but do however have high viscosities, which is a problem in the case of industrial use

[14].

As a possible solution to the mentioned problems with ATPS, Kumar et al. [15] suggested the use

2

of smart polymers. These are characterized by their ability of undergo large reversible chemical and

physical changes as a response to small environmental variations. Such molecules can be sensitive

to factors such as temperature, pH, electric or magnetic field and light intensity [16]. One specific

type of such materials are the Hyperbranched Polymers (HBP) – compounds that can carry special

functional groups and show no denaturation effect on the biomolecules. HBP can be used as phase

forming components in ATPS originating systems with lower viscosity and melting point, and higher

specificity [13]. Application of HBP in ATPS has shown promising potential [15], which encourages

the study of these systems.

The design of an extraction using ATPS is a time consuming process that requires enormous

experimental efforts in order to characterize the behaviour of each component in the mixture. In

addition, when a system has low productivity, it is necessary to restart the process. Thus, for the

optimization of extraction processes with ATPS, a modelling of these systems is required.

Therefore, this work will focus on answering three main questions:

1. Can lysozyme be purified with aqueous polymer-polymer systems composed by linear PEG

6000, 8000 and Dextran?

2. Can the lysozyme partitioning be modelled with an Lattice Cluster Theory (LCT) model in asso-

ciation with the Wertheim theory?

3. Can systems composed by HBP also be modelled accurately?

The modelling will be based on a version of the LCT applicable for multicomponent polymer solu-

tions combined with the Wertheim theory so as to account for the associative interactions [13].

1.2 Thesis Outline

Firstly, the state of the art of the studied field is presented. An introduction to aqueous two phase

systems is made, followed by a summary of hyperbranched polymers’ history, their applications and

importance. Ensuing, the protein partitioning behaviour in aqueous two phase systems is briefly

explained. The fundamental thermodynamics of these systems are also presented. Finally the state

of the art on aqueous two phase systems’ modelling is summarized.

The experimental setup of this work is then described. The used materials are discriminated and

characterized. The high-performance liquid chromatography and spectrophotometry methods are

explained in detail, as are the experimental procedures followed in the analysis. In this section the

choice of method is also explained.

The modelling chapter explains, in a summarized way, the applied models, Lattice Cluster Theory

(LCT) and Wertheim Theory, and presents the correspondent equations.

Afterwards, the final results are presented. Aqueous two phase systems containing two linear

PEG polymers, dextran and two hyperbranched polymers are studied experimentally and adjusted

to a LCT+Wertheim theory model. Furthermore, the lysozyme partitioning on the linear polymers

3

based systems is measured and adjusted to a quaternary LCT+Wertheim theory model. The obtained

results are analysed and discussed.

Finally, the last chapter contains the conclusions of the work and suggests future developments

on the topic.

The work behind this thesis was performed in the Fluid Separation Laboratory of the Department

of Biochemical and Chemical Engineering in the Technical University of Dortmund, Germany.

4

2State of the Art

Contents2.1 Aqueous Two Phase System (ATPS) . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Hyperbranched polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Protein partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Fundamental Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Modelling of ATPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5

In an attempt to describe the phase equilibria in ATPS, different models were developed, which

can be segregated based on divergent schools of thought. The first modelling approaches were

based on the Othmer-Tobias [17] and Bancroft [18] equations, which required an input of experimental

data and several adjusted parameters to model the tie-lines. Other models are based on osmotic

viral expansions, reminiscent of the work of Edmond and Ogston [19][20]. These do not require

experimental data input, but involve up to three adjustable parameters to describe the interaction

between the different components, and an extra one to account for the temperature influence.

Besides the correlation equations, thermodynamic models using Equation of State (EOS) and

the Gibbs excess energy (GE) equations where also introduced to perform calculations in order to

characterize the ATPS. One possible way is the use of EOS, such as Statistical Association Fluid

Theory (SAFT)-family equations, which originated from a perturbation theory inspired by Wertheim

papers [21]. The EOS models are useful when modelling different phase diagrams with polymers

present in the mixture, and normally pure component data are used to fit the model parameter of an

EOS as density or vapour pressure, but depend upon high calculation efforts and the parameters of

pure components must be fitted to phase equilibria data.

The GE models have also been applied to calculate the phase behaviour of ATPS. These models

can take into account short range interactions, such as the Non Random Two Liquids (NRTL), ex-

tended NRTL, Wilson or Universal Quasichemical (UNIQUAC) models, or long range interactions, in

the case of Debye-Hueckle and Pitzer-Debye-Hueckle [22]. The drawback of the GE models is the

lack of associative interactions which are of great importance for the thermochemical modelling of

liquid systems.

Lastly, there are also models based on extensions of lattice theories (also GE models) such as

the Flory-Huggins (FH) theory [23] [24], which is the classical way of describing phase behaviour in

polymer solutions. However this theory is a simple mean-field approximation that ignores the details

of the polymer structure, and therefore, is not suitable for non-linear polymers. The LCT is an exten-

sion of the FH theory, developed by Freed and co-workers [25–29], that takes into account polymer

structure.

Kulaguin Chicaroux and Zeiner [13] published a GE model based on the LCT to calculate the

ATPS taking into account on the one hand the molecular structure, derived from the LCT, and on the

other hand the associative interactions by integrating the Wertheim association theory [30, 31].

2.1 Aqueous Two Phase System (ATPS)

As mentioned before, ATPS are formed by mixing two hydrophilic, incompatible components, such

as a salt and a polymer, a salt and an alcohol, two hydrophilic polymers or two surfactants in water

above a critical concentration [7]. In most cases, both aqueous phases contain 50 to 90 wt% of

water, and the type and concentration of the components in the mixture is a decisive factor for phase

formation. Physical properties such as density, interfacial tension or viscosity of phases or between

them have a strong dependence on the Phase Forming Components (PFC).

6

Generally the Liquid-Liquid Equilibrium (LLE) of an ATPS at constant temperature and pressure

is described by a ternary diagram, exemplified in Figure 2.1. With one point within the triangular

diagram, the composition in mass fraction or mole fraction can be read out. In the diagram, the curve

represents the binodal curve which separates the immiscible region (grey) from the homogeneous

one-phase region (white). Inside the grey region all the mixing compositions correspond to a tie-line

(broken line) and originate a system with two phases in equilibrium, each with the composition given

by the point where the tie-line intercepts the binodal curve. At the critical point (•), the tie line length

is zero. The mass fraction or mole fraction of every component in the two phases is equal.

Figure 2.1: Schematic of a ternary diagram. The solid line represents the binodal curve of the system andbroken lines represent the tie-line. The white region represents the compositions that form a miscible one-phasemixture and the grey region represents the compositions that form an heterogeneous two-phase mixture. The

full circle (•) corresponds to the critical point.

A possible approach to characterize and study ATPS is the Tie Line Length (TLL), which is used

to compare the physicochemical differences between the two phases [7]. In an aqueous two-phase

diagram, a Tie Line (TL) is a straight line between two points on the binodal curve, connecting the

two corresponding phases (top and bottom phase concentration) for a specific mixing point. It can be

calculated using the Pythagoras theorem, (2.1).

TLL =√

(C1,TP − C1,BP )2 + (C2,TP − C2,BP )2 + ...+ (Cn,TP − Cn,BP )2 (2.1)

Where 1,2...n are the PFC of the mixture, and Ci,TP and Ci,BP correspond to the concentration of

the component in the top and the more dense bottom phases, respectively. The binodal curve of an

ATPS changes with different factors such as the type of the PFC, the type of additional solutes used,

or the temperature. As a consequence, the TL is also affected by these parameters, not only in its

length but also in its slope. Additionally, the TLL can also be used to calculate the phase ratio of the

systems with the lever rule, knowing the mixing point [32].

The first polymer-polymer ATPS publication was in 1896 by Beijerinck [33], which described the

7

formation of an emulsion after mixing a starch solution with a gelatin solution. The first polymer-

salt ATPS was discovered by accident by Per-Ake Albertsson [34]. After the discovery, in the 50s

Albertsson studied the partitioning of proteins and cell particles in ATPS of polymer-polymer and

polymer-salt [35][36], and in the following years he also studied low molecular weight substances,

polyelectrolytes, nucleic acids, and membrane vesicles, which are non-soluble compounds [37].

Consecutive to his research, many groups continue investigating the ATPS application in biomolecule

purification with focus in different topics such as factors influencing the scale-up, the partitioning, or

process variants [38] [7] [39].

The growing number of publications regarding ATPS and proteins since 1970 can be observed in

Figure 2.2.

1 9 7 0 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 50

2 5

5 0

7 5

1 0 0

1 2 5

Numb

er of

public

ation

s

Y e a r

Figure 2.2: Number of publications containing ”Aqueous Two Phase Systems” and ”Protein” from 1970 to 2014.Date: 26th March 2015, sourse: www.scopus.com

As can be seen in Figure 2.2, the number of publications shows a steady increase, and since the

number of publications correlates to the research effort put into this topic, it is safe to assume that

the interest is still growing. This strong increase can be partly explained by the more recent study of

the application of ATPS for the purification of biopharmaceuticals and biocatalysts by several groups,

such as the ones of Aires-Barros [40], Rita-Palomares [41] and Asenjo [42].

2.2 Hyperbranched polymers

In the end of the 19th century, Berzelius reported the synthesis of a resin from tartaric acid and

glycerol – the first reported synthesized hyperbranched macromolecule [43]. In 1909, Baekeland

introduced the first commercial synthetic plastics, phenolic polymers, commercialized through his

Bakelite Company [44]. In the 1940s, Flory et al. [45][46][47] developed the ”degree of branching”

8

and ”highly branched species” concepts, but the term ”Hyperbranched Polymer” was first used in 1988

by Kim and Webster [48].

HBP are highly branched macromolecules with three-dimensional dendritic architecture. Due to

their unique physical and chemical properties and potential applications in various fields from drug-

delivery to coatings, interest in HBP is growing rapidly [49].

HBP are one type of dendritic polymers, which are the fourth major class of polymers’ architecture,

and consist of six subclasses [50], illustrated in Figure 2.3:

1. dendrons and dendrimers;

2. linear-dendritic hybrids;

3. linear-dendritic hybrids

4. dendrigrafts or dendronized polymers;

5. hyperbranched polymers;

6. multi-arm star polymers;

7. hypergrafts or hypergrafted polymers.

Figure 2.3: Schematic description of dendritic polymers [49].

What distinguishes these groups is the degree of structural control during the synthesis. HBP are

the most irregular dendritic polymers.

The main differences between linear and HBP are the glass temperature (temperature at which

occurs a reversible transition in amorphous materials from a hard and relatively brittle state into a

molten or rubber-like state), the viscosity and the solubility.

9

The glass temperature is a function of the backbone, the number of end-groups, and the number

of branching points. The glass temperature lowers with the increase of end-groups, while it increases

with the number of branching points. Markedly, the influence of end-groups for a linear polymer

of infinite molar mass disappears while for dendrimers it converges to a certain value, if the glass

temperature is affected by the polarity of end-groups [51].

One of the most interesting physical properties of HBP is their considerably different viscosity

characteristics in comparison with their linear analogues. Hyperbranched macromolecules in solution

reach a maximum of intrinsic viscosity as a function of molecular weight as their shape changes,

however the conditions for the existence of this maximum are still not clear [52]. Moreover, the melt

viscosity of linear polymers has been shown to increase linearly with logarithm of molar mass up to

a critical molar mass where the viscosity drastically increases [53]. This behaviour is related to the

enlargement of the polymer chain with the molar mass, which has been proven not to occur in the

case of the HBP [54].

The solubility of dendritic polymers with a higher generation (number of repeated branching cy-

cles that are performed during its synthesis) depend largely on the characteristic of the end groups,

therefore, modifying these groups permits to control influence of their solubility [55].

Due to their unique properties and easy synthesis, HBP have a wide range of potential appli-

cations, from being used as nanomaterials for host-guest encapsulation [56], to the fabrication of

organic-inorganic hybrids [57], as nanoreactors, or as biocarriers and biodegradable materials [49].

Some other application examples are their use as rheology modifiers or blend components [58], as

the base for various coating resins, or as novel polymeric electrolytes or ion-conducting elastomers

[49].

Different models have been proposed to predict thermodynamic properties and phase equilibria

of mixtures containing hyperbranched or dendritic polymers. The branched Perturbed Chain Polar-

Statistical Association Fluid Theory model was used to calculate phase equilbria of HBP by Kozlowska

et al. [59]. Lattice Cluster Theory (LCT) was used to calculate the liquid-liquid phase equilibria of

HBP solutions and to determine the activity coefficients of dendrimer solutions [60][61]. UNIFAC-FV

(Universal Quasichemical Functional Group Activity Coefficients- Free Volume) approach was also

tested to calculate vapour-liquid phase equilibria of HBP solution [62].

2.3 Protein partitioning

Proteins can either be separated from cell debris or purified from other proteins using two-phase

partitioning. Most soluble and particulate matter will partition to the lower, more polar phase, whilst

proteins will partition to the top, less polar and more hydrophobic phase, usually Polyethylene Glycol

(PEG) [11]. The partition coefficient can be manipulated in order to separate proteins from one

another. It is influenced by the average molecular weight of the polymers, the type of ions in the

system, the ionic strength of the salt phase or addition of an additional salt such as NaCl. Affinity

partitioning, a method for the purification of proteins containing specific ligand binding receptor sites,

10

can also be used to increase the degree of purification [63].

The partition coefficient, KP , can be calculated with Equation (2.2).

KP =Ci,BPCi,TP

(2.2)

Where Ci,TP and Ci,BP correspond to the equilibrium concentration of the protein in the top and

bottom phases, respectively.

The mechanism governing partition can be described qualitatively as follows: a protein interacts

with the surrounding molecules within a phase via various types of interactions, such as hydrogen,

ionic, and hydrophobic interactions, together with other weak forces. The net effect of these interac-

tions is likely to be different in the two phases and therefore the protein will preferentially partition to

one phase.

The properties of proteins, such as hydrophobicity, electrochemical interactions, molecular size,

shape and surface area, biospecific affinity and conformation, can be exploited individually or in con-

junction to achieve an effective separation [64][11]. Thus, the overall partition coefficient can be

expressed in terms of all these individual factors:

KP = K0 ·Khfob ·Kel ·Kbiosp ·Ksize ·Kconf (2.3)

where hfob, el, biosp, size and conf stand for hydrophobic, electrochemical, biospecific, size and

conformational contributions to the partition coefficient, and K0 includes other factors.

In a polymer-polymer ATPS there are factors that also influence the partitioning behaviour, namely

the pH of the mixture, the molecular weight of the polymers, their concentration and the addition of a

salt such as NaCl [65] [11].

Specifically, the larger the molecular weight of the PEG, the lower the value of the partition co-

efficient [11]. Boncina et al. [66] studied lysozyme solubility in PEG solutions and observed that it

decreases linearly with the increase of PEG concentration. Furthermore, the solubility is lower for a

polyethylene glycol with a higher degree of polymerization. The solubility decrease is correlated with

the hydrophobic character of PEG molecules, which increases as the polymer’s molecular mass does

[67].

2.4 Fundamental Thermodynamics

Considering the systems of Figure 2.4 with two phases, α and β, and n pure components, the

equilibrium is reached for specific thermal, mechanical and chemical conditions described by the

Equations (2.4) to (2.6) [68].

11

µiα

µiβ

α

β

P T

Figure 2.4: Equilibrium between two phases for a pure component.

Tα = T β (2.4)

Pα = P β (2.5)

µαi = µβi ∀ i = 1, ..., n (2.6)

The equilibrium of the two phases is only possible if a list of requirements is fulfilled. For one, both

phases must share the same temperature – thermal equilibrium (2.4). Secondly, the pressure of the

phases must be the same – mechanical equilibrium (2.5). Lastly there must be equilibrium of matter,

i.e., the transition of mass between phases has to be the same and, as a result, the composition of

each component will remain constant in each phase (2.6).

Therefore, to determine the thermodynamic equilibrium of the system the chemical potential of

each component must be known, and for real solutions it is defined as shown in Equation (2.7).

µi =

(∂G

∂ni

)P,T,nj 6=i

(2.7)

Equation (2.7) shows that once the Gibbs energy is known, the chemical potential can be calcu-

lated. Several different models, either empirical or based on theories of the liquid state, have been

developed since the 19th century aiming to calculate the excess Gibbs free energy. These models will

be introduced on Chapter 2.5.

The choice of the model to use in each situation is a complex problem that requires a careful analy-

sis of the chemical and structural nature of the mixture components, the application, the experimental

data available, among others.

2.5 Modelling of ATPS

2.5.1 Empirical Equations

The empirical equations for calculating equilibrium of three components on two phases are divided

into two main groups, the Othmer-Tobias equation [69] and the Bancroft equation [70]. This method

has the advantage of combining the simple applicability of an empirical approach to a high precision.

12

Nevertheless, the use of these equations carries some drawbacks. For one, they can only be

applied to systems with three components, and since a single equation is being used to calculate the

composition of three components in two phases, plus two empirical parameters, the binodal curve

of the system must be known. The binodal curve can also be calculated via empirical equations,

however three or four additional empirical parameters are needed [71][72]. As the parameters do not

require any thermodynamic background, they must be adjusted for each new condition, which is why

empirical models cannot be used for prediction.

2.5.2 Osmotic viral equation

Although different versions of the osmotic viral equation can be applied to model ATPS, the first

adaptation by Edmond and Ogston to PEG-dextran systems in 1968 is the most popular due to its

simplicity and accuracy [19]. This equation is based on the osmotic viral expansions from McMillan

and Mayer, developed in 1945 [73].

The key ideas of the osmotic viral equation are, firstly, that the chemical potential of a solute can

be described by a Taylor series expansion of the solute concentration; secondly, that the chemical

potential of a solvent can be calculated with all the solutes’ potentials and the Gibbs-Duhem equation.

For an ATPS equilibrium with one solvent, water, and two solutes, three parameters are necessary:

two binary osmotic viral coefficients of the solutes, obtained by fitting to solvent activities, plus one

osmotic cross viral coefficient, obtained by fitting to LLE data. It is usual to fit the three mentioned

parameters only to LLE data, ignoring the equilibrium, and for that reason the viral coefficients that

are published only apply to LLE.

In the same manner as the empirical equations introduced in Section 2.5.1, the osmotic viral

equation cannot be used as a predicting tool, since the viral osmotic coefficients must be defined for

each system condition.

2.5.3 Equations of state

By using equations of state to model ATPS, the phase composition and volumetric properties can

be obtained with the model, which allows for an easier planning of the extraction process, as the

density of both phases influences the phase separation. Also, this method is able to predict without

interaction parameters or experimental data.

The first application of equations of state for ATPS modelling was made by Naeem and Sad-

owski (47), when they employed polyelectrolyte Perturbed-chain Statistical Associating Fluid The-

ory (PC-SAFT) for a system of polymer-polyelectrolyte and salt. Secondly, Valvary et al. [74] applied

the hard sphere chain for systems containing PEG and salts. This application in particular requires

an enormous amount of binary parameters which are functions of the molecular weight of the poly-

mer, of temperature, and even of the specific experimental-data reference. Moreover every salt was

described with its own parameter set, which again increased the amount of required parameters. As

a consequence, this specific method cannot yet be used as predictive model [75].

13

2.5.4 Activity coefficient models

In 1895, Max Margules modelled the Gibbs free energy of a solution with an empirical approach

[76], and since then, many activity coefficient models have been developed for modelling phase prop-

erties. In 1985, the first activity coefficient model for an ATPS was Flory-Huggins (FH) solution theory

[23] [24] by Walter et al. [39]. Later, in 1988 UNIQUAC was applied for ATPS with two polymers [77].

Viral Equation Relative Surface (VERS) was applied by Grossmann et al. [78] to model ATPS with

PEG and dextran in 1993. In 2002, Zafarani-Moattar and Sadeghi [79] obtained a novel expression

with three terms: short-range, combinatorial and long-range electrostatic interactions term, by com-

bining a model developed by Chen with Debye-Hueckel [80]. The local composition approach has

been widely used, with several adaptations for different short-range interactions (UNIQUAC , Wilson

[81]).

The main advantage of this approach is its high accuracy when modelling aqueous solutions,

electrolyte solutions, and ATPS of water with two solutes. As a result of considering short-range,

long-range and combinatorial terms in these models, it is possible to predict systems with changing

molecular weights [81].

As a limitation, it should be considered that different temperatures can only be taken into ac-

count when using activity coefficient models if different interaction parameters are added for each

temperature [81]. Since local composition concepts are used in these calculations, it is necessary to

experimentally determine the volumetric characteristics of the phase forming components. Further-

more, the complexity of the model increases with the number of parameters because of the need to

derive the equations adapted to the local composition model.

In the following Section 2.5.4.A the activity coefficient model, Flory-Huggins (FH) Theory, will be

presented.

2.5.4.A Flory-Huggins Theory

The Raoult’s law of ideal solutions states that the vapour pressure of a solvent above a solution is

equal to the vapour pressure of the pure solvent at the same temperature scaled by the mole fraction

of the solvent present [82]:

Psolution = XsolventPosolvent (2.8)

This law was proven unsuitable to describe polymer solutions when the experimental data of

Vapour-Liquid Equilibrium (VLE) did not fit the predictions [83]. For this reason, in an attempt to

better describe polymer solutions, in the early 40s, Flory and Huggins [83, 84] developed individually

a simple lattice theory, that would come to be known as the Flory-Huggins theory.

This lattice theory 2.5 was presented with the following assumptions:

1. a quasi-solid (properties between solid and liquid) lattice in the liquid,

2. polymer segments and solvent molecules’ interchangeability in the lattice cells,

14

3. independence on composition,

4. no polydispersity (all polymer molecules are assumed to be the same size) and

5. concentration of polymer in a cell neighbourhood considered to be equal to the all-over average

concentration.

Pure polymer Pure solvent Homogeneous solution

Figure 2.5: Illustration of the distribution of chains of polymers and a solvent in a lattice.

In order to calculate the Gibbs free mixing energy, it is necessary to estimate a residual part

(∆Gres) and a combinatorial part (∆Gcomb) in (2.9).

∆Gres + ∆Gcomb = (∆H − T∆Sres)− T∆Scomb (2.9)

where ∆Sres corresponds to the residual mixing entropy and ∆Scomb to the combinatorial mixing

entropy. In the FH theory, the residual portion is given purely by enthalpic contributions (∆H), and

the combinatorial portion is estimated by the positioning of the molecules on the lattice (∆Scomb).

In order to explain the basic concepts of this theory, the calculations for a binary mixture will be

described as an example.

Residual contribution

For estimating the mixing enthalpy,

∆Gres = ∆H =∆ε12z

2Φ1Φ2 (2.10)

the interaction energy ∆ε12 is defined as:

∆ε12 = ε11 + ε22 − 2ε12 (2.11)

where ε11 and ε22 describe the interaction between segments of the same type, polymer and

solvent accordingly, and ε12 describes the interaction energy between solvent and polymer.

In equation (2.10), Φi is the segment fraction of each component, defined as

Φ1 =N1M1

NLΦ2 =

N2

NL, NL = N1M1 +N2 (2.12)

where Mi is the chain length of the component i, Ni is the number of molecules of component i,

and NL is the total number of lattice sites. z is the coordination number of the lattice, i.e., the number

15

of lattice sites adjacent to each segment, which was derived by Flory [23] and Huggins [24] with the

assumption:

z →∞ and ∆ε→ 0 ⇒ ∆εz

2→ finite (2.13)

It is common to write this parameter as the FH parameter χ:

χ =∆εz

2(2.14)

Combinatorial contribution

In a lattice, the molecules can be distributed and redistributed, and it is possible to estimate the

combinatorial part of the Gibbs free mixing energy with the Boltzmann relation, Equation (2.16), and

the number of all possible configurations of the system, Ω, neglecting molecule interaction, with kB

being the Boltzmann constant.

The entropy of mixing for a binary mixture corresponds to:

∆S = Smix − S1 − S2 (2.15)

in which Smix, S1 and S2 are the entropy of the mixture, and components 1 and 2. Each of these

values can be determined through Equation (2.16).

S = kB lnΩ (2.16)

Since components 1 and 2 are the same size and each molecule occupies one single lattice, the

number of possible dispositions in each case is only one, therefore:

Ω = 1→ lnΩ = 0→ S1 = S2 = 0 (2.17)

This is not the case for the entropy of the mixture. In a binary mixture, if the solvent and solute are

the same size, Ω can be calculated as is shown in Equation (2.18).

Ω =N !

N1!N2!(2.18)

with Ni being the number of molecules of component i in the mixture, and N the total number of

molecules.

N = N1 +N2 (2.19)

Inserting this calculation in the Boltzmann relation,

S = kB [ln(N !)− ln(N1!)− ln(N2!)] (2.20)

and resorting to the Stirling approximation:

ln(x!) = xln(x)− x (2.21)

16

the combinatorial contribution can be calculated as:

∆Scomb = −kB[N1ln

(N1

N

)+N2ln

(N1

N

)](2.22)

and, finally, considering the mole fraction,

xi =NiN

(2.23)

it can be expressed by Equation (2.24).

∆Scomb = −R [x1ln (x1) + x2ln (x2)] (2.24)

Since in a polymer solution the sizes of solute and solvent have a large difference, Flory [23] and

Huggins [24] introduced the idea of dividing the polymers into pieces – chain segments. Considering

that the solute molecules and the created segments have the same size, it is then possible to use the

Boltzmann relation to calculate the combinatorial entropy.

The number of segments, M , depends on both the polymer and the solvent molecular sizes, and

can be calculated with Equation (2.25).

M =MM polymer

MM solute(2.25)

where MM polymer and MM solute are the molar masses of the polymer and solute respectively.

The last required step to be able to apply the Boltzmann relation to a polymer solution is consider-

ing the strong bonds between the individual segments of the polymers, i.e., the polymer disposition in

the lattice should be in a way that all the segments have at least two neighbour segments, excluding

the first and the last, which only need to have one. Therefore, for polymer solutions, considering once

again the definition (2.15), the entropy of the pure polymer is no longer zero (Ω > 1), and the entropy

of the mixture must be calculated with a different expression.

The derived expression for the combinatorial part of the entropy of mixing can be found in Equation

(2.26).

∆Scomb = −k[N1ln

(MN1

N2 +MN1

)+N2ln

(N2

N2 +MN1

)](2.26)

Applying the definition of segment fraction (2.12), the segment mixing entropy can be written as

∆Scomb = −R[

Φ1

Mln(Φ1) + Φ2ln(Φ2)

](2.27)

Finally, the FH mixing energy is:

∆G = −RT[

Φ1

Mln(Φ1) + Φ2ln(Φ2)

]+ χΦ1Φ2 (2.28)

FH and related theories are still widely used for the thermodynamic description of polymer solu-

tions because they present several advantages. While classic FH theory successfully explains the

17

behaviour of long-chain polymers in the liquid state and gives mechanistic insight into the phase

formation process [85], it is inadequate in several respects.

There is a concentration range in which the FH theory is expected to be applied, due to the mean

field approximation used as the basis of the calculations. On the one hand, there is a minimum

concentration from which the solution can be considered to have a uniform density of segments; on

the other hand, given the lack of consideration for the interactions between non-successive polymer

segments, the solution can also be sufficiently diluted so that a polymer segment is approximately

surrounded only by solvent, and is therefore separated from its polymer neighbours.

Futhermore, due to the employment of a simple mean-field approximation that effectively ignores

the details of the polymer chain connectivity, it cannot distinguish between linear, star, branch, and

other polymer architectures [29].

The FH expression for the χ parameter, Equation (2.14), provides little further insight into the

physical features that control polymer miscibility. Actually, χ is described as inversely dependent on

the temperature, as well as independent of the composition, the molecular weights, and the pressure

of the mixture. However, χ is often found to be empirically dependent on the last three parameters,

and has shown a dependence on temperature better described by the relationship χ = A+B/T [29],

consequence of the non-combinatorial contributions not considered (volume, equation of state, and

packing effects). The contradictions between theory and experimental data implies that, although FH

is applicable in specific situations, the χ parameter is purely empirical and is inadequate for more am-

bitious predictive purposes. In the literature, several extensions of the FH theory can be found that try

to describe the χ-parameter depending on concentration and temperature, such as the Koningsveld-

Kleintjens Model and the Prigogine-Flory-Patterson Theory [86], [87].

FH specifies that monomers of different polymers and solvent molecules all occupy a single lattice

site, ignoring the monomer structure, e.g. the molecular size and shape, and as a consequence, the

influence on the mixture thermodynamics [29]. Moreover it does not consider the excess volume.

In order to correct some of the mentioned deficiencies, Freed and co-workers developed the LCT,

based on FH theory, that will be introduced in the following Section.

18

3Experimental Setup

Contents3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Determination of the binodal curves . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Introduction to High Performance Liquid Chromatography . . . . . . . . . . . . . 22

3.4 HPLC method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5 Calibration of the polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.6 Determination of Tie Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.7 Partitioning of the Lysozyme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

19

In this chapter, the experimental methods to determine liquid-liquid phase equilibria, the binodal

curve and tie-lines of the studied ATPS and the lysozyme partitioning are presented. Firstly, the

materials used for the experiments are characterized.

3.1 Materials

3.1.1 Polymers

In this study PEG 6000, PEG 8000 and dextran were used as the linear polymers to form the

ATPS, while PFLDHB-G2-PEG6k-OH (G2) and PFLDHB-G3-PEG6k-OH (G3) were applied as the

branched polymers. All the chemicals were used without further purification. With the help of weak

heating and magnetic stirring, all polymers can be dissolved in water quickly.

The linear PEG polymers share the chemical formula HO(C2H4O)nH. PEG 6000, from Merck

Schuchardt OHG, Hohenbrunncan, Germany, can be characterized as a white or almost white solid

with a waxy or paraffin-like appearance. PEG 8000 is a white waxy powder from AMRESCO, 6681

Cochran Rd, United States.

The chemical formula of dextran is (C6H10O5)n and at room temperature it is a white power. It is

produced by Carl Roth GmbH + Co. KG, Karlsruhe.

All the mentioned polymers were stored at room temperature in a closed container opened only

for experiments.

The HBP both have the appearance of a white crystal and are produced by Polymer Factory

Sweden AB. The chemical structure of these polymers is presented in Figures 3.1 and 3.2.

The HBP were stored in an airtight container to protect from air humidity at 4°C, just opened for

the experiments.

Figure 3.1: Idealized structure of G2 [88].

20

Figure 3.2: Idealized structure of G3 [88].

In Table 3.1, the used polymers are further characterized.

Table 3.1: Characteristics of the used polymers.

Sample Molar mass MW (g/mol) Polydispersity MW /Mn Number of –OH per molecule

PEG 6000 5600-6600 – 2PEG 8000 7000-9000 – 2

Dextran 35000-45000 – –PFLDHB-G2-PEG6k-OH 6696 1,42 8PFLDHB-G3-PEG6k-OH 7625 1,3 16

3.1.2 Lysozyme

In this work, lysozyme from hen egg white, EC 3.2.1.17, purchased from SIGMA-ALDRICH CHEMIE

GmbH, Steinheim was used. The lysozyme has an average molar mass of 14600 g/mol and an activity

of 120 000 U/mg. The lysozyme is a lyophilized powder and it was stored at 4°C.

3.1.3 Solvents

For the experiments, deionised water was used as solvent to prepare all the solutions.

3.2 Determination of the binodal curves

Usually, there are three ways to determine the binodal curve for an ATPS, which are cloud-point

method, and turbidometric titration [89]. In turbidometric titration a series of systems are prepared

and titrated until a one-phase system is formed, the binodal lies just above this point. With the cloud

point method a concentrated stock of component 1, i.e., polymer X is added to a concentrated stock of

component 2, i.e., polymer Y. The solution is repeatedly taken above and below the cloud point. The

determination of nodes is accomplished by preparing a series of systems lying on different tie-lines

and analysing the concentration of components in the top and bottom phase. They all follow the same

21

principle: when the mixture is turbid, immiscibility happens; when the mixture is clear, it is still in the

homogeneous area.

In this work, the commonly used cloud point method was selected to determine the binodal curve.

Pure polymer aqueous solutions were prepared with a fixed compositions. The solution of one of the

polymers was added drop-wise into a solution of a different polymer with a known mass, by using a

syringe. The mixture was continuously stirred using a magnetic stirrer. After the addition of 3 ml, the

mixture was observed to determine if it turned turbid in the following 1-2 minutes. Since it did not turn

turbid, the last step was repeated until two phases formed, thus turning the mixture turbid. When the

point on the binodal curve was obtained, observed by the turbidity of the mixture, the added weight

was noted and 5 ml more were added. To obtain the second point of the binodal curve, deionized

water was added by the same method until the mixture turned clear. The two steps were repeated in

order to obtain the binodal points with a higher polymer B composition. The remaining binodal curve

can be determined by exchanging the polymers, i.e., adding the solution of polymer B to the solution

of polymer A. The experiment was conducted at room temperature.

The turbidometric titration was performed for the systems PEG 6000 – Dextran – Water, PEG 8000

– Dextran – Water and G2 – Dextran – Water. The weighing amount of polymers and water and wt%

can be seen in Appendix B. Results will be shown and discussed in Section 5.

3.3 Introduction to High Performance Liquid Chromatography

To determine the concentrations of linear branched polymers in ATPS, size exclusion chromatog-

raphy (SEC) equipped with refractive index detector (RID) was applied.

Solvent reservoir and filter

Pump to produce high pressure

HPLC tubeSample

injectionDetector

Processing unit and display

Waste

Signal to processorColumn oven

In-line degasser

Solvent and sample delivery system Separation system Detection system

Figure 3.3: Flow Sheet of HPLC based on [90].

Size Exclusion Chromatography (SEC) has been regularly used as a type of HPLC since 1959,

when Porathand Florian investigated a cross-linked dextran gel to separate proteins [90]. SEC is used

primarily for the analysis of large molecules such as proteins or polymers. SEC works by trapping

the smaller molecules in the pores of a particle, and allowing the larger ones to simply pass by the

22

pores as they are too large to enter them. Therefore, the larger molecules flow through the column

quicker than the smaller ones, meaning that the smaller the molecule, the longer the retention time. A

chromatogram is shown in Figure 3.4 as an example. The concentration of phase forming component

in the injected liquid can be determined by analysis of the areas of peaks with a data analysing tool,

as the peak area is proportional to its concentration.

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0

0 , 0

0 , 5

1 , 0

1 , 5

2 , 0

RI (Vo

lts)

T i m e ( m i n u t e s )

Figure 3.4: Example of a typical chromatography diagram.

In this study, the column was tempered at 80°C with the help of an isothermal oven. The eluent,

deionised water, was filtrated with GHP membrane disc 47mm, 0,45µm, supplied by Pall Corporation,

USA, before being pumped into the HPLC.

The software and apparatus used are presented in Table 3.2.

Table 3.2: My caption

Software/Apparatus Model and Manufacturer

Intelligent Pump L-6200; Merck-Hitachi, Darmstadt and San Jose

Interface D-6000A; Merck-Hitachi, Darmstadt and San Jose

Refractive Index Detector (RID) K-2301; Dr. Ing. Herbert Knauer GmbH, Berlin

Chromatography Column SUPREMA analytical in Water; PPS Polymer Standards Service GmbH, Mainz

Intelligent Auto Sampler AS-4000; Merck-Hitachi, Darmstadt and San Jose

Isothermal Column Oven CTO-6AS; Shimadzu Deutschland GmbH, Duisburg

Software D-7000; Merck-Hitachi, Darmstadt and San Jose

The measured samples were prepared with Millipore water, the mentioned polymers and the pro-

tein lysozyme. Before measurement, the samples were diluted using with Millipore water. Before the

samples were injected into the vials, they were filtrated with a syringe filter of 25mm with 0,45mm

cellulose acetate membrane, purchased from VWR International, USA.

The RID measured the values used by the computer software to later create the chromatograms.

The chromatograms were analysed using the data analysis software OriginLab 9.0. To analyse the

23

peak areas and calculate the concentration of the solution, the built-in analysing tool named Peak

Analyzer was used.

3.4 HPLC method

Besides the mentioned separation by size, polymers are also prone to interact with surface charged

sites of the chromatographic stationary phase. These ionic interactions can result in the absorption of

the polymers, shifts in retention time or asymmetry. The mobile and stationary phase are selected in

order to avoid non-ideal interactions. [91] In this work, an ideal system for the study of polymers was

used. The mobile phase was deionised water and the stationary phase was a polyhydroxymethacry-

late copolymer network. No buffer was used.

Other factors can be used to manipulate SEC separations, such as flow rate, volume load and

temperature of the column. Adjustment of these factors can impact resolution, analysis time, and/or

sensitivity.

A high temperature operation has a low solvent viscosity and high diffusivity of the polymer

molecules [92]. In the used column, the analysed polymers have bordering retention times, so to

optimize the resolution the maximum column temperature, 80°C, was used.

Different flow rates were tested in order to optimize the chromatographic process. The selection

of the flow rate to use was made considering that the peaks of the analysed polymers need to have

retention times that ensure a good area of analysis. Although polymers are more effectively separated

at lower flow rates, the time consumption increases with decreasing flow rate. This should be avoided

because of the great number of measurements made in this work. In Table 3.3, the retention times

corresponding to different flow rates are presented, for the aqueous solutions of PEG 6000 and dex-

tran, as well as the calculated time differences. Millipore water was used as the eluent and washing

liquid for the auto sampler.

According to the results shown in Table 3.3, at 0,2 ml/min the two polymers can already be sepa-

rated with an appropriate retention time difference, as is shown in Figure 3.5. To reduce the measuring

time, a flow rate of 0,20 ml/min is used and the corresponding stop time is 62 minutes.

Table 3.3: Retention time differences between PEG 6000 and dextran for different flow rates at 80 °C.

flow rate (ml/min) retention time (min) Difference (min)

0,15 79,7 7,086,7

0,2 52,1 6,058,1

0,23 45,3 3,949,2

24

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5- 0 , 1

0 , 0

0 , 1

0 , 2

0 , 3

0 , 4

RI (vo

lts)

T i m e ( m i n u t e s )

Figure 3.5: Chromatogram obtained from a PEG 6000 – Dextran aqueous solution at 80°C with a flow rate of0,2 ml/min.

In the chromatogram, the first peak corresponds to PEG 6000 and the second one to dextran.

For the measurements of the remaining used solutions (PEG 8000 – dextran, G2 – dextran and

G3 – dextran) the same method was used. Since the peaks showed a good resolution, as can be

observed in Figure 3.6, no other methods were tested to measure these polymers’ concentrations.

The calibration was confirmed by performing test measurements. Despite using the same method,

the measuring time had to be extended, as the retention time of these polymers is longer. In Table 3.4,

a summary of the method and measurement time is presented.

25

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 50 , 00 , 20 , 40 , 60 , 81 , 0

RI (vo

lts)

T i m e ( m i n u t e s )(a) PEG 8000 – dextran 40

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0- 0 , 10 , 00 , 10 , 20 , 30 , 40 , 50 , 60 , 7

RI (vo

lts)

T i m e ( m i n u t e s )(b) G2 – dextran 40

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 00 , 00 , 20 , 40 , 60 , 81 , 01 , 21 , 41 , 6

RI (vo

lts)

T i m e ( m i n u t e s )(c) G3 – dextran 40

Figure 3.6: Chromatogram obtained from the studied aqueous solution at 80°C with a flow rate of 0,2 ml/min.

In Figure 3.6 it is possible to observe several peaks with retention times different from the peaks

used to analyse the polymers of the mixture, which are a consequence of the polydispersity of the

HBP and dextran. Most of these peaks can be ignored as they have very different retention times

comparing to the main peaks, except the peak with a retention time of approximately 67 min (seen

26

Table 3.4: Summary of the methods and measurement times.

Flow rate (ml/min) Temperature (°C) Measurement time (min)

PEG 6000 – Dextran 0,2 80 62PEG 8000 – Dextran 0,2 80 64

G2 – Dextran 0,2 80 70G3 – Dextran 0,2 80 70

in (b) and (c) of Figure 3.6), which has some interference with the HBP peak. However, as it also

appears on the calibration chromatograms without compromising the quality of the calibration curve,

it was considered not to interfere with the measurement.

3.5 Calibration of the polymers

It is possible to relate the HPLC measured peak area with the concentration of the component

responsible for this peak, and when the range of concentrations is small, the relationship between both

is considered linear. To relate the peak area with the components’ concentration, a calibration curve

was made for each of the used polymers. The calibration was performed for a concentration range

of 0,01 to 0,2 wt% for PEG 6000, PEG 8000 and the HBP G2 and G3. For dextran the concentration

range was of 0,01 to 0,3 wt%.

In this step, Millipore water was used as diluter, eluent and washing liquid for the auto sampler. All

the solutions were prepared at room temperature. The measurements were made in a balance scale

with an accuracy of 0.0001 g.

Bulk solutions were prepared for each polymer, with the higher concentrations shown in Table 3.5.

The remaining solutions were prepared by diluting the bulk solutions with water, and these are pre-

sented in Tables 3.6 to 3.10.

To determine the standard curves, the areas in the chromatography diagrams for each polymer

with different concentrations were analysed with the use of OriginLab 9.0.

Table 3.5: Prepared bulk solutions for calibration of the polymers.

Solution mpolymer mwater (wt %)

1 PEG 6000 0,1030 50,1103 0,20552 PEG 8000 0,1016 50,0834 0,20283 Dextran 0,1013 50,3368 0,20124 Dextran 0,0619 20,7532 0,29825 G2 0,1024 50,0047 0,20476 G3 0,1063 50,4473 0,2107

27

Table 3.7: Prepared PEG 8000 Samples for Calibration. Bulk solution 2 was used.

Solution Bulk solution (g) Water (g) (wt %)

12 11,8230 16,0122 0,151813 8,0039 16,3893 0,099114 3,9969 16,2836 0,049815 1,9957 16,4616 0,024616 0,7878 16,0002 0,0101

Table 3.6: Prepared PEG 6000 Samples for Calibration. Bulk solution 1 was used.


7 11,7196 16,0232 0,15038 8,0130 15,9916 0,10309 4,0327 16,0443 0,051710 2,0164 16,0104 0,025911 0,7821 16,0113 0,0100

Table 3.8: Prepared Dextran Samples for Calibration. Bulk solution 3 was used.


17 8,0194 16,0438 0,100618 3,9326 15,8570 0,049919 0,7852 15,9970 0,0099

Table 3.9: Prepared G2 Samples for Calibration. Bulk solution 5 was used.


20 8,0200 16,0078 0,102621 4,0004 16,0896 0,050922 0,8737 16,1837 0,0111

Table 3.10: Prepared G3 Samples for Calibration. Bulk solution 6 was used.


23 8,0646 16,9858 0,100024 4,0441 16,1970 0,052625 0,8237 16,0342 0,0108

3.6 Determination of Tie Lines

The tie lines are determined with the help of HPLC to measure the concentration of each compo-

nent in the separated phases.

Firstly, within the binodal curve, some ATPSs for each system were prepared. The prepared sys-

tems are described in Table 3.11. Then the prepared solutions were stirred with magnets stirring for

1-3 hours and put in a 25°C water bath for 72 hours to reach equilibrium – complete phase separation.

28

After 72 hours, the two phases were separated with a syringe. Considering the limited interval

of calibration, both the top and bottom phases were diluted with an appropriate amount of Millipore

water, to make sure that the concentration after dilution of each component was located within the

calibration interval. Thus, the concentration of each component in the two phases can be measured

with HPLC.

To control the quality of the tie lines, the Lever Rule was applied. When the de-mixing point of the

ATPS lies on the tie line, which was created by connecting two composition points for each phase,

experiments were performed with acceptable accuracy.

Table 3.11: Composition and measured values of the components of the systems used to obtain the tie lines.

System PEG (g) Dextran (g) Water (g) PEG (wt %) Dextran (wt %) Water (wt %)

PEG 60001 0,3381 0,6031 5,0966 5,5997 9,9887 84,41152 0,4581 0,6187 4,9861 7,5558 10,2047 82,23953 0,4775 0,6805 4,8509 7,9465 11,3249 80,7286

PEG 80001 0,3614 0,6689 6,9768 4,5135 8,3538 87,13272 0,5000 0,6851 6,837 6,2328 8,5402 85,22713 0,6064 0,7203 6,6904 7,5638 8,9845 83,4516

G2 1 0,6021 0,6124 4,8089 9,9960 10,1670 79,83702 0,4518 0,6269 4,9347 7,5132 10,4251 82,0617

G3 1 0,6014 0,607 5,1562 9,4491 9,5371 81,01372 0,4503 0,6184 4,9548 7,4757 10,2665 82,2578

3.7 Partitioning of the Lysozyme

The goal of this work is to study the partitioning of lysozyme in the chosen systems: PEG 6000 –

dextran – water, PEG 8000 – dextran – water, G2 – dextran – water and G3 – dextran – water.

Two tie-lines were analysed for each type of system. The systems were prepared with two

lysozyme concentrations, 0,3 and 1 wt %. These concentrations were chosen as they are below

the lysozyme solubility in water and in PEG 6000/8000 aqueous solutions.

The solubility in PEG 20000 solutions can be estimated by Boncina et al. correlations [93] for

a temperature of 25°C, 0,20M of NaCl and pH of 4 and 6, obtaining 24,2 and 2,1 wt %. As the

solubility of lysozyme in PEG solutions increases with the polymerization [93] and decreases with the

salt concentration [94][93], it is possible to assume that for solutions of PEG with molar masses of

6000 and 8000 and no dissolved salts, the lysozyme solubility is higher than 1 wt %.

Howard et al. [94] measured the solubility of lysozyme in aqueous solutions, in the presence of

NaCl. For a pH of 7, 25°C and 1,5 wt % of NaCl, the measured lysozyme solubility was 1,8 wt %.

As mentioned before, and has been proven by Howard et al., the solubility decreases with the salt

concentration, therefore the lysozyme concentration in water is higher than 1 wt %.

The solubility in dextran was not considered since no relevant information was found on the topic.

The lysozyme solubility in solutions with the used HBP is not known, and for that reason the same

concentrations were used.

29

In order to know the partitioning of the lysozyme, the concentration on the top and bottom phases

of the prepared systems must be measured. For this, different methods were attempted.

Firstly the HPLC was performed using the previous column. Since the column used is applicable

to neutral and anionic polymers from 100 to 30 000 000 Da, an applicability to the lysozyme measure-

ment was expected for pHs higher than the lysozyme’s isoelectric point (at which the lysozyme has

a negative charge). The column is stable in a pH range of 1,5 to 13 and the isoelectric point of the

lysozyme is 11,2 [95]. To choose the method’s pH, a range of 7 (lysozyme charge of +7) to 12 (charge

lower than -2) was tested. The tested lysozyme solutions were prepared with a concentration of 0,2

wt %. Mixtures with dextran and PEG 6000 were also tested. None of the attempts was successful.

Secondly, a silica column usually used for biomolecules analysis was tried, TSKgel G3000SWxl

purchased at Tosoh Bioscience GmbH, Stuttgart. The TSKgel column has a calibration range of

10000 to 500000 Da and operates at a pH of 2,5 to 7,5. The results were also not optimal.

For that reason the problem was approached using a different method: Spectrophotometry.

Spectrophotometry is a method to measure the light absorbance of a chemical substance, by

measuring the intensity of light as a beam of light passes through the sample solution. The basic

principle is that each compound absorbs or transmits light over a certain range of wavelengths [96].

A spectrophotometer is used to measure the amount of photons (the intensity of light) absorbed after

it passes through the sample solution. A spectrophotometer, in general, consists of two devices: a

spectrometer and a photometer. A spectrometer is a device that produces, typically disperses and

measures light. A photometer is a photoelectric detector that measures the intensity of light.

Knowing the intensity of the light before and after it passes through the sample, the transmittance,

T, can be calculated using Equation 3.1,

T =ItI0

(3.1)

where Io and It correspond to the light intensity before and after the beam of light passes through

the cuvette, respectively. Transmittance is related to the amount of photons that is absorbed, and is

designated as absorbance, A, by Equation 3.2.

A = −log(T )− log(ItI0

)(3.2)

Having the absorbance, the concentration of the component being measured can be determined

using Lambert-Beer Law, written as:

A = εlC (3.3)

where ε is the absorption coefficient, l is the path length, and c is the concentration.

Since proteins absorb light at a specific wavelength, a spectrophotometer can be used to directly

measure the concentration of a protein in solution. The number and type of amino acids of the protein

affect the absorption [96].

30

The typical Ultraviolet (UV) absorption spectrum of a protein can be divided in three distinct re-

gions: the far-UV region, below 210 nm; the region between 210 nm and 240 nm; and the near-UV

region, above 250 nm. In a protein, absorption in the far-UV region is caused by peptide bonds,

and in the near-UV region by the transfer of electron between the π-orbitals of aromatic amino acids.

The maximum absorption peaks centre around 295, 275 and 260 nm for tryptophan, tyrosine and

phenylalanine, respectively. In general, protein absorption of long-wavelength radiation is maximal at

around 280 [97].

The software and apparatus used are presented in Table 3.12.

Table 3.12: Information about apparatus and Software in spectrophotometry.

Software/Apparatus Model and Manufacturer

Spectrophotometer UVmini-1240 UV-Vis; Shimadzu Corporation,Kyoto Prefecture, Japan

Cuvette BRAND UV-Cuvette UV-Transparent Spectrophotometry; 11 Bokum Road12,5 x 12,5 x 45 mm

Software NEW UV DATA MANAGER; Shimadzu Corporation,Kyoto Prefecture, Japan

In this work the polymer absorption was also taken into account. In order to do that, the influence

of PEG and dextran in the spectrum of a lysozyme solution from 200 nm to 330 nm was evaluated.

Solutions with dextran concentrations ranging from 0 to 5 wt % where prepared (Table 3.13), and the

UV spectrum of each solution was measured. The solutions were prepared with Millipore water. A

initial aqueous solution of 0,2 wt % was prepared and mixed with a magnetic stirrer. The subsequent

solutions where obtained by adding a dextran solution of approximately 25 wt %, while mixing with

the magnetic stirrer. Four additions were made, obtaining the compositions presented in Table 3.13.

After every new addition a sample of 1 ml is taken from the mixture with a syringe, measured in the

spectrophotometer. The data was saved with the help of the optional NEW UV DATA MANAGER

software.

In Figure 3.7 the influence of dextran can be observed.

31

2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 00 , 00 , 20 , 40 , 60 , 81 , 01 , 21 , 41 , 61 , 82 , 02 , 2

Abs

W a v e l e n g t h

Figure 3.7: Dextran influence in the lysozyme UV spectrum. The lighter the colour of the line, the higher thedextran concentration. The composition of the analysed solutions can be found in the Table 3.13.

Table 3.13: Composition of the solutions analysed in Figure 3.7.

Solution Lysozyme (wt %) Dextran (wt %)

0 0,0203 0,00001 0,0194 1,11712 0,0181 2,83463 0,0171 4,08674 0,0162 5,1962

Even though the lysozyme concentration decreases from 0,020 to 0,016 wt %, the absorbance in

the 280 nm wavelength increases with the dextran concentration. The same evaluation was made

for the PEG linear polymers, and, although less influential, similar results were observed. The ab-

sorbance variation can be a result of the absorption of the polymers, a conformational change of the

protein caused by the interactions with the polymer, or both.

The polymers’ influence precludes the measurement of the lysozyme concentration for the wave-

length of 280 nm, showed in Figure 3.7, the second maximum of the spectrum will be considered,

220 nm. To verify if the polymers have a negligible influence on the absorbance at 220 nm, measure-

ments of the lysozyme concentration were made with solutions of a known polymer concentration.

The measurements were also made for 280 nm, to compare the results.

A lysozyme stock solution was prepared with a concentration of 0,2 wt %, weighting the lysozyme

mass and dissolving it in Millipore water. The remaining solutions were prepared by diluting the stock

solution with Millipore water.

Firstly, the maximum lysozyme concentration for the applicability of the Lambert-Beer Law was

determined. The absorbance of the prepared solutions was measured and the values are presented

in Figure 3.8. Based on the data of Figure 3.8, the concentration range for 220 and 280 nm can be

defined as 0,001 to 0,01 wt % and 0,001 to 0,03 wt %, respectively.

32

0 , 0 0 0 , 0 2 0 , 0 4 0 , 0 6

0 , 0

0 , 5

1 , 0

1 , 5

2 , 0

Abs

L y s o z y m e ( % ( w / w ) )

Figure 3.8: Absorbance of lysozyme at 220 (squares) and 280 (triangles) nm.

Secondly, calibration curves where determined for lysozyme solutions with 1 and 7 wt % of dextran.

The solutions were prepared by adding a known amount of solid dextran to lysozyme solutions with a

known concentration.

The obtained points for the solutions with 1 and 7 wt % of dextran are presented in Figure 3.9. As

expected, for 280 nm the presence of dextran is noticeable by an increase in the interception value of

the line that describes the points’ tendency for the two dextran concentrations studied.

0 , 0 0 0 0 , 0 0 5 0 , 0 1 0 0 , 0 1 50 , 0

0 , 5

1 , 0

1 , 5

2 , 0

Abs

L y s o z y m e ( % ( w / w ) )

(a) Absorbance at 220 nm.

0 , 0 0 0 0 , 0 0 5 0 , 0 1 0 0 , 0 1 50 , 0

0 , 1

0 , 2

0 , 3

0 , 4

0 , 5

0 , 6

Abs

L y s o z y m e ( % ( w / w ) )

(b) Absorbance at 280 nm.

Figure 3.9: Influence of dextran concentration in the measurement of lysozyme concentration. Squarescorrespond to solutions with no dextran; circles and triangles correspond to solutions with 1 and 7 wt % dextran,

respectively.

The points obtained at 220 nm prove that, if the dextran concentration is lower than 1 %, the

measurement is not influenced by its presence. As the PEG polymers showed a lower influence on

the spectrum, the same assumption was made for these polymers.

Considering the results of Figure 3.9, the dilutions made before the measurement of lysozyme in

the bottom and top phases of the ATPS containing linear polymers guarantee combined concentra-

tions (dextran + PEG) lower than 1 wt %.

33

For the measuring of the HBP a different method was a attempted. The HBP absorbed UV light

at 220 nm. To account for this absorption a calibration curve for G2 was made, with which, knowing

the concentration of HBP in the systems, the absorbance contribution of these polymers can be

subtracted. The calibration was performed in a concentration range of 0,01 to 0,2 wt %.

A bulk solution was prepared by weighing a certain amount of polymer on a scale with an accuracy

of 0,0001 g and dissolving it with water. Other samples with lower concentration were diluted from

the bulk solution by adding certain amounts of water. Four solutions with different concentrations for

each polymer were prepared (as shown in Table 3.14).

Table 3.14: Prepared G2 samples for calibration in spectrophotometer.

Solution Dilution (g) G2 (mg) Water (g) (wt %)

Bulk solution 1 - 0,0113 5,122 0,22011 1,0147 of bulk sol. 1 2,2337 4,0227 0,04432 0,9927 of bulk sol. 1 2,1852 4,0366 0,00883 1,0024 of bulk sol. 1 2,2066 5,4997 0,00134 1,9099 of bulk sol. 1 4,2043 2,1788 0,1028

To test this method, the absorbance of two solutions with a known concentration of G2 and

lysozyme was measured, and the lysozyme concentration was calculated and compared with the real

one. The solutions were prepared by mixing a weighed amount of bulk solution 1 from Table 3.14, and

2 from Table 3.18 with Millipore water. The weighed amounts and final concentrations are presented

in Table 3.15.

Table 3.15: Prepared solutions to test the lysozyme measurement method in samples containing G2. BSstands for bulk solution.

Test solutions BS 1 (Table 3.18 (g) BS 2 (Table 3.14 (g) Water (g) Lysozyme wt % G2 wt %

1 0,2954 1,9927 1,9937 6,774E-03 4,785E-022 0,2017 2,9232 0 6,338E-03 4,148E-02

The systems were prepared with the same procedure as the one explained in section 3.6, with

the addition of lysozyme, which was measured and added to the mixture at the same time as the

polymers.

After mixing the systems with a magnetic stirrer and settling, the phases were separated as de-

scribed in section 3.6. ATPS consisting of PEG, Dextran, HBP, Millipore water and lysozyme were

prepared. The results in percentage of individual component are recorded in Tables 3.16 and 3.17.

Systems A correspond to a lysozyme concentration of 0,3 wt %, and systems B to a 1 wt % concen-

tration. System 1 corresponds to the shortest tie-line, nearer the critical point.

34

Table 3.16: Composition of prepared systems with lysozyme and linear polymers. The A correspond to systemswith 0,3 wt % of lysozyme and the B to systems with 1 wt %. System 1 is

System PEG (g) Dextran (g) Lysozyme (g) Water (g) Total mass (g) PEG (wt %) Dextran (wt %) Lysozyme (wt %) Water (wt %)

PEG 6000 (1)

A1 0,456 0,617 0,019 4,911 6,003 7,598 10,272 0,312 81,818A2 0,477 0,680 0,018 4,896 6,071 7,864 11,195 0,297 80,644B1 0,461 0,618 0,061 4,869 6,009 7,678 10,284 1,015 81,022B2 0,474 0,679 0,062 4,777 5,992 7,908 11,329 1,033 79,730

PEG 8000 (1)

A1 0,372 0,516 0,018 5,076 5,982 6,218 8,626 0,304 84,852A2 0,451 0,538 0,018 5,030 6,037 7,474 8,910 0,298 83,319B1 0,375 0,526 0,062 5,050 6,012 6,232 8,747 1,028 83,993B2 0,454 0,543 0,060 4,960 6,017 7,539 9,019 1,002 82,440

PEG 6000 (2)

A1 0,459 0,620 0,018 4,917 6,014 7,626 10,303 0,303 81,768A2 0,476 0,679 0,018 4,839 6,012 7,911 11,299 0,299 80,491B1 0,458 0,617 0,060 4,865 6,000 7,625 10,287 0,998 81,090B2 0,476 0,679 0,060 4,791 6,006 7,924 11,309 0,992 79,775

PEG 8000 (2)

A1 0,373 0,517 0,018 5,209 6,116 6,095 8,454 0,291 85,160A2 0,450 0,547 0,019 5,113 6,129 7,346 8,930 0,303 83,421B1 0,378 0,516 0,061 5,092 6,047 6,258 8,532 1,009 84,202B2 0,452 0,546 0,061 4,971 6,030 7,500 9,059 1,007 82,434

Table 3.17: Composition of prepared systems with lysozyme and HBP. The A correspond to systems with 0,3wt % of lysozyme and the B to systems with 1 wt %.

System HBP (g) Dextran (g) Lysozyme (g) Water (g) Total mass (g) HBP (wt %) Dextran (wt %) Lysozyme (wt %) Water (wt %)

G2

A1 0,720 0,730 0,018 4,546 6,014 11,968 12,138 0,306 75,588A2 0,453 0,624 0,019 4,919 6,014 7,532 10,370 0,319 81,779B1 0,722 0,724 0,061 4,511 6,017 11,990 12,035 1,012 74,962B2 0,451 0,618 0,061 4,885 6,015 7,499 10,274 1,009 81,218

G3 A1 0,721 0,721 0,018 5,270 6,731 10,715 10,715 0,273 78,296A2 0,455 0,621 0,018 4,916 6,009 7,568 10,327 0,298 81,807

For the linear polymers, duplicates were made for each system. For the HBP, no duplicates were

made. The systems with G3 and 1 wt % of lysozyme were also not made, as a result of the incapacity

to measure lysozyme concentration in this system, after partitioning.

To measure the lysozyme concentration in each phase, the solutions were diluted with Millipore

water with the dilution factors presented in Tables B.24 to B.27.

Before each composition is measured in the spectrophotometer, a calibration is essential. The

calibration was carried out with a concentration range of 0,001-0,01 wt % of lysozyme.

The calibration solutions were prepared from two bulk solutions, a first one with 0,2 wt % of

lysozyme and a second one with 0,1 wt %. The lysozyme was dissolved in water and the amount

of both was weighted on a scale with accuracy of 0,0001 g. Other samples with lower concentration

were diluted from the bulk solution by adding the amounts of water indicated on Table 3.18. The two

bulk solutions were prepared on different days, and the measurement of respecting diluted solutions

also, confirming the applicability of the calibration. Nine solutions with different concentrations were

prepared (as shown inTable 3.18).

35

Table 3.18: Prepared lysozyme samples for calibration in spectrophotometer.

Solution Dilution (g) Lysozyme (mg) Water (g) (w- %)

Bulk solution 1 - 0,0503 24,9981 0,20081 0,5410 of bulk sol. 1 1,0864 10,1215 0,01072 0,2889 of bulk sol. 1 0,5801 10,1344 0,00573 0,1222 of bulk sol. 1 0,2454 10,0091 0,00254 0,0656 of bulk sol. 1 0,1317 10,3680 0,00135 0,4118 of bulk sol. 1 0,8269 10,3666 0,0080

Bulk solution 2 - 0,0499 50,7701 0,09826 1,0419 of bulk sol. 2 1,0230 9,9630 0,01037 0,7987 of bulk sol. 2 0,7842 10,0888 0,00788 0,5305 of bulk sol. 2 0,5209 12,5136 0,00429 0,2006 of bulk sol. 2 0,1970 19,4468 0,0010

36

4Model

Contents4.1 Lattice Cluster Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Wertheim theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

37

4.1 Lattice Cluster Theory

In this chapter the model used, a version of the LCT applicable for a multicomponent polymer

solution/blend, will be introduced.

Freed and co-workers [25–29] improved the FH theory by identifying and understanding its de-

ficiencies, and calculating corrections. On the basis of de Gennes’ work [98] treating long chain

molecules as a self-avoiding walk on a lattice by the use of spins they developed the LCT for long

chain molecules with different architectures. The main amendments will now be addressed.

As mentioned in Section 2.5.4.A, the FH lattice model treats the monomers as structureless units.

The LCT overcomes this limitation by allowing monomers to occupy several neighbouring lattice sites

to mimic the sizes, shapes and structure of the actual molecules, as can be seen in Figure 4.1 [29].

PIBPEPPPPE

Figure 4.1: United atom group models for monomers of poly(ethylene) (PE), poly(propylene) (PP), poly(thylenepropylene) (PEP) and poly(isobutylene). Circles represent CHn groups, solid lines designate C - C bonds inside

the monomer, and dotted lines indicate C - C bonds linking the monomer to its neighbours along the chain.

The non-combinatorial contribution of the model is generated analytically and accounts for the

compositions, molecular weights, nearest neighbours, attractive van der Walls interactions, and tem-

perature. This way, the use of the purely empirical FH parameter is avoided.

In this study, a model from Kulaguin and Zeiner [13] is used.

The LCT derives in the form of a cluster expansion in the inverse coordination number 1/z and the

reduced interaction energy ∆εij/kBT . Using Tables I-III [26] and the corrections given in [27], Equa-

tion (4.1) is defined for the Gibbs free energy contribution of the LCT, GLCT , for an incompressible

LCT with multi-components.

GLCTNLRT

=

n∑i=1

ΦiMi

ln (Φi)−∆S

NLRT− ∆E1

NLRT− ∆E2

NLRT(4.1)

The first term of Equation (4.1) emerges as the contribution of the classical FH entropy, ∆S is the

non-combinatorial correction term of the entropy, and ∆E1 and ∆E2 are the energy contributions of

first and second order.

The correction term of the entropy and the energy contributions are calculated with the use of

Equations (4.2)-(4.4).

∆SNLRT

= 1z

n∑k=1

n∑λ=1

XS1,kλΦkΦλ− 2

z2

n∑k=1

n∑λ=1

XS2,kλΦkΦλ + 1

z2

n∑k=1

n∑λ=1

XS3,kλΦkΦλ

+ 4z2

n∑k=1

n∑λ=1

n∑µ=1

XS4,kλµΦkΦλΦµ + 2

z2

n∑k=1

n∑λ=1

n∑µ=1

n∑η=1

XS5,kλµηΦkΦλΦµΦη

(4.2)

38

∆E1

NLRT= 1

z

n∑k=1

n∑λ=1

n∑µ=1

Xε1,kλµ∆εkλΦkΦλΦµ + 1

z

n∑k=1

n∑λ=1

Xε2,kλΦkΦλ

n∑µ=1

∆εkµΦµ

+ 1z

n∑k=1

n∑λ=1

Xε3,kλΦkΦλ

n∑µ=1

n∑η=1

∆εµηΦµΦη + 1z

n∑k=1

n∑λ=1

Xε4,kλΦkΦλ

n∑µ=1

∆ελµΦµ

− 2z

n∑k=1

n∑λ=1

n∑µ=1

Xε5,kλµΦkΦλΦµ

n∑τ=1

n∑η=1

(∆ετη − 2∆εkτ ) ΦτΦη

− 12

n∑k=1

Xε6,kΦk

n∑µ=1

n∑η=1

(∆εµη − 2∆εkµ) ΦµΦη − z4

n∑µ=1

n∑η=1

∆εµηΦµΦη

(4.3)

∆E2

NLRT=

n∑k=1

Xε2

1,kΦkn∑µ=1

∆ε2kµ4 Φµ +

n∑k=1

n∑λ=1

Xε2

2,kλΦkΦλn∑µ=1

n∑η=1

∆εkµ∆εµη2 ΦµΦη

+n∑k=1

n∑λ=1

Xε2

3,kλΦkΦλn∑µ=1

n∑η=1

∆εkµ∆εkη4 ΦµΦη

+k∑k=1

k∑λ=1

Xε2

4,kλΦkΦλk∑µ=1

k∑η=1

k∑ω=1

k∑τ=1

∆εωτ∆εµη4 ΦµΦηΦωΦτ

+k∑k=1

k∑λ=1

Xε2


k∑η=1

k∑ω=1

∆εµη∆εηω4 ΦµΦηΦω

+k∑k=1

k∑λ=1

Xε2


k∑η=1

k∑ω=1

∆εkµ∆εηω2 ΦµΦηΦω

+k∑k=1

k∑λ=1

Xε2


k∑η=1

(∆ε2kλ

4 −∆εkµ∆εkλ + ∆εkµ∆ελη − ∆εkµ∆ελµ2 +

∆εkλ∆εµη2

)ΦµΦη +

k∑k=1

Xε2

8,kΦkk∑µ=1

k∑η=1

∆ε2µη8 ΦµΦη

+ z4

k∑µ=1

k∑η=1

k∑ω=1

k∑τ=1

(∆εµη∆εωτ

4 − ∆εµη∆εηω2 +

∆ε2µη4

)ΦµΦηΦωΦτ

(4.4)

The calculated corrections are implemented in the model used, as the terms XSi , Xε

i and Xε2

i ,

defined by Equations eqs. (A.1) to (A.5), eqs. (A.6) to (A.11), and eqs. (A.12) to (A.18) [13], that can

be found in Appendix A, including a temperature-independent contribution to the χ parameter that

arises from the corrections introduced by the chain connectivity and excludes volume constraints.

In the X terms, two structural parameters, b3,i and b4,i – the number of branching points of three

and four – are introduced in order to account for the chains’ architecture. The use of this structural

parameters assumes that there are at least two segments between two branching points, which for

the used hyperbranched polymer this assumption is fulfilled. To consider the short chain branching

the equations given in [99] have to be used. The advantage of the equations of this work is the simple

way of describing the architecture and the reduced number of parameters.

In the framework of LCT, the interaction parameter ∆εij is related to one contact point between

segments. Hence, the product of coordination number and interaction energy describes the interac-

tion of one segment. When the coordination number z tends to infinity (z →∞), Equations (4.2)-(4.4)

tend to zero (∆E1,∆E2,∆S → 0), i.e., the entropic LCT-contribution is reduced to the classical FH

entropy and, in case the interaction energy also tends to zero (∆εij → 0), the energy contributions

are reduced to the FH χ−parameter.

39

4.2 Wertheim theory

The LCT presented in the previous chapter 4.1 has a disadvantage that cannot be ignored in the

systems to be studied in this work, which is the inability to describe the molecules’ association. This

is particularly important as the Dextran T40 molecules have 3 OH-groups per glucose unit and the

PEG/HB has the association sites on the oxygen.

The association between molecules in the mixtures is usually described based on one of two

approaches. The ”chemical theory” assumes the formation of hydrogen bonds as a chemical reaction,

and the ”physical theory” calculates the association contributions using integral equations consisting

of an interaction potential to illustrate the association interactions [100].

Wertheim [30, 31] developed one ”physical theory” that treats the associative bonds as directional

forces between two association sites. This theory takes into account self and cross associations, i.e.,

between molecules of the same type and different types. The Wertheim theory was transferred on

a fully occupied lattice, so an incompressible fluid is regarded. As a result of the application of the

Wertheim theory, the Gibbs energy has the extra addition (4.5)[101].

GassoNLRT

=∑i

Φi

[∑Ai

[ln (XAi)−

XAi

2

]+

1

2Nassoi

](4.5)

Where Nassoi is the number of association sites per segments of component i, and XAi are the

non-bonded segment fractions.

To apply this theory it is necessary to identify every associative site in the studied molecules [30,

31], which are divided by class according to the type of group that is responsible for the association,

such as OH, amine or carbonyl. The non-bonded segment fractions can be calculated with Equation

(4.6) [102][101]

XAi =

1 +∑j

∑Bj

ΦjXBj∆ij

−1

(4.6)

The cross association strength between two molecules ∆ij is defined as:

∆ij = Kassoij

[exp

(εassoij

kBT

)− 1

](4.7)

where Kassoij is the association volume and εassoij is the association energy between two segments

of two different components. These cross association parameters are calculated based on the self

association ones, that must be fitted to experimental data:

Kassoij =

Kassoii +Kasso

jj

2(4.8)

εassoij = (1− kij)√εassoii εassojj (4.9)

where the parameter kij is introduced to consider the deviation of the association energy from

the geometrical mixing rule, i.e., the difference between√εassoii εassojj and εassoij ; Kasso

ii or Kassojj , and

40

εassoii or εassojj are the association volumes and the association energies of one single component,

respectively.

Finally, the total Gibbs free energy of the systems, when accounting for the architecture and the

association interaction, is defined as:

GmixNLRT

=GassoNLRT

+GLCTNLRT

(4.10)

41

5Results and Discussion

Contents5.1 Liquid-liquid equilibria for the lysozyme-water system . . . . . . . . . . . . . . . 43

5.2 Liquid-liquid equilibria for ternary systems . . . . . . . . . . . . . . . . . . . . . . 44

5.3 Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

42

In this chapter, solutions of two linear PEG polymers and two Hyperbranched Polymers (HBP) are

studied. To describe the architecture of the HBP, the number of branching points of two of these, and

the number of segments will be used as structural parameters. Moreover, the partitioning of lysozyme

will be studied in the linear system and modelled with a quaternary LCT combined with the Wertheim

theory.

5.1 Liquid-liquid equilibria for the lysozyme-water system

Figure 5.1: Lysozyme structure illustration [103]

In the following chapter, the parameters describing the LLE of the binary subsystem lysozyme-

water will be adjusted to experimental data with the LCT in combination with the Wertheim theory.

This step will facilitate the parameter adjustment in the quaternary system, where the partitioning of

the lysozyme will be calculated.

For the modelling of the LLE of lysozyme solution, a linear structure will be considered and the

3D configuration will not be taken into account. The number of segments was defined based on the

amino acids of the protein, so it equals 147, and the branching parameters are zero. The binary

interaction, association and LCT parameters were fitted to the experimental results.

The LLE experimental data, taken from Taratuta et al [104], and the modelled data are shown in

Figure 5.2.

43

0 , 0 0 0 , 0 5 0 , 1 0 0 , 1 5 0 , 2 0 0 , 2 5 0 , 3 0 0 , 3 5 0 , 4 0 0 , 4 5 0 , 5 0 0 , 5 52 6 4

2 6 6

2 6 8

2 7 0

2 7 2

2 7 4

2 7 6

2 7 8

2 8 0

Temp

eratur

e (K)

C o n c e n t r a t i o n ( % ( w / w )

Figure 5.2: Liquid-liquid equilibrium of aqueous lysozyme solution. Symbols are experimental data []; Thebroken line is the model. Experimental data taken from Taratuta et al [104], from solutions in phosphate buffer

with a pH of 7.

Table 5.1: Binary interaction, association and LCT parameters for the aqueous lysozyme solution.

Binary interaction energy (∆εijkB

) [K] -25

Association energy ( εassoij

kB) [K] 559

Association parameter (Kassoij ) 0,1

Deviation of the geometrical mixing rule (kij) 0,1

5.2 Liquid-liquid equilibria for ternary systems

In this chapter, the ternary systems of water/dextran-T40 and PEG 6000, 8000, G2 or G3 are

studied. The experimental and modelled results will be shown.

5.2.1 Calibration for tie-line determination

After selection of the appropriate HPLC method, the calibration lines were investigated according

to the procedure introduced in section 3.4. Results are displayed in x-y diagram with the x-axis

standing for the weight percentage of prepared polymer solutions, and the y-axis standing for the

area values obtained from the OriginLab evaluation. In the calibration diagrams, the relations between

evaluated areas and corresponding concentrations are presented with filled dots. Calibration results

of linear polymers and HBP are displayed in Figure 5.3 and Figure 5.4, respectively.

44

0 , 0 0 0 , 0 5 0 , 1 0 0 , 1 5 0 , 2 0 0 , 2 50

1

2

3

4

5

6Are

a

C o n c e n t r a t i o n w t %

(a) PEG 6000a= -0,32±0,05; b= 28,9±0,4

R2=0,99795

0 , 0 0 0 , 0 5 0 , 1 0 0 , 1 5 0 , 2 0 0 , 2 50

1

2

3

4

5

6

Area


(b) PEG 8000a= -0,3759±0,03; b= 28,8±0,3

R2=0,99858

0 , 0 0 0 , 0 5 0 , 1 0 0 , 1 5 0 , 2 0 0 , 2 5 0 , 3 0 0 , 3 50123456789

1 0

Area


(c) Dextrana= 0,03±0,01; b= 29,06±0,09

R2=0,99982

Figure 5.3: Calibration Diagram for the linear polymers. The data is presented in the Table B.1. Therepresented calibration curve is defined by y = ax+ b.

0 , 0 0 0 , 0 5 0 , 1 0 0 , 1 5 0 , 2 0 0 , 2 50

1

2

3

4

5

6

Area


(a) G2a= -0,07±0,05; b= 17,0±0,4

R2=0,99564

0 , 0 0 0 , 0 5 0 , 1 0 0 , 1 5 0 , 2 0 0 , 2 50

1

2

3

4

5

6Are

a


(b) G3a= -0,06±0,04; b= 18,8±0,4

R2=0,99743

Figure 5.4: Calibration Diagram for the HBP. The data is presented in the Table B.2. The representedcalibration curve is defined by y = ax+ b.

All the calibration curves have a good R-square. The curves do not have an interception value of

zero, which can be explained by the low sensibility of the HPLC method to these polymers, probably

caused by their polydispersity. The polydispersity causes the different molar size polymer segments

to elute the column in various retention times, and consequently, not all the polymer is accounted for

in the measured peak. This effect is more noticeable in the PEG polymers, for which the samples with

the lower concentration (0,01 wt % in Table B.1) result in an almost null measured area.

5.2.2 Tie-line modelling

With the help of the Programming Software Free Pascal V2.6.4, the LLE will be calculated. The

LCT+Wertheim model, which has been introduced in the theoretical part, has already been imple-

mented to the program by Laboratory of Fluid Separations, TU Dortmund. Therefore, no program-

45

ming work is required any more. The only work that needs to be done is calculating with this already

existing program.

Firstly, the systems with linear polymers (PEG 6000/Dextran 40 and PEG 8000/Dextran 40) are

calculated maintaining the LCT and Wertheim parameters coherent. Secondly, a similar work will be

done for the systems with HBP, taking into account extra structural parameters this time.

The association parameters, association energy ( εassoii

kB) and association volume (Kasso

ii ) of the pure

solvent and the linear polymers were the first to be defined, based on former articles [13], and are

shown in Table 5.2

Table 5.2: Association parameters of water and linear polymers taken from [13].

Association energy PEG 6000 750

Association energy PEG 8000 750

Association energy Dextran 869

Association energy water 1512

Association volume PEG 6000 0,009

Association volume PEG 8000 0,009

Association volume Dextran 0,012

Association volume water 0,01

In the calculations for the linear polymer systems, the structural parameters taken into account are

the molar mass of each component, MM i, and the corresponding number of segments, Mi. In this

case, give the linear structure, the number of branching points of 3, b3,i, and 4, b4,i is zero. For the

PEG polymer the number of segments is calculated by setting the segment size as the molar mass of

the solvent, in this case water, meaning that each segment has a molar mass of 18 g/mol. Then, the

number of segments of each polymer is calculated as shown in Equation (5.1).

Mi =MM i

18(5.1)

The dextran molecule has rings as part of its structure, which cannot be described by the LCT.

Considering that the space occupied by the glucose rings cannot be disregarded, for each ring an

extra segment is accounted for. Thus, the number of segments per glucose is set as 7 – the number

of carbons plus one.

The interaction energies show a dependence on molar mass that was described for PEG, dextran

and water by Kulaguin Chicaroux and Zeiner [105] by Equations (5.2) to (5.4).

εPEG−water

kB= −7, 143× 10−5K ·mol

g·MM,PEG − 4, 771 K (5.2)

εDex−waterkB

= −5, 727× 10−5K · gmol

·MM,Dex − 5, 229 K (5.3)

εPEG−Dex

kB= 8, 166× 10−5 ·MM,Dex + 9, 884 K (5.4)

46

The dependence shown was used for an initial calculation of these parameters, followed by an

adjustment to the experimental data. In Table 5.3 the parameters calculated with the Equations (5.2)

to (5.4) are presented next with the adjusted ones.

Table 5.3: Interaction parameters of LCT+Wertheim for systems with linear polymers.. Calculated byEquations (5.2) to (5.4) and adjusted to the experimental results.

Calculated Adjusted Difference (%)

PEG 6000 - water -5,2 -5,4 4PEG 8000 - water -5,3 -4,8 11

Dextran - water -7,3 -9,5 23Dextran - PEG 6000 12,9 14,5 11Dextran - PEG 8000 12,9 13,5 4

The adjusted parameter that shows a bigger difference with the calculated is the value that de-

scribes the interaction between dextran and water. This can be related with the polydispersity of the

dextran (35000-45000), which is not taken into account by the model.

In addition to the molecular structure parameters, the coordination number z also needs to be

fixed. It describes the number of neighbour segments or next segments in the liquid. Originally, the

LCT was developed at z=6, as a cubic lattice [25]. In this work, the coordination is also considered as

6.

The modelled ATPS and the correspondent experimental data are illustrated in Figure 5.5, and the

used values can be found in Table 5.4.

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0

D e x t r a nW a t er

P E G 6 0 0 0

(a) ATPS consisting of PEG 6000 – dextran 40 – water.

0 5 1 0 1 5 2 0 2 5 3 0

7 0

7 5

8 0

8 5

9 0

9 5

1 0 0 0

5

1 0

1 5

2 0

2 5

3 0


P E G 8 0 0 0

(b) ATPS consisting of PEG 8000 – dextran 40 – water.

Figure 5.5: Experimental and LCT+Wertheim points of ATPS consisting of linear polymers, in wt % at 298.15K:Symbols are experimental data []; The broken lines are the measured tie lines; the full lines are the modelled

tie lines and binodal curve. The parameters used are presented in ??

Comparing the modelling results and the experimental data, it can be stated that the binodal curve

can be described in good accordance with experimental data, but there are some deviations of the

47

Table5.4:

Sum

mary

ofLCT

andW

ertheimA

ssociationparam

etersetforlinearpolymers.

Com

ponentpropertiesS

tructuralparameters

Interactionparam

eters(∆εij

kB

)A

ssociationparam

eters

Association

Energy

Association

Volume

MMPEG

6000

6000MPEG

6000

333P

EG

6000-Dextran

14,5P

EG

6000750

PE

G6000

0,009

MMPEG

8000

8000MPEG

8000

444P

EG

8000-Dextran

13,5P

EG

8000750

PE

G8000

0,009

MMDextra

n37000

MDextran

1597D

extran-water

-9.5D

extran869

Dextran

0,012

PE

G6000-w

ater-5,4

Water

1512W

ater0.01

PE

G8000-w

ater-4,8

kasso

ijP

EG

6000-Water

0

kasso

ijP

EG

8000-Water

0

kasso

ijP

EG

6000-Dextran

0,045

kasso

ijP

EG

8000-Dextran

0,045

kasso

ijD

extran-water

0

48

calculated tie lines and the experimental ones. The bigger deviations correspond to the tie-lines near

the critical point, which are obtain with a bigger error experimentally, give that the equilibrium is more

difficult to achieve. Moreover, the tie-lines near the critical point were only measured once, making

the results less reliable than the other two.

Although there are deviations in the tie lines, the agreement between experimental and modelling

data is good for the linear system. Therefore, this LCT-Wertheim model can be applied to describe

liquid-liquid equilibrium of PEG6000-Dextran-water and PEG8000-Dextran-water system, and it will

be used to calculate the lysozyme partitioning in these systems.

In contrast to the simple architecture of the linear polymers, the HBP architecture must be specified

in a more complex manner in the calculation. The architecture will not be considered an adjustable

parameter, but rather it will be determined by the chemical structure of the molecules, similar to

former articles [13]. Firstly, the polymers’ architecture will be inspected in order to define the number

of branching points of 3, b3, and 4, b3, for each HBP.

The first considered HBP is G2, and its idealized structure can be seen in Figure 3.1. This polymer

is a hyperbranched polyester of pseudo generation 2, i.e., with one branching level in one of the ends.

It is composed by a core of PEG with a theoretical molar mass of 6000 and its branching units are

2,2-bis(methylol)propionic acid (bis-MPA).

The number of segments of the HBP were defined considering that each bis-MPA molecule, with

a molar mass of 133, occupies 5 segments of the lattice, thus defining that each segment has a molar

mass of 27:

Segment size =MM,MPA

5(5.5)

therefore the G2 molecule has a total of 248 segments. Regarding the architecture, this HBP has

only one branching point of 3, thus b3 = 1 and b4 = 0.

The G3 is represented in Figure 3.2 and it is also a hyperbranched polyester composed by a core

of PEG with a theoretical molar mass of 6000 and branching units of bis-MPA. This HBP is of pseudo

generation of 3, with 2 branching point levels. Once again, the segment size is 27, by the same

consideration, therefore G3 has a total of 346 segments. As this HBP has 3 branching points of 3,

b3 = 3.

The interaction and association parameters where adjusted to the experimental data.

The calculated and experimental values for both polymers are presented in Figure 5.6 and the

used adjusted parameters can be found in Table 5.5.

49

0 5 1 0 1 5 2 0 2 5 3 0 3 50

5

1 0

1 5

2 0

2 5

3 0

3 56 5

7 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P F L D H B - G 2 - O H

(a) ATPS consisting of G2 – dextran 40 – water.

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P F L D H B - G 3 - O H

(b) ATPS consisting of G3 – dextran 40 – water.

Figure 5.6: Experimental and LCT+Wertheim points of ATPS consisting of HBP, in wt %: Symbols areexperimental data []; The broken lines are the measured tie lines; the full lines are the modelled tie lines and

binodal curve. The used parameters are presented in Table 5.5

Comparing the modelling results and the experimental data, it can be stated that, for the ATPS

formed by G2 polymer, the binodal curve can be described in good accordance with experimental

data, but there are big deviations between the calculated tie lines and the experimental ones. This

can be explained by the chosen structural parameters, as these are the very influential parameters

in the tie-line slope. Although defining the bis-MPA monomer as occupying five segments in the

lattice allows for good tie-line calculations for the G3 system, as can be seen in Figure 5.6b, this

consideration did not apply for the G2 system. One reason for this could be the polydispersity of the

HBP and the dextran. Consideration of dispersity can be an option to optimize the model.

Similar systems, as PEG4000-dextran110, PEG10000-dextran40 and PEG10000-dextran110, can

also be modelled with LCT and Wertheim theory [105]. Although deviations appear in some systems,

this model can be accepted to describe the LLE of ATPS consisting of two polymers.

Additionally, a comparison can be made between the linear and the hyperbranched systems. Con-

sidering the molar mass similarity, in Figure 5.7 the PEG 6000 system is compared with G2 and the

PEG 8000 with G3. Comparing the ATPS based on the HBP and the ATPS including the PEG 6000

and 8000, it can be seen that the ATPS containing linear polymers has steeper tie lines. One disad-

vantage of the ATPS based on HBP is that the weight fraction of HBP polymer of the top (HBP-rich)

phase is higher than in the ATPS containing linear polymers, which results in a higher requirement of

HBP to form an ATPS. This fact is confirmed by the translation of the critical point in the ternary sys-

tem to the right, meaning the minimum required amount of polymers to form an ATPS in both cases,

(a) and (b) Figure 5.7, is larger for the systems containing HBP.

50

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P E G 6 0 0 0 / G 2

(a) G2 vs PEG 6000.

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P E G 8 0 0 0 / G 3

(b) G3 vs PEG 8000.

Figure 5.7: Comparison can be made between the linear and the hyperbranched systems, in wt % at 298.15K:full line corresponds to the HBP systems; broken lines correspond to the linear polymers’ systems.

51

Table5.5:

Sum

mary

ofLCT

andW

ertheimA

ssociationparam

etersetfortheH

BP

.

Com

ponentpropertiesS

tructuralparameters

Interactionparam

eters(∆εij

kB

)A

ssociationparam

eters

Association

Energy

Association

Volume

MMG

26696

MG

2248

G2-D

extran20

G2

785G

20,0055

MMG

37625

MG

3346

G2-W

ater-5

G3

779G

30,009

G3-D

extran15

kasso

ijG

2-Water

0

G3-W

ater-6

kasso

ijG

3-Water

0

kasso

ijG

2-Dextran

0,085

kasso

ijG

3-Dextran

0,045

52

5.3 Partitioning

In this section, the partitioning of the lysozyme in the ATPS with the linear polymers PEG 6000,

8000 and dextran will be studied. The partition was measured experimentally and modelled with a

quaternary LCT model in combination with the Wertheim theory.

5.3.1 Calibration for lysozyme quantification

A calibration was necessary before the partitioning coefficients could be determined. Results are

displayed in an x-y diagram with the x-axis standing for the weight percent of the prepared lysozyme

solutions while the y-axis stands for the the absorbance of the solution. Results of calibration for

partitioning investigation are illustrated in Figure 5.8.

0 , 0 0 0 0 , 0 0 4 0 , 0 0 8 0 , 0 1 20 , 0

0 , 5

1 , 0

1 , 5

2 , 0

Abs

L y s o z y m e w t %

Figure 5.8: Calibration diagram for the lysozyme. The data is presented in the Table B.3. The representedcalibration curve is defined by y = (144±3)x + (0,04±0,02). R2=0,99654.

In order to account for the HBP absorbance a calibration curve was made for the G2 molecule.

Results are displayed in an x-y diagram with the x-axis standing for the weight percent of the prepared

G2 solutions while the y-axis stands for the the absorbance of the solution. Results of the calibration

are illustrated in Figure 5.9.

53

0 , 0 0 0 , 0 2 0 , 0 4 0 , 0 6 0 , 0 8 0 , 1 0 0 , 1 20 , 0

0 , 5

1 , 0

1 , 5

Abs

G 2 w t %

Figure 5.9: Calibration diagram for G2 spectrometry. The data is presented in the Table B.3. The representedcalibration curve is defined by y = (11,9±0,2)x + (0,025±0,009). R2=0,99943.

To test the applicability of the presented calibration curve, two test solutions were prepared with

previously known lysozyme and G2 concentrations. Knowing the G2 concentration, CG2, the corre-

sponding absorbance, Acalc, was calculated with the calibration curve, and subtracted to the mea-

sured absorbance of the prepared solutions solutions, Ameas, obtaining an estimated absorbance,

Aest.

Aest = Ameas −Acalc (5.6)

With the estimated absorbance and the lysozyme calibration curve presented in Figure 5.8, the

lysozyme concentration was calculated and compared with the real one. In Table 5.6 the calculated

values are presented. To avaluate the applicability of the method, an error was calculated as:

Error (%) =|CLys,est − CLys,exp|

CLys,exp× 100 (5.7)

Where CLys,est is the estimated concentration of lysozyme and CLys,exp is the known experimental

concentration.

Table 5.6: Prepared and calculated concentrations, measured and calculated absorbances, and error fo thesolutions used on the explained test.

Experimental Estimated

Test solutions Lysozyme wt % G2 wt % Acalc Ameas Aest Lysozyme wt % Error (%)

1 6,774E-03 4,785E-02 0,571 1,670 1,099 7,29E-03 7,62 6,338E-03 4,148E-02 0,495 1,420 0,925 6,08E-03 4,1

Analysing the results, it can be considered that the lysozyme concentration can be estimated with

less than 10 % of error. This error can be related with the cumulative experimental error throughout

the procedure.

54

5.3.2 Modelling

The lysozyme partitioning was investigated by preparing systems with mixing points previously

studied and adding the lysozyme in two different concentrations, 0,3 and 1 wt % (designated A and B,

respectively) in order to evaluate the influence of the lysozyme concentration in the partitioning. For

each type of system, PEG 6000 – dextran, PEG 8000 – dextran, G2 – dextran and G3 – dextran, two

mixing points far from the critical point were chosen. This was defined in order to study the influence

of the TLL in the partitioning. The compositions of the prepared systems are presented in Tables

3.16 and 3.17, and the measured values can be found in Appendix B. Systems A correspond to a

lysozyme concentration of 0,3 wt %, systems B to a 1 wt % concentration. Systems 1 correspond to

the shortest tie-line, nearest to the critical point.

After mixing and settling, two transparent phases were obtained. In the systems with 1% of

lysozyme a white deposit was detected in the interface, resulting of lysozyme precipitation.

To ensure the values of the experimental points, each system was prepared twice, but the study

of the results was made with the average values of partitioning obtained for each system, presented

in Table 5.7.

Table 5.7: Average mixing point of the partitioning experiments.

PEG (%-w) Dextran (%-w) Lysozyme (%-w) Water (%-w)

PEG 6000 (1) 7,612 10,288 0,307 82,100PEG 6000 (2) 7,903 11,275 0,299 80,523PEG 8000 (1) 6,157 8,585 0,298 84,960PEG 8000 (2) 7,410 8,920 0,301 83,370

In Figures 5.10 to 5.12, the measured tie-lines with lysozyme can be compared with the ones

measured before, without lysozyme. For the linear and HBP, the tie-lines show no deviation from the

ones measured without lysozyme.

55

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P E G

(a) 0,3 wt % of lysozyme

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P E G

(b) 1 wt % of lysozyme

Figure 5.10: Experimental tie-lines of ATPS consisting of PEG 6000 – dextran 40 – water – lysozyme. Thevalues are presented in Tables B.16 to B.19.

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P E G

(a) 0,3 wt % of lysozyme

0 5 1 0 1 5 2 0 2 5 3 00

5

1 0

1 5

2 0

2 5

3 07 0

7 5

8 0

8 5

9 0

9 5

1 0 0


P E G

(b) 1 wt % of lysozyme

Figure 5.11: Experimental tie-lines of ATPS consisting of PEG 8000 – dextran 40 – water – lysozyme. Thevalues are presented in Tables ?? to ??.

56

0 5 1 0 1 5 2 0 2 5 3 0 3 50

5

1 0

1 5

2 0

2 5

3 0

3 56 5

7 0

7 5

8 0

8 5

9 0

9 5

1 0 0


G 2

(a) ATPS consisting of G2

0 5 1 0 1 5 2 0 2 5 3 0 3 50

5

1 0

1 5

2 0

2 5

3 0

3 56 5

7 0

7 5

8 0

8 5

9 0

9 5

1 0 0


G 3

(b) ATPS consisting of G3

Figure 5.12: Experimental tie-lines of ATPS consisting of HBP – dextran 40 – water – lysozyme. The values arepresented in Tables ?? to ??.

The partition coefficient of the lysozyme, KP , was calculated with Equation (2.2) and the TLL

using Equation (2.1).

The obtained partition coefficients for ATPS with linear polymers as phase forming components

are presented in Figure 5.13, with the correspondent deviations. One possible way to interpret the

results is to consider that each pair of points illustrating the partitioning in systems containing the

same phase forming polymers and the same lysozyme concentration, has a tendency. This way, it is

possible to observe that for a lower protein concentration, 0,3 wt %, the partition coefficient increases

with the TLL, but for a higher protein concentration, 1 wt %, the opposite occurs. In both cases, more

partitioning is observed for an increasing TLL. Furthermore, the partitioning behaviour depends on

the molar weight of the PEG used, since in the systems formed by PEG 6000 the lysozyme partitions

to the bottom but in the case of PEG 8000 it partitions to the top.

57

1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 80 , 8 00 , 8 50 , 9 00 , 9 51 , 0 01 , 0 51 , 1 01 , 1 51 , 2 01 , 2 5

Partit

ion

T L L

Figure 5.13: Partition coefficient experimentally obtained for ATPS formed by linear polymers PEG 6000 –Dextran (squares) and PEG 8000 – Dextran (triangles). The filled symbols correspond to systems with 0,3 wt %of lysozyme and the unfilled ones correspond to systems prepared with 1 wt % of lysozyme. The used data is

presented in Table B.28 of the Appendix.

It is known that the partition may be influenced by the concentrations and molecular mass of the

phase-forming polymer[65]. Moreover, the lysozyme solubility in PEG solutions decreases linearly

with the increase of PEG concentration, and the solubility is lower for a polyethylene glycol with a

higher degree of polymerization [66].

These studies are in agreement with the results obtained for the systems with 0,3 wt % of lysozyme

(filled symbols in Figure 5.13). For a higher concentration of PEG, longer TLL, a larger amount of

lysozyme partitions to the bottom phase, which can be explained by the solubility decrease in the

PEG phase. Moreover, the systems with PEG 8000 show a higher partitioning behaviour for a given

TLL: for a TLL of approximately 23 wt %, the PEG 8000 system has a KP of 1,15; for a similar TLL,

24,5 %, the lysozyme in the PEG 6000 system has a KP of 1,03.

However, the measured concentrations for the systems with 1 wt % of lysozyme were unexpected.

Although the protein shows a lower partitioning to the PEG phase when the polymer molar mass

is higher, the partition coefficient is lower than 1, which means that the lysozyme partitions to the

top phase (PEG) instead of the bottom. Also the KP decreases with longer TL, i.e., more lysozyme

partitions to the PEG phase where it has a higher amount of PEG. These results are not consistent

with the mentioned studies.

A reason for the unexpected results with a higher protein concentration may be the precipitation of

some of the protein in the interface of the systems. Since the solubility in the PEG solution was verified

in literature, a possible explanation may be a low solubility in the dextran phase. This would cause

58

the protein to precipitate when in contact with that phase, lowering the partitioning coefficient. This

effect would be more significant as the TLL increases, since then the dextran concentration increases

as well. Furthermore, in Figure 5.13 it is possible to observe a tendency of the points with higher

protein concentration, which suggests an independence from the PEG molar mass, and agrees with

the given interpretation.

Knowing the partitioning behaviour of lysozyme, a modelling attempt was made. A quaternary

LCT model in combination with the Wertheim theory was used. At this stage, the studied ATPS are

already well described by the model with the adjusted parameters presented in Section 5.2, and the

interaction and association parameters of lysozyme in a water solution are adjusted as well, and can

be found in Section 5.1. Therefore, the interaction between the lysozyme and the phase forming

polymers is what still needs to be modelled.

For each system, PEG 6000 – dextran – water and PEG 8000 – dextran – water, the partition for

one of the tie lines was adjusted. To test the model, the partitioning for the second tie line was calcu-

lated and compared to the measured value. In Figure 5.14 the results for a lysozyme concentration

of 0,3 wt % are presented.

1 5 2 0 2 5 3 0

1 , 0

1 , 1

1 , 2

Partit

ion co

efficie

nt

T L L

Figure 5.14: Partition coefficient experimentally obtained for ATPS formed by linear polymers PEG 6000 –Dextran – water and PEG 6000 – Dextran – water (filled symbols), and values calculated by the LCT+Wertheim

(unfilled symbols), for a lysozyme concentration of 0,3 wt %.

Comparing the modelling results with the experimental data regarding the systems with 0,3 wt %

of lysozyme, the model can be considered to describe the partitioning behaviour of the lysozyme in

good accordance with the experimental data. Therefore, using the LCT+Wertheim model, the phase

behaviour of quaternary systems can be described with an acceptable accuracy.

In Figure 5.15, the results for a lysozyme concentration of 1 wt % are presented. The calculated

59

results do not fit the ones obtained experimentally, which can be explained by the already mentioned

protein’s precipitation. In this work, the lysozyme concentration in the systems was chosen based

on literature information in comparable systems. In order to test the model used for higher lysozyme

concentrations, solubility measurements should be made for the conditions used in this work.

1 5 2 0 2 5 3 00 , 8

0 , 9

1 , 0

1 , 1

1 , 2

Partit

ion co

efficie

nt

T L L

Figure 5.15: Partition coefficient experimentally obtained for ATPS formed by linear polymers PEG 6000 –Dextran – water and PEG 6000 – Dextran – water (filled symbols), and values calculated by the LCT+Wertheim

(unfilled symbols), for a lysozyme concentration of 1 wt %.

Regarding the ATPS formed by HBP, a lot of precipitation was observed, and for that reason the

obtained results were not modelled, since they do not represent the real behaviour of lysozyme in

the ATPS based on G2 and G3. This problem could be solved by a test on the lysozyme solubility

in solutions with G2 and G3 polymers. The calculated lysozyme concentrations are presented in

Table 5.8

Table 5.8: Absorbance and lysozyme concentration on the top and bottom phases of ATPS containing G2. TheA correspond to systems with 0,3 wt % of lysozyme and the B to systems with 1 wt %.

A B

System 1 System 2 System 1

Top Bottom Top Bottom Top Bottom

Ameas 0,655 0,344 0,592 0,390 0,512 0,206G2 wt% 4,77E-02 6,60E-03 3,71E-02 1,32E-02 2,46E-02 3,24E-03Acalc 0,569 0,079 0,442 0,157 0,293 0,039Aest 0,086 0,265 0,150 0,233 0,219 0,167

Lysozyme wt % 0,110 0,247 0,246 0,218 1,02 0,304

As expected, in five out of the six separated phases the concentrations are lower than in the initial

prepared mixtures (Table 3.17), result of the protein precipitation. Given the obtained results for these

60

systems, no further measurements were made for ATPS containing HBP.

61

6Conclusions and Future Work

63

Within this work, the phase behaviour of ATPS composed of linear polymer (PEG 6000/PEG

8000/dextran) was analysed, as well as the novel ATPS containing branched polymers (G2/G3). The

LLE diagrams of the systems were determined by the investigation of the binodal curves and tie-lines.

The partitioning behaviour of lysozyme in the PEG 6000 – dextran – water system and PEG 8000

– dextran – water systems was investigated. Additionally, the quaternary systems containing both

lysozyme and HBP were also investigated.

With all the experimental results of the LLE, a thermodynamic calculation model with Lattice Clus-

ter Theory (LCT) combined with Wertheim theory was adjusted to describe the equilibrium of the

systems with linear and branched polymers, as well as the partitioning of the lysozyme in the linear

systems.

Parameters in the model were determined in order for the calculated results to match the experi-

mental data in the most precise way.

The obtained tie-lines have acceptable deviations to the demixing points. Reasons for these neg-

ligible deviations can be the non-complete phase separation and the non-optimized HPLC method.

Comparing the experimental and modelled results regarding the binodal curves for systems contain-

ing linear and branched polymers, it can be seen that the tie-lines of the systems containing branched

polymers have steeper tie lines, which means that the minimum required amount of polymers to form

the system is higher when using HBP. This is one disadvantage of using HBP as phase forming

components. Additionally G2 and G3 polymers are more expensive than the used linear polymers.

Therefore, in case the HBP based systems show an improvement on the partitioning of a product, an

economic analysis would have to be made in order to understand if the improvement is worth the extra

cost. Moreover, the viscosity of the formed phases has an important influence in the phase separation

time, thus viscosity measurements should be made in order to better optimize the process.

Modelling with LCT and Wertheim theory for binodal curves and tie lines can achieve a good

accordance between experimental and calculated data for the systems containing linear polymers. In

this case the association parameters are constant for both PEG 6000 and PEG 8000, and based on

literature, and the structural parameters were calculated taking into account the molar mass of the

polymers. The interaction parameters were adjusted for each polymer and compared with the ones

calculated through equations that describe a relation between the interaction parameters and the

molar mass of the interacting polymers, defined by Kulaguin Chicaroux and Zeiner. The comparison

showed that the most important deviation corresponded to the dextran – water interaction, which can

be a result of the polydispersity of this polymer.

The modelling of the systems containing HBP was made by adjusting all the interaction and as-

sociative parameters related with the G2 and G3 polymers to the obtained experimental data. The

structural parameters were defined by the polymers’ structure and the segment size was determined

based on the system containing G3, in order to adjust the tie-line slope to the experimental results.

This parameter was also used to calculate the G2 based ATPS. The binodal curve was well fitted in

both systems, although the tie-lines for the G2 system showed some deviation to the experimentally

obtained data. This can be explained by the polydispersity of the HBP, which is not considered in the

64

model.

The lysozyme partitioning in systems containing linear polymers with a low protein concentration

was also successfully modelled, using a quaternary LCT+Wertheim model. The interaction and as-

sociation parameters between lysozyme and water were adjusted to literature data. The structural

parameters were defined considering the biomolecule as a linear polymer with an amino acid per

segment. The interaction and association parameters between the lysozyme and the polymers were

determined by adjustment of the partitioning to the experimental data. The modelled partitioning

behaviour was in good accordance with the experimental data.

It was not possible to measure the lysozyme concentration in the HBP based systems, because

a part of the protein precipitated. In order to better study and compare the partitioning behaviour of

biomolecules in ATPS containing HBP, solubility measurements should be made. The binodal curve

and tie-lines were not influenced by the presence of lysozyme in any of the systems.

In further research, dispersity of the polymer can be considered in the model. This way, a higher

accuracy could be achieved. Furthermore, as in the past [13], the model was successfully applied to

calculate linear polymers based systems. Moreover in the present work it was also applied to HBP

based systems. Therefore, it can be considered that the model has great potential to help with a more

economically favourable development of novel ATPS.

65

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ALCT correction terms

XS1,kλ =

(1− 1

Mk

) [1Mk− 1

Mλ

](A.1)

XS2,kλ =

(1− 1

Mk

) [1Mk

(2b3,k + 6b4,k − 3)− 1Mλ

(2b3,λ + 6b4,λ − 3)]

(A.2)

XS3,kλ =

(1− 2

Mk+

b3,kMk

+3b4,kMk

) [1Mk

(2− b3,k − 3b4,k)− 1Mλ

(2− b3,λ − 3b4,λ)]

(A.3)

XS4,kλµ =

(M2k−5Mk−2b3,k−6b4,k+6

2Mk

) [1

MλMµ− 1

Mλ− 1

Mµ− 1

M2k

+ 2Mk

](A.4)

XS5,kλµη =

(1− 1

Mk

) [(3−3Mµ−10Mη)Mλ+(3−10Mη)Mµ+10Mη−3

3MλMµMη+

(Mλ+Mµ−1)Mk

MλMµ+(

263 −

163Mk

+ 1M2k

)1Mk− 2

(A.5)

Xε1,kλµ = 1

Mλ

(1− 1

Mk

) [2Mλ−2Mµ

+ 2b3,λ + 6b4,λ −Mλ − 1]

(A.6)

Xε2,kλ = 2

Mλ

(1− 1

Mk

)[2Mλ − b3,λ − 3b4,λ −MkMλ +Mk − 1] +

2b3,k+6b4,k−3Mk

+ 1 (A.7)

Xε3,kλ = 1

Mλ

(1− 1

Mk

)[2b3,λ + 6b4,λ −Mk + (Mk −Mλ + 2)Mλ − 3] +

3−2b3,k−6b4,k2Mk

− 12 (A.8)

Xε4,kλ = 2

Mλ

(1− 1

Mk

) [4− b3,λ − 3b4,λ +M2

λ − 4Mλ

](A.9)

Xε5,kλµ = 1

Mλ

(1− 1

Mk

) [1−Mλ−Mµ

Mµ+Mλ

](A.10)

Xε6,k =

(1− 1

Mk

)(A.11)

Xε2

1,k = 1Mk

(b3,k + 3b4,k − 1) (A.12)

Xε2

2,kλ = 1Mk

(2Mλ− b3,k − 3b4,k − 2Mk

Mλ+ 2Mk − 1

)(A.13)

Xε2

3,k = 1Mk

(2Mk − b3,k − 3b4,k − 2Mk

Mλ+ 2

Mλ− 1)

(A.14)

Xε2

4,kλ = 1Mk

(3Mλ− b3,k − 3b4,k − 3Mk

Mλ+ 7Mk

2 − 52

)(A.15)

A-1

Xε2

5,kλ = 1Mk

(b3,k + 3b4,k + 2Mk

Mλ− 2

Mλ− 3Mk + 2

)(A.16)

Xε2

6,kλ = 1Mk

(b3,k + 3b4,k − 4Mk + 4Mk

Mλ− 4

Mλ+ 3)

(A.17)

Xε2

7,kλ = 1Mk

(Mk − Mk+Mλ−1

Mλ

)(A.18)

Xε2

8,k = 1Mk

(Mk − 1) (A.19)

A-2

BExperimental data

B.0.3 Calibration

Table B.1: Calibration data for the linear polymers.

PEG6000 PEG8000 Dextran

Concentration(wt%) Area Concentration

(wt%) Area Concentration(wt%) Area

0,20555 5,60165 0,20124 5,820550,20555 5,61567 0,20286 5,56172 0,20124 5,887360,10299 2,57547 0,09907 2,46163 0,10059 2,943670,10299 2,55205 0,09907 2,48987 0,10059 2,942880,05166 1,06199 0,04979 1,01198 0,04991 1,471150,05166 1,10589 0,04979 1,00754 0,04991 1,524040,02589 0,38414 0,02459 0,29426 0,00988 0,325860,02589 0,35823 0,02459 0,29983 0,00988 0,292670,15034 4,09049 0,15177 3,87341 0,29827 8,72340,15034 4,11892 0,15177 4,02578 0,29827 8,694760,01004 0 0,01012 0,114890,01004 0,09347 0,01012 0

B-1

Table B.2: Calibration data for the HBP.

G2 G3

Concentration(wt%) Area Concentration

(wt%) Area

0,20478 3,27717 0,21071 3,782680,20478 3,55831 0,21071 4,028860,1026 1,67679 0,10004 1,820570,1026 1,67147 0,10004 1,80323

0,05092 0,74955 0,05261 0,900820,05092 0,75902 0,05261 0,893120,01106 0,16147 0,01082 0,173930,01106 0,14277 0,01082 0,17628

Table B.3: Calibration data for lysozyme.

Concentration(%wt) Absorbance

0,01073 1,56260,00572 0,84840,00245 0,38070,00127 0,26980,00798 1,2450,01027 1,530,00777 1,1880,00416 0,6540,00101 0,167

Table B.4: Calibration diagram for G2 spectrometry.

Concentration wt % Absorbance

0,0443 0,5680,0088 0,1280,0013 0,0330,1028 1,242

B.0.4 Systems without lysozyme

Table B.5: Experimental data of ATPS system PEG6000 – dextran – water, for tie-line 1.

PEG6000 Dextran Dilution factor Composition (wt%)

Area Concentration Area Concentration PEG6000 Dextran Water

TOP 2,323 0,09166 0,9890 0,03310 0,0107 8,540 3,087 88,372,317 0,09144 0,9886 0,03308

BOTTOM 0,2398 0,01947 5,654 0,1936 0,0114 1,831 16,87 81,300,3244 0,02240 5,611 0,1921

B-2




TOP 3,153 0,1204 0,4331 0,01397 0,0103 11,64 1,332 87,023,144 0,1201 0,4210 0,01355

BOTTOM 0,03372 0,01233 6,962 0,2386 0,0103 1,194 23,27 75,540,03198 0,01226 7,015 0,2404




TOP 3,561 0,1346 0,3267 0,01030 0,0103 13,11 1,016 85,873,556 0,1344 0,3338 0,01055

BOTTOM 0 0,01116 8,545 0,2931 0,0116 0,9609 25,30 73,740 0,01116 8,585 0,2945




TOP 1,320 0,05888 1,652 0,05590 0,0103 5,764 5,386 88,851,347 0,05980 1,625 0,05499

BOTTOM 0,3332 0,02462 3,546 0,1211 0,0103 2,523 11,79 85,680,4115 0,02734 3,566 0,1218




TOP 2,369 0,09531 0,6324 0,02083 0,0102 9,290 2,024 88,692,355 0,09482 0,6258 0,02060

BOTTOM 0 0,01305 5,782 0,1980 0,0107 1,223 18,51 80,260 0,01305 5,756 0,1971




TOP 2,991 0,1169 0,3466 0,01099 0,0103 11,39 1,088 87,522,995 0,1170 0,3569 0,01135

BOTTOM 0 0,01305 6,981 0,2393 0,0107 1,221 22,44 76,340 0,01305 7,020 0,2406

B-3

Table B.11: Experimental data of ATPS system G2 – dextran – water, for tie-line 1.

PEG Dextran Dilution factor Composition (wt%)

Area Concentration Area Concentration PEG Dextran Water

TOP 2,945 0,1774 0,2495 0,007650 0,0111 16,33 0,6442 83,033,046 0,1834 0,2187 0,006589

BOTTOM 0,1493 0,01283 7,512 0,2575 0,0106 1,287 24,42 74,290,1770 0,01446 7,590 0,2602




TOP 2,239 0,1359 0,4627 0,01498 0,0101 13,63 1,507 84,872,310 0,1401 0,4788 0,01554

BOTTOM 0,3581 0,02513 6,143 0,2104 0,0107 2,316 19,71 77,980,3464 0,02444 6,167 0,2113




TOP 5,508 0,2967 0,6307 0,02077 0,0203 14,97 1,023 84,015,766 0,3104 0,6297 0,02073

BOTTOM 0,4520 0,02717 13,43 0,4613 0,0202 1,574 21,08 77,340,6286 0,03658 11,43 0,3925




TOP 4,166 0,2251 0,1329 0,003637 0,0111 20,38 0,3352 79,294,225 0,2283 0,1382 0,003822

BOTTOM 0,1548 0,01133 8,383 0,2875 0,0099 1,064 28,91 70,020,1262 0,009804 8,362 0,2868




TOP 4,821 0,2600 0,9609 0,03213 0,0201 13,03 1,620 85,354,883 0,2633 0,9853 0,03297

BOTTOM 0,7063 0,04072 11,38 0,3908 0,0207 1,865 18,90 79,240,6286 0,03658 11,43 0,3925

B-4

B.0.5 Systems with Lysozyme

Table B.16: Experimental data of ATPS system PEG6000 – dextran – water with 0,3 wt% lysozyme, for tie-line1.


Area Concentration Area Concentration PEG6000 Dextran Water Lysozyme

TOP 3,307 0,1258 0,3931 0,01259 0,0105 12,05 1,214 86,42 0,32003,371 0,1280 0,4041 0,01297

BOTTOM 0,05171 0,01295 7,880 0,2702 0,0116 1,095 23,31 75,28 0,31360,03702 0,01244 7,887 0,2704




TOP 3,693 0,1392 0,3164 0,009952 0,0108 1,172 24,89 73,63 0,30913,630 0,1369 0,3347 0,01058

BOTTOM 0,04249 0,01263 7,816 0,2680 0,0108 12,79 0,9511 85,95 0,30980,04292 0,01264 7,843 0,2689

Table B.18: Experimental data of ATPS system PEG6000 – dextran – water with 1 wt% lysozyme, for tie-line 1.



TOP 3,420 0,1297 0,3618 0,01151 0,0107 12,01 1,139 85,88 0,97143,371 0,1280 0,4031 0,01293

BOTTOM 0,04939 0,01287 7,979 0,2736 0,0116 1,120 23,64 74,17 1,0740,05534 0,01307 7,980 0,2737




TOP 3,738 0,1407 0,3298 0,01041 0,0108 13,05 0,9323 84,92 1,0953,778 0,1421 0,3118 0,009794

BOTTOM 0,01498 0,01168 8,308 0,2849 0,0113 1,069 25,25 72,58 1,1020,03828 0,01248 8,330 0,2857


PEG 8000 Dextran Dilution factor Composition (wt%)

Area Concentration Area Concentration PEG Dextran Water Lysozyme

TOP 2,164 0,08818 0,7145 0,02345 0,0132 7,159 1,689 90,84 0,31232,542 0,1013 0,6511 0,02125

BOTTOM 0 0,01305 5,732 0,1969 0,0116 1,122 16,88 81,74 0,25610 0,01305 5,697 0,1957

B-5




TOP 3,420 0,1318 0,4152 0,01310 0,0102 12,85 1,262 85,58 0,30493,380 0,1304 0,4023 0,01265

BOTTOM 0 0,01305 7,572 0,2606 0,0106 1,237 24,72 73,79 0,25820 0,01305 7,586 0,2610




TOP 2,558 0,1019 0,5773 0,01870 0,0112 9,080 1,616 88,23 1,0762,542 0,1013 0,5415 0,01746

BOTTOM 0 0,01305 5,760 0,1979 0,0105 1,239 18,63 79,11 1,0210 0,01305 5,659 0,1944




TOP 3,098 0,1206 0,3329 0,01025 0,0112 11,01 0,9509 87,06 0,97813,134 0,1219 0,3459 0,01070

BOTTOM 0 0,01305 6,885 0,2368 0,0108 1,207 21,84 75,89 1,0640 0,01305 6,849 0,2355

B.0.6 Partitioning data

Table B.24: Experimental lysozyme concentration used to calculate the partition coefficients for systems withPEG 6000 - first measurement.

System S61Atop S61Abot S62Atop S62Abot S61Btop S61Bbot S62Btop S62Bbot

Abs 1,003 0,734 0,333 0,344 1,053 0,729 1,001 0,939Calc. Conc. 6,62E-03 4,75E-03 1,97E-03 2,05E-03 6,96E-03 4,72E-03 6,60E-03 6,17E-03

Dilution 33,2908 65,0054 134,1150 135,8805 149,7043 198,7671 158,7876 152,5725Phase conc. 0,258 0,271 0,264 0,278 1,049 0,947 1,049 0,942

Table B.25: Experimental lysozyme concentration used to calculate the partition coefficients for systems withPEG 6000 - second measurement.


Abs 0,294 0,343 0,260 0,312 1,053 0,729 1,133 0,758Calc. Concentration 1,70E-03 2,04E-03 1,47E-03 1,83E-03 6,96E-03 4,72E-03 7,52E-03 4,92E-03

Dilution 151,7738 132,5944 129,0917 111,4261 149,7043 198,7671 139,1991 183,6007Phase concentration 0,258 0,271 0,189 0,204 1,043 0,938 1,047 0,903

B-6

Table B.26: Experimental lysozyme concentration used to calculate the partition coefficients for systems withPEG 8000 - first measurement.




Table B.27: Experimental lysozyme concentration used to calculate the partition coefficients for systems withPEG 8000 - second measurement.




Table B.28: Experimental partition coefficients and deviation for the ATPS formed by linear polymers: PEG6000 – dextran – water and PEG 8000 – dextran – water. The partition coefficients were calculated with the

data from Tables B.24, B.25, B.26 and B.27.

S61A S62A S61B S62B S81A S82A S81B S82B

First measurement 1,020 1,051 0,899 0,899 1,003 1,191 0,952 0,917Second measurement 1,040 1,075 0,902 0,863 1,084 1,153 0,922 0,903Average 1,030 1,063 0,901 0,881 1,044 1,172 0,937 0,910Deviation 0,010 0,012 0,002 0,018 0,057 0,027 0,021 0,010

B-7

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