Experimental and Prediction Approaches to Determine

Dissociation Constants (pKa) of Amines

A Thesis

Submitted to the Faculty of Graduate Studies and Research

In Partial Fulfillment of the Requirements

For the Degree of

Master of Applied Science

in

Process Systems Engineering

University of Regina

By

Gao Liu

Regina, Saskatchewan

August, 2018

Copyright 2018: G. Liu

UNIVERSITY OF REGINA

FACULTY OF GRADUATE STUDIES AND RESEARCH

SUPERVISORY AND EXAMINING COMMITTEE

Gao Liu, candidate for the degree of Master of Applied Science in Process Systems Engineering, has presented a thesis titled, Experimental and Prediction Approaches to Determine Dissociation Constants (pKa) of Amines, in an oral examination held on August 8, 2018. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material.

External Examiner: Dr. Mohamed El-Darieby, Software Systems Engineering

Supervisor: Dr. Amr Henni, Process Systems Engineering

Committee Member: Dr. Hussameldin Ibrahim, Process Systems Engineering

Committee Member: Dr. Amgad Salama, Process Systems Engineering

Chair of Defense: Dr. James Daschuk, Kinesiology and Health Studies

i

Abstract

This research work studied the dissociation constants (pKa) of eight amines [N-(2-

Aminoethyl)-1,3-propanediamine, Bis[2-(N,N-dimethylamino)ethyl] ether, 2-

Methylpentamethylene diamine, N,N-Dimethyldipropylenetriamine, 3,3’-Diamino-N-

methyldipropylamine, 2-[2-(Dimethylamino)ethoxy]ethanol, 2-(Dibutylamino)ethanol,

and N-Propylethanolamine] within a temperature range of 298.15K – 313.15K, using the

potentiometric titration method. The thermodynamic quantities including the standard

state enthalpy change (∆H0) and the standard state entropy change (∆𝑆0) for the

dissociation process were determined via Van’t Hoff equation. The pKa values reflected

the basicity of amines and results showed that all studied amines had a stronger basicity

than methyldiethanolamine (MDEA)

The pKa values of series of amines (25 compounds) relevant to CO2 capture were

predicted based on the feedforward artificial neuron network (ANN) with the

backpropagation algorithm. Eight parameters were used as the input data, and these

parameters were divided into two categories: (a) molecular weight, critical pressure and

critical pressure as inputs that were used to identify the compound; (b) temperature and

physical properties as inputs including density, viscosity, surface tension and refractive

index that were used to correlate pKa values. An optimized architecture of 8-5-7-1 was

selected and predicted outputs were in a good agreement with targets, whose regression

coefficient was 0.99424 and mean squared error for training, validation and test process

was 2.20E-05, 0.0094 and 0.0078, respectively.

To compromise the flexibility of the ANN model, the other architecture of 6-5-7-

1 which reduced density and viscosity as inputs was selected, and it had a regression

ii

coefficient was 0.99216 and mean squared error for training, validation and test process

was 4.40E-05, 0.0045 and 0.0203, respectively.

iii

Acknowledgements

First and foremost, I would like to express my gratitude to my supervisor, Dr.

Amr Henni, for his support and guidance throughout my research. He introduced and

helped me to start my life in process systems engineering. His encourage and patience

enable me to accomplish the challenges in my research. Secondly, I wish to thank my

dear parents. Without their love, support and encouragement, I would never have enjoyed

so many opportunities. Finally, I am grateful for the generous assistance of our group

members and emotional support of my friends.

I would like to acknowledge the financial and academic support of Faculty of

Graduate Studies and Research and the Faculty of Engineering and Applied Science.

I also would like to thank my committee members for taking time to review my

thesis and giving me valuable feedback.

iv

Table of Contents

Abstract ................................................................................................................................ i

Acknowledgements ............................................................................................................ iii

Table of Contents ............................................................................................................... iv

List of Tables ..................................................................................................................... vi

List of Figures .................................................................................................................. viii

Chapter 1: Introduction ....................................................................................................... 1

1.1 General background of CO2 capture and storage (CCS) .............................. 1

1.2 Amine-based absorption for CO2 capture ..................................................... 9

1.3 The importance of pKa of amines ............................................................... 13

1.4 Scope of work ............................................................................................. 15

Chapter 2: Experimental determination and PDS prediction of pKa of amines ............... 16

2.1 Introduction ................................................................................................. 16

2.2 Chemicals and apparatus............................................................................. 17

2.3 Experimental procedure .............................................................................. 19

2.4 Results and discussion ................................................................................ 20

2.5 PDS prediction of pKa values of protonated amines and related updates ... 34

Chapter 3: Artificial Neural Network Application in pKa Predictions of Amines ........... 39

3.1 Soft modeling .............................................................................................. 39

3.2 Artificial Neural Network Overview .......................................................... 42

v

3.2.1 Feed-forward Neural Network ............................................................. 42

3.2.2 Backpropagation algorithm .................................................................. 44

3.3 Parameter selection and data collection ...................................................... 47

3.4 Modeling and Results ................................................................................. 54

3.4.1 Modeling with all input parameter ....................................................... 54

3.4.2 Modeling with reduced input parameter .............................................. 63

Chapter 4: Conclusion and Recommendations ................................................................. 71

References ......................................................................................................................... 74

Appendix A: Experimental Determination of Physical Properties of Amines ................. 80

Appendix A-1: Density Measurement .............................................................. 80

Appendix A-2: Viscosity Measurement............................................................ 81

Appendix A-3: Refractive Index Measurement ................................................ 83

Appendix A-4: Surface Tension Measurement ................................................. 84

Appendix B: Estimation of Critical Properties of Amines ............................................... 85

vi

List of Tables

Table 1. 1 Currently operating large-scale CCS plants in North America.. ....................... 5

Table 1. 2 CO2 removal targets in primary industrial process. .......................................... 8

Table 1. 3 Some commercially well-known amines used for CO2 capture ...................... 13

Table 2. 1 Molecular structures and purities of amines used in this work ........................ 18

Table 2. 2 Measured pH values of buffer solution at required temperature ..................... 19

Table 2. 3 Constants of Debye-Huckel equation at different temperature. ...................... 21

Table 2. 4 Kw and pKw ranging from 298.15K to 313.15K .............................................. 22

Table 2. 5 Determination of pKa value of MDEA at 298.15 K ........................................ 24

Table 2. 6 pKa1 values of 9 amines at different temperature ............................................ 26

Table 2. 7 pKa2 values of 5 amines at different temperature ............................................ 27

Table 2. 8 pKa3 values of 3 amines at different temperature ............................................ 27

Table 2. 9 Thermodynamic quantities for first dissociation of amines ............................. 33

Table 2. 10 Thermodynamic quantities for second dissociation of amines ...................... 33

Table 2. 11 Thermodynamic quantities for third dissociation of amines ......................... 34

Table 2. 12 Parameters for pKa prediction using PDS, new PDS and QSSG methods .... 36

Table 2. 13 Base weakening effect according to the PDS method ................................... 37

Table 2. 14 Base weakening effect according to new PDS method ................................. 38

Table 2. 15 Base weakening effect according to the QSSG method ................................ 38

Table 3. 1 Collected data information ............................................................................... 50

Table 3. 2 Critical properties of amine used in modeling ................................................. 53

Table 3. 3 Weights and biases for the first hidden layer ................................................... 58

Table 3. 4 Weights and biases for the second hidden layer .............................................. 60

vii

Table 3. 5 Weights and bias for the output layer .............................................................. 60

Table 3. 6 Performance of ANN models .......................................................................... 64

Table 3. 7 Weights and biases for the first hidden layer of the new model ...................... 68

Table 3. 8 Weights and biases for the second hidden layer of the new model ................. 69

Table 3. 9 Weights and bias for the output layer of the new model ................................. 70

Table A-1. 1 Densities of studied amines ......................................................................... 80

Table A-2. 1 Viscosities of studied amines ...................................................................... 82

Table A-3. 1 Refractive indices of studied amines ........................................................... 83

Table A-4. 1 Surface tensions of studied amines .............................................................. 84

Table B. 1 Group contribution of critical properties ......................................................... 85

viii

List of Figures

Figure 1. 1 Map of global CCS facilities in operation and under construction. ................. 4

Figure 1. 2 Diagram of primary CO2 capture technology ................................................... 6

Figure 1. 3 Flow diagram of a typical CO2 capture plant using a chemical absorbent ....... 9

Figure 2. 1 Titration curve of MDEA at different temperature ........................................ 23

Figure 2. 2 Comparison of the ionization constants of MDEA at different temperature.. 25

Figure 2. 3 ln(Ka1) vs 1/T for amines ................................................................................ 30

Figure 2. 4 ln(Ka) vs 1/T for studied amines ..................................................................... 32

Figure 3. 1 A basic structure of an ANN model ............................................................... 43

Figure 3. 2 Performance of ANN model with a single hidden layer of different number 56

Figure 3. 3 Performance of ANN model with different number of neurons in the second

hidden layer. ...................................................................................................................... 57

Figure 3. 4 pKa function fitting neural network ................................................................ 61

Figure 3. 5 Performance improvement ............................................................................. 61

Figure 3. 6 Regression plot for pKa prediction ................................................................. 62

Figure 3. 7 Error histogram ............................................................................................... 63

Figure 3. 8 Performance improvement of the new selected ANN model ......................... 66

Figure 3. 9 Regression plot of the new selected ANN model ........................................... 66

Figure 3. 10 Error histogram of the new selected ANN model ........................................ 67

1

Chapter 1: Introduction

1.1 General background of CO2 capture and storage (CCS)

Fossil fuels, including coal, petroleum and natural gas, act as crucial primary

energy and the largest portion of fossil fuel usage is to produce electricity. Nowadays,

60% of global electricity production is dependent on fossil fuel for energy generation [1].

Meanwhile, electricity production plays an important role in anthropogenic carbon

dioxide (CO2) emission, which accounts slightly more than 40% of the global CO2

emission [1-3]. Moreover, coal-fired plants contribute around 31% of global CO2

emission among all types of fossil fuels [3].

CO2 is the most influential greenhouse gas (GHG), which can trap the infrared

radiation emitted by the atmosphere and cause temperature increase. “The greenhouse

effect” can prevent the temperature of earth surface to drop below freezing, however,

increased concentration of GHG in the atmosphere is dangerous and harmful[4]. Global

warming of about 2 oC has a higher risk to cause more frequent extreme heat events,

extreme daily precipitation, more frequent low-snow years, and shifts toward earlier

snowmelt runoff over much of the western USA and Canada [5]. In 2014, CO2

concentration was reported to have an average growth of 2 ppm/s and have an

approximate increase of 40% since 1850 [5]. Even though more and more countries and

unions start to pay attention to climate issues and implement policy to reduce fossil fuel

usage, the world is not likely to transition completely away from fossil fuels in the

necessary time frames. The amount of fossil fuels burnt annually always reaches a new

record since 1992, except the only year of 2009 owing to the global recession [6]. The

ideal clean energy including solar and wind currently contributes less than 5% of gross

2

electricity generation [6]. Even though it is proposed to rise to 17% by 2040, the sector of

fossil fuels will equate to 50% and still maintain the primary sector in electricity

generation [6]. Therefore, their usage is expected to keep increasing because of a high

efficiency and low costs for power generation.

195 countries adopted the Paris Agreement at the COP 21 in Paris in December

2015 [2, 3]. The Paris Agreement targets to limit average global atmospheric temperature

increase to well-below 2 ˚C (commonly stated as 1.5 ˚C) by 2050, and meanwhile

achieve net-zero emissions which refers to a balance between emissions sources and

sinks [2, 3]. Global CO2 emissions have been increasing since 1960 and hit all-time

records in the last two years [6]. At current rates of GHG emissions worldwide without

any climate change mitigation policies, it is estimated as 20 years to exceed the 2°C limit

with 50% likelihood [5]. To avoid a 1.5 °C increase with 66% likelihood, there are only

six years left [5]. However, the world is way off track in meeting the Paris Agreement

climate goals. Due to the limitation in renewables and current high demand of fossil fuels

in widely industry, there is an urgency to deploy CO2 capture and storage (CCS)

technologies swiftly and at scale. It is predicted by International Energy Agency (IEA)

that 14% of cumulative emissions reductions by 2060 must derive from CCS to reach

Paris climate targets [6].

The idea of CO2 capture was first motivated for the economic value of CO2 gas.

CO2 is a valuable feedstock in food industry for carbonated beverage, enhanced oil

recovery (EOR) and the production of dry ice [2-4, 6]. Moreover, it became a potential

technology for mitigation of CO2 emissions and counteracting global warming.

3

Global CCS institute defines large-scale integrated CCS facilities as facilities

involving the capture, transport, and storage of CO2 at a scale of at least 800,000 tonnes

annually for a coal-based power plant or at least 400,000 tonnes annually for other

emissions-intensive industrial facilities [6]. Figure 1.1 indicates CCS facilities in

operation and under construction at large and smaller scale in the power and industry

sectors. There are 17 operating CCS plants across the United States, Canada, Norway,

Brazil and Saudi Arabia by November 2017, and these facilities have capability of

capturing more than 30 million tonnes per annum (Mtpa) [6]. In addition, 20 CCS plants

either are being in construction or in development around the world attest [6]. Other than

North America, Asia and Australia start to pay more attention to develop CCS plants. In

March 2017, China began to construct Yanchang CCS plant in Shaanxi Province, central

China [6]. This large-scale CCS construction is a milestone in China and Asia. CO2

capture will take place at two separate gasification facilities with a total CO2 capture

capacity of around 0.4 Mtpa [6]. Furthermore, China has confirmed CCS as a crucial

technology to reduce industrial greenhouse gas emissions in their provincial 13th five-

year plans and more facilities are planned across 8 provinces [6]. All of 37 CCS facilities

are estimated to be capable of capturing approximately 65 Mtpa of CO2 in total [6].

The USA and Canada dominate activity in CCS development as listed in Table

1.1. It is well known that the Terrell gas processing facility in west Texas, USA, was the

first CCS plant and captured CO2 was distributed to enhanced oil recovery since the early

1970s [6]. It can be seen that 75% of these plants began to be operated in 21th century,

which reflects the fact that CO2 reduction garner the attention and support with the social

development and CCS is one of the most promising technologies to reach this goal.

4

Weyburn-Midale plant located in Saskatchewan, Canada, is the first large-scale CCS

facility in Canada, and is an international collaborative effort between the USA and

Canada to study the CCS feasibility in EOR field [6]. In 2011, Saskpower, a provincial

owned utility of Saskatchewan, started the coal-fired Boundary Dam Power Station Unit

3 generating plant by using post-combustion CO2 capture technology [6]. Around 90% of

CO2 emission can be reduced and it reaches an annual CO2 capture capacity of 1 million

tonnes after this CCS plant became into operation in 2014 [6]. In addition, this project

had a saving of as much as 30%, which also identifies that costs for construction of an

alike facility will keep declining as more facilities come on stream [6].

Figure 1. 1 Map of global CCS facilities in operation and under construction [6].

: Power sectors; : Industry sector.

However, CCS still faces many challenges, one of the most concerned issues is

that implementation of CCS is not economically beneficial so far in general. Especially

5

CO2 capture part could contribute up to 80% of the total cost of a complete CCS system

involving capture, transportation and storage[1, 2]. For instance, the cost of electricity

could increase by 65% for post-combustion in coal-fired plants[3]. On the other hand,

current CO2 capture technologies are likely to lead a significant decrease in combustion

efficiency and the increase in electricity prices[1, 2, 4]. Therefore, there is an increasing

number of research and development (R&D) efforts focused on reducing CCS costs and

energy penalty.

Table 1. 1 Currently operating large-scale CCS plants in North America. Adapt from [6].

The heart of CO2 emission of coal-fired plants is fuel combustion, therefore, there

are three major categories to prepare the CO2 for capture according to the combustion

process: post-combustion, pre-combustion and oxy-fuel technology, as shown in Figure

Facility name Country

CO2 captured in

Mtpa

Operation

date Industry

Terrell USA 0.4-0.5 1972 Natural gas processing

Enid Fertilizer USA 0.7 1982 Fertiliser production

Shute Creek USA 7 1986 Natural gas processing

Great Plains

Synfuel Plant and

Weyburn-Midale

USA

CANADA 3 2000 Synthetic natural gas

Century USA 8.4 2010 Natural gas processing

Air Products Steam

Methane Reformer USA 1 2013 Hydrogen production

Coffeyville USA 1 2013 Fertiliser production

Lost Cabin USA 0.9 2013 Natural gas processing

Boundary Dam CANADA 1 2014 Power generation

Quest CANADA Approx. 1.0 2015 Hydrogen production

Petra Nova USA 1.4 2017 Power generation

Illinois USA 1 2017 Ethanol production

6

1.2[2, 4, 7-10]. The post-combustion technology is to remove CO2 directly from flue gas

mixture after the fuel combusts with air. The pre-combustion includes integrated

gasification combined cycle (IGCC) and means to develop a low carbon-intensive

combustion system[10]. The gasified coal is firstly transformed into hydrogen (H2) and

carbon monoxide (CO), which are called syngas together, and then CO is converted into

CO2 and is captured from H2[2, 7, 10]. The oxyfuel combustion reduces the carbon

intensity by applying pure oxygen instead of air to produce a highly-concentrated CO2

stream[2, 7, 10]. Among these capture approaches, post-combustion is the most mature

technology and has taken place commercially for decades, as it is convenient and less

costly to be retrofitted to an existing power plant[2, 10].

Figure 1. 2 Diagram of primary CO2 capture technology from various hydrocarbon-based

energy conversion processes. Taken from [10].

7

Typical separation methods include absorption, adsorption, and membrane. The

selection of CO2 separation technologies for post-combustion in power plants depends on

many factors, such as the concentration of CO2 in the gas mixture, chemical environment

of CO2 (the presence of water vapor, acid species and particulate matter) and physical

environmental of CO2 (temperature and pressure)[7, 10]. Comparing to other two

separation technologies, absorption is most mature and typically used for currently

operating power plants. According to principles of absorb process, it can be classified

into physical absorption and chemical absorption.

Absorbents of physical absorption are usually organic compounds which have a

strong ability to absorb CO2 without any chemical reaction. Typical absorbents are

methanol, polyethylene glycol ethers and ionic liquid [2, 4, 7-10]. Physical absorption is

based on Henry’s law for flue gas application, which is a sufficiently dilute system[7,

10]. Due to the mass transfer driven only by the physical process, it requires a high CO2

partial pressure and this approach is typically favoured when CO2 partial pressure is

above 1.4 MPa [11]. The main benefit of the physical absorption is the lower energy

requirement for absorbent regeneration as it can be easily achieved by flashing along with

less corrosion [2, 4, 8-11]. However, the main limits of physical absorption include

difficulty in obtaining the high CO2 removal target and relatively low rate of mass

transfer of CO2 [2, 4, 8, 10, 12].

Chemical absorption has a high rate of mass transfer of CO2 to efficiently separate

it from gas steam, as a result of additional driving force from chemical reaction [2, 4, 7,

8, 10-12]. It also requires a lower CO2 partial pressure and is usually favoured at a lower

partial pressure of 0.4-0.7 MPa [12]. The partial pressure of CO2 in a typical flue gas

8

mixture is approximately 0.012 MPa in post-combustion power plants, therefore,

chemical absorption is more applicable for CO2 capture owing to such a low CO2 partial

pressure in flue gases [10]. Moreover, comparing to physical absorption, it is able to

achieve a much lower level of CO2 concentration in treated gas by a smaller amount of

absorbent [4, 7, 11, 12]. Table 1.2 shows CO2 removal targets in some industrial process.

Table 1. 2 CO2 removal targets in primary industrial process. Adapt from [7].

Industrial process CO2 removal target

Natural Gas purification < 1% CO2

Hydrogen Manufacture < 0.1% CO2

Syn-gas for chemicals (H2/CO) <500 ppm

Coal Gasification 500 ppm

LNG Feedstock <50 ppm

Ammonia Manufacture < 16 ppm CO2 + CO

Ethylene Manufacture 1 ppm

Figure 1.3 shows a schematic process flow of a typical CO2 capture plant through

chemical absorption. The procedure can be divided into two parts as absorption and

regeneration. For absorption part, the fuel gas enters a cooler firstly to decrease its

temperature, which benefits the CO2 solubility in the chemical solution. And then cooled

gas enters the bottom of the absorber. In the absorber, feed gas contacts a counter-current

lean solution flow and CO2 is absorbed by chemical solvent, meanwhile, the lean solution

becomes rich solution as it travels down the column and leaves from the bottom of the

absorber. The treated gas leaves the absorber from its top and will undergo further

process. For regeneration part, rich solution needs be heated firstly and pumped to the top

of the stripper. In the stripper, CO2 is driven out when the rich solution travels down the

stripper because of the high temperature and low pressure inside, and it leaves the

9

stripper from the top. The lean solution is cooled and pumped back to the top of the

absorber. A lean-rich heat exchanger links absorption part and regeneration part as a

bridge. The operation pressure is around 1.0 bar and the temperatures in the absorber and

stripper are generally in the ranges of 40–60 °C and 120–140 °C, respectively [7, 10, 11].

In addition, this heat exchanger makes the process less expensive because it can reduce

the reboiler duty by recovering some heat from the lean solution.

Figure 1. 3 Flow diagram of a typical CO2 capture plant using a chemical absorbent [10].

1.2 Amine-based absorption for CO2 capture

Although it is the most mature technology and has been commercialized for many

decades, CO2 capture based on the chemical absorption still faces some problems such as

a high energy consumption in desorption and high corrosion for equipment [2, 4, 7-12].

Therefore, the selection of a chemical solvent plays a key role in CO2 capture by

chemical absorption. The ability of amines to react reversibly with CO2 makes them the

most promising candidates for commercial application for post-combustion CO2 capture

10

technology before 2030 [6]. Amines, ammonia derivatives, can be classified into primary,

secondary and tertiary amines regarding to the number of hydrogen atoms that have been

replaced on the ammonia molecule. Primary amines are amines which have only one

hydrogen atom replaced by another atom on the amino group. Similarly, secondary

amines have two hydrogen atoms replaced on the amino group and tertiary amines do not

have any hydrogen atom on the amino group. The basicity of the amino group of amines

promotes the CO2 absorption through Brønsted type acid-base reaction.

For primary and secondary amines, principal reactions occurring in the absorber are to

form zwitterion at first and then form carbamates or carbonates as shown in equation 1.1-

1.4 [13].

CO2 + R1R2NH ⇌ R1R2NH+COO- Eqn. 1.1

R1R2NH+COO- + B ⇌ R1R2NCOO- + BH+ Eqn. 1.2

The overall reactions:

CO2 + R1R2NH ⇌ R1R2NCOOH Eqn. 1.3

R1R2NCOOH + R1R2NH ⇌ R1R2NCOO- + R1R2NH2+ Eqn. 1.4

For tertiary amines, they react with CO2 in a different way since nitrogen has

bonds with three substitute groups and is not available to form carbamates. Instead, they

react with CO2 and produce bicarbonates, as shown in equation 1.5 [2, 4].

CO2 + R1R2R3N + H2O ⇌ R1R2 R3NH+ + HCO- Eqn. 1.5

11

Amines have different number of amino groups also can be classified into

different categories, in which way amines containing one, two or three amino groups are

called mono-, di-, or triamine. As nitrogen atoms in amino groups act as reactive centers,

polyamines will react with more amount of CO2 and result in improving the efficiency of

CO2 removal. Moreover, alkanolamines, who have at least one hydroxyl group, are a set

of amines commonly regarded as the most promising amines for post-combustion CO2

capture. Hydroxyl group can not only improve the solubility of amines in water, but also

reduce their vapor pressure [4]. Most widely investigated and commercially used

alkanolamines for CO2 chemical absorption include monoethanolamine (MEA),

diethanolamine (DEA), methyldiethanolamine (MDEA) and 2-amino-2-methyl-1-

propanol (AMP) [2, 4, 7-12, 14]. However, these conventional amines have some

shortcomings. MEA, a benchmark primary amine, has limited CO2 absorption capacity

(CO2 loading) known as 0.5 mole of CO2 per mole of amine [4, 10, 14-17]. Meanwhile,

they require more energy to be regenerated [18]. MDEA has a greater CO2 absorption

capacity (1.0 mole of CO2 per mole of amine) and much lower heat requirement for

regeneration, while it has drawback on a 1.3-4.0 times lower reaction rate with CO2 as

compared to MEA [14]. As it is a tertiary amine, MDEA absorbs CO2 by promoting the

hydrolysis of CO2 in formation of bicarbonates instead of the direct chemical reaction

with CO2 [4, 13, 14]. AMP is a sterically hindered amine, and directly reacts with CO2

and produce carbamate at first. The product through this reaction step is very unstable

and readily undergoes further hydrolysis that results in the formation of a bicarbonate

[10]. Recently, the group of Dr. Rochelle focus on the research of piperazine (PZ) and its

derivatives application for CO2 capture [14-17]. Piperazine is a sterically hindered

12

diamine, and it has a much greater CO2 absorption ability as compared to all other

conventional amines. However, the low solubility (14 wt% at 20 oC) of piperazine in

water challenges its application in large scale of plants [14]. Table 1.3 lists structures of

amines mentioned above.

Along with the capital cost of post-combustion facility, operation costs are related

certain factors, such as initial solvent cost, heat duty, solvent volatility and degradation

and equipment experience with corrosion, foaming or other operating problems.

According to the US DOE CO2 capture goal, a 90% CO2 capture efficiency with a less

than 35% increase in cost is needed to achieve for post-combustion [19]. On the other

hand, the toxicity and influence on environment of amines should also be taken into

consideration. Therefore, intensive R&D work focuses on the investigation of amine-

based solvents (single or blended) with both good physical and chemical properties. For

example, a desired solvent should have a high CO2 capacity and kinetic rate, low to

moderate viscosity, stable thermal and chemical properties, and less toxicity and

influence on environment.

13

Table 1. 3 Some commercially well-known amines used for CO2 capture

Chemical Type Structure

Monoethanolamine

(MEA)

Primary

Diethanolamine

(DEA)

Secondary

Methyldiethanolamine

(MDEA)

Tertiary

2-amino-2-methyl-

propanol

(AMP)

Sterically hindered

Piperazine

(PZ)

Cyclic

1.3 The importance of pKa of amines

Brønsted-Lowry theory of acid and bases defined a base is a species having a

tendency to accept a proton, therefore, for every base, B, has the relationship with its

conjugate acid, BH+ as shown in equation 1.6 [20, 21]:

BH+ ⇋ H+ + B Eqn. 1.6

For amine-based absorption, CO2 reacts with water and produces bicarbonate ion

and carbonate ion as shown in equation 1.7 and 1.8. As the presence of H3O+, it promotes

the formation of protonated amines as represented in equation 1.9 [14, 17].

2H2O + CO2 ⇋ H3O+ + HCO3− Eqn. 1.7

HCO3− + H2O ⇋ H3O+ + CO3

2− Eqn. 1.8

R1R2R3NH+ + H2O ⇋ H3O+ + R1R2R3N Eqn. 1.9

14

Acid dissociation constant, Ka, quantitatively reflects the strength of an acid in

solution. It is given by the thermodynamic equilibrium constant for a dissociation

reaction in the context of acid-base reactions. For an amine, Ka of its conjugate acids,

BH+, is generally used to represent the basicity of this amine. According to equation 1.6,

Ka of BH+ can be expressed in equation 1.10 [20, 21]:

Ka={𝐻+}{𝐵}

{𝐻𝐵+} Eqn. 1.10

Where {} represents the activity of each ionic species. Since the activity of a

species can be represented as the product of its activity coefficient (γ) and concentration,

equation 1.10 can be derived into 1.11 [20, 21].

Ka=[𝐻+][𝐵]

[HB+]×

γH+𝛾𝐵

γHB+ Eqn. 1.11

In general, Ka is a clumsy number as its calculation involves complicated

numbers, thus it has become customary to represent the Ka by its negative logarithm and

this new represent is called pKa. Finally, pKa is calculated in the form as shown in

equation 1.12 [20, 21].

pKa = pH + log[BH+]γB

[B]γHB+ Eqn. 1.12

As it is said above, pKa of conjugate acid of an amine is a quantitative measure of

the strength its strength to release a proton in solution, thus the greater the pKa value, the

weaker the substance as an acid. In other word, amine has greater basicity if its conjugate

acid has a higher pKa value.

15

Numerous studies about pKa have been done to help researchers understand the

behavior of substances in chemical reactions. These knowledges have great help in many

fields, such as spectrophotometry, pharmacology, organic synthesis and analytical

chemistry [20, 21]. Absolutely, pKa also plays a crucial role in the screen of amines by

investigating the performance of amines in CO2 capture process. Sharma et al. reported

the relationship between pKa of some amines and rate constants in CO2 capture for power

generation [22]. Versteeg et al. found the linear correlation between the logarithm of

second order rate constants in formation of zwitterion and pKa of amines [23]. Sumon et

al. studied the relationship between activation energies of amines and pKa [24]. Aboaba et

al. correlated the absorption kinetic constant of CO2 into some tertiary amines with their

pKa [25].

1.4 Scope of work

In this work, pKa of conjugate acids of 8 novel amines from 25 oC to 40 oC with a

5 oC-increment has been experimentally measured by potentiometric titration. Along the

experimental method, artificial neural network (ANN) was applied to establish a model

that can be used to predict pKa of amines and compared to existing PDS method and its

updates. To assist the prediction of pKa values, several physical properties of 8 amines

have also been experimentally measured in the same temperature range.

16

Chapter 2: Experimental determination and PDS prediction of pKa of amines

2.1 Introduction

Typical methods to determine pKa include potentiometric titration, ultraviolet

spectrophotometry, conductimetric titration and magnetic resonance [20]. Among these

methods, potentiometric titration is the most convenient and widely used in the pH range

of 2.00 to 11.00 [20, 26, 27]. In general, determination of pKa can be finished in 20

minutes through pH measurement by using a pH meter [20]. A pH meter consists of one

reference electrode and one pH electrode. The reference electrode has a known and

constant potential, while the potential of pH electrode is changeable with the

thermodynamic activity of hydrogen ions in solution [20]. The circuit in the cell is

complete via two electrodes and activity of hydrogen ions can be measured through the

potential difference between two electrodes [20]. The potential between two electrodes is

detected by a potentiometer, and there is a relationship between the potential and activity

of hydrogen ions derived from Nernst equation, as shown in equation 2.1 [20].

E = −RT

Fln {H+} Eqn. 2.1

Where E is potential in volt, T is the absolute temperature in Kelvin, R is the gas

constant and F is the Faraday.

For instance, pH of the solution at 25 oC is calculated in the form of equation 2.2

[20].

pH = log{H+} =Ecell−Eref

0.0592 Eqn. 2.2

17

The potential is sensitive of temperature as indicated in equation 2.1, therefore, it

is essential to do the calibration of electrodes at each target temperature for an accurate

measurement [20, 26, 27].

2.2 Chemicals and apparatus

Nine amines used in this work were purchased from Sigma-Aldrich Canada.

MDEA was used to validate the instrument and experiment method by comparing results

with literature. Hydrochloric acid (HCl) of 0.10 mol/L as the titrant was purchased from

VWR International. Table 2.1 lists detailed information of 9 amines including their

molecular structures and purities. A pH meter of model 270 pH/ion/conductivity/titration

controller manufactured by Denver Instrument was used to determine pH values. The pH

meter was calibrated at each required temperature by using buffers with pH values of

4.00 (± 0.01), 7.00 (± 0.01), and 10.00 (± 0.01), respectively. The buffer solutions were

supplied by VWR International and their measured values at required temperature were

listed in Table 2.2. A jacket beaker connected to a water bath with a thermostat controller

was used to make the solution reach the required temperature keep it steady during the

experimental procedure. In order to prevent chemical reaction between amines and tiny

amount of CO2 in the air, ultra-high purity (≥ 99.99%) nitrogen purchased from Praxair

was used to blanket the solution throughout the potentiometric titration.

18

Table 2. 1 Molecular structures and purities of amines used in this work

Structure Chemical Name CAS

Number

Purity

Methyldiethanolamine

(MDEA)

105-59-9 99%

N-(2-Aminoethyl)-1,3-

propanediamine

(n-2AOE13PDA)

13531-52-7 97%

Bis[2-(N,N-dimethylamino)ethyl]

ether

(2DMAOEE)

3033-62-3 97%

2-Methylpentamethylene diamine

(2-MPMDA)

15520-10-2 99%

N,N-Dimethyldipropylenetriamine

(DMAPAPA)

10563-29-8 99%

3,3′-Diamino-N-

methyldipropylamine

(DAOMDPA)

105-83-9 96%

2-[2-(Dimethylamino)ethoxy]ethanol

(DMAOEOE)

1704-62-7 98%

2-(Dibutylamino)ethanol

(DBEA)

102-81-8 99%

N-Propylethanolamine

(PEA)

16369-21-4 98%

19

Table 2. 2 Measured pH values of buffer solution at required temperature

Temperature (K)

pH

Buffer 1 Buffer 2 Buffer 3

298.15 4.00 ± 0.01 7.00 ± 0.02 10.00 ± 0.02

303.15 4.01 ± 0.01 6.99 ± 0.02 9.94 ± 0.03

308.15 4.02 ± 0.02 6.99 ± 0.02 9.90 ± 0.03

313.15 4.02 ± 0.02 6.97 ± 0.02 9.85 ± 0.03

2.3 Experimental procedure

Before running each experiment, the reliability of the pH meter was checked by

calibrating with three standard buffer solutions with known pH values. The desired

temperature was achieved by adjusting the thermostatic controller, until the actual

detected temperature of solution in the jacket beaker reached the required temperature.

The fresh aqueous solution of amines with a concentration of 0.01 mol/L were

prepared at the beginning of every measurement with double distilled water made from

the laboratory. After 50 mL of the dilute solution of an amine was transferred into the

jacket beaker, a piece of parafilm was immediately used to cover the top of the beaker. In

addition, a slow stream of ultra-high purity N2 was introduced into the beaker to prevent

the amine solution from the contamination of trace CO2 in the air. However, it should be

noticed that the outlet of N2 must be above the solution and the stream of N2 should be

controlled to blow the solution very gently.

20

For monoamines including MDEA, DMAOEOE, DBEA and PEA, ten portions of

0.5 mL of HCl were gradually added into the amine solution. The pH value was recorded

once the reading got stable. In order to prevent carryover contamination of the tested

solution, the pH electrode was thoroughly rinsed with deionized water and softly wiped

dry via kimiwipes between two experimental runs. Three runs were repeated for one

target amine at one desired temperature and the average of their calculated pKa values

was reported. For diamines including 2DMAOEE and 2-MPMDA, twenty portions of 0.5

mL of HCl were used for titration. Thirty portions of 0.5 mL of HCl were titrated for

triamines including n-2AOE13PDA, DMAPAPA and DAOMDPA.

2.4 Results and discussion

The method used to obtain the pKa values of MDEA, 2DMAOEE and

DMAPAPA from experimental work will be explained in this section, and the similar

procedure was used to calculate the pKa values of other amines including monoamines,

diamines and triamines.

MDEA in aqueous solution can ionize into protonated MDEA (MDEAH+) as

shown in equation 2.3, and pKa of MDEAH+ can be written in the form of equation 2.4.

Equation 2.4 is valid under the assumption that ionic strength of the solution is zero,

which means the solute is infinite dilute [20]. For a more accurate pKa result, calculated

pKa through equation 2.4 needs be corrected by taking effects of activity coefficients into

consideration [20]. Debye-Huckel equation is used to calculate the activity coefficient of

the ionized species (𝛾𝐵𝐻+), as shown in equation 2.5 [20]. Finally, corrected pKa (pKaT) is

calculated as shown in equation 2.6 by combining equation 2.4 with 2.5.

MDEA + H3O+ ⇋ MDEAH+ + H2O Eqn. 2.3

21

pKa = pH + log[MDEAH+]

MDEA Eqn. 2.4

-log(𝛾𝐵𝐻+) =

AZi2I0.5

1+BkiI0.5 Eqn. 2.5

pKa𝑇 = pH + log[MDEAH+]

MDEA

𝐴𝑍𝑖2𝐼0.5

1+𝐵𝑘𝑖𝐼0.5 Eqn. 2.6

Where A and B are constants of the Debye-Huckel equation, which is dependent

on dielectric constant and temperature, Zi is the charge of the ion, and ki is the ionic size

parameter, which represents the mean distance of approach of the ions. A and B can be

obtained from the literature and summarized in Table 2.3 [28]. k0 is also found in

literature as 4.5 × 10-8 cm [29].

Table 2. 3 Constants of Debye-Huckel equation for aqueous solution at temperature

ranging from 298.15K to 313.15K. Taken from [28].

Temperature (K) A (mol-1/2L1/2) B (× 108 cm-1)

298.15 0.5092 0.3286

303.15 0.5141 0.3297

308.15 0.5190 0.3307

313.15 0.5241 0.3318

The ionic strength (I) is defined in equation 2.7 [20],

I=0.5Σ(CiZi2) Eqn. 2.7

Where Ci is molarity of an ion species and Zi is its charge.

22

When titrant HCl solution was added into MDEA solution, there was a charge

balance as shown in form of equation 2.8 [26].

Charge balance: CH+ + CMDEAH+ = COH− + CCl− Eqn. 2.8

In the mixture solution, the ionic strength can be calculated as shown in equation

2.9 by substituting equation 2.8 into equation 2.7 [26].

I= 0.5 (CH+ × 12 + CMDEAH+ × 12 + COH− × 12 + CCl− × 12)

= 0.5(CH+ + CMDEAH+ + COH− + CCl−)

= COH− + CCl− Eqn. 2.9

The concentration of OH- is insignificant and can be negligible if the pH remains

between 4 and 10 when 0.01 M solution is being titrated [20]. Otherwise, it can be

calculated through equation 2.10, and equilibrium constants (Kw) for ionization of water

at different temperature are listed in Table 2.4.

COH− = 10pKw−pH Eqn. 2.10

Table 2. 4 Kw and pKw ranging from 298.15K to 313.15K. Taken from [30].

Temperature (K) Kw× 1015 pKw

298.15 9.91 14.00

303.15 14.39 13.84

308.15 20.42 13.69

313.15 28.51 13.54

23

Combining all calculation together, pKa values of MDEA are determined, and an

example of pKa of MDEA at 298.15 K is shown in Table 2.5. Figure 2.1 shows the

titration curve of MDEA.

Figure 2. 1 Titration curve of MDEA at different temperature

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0

pH

Volume of titrant HCl (mL)

298.15K

303.15K

308.15K

313.15K

24

Table 2. 5 Determination of pKa value of MDEA at 298.15 K

Titrant 0.1 M

HCl (mL)

pH [MDEAH+]

[MDEA] log

[MDEAH+]

[MDEA]

Thermodynamic

correction

pKa

0.0 10.21 - - - -

0.5 9.50 0.11 -0.95 -0.02 8.53

1.0 9.18 0.25 -0.60 -0.02 8.56

1.5 8.94 0.43 -0.37 -0.03 8.54

2.0 8.76 0.67 -0.18 -0.03 8.55

2.5 8.56 1.00 0.00 -0.03 8.53

3.0 8.41 1.50 0.18 -0.03 8.56

3.5 8.22 2.33 0.37 -0.04 8.55

4.0 7.99 4.00 0.60 -0.04 8.55

4.5 7.63 9.00 0.95 -0.04 8.54

5.0 3.81 - - - -

Average 8.55

Van’t Hoff equation, equation 2.11, describes the relationship between ionization

constant (Ka), the standard state enthalpy change (∆H0) and standard state entropy

change (∆𝑆0) [13]. According to Van’t Hoff equation, it can be found ln(Ka) has a linear

relationship with 1/T. Therefore, ln(Ka) vs 1/T is plotted in Figure 2.2 and compared with

data in literature. ln(Ka) of MDEA has an average absolute percentage deviation

(AAD%) of 0.18% with Rayer [26], 0.20% with Tagiuri [27], 0.16% with Kamps [31],

0.35% with Kim [13], and 0.10% with Littel [32]. Results are in a good agreement with

25

literature. Dissociation constants of 8 protonated amines and MDEA were calculated by

following procedure described before, and final results were summarized in Table 2.6 to

2.8.

ln(Ka)= −∆H0

RT+

∆S0

R Eqn. 2.11

Figure 2. 2 Comparison of the ionization constants of MDEA at temperature ranging

from 298.15 K to 313.15 K.

26

Table 2. 6 pKa1 values of 9 amines at different temperaturea

Chemical

pKa1

298.15K 303.15K 308.15K 313.15K

Methyldiethanolamine

(MDEA)

8.55 8.48 8.37 8.32

N-(2-Aminoethyl)-1,3-propanediamine

(n-2AOE13PDA)

10.25 10.18 10.04 9.94

Bis[2-(N,N-dimethylamino)ethyl] ether

(2DMAOEE)

9.60 9.49 9.42 9.37

2-Methylpentamethylene diamine

(2-MPMDA)

10.62 10.44 10.27 10.10

N,N-Dimethyldipropylenetriamine

(DMAPAPA)

10.38 10.25 10.13 9.99

3,3′-Diamino-N-methyldipropylamine

(DAOMDPA)

10.45 10.31 10.17 10.08

2-[2-(Dimethylamino)ethoxy]ethanol

(DMAOEOE)

9.05 8.96 8.85 8.74

2-(Dibutylamino)ethanol

(DBEA)

9.87 9.72 9.61 9.45

N-Propylethanolamine

(PEA)

9.83 9.68 9.56 9.42

27

Table 2. 7 pKa2 values of 5 amines at different temperaturea

Chemical

pKa2

298.15K 303.15K 308.15K 313.15K

n-2AOE13PDA 8.74 8.61 8.47 8.27

2DMAOEE 7.90 7.85 7.74 7.70

2-MPMDA 9.07 8.92 8.73 8.56

DMAPAPA 8.86 8.73 8.61 8.47

DAOMDPA 9.13 9.02 8.88 8.77

Table 2. 8 pKa3 values of 3 amines at different temperaturea

Chemical

pKa3

298.15K 303.15K 308.15K 313.15K

n-2AOE13PDA 5.38 5.26 5.18 5.05

DMAPAPA 6.78 6.67 6.56 6.41

DAOMDPA 6.32 6.28 6.21 6.15

aStandard uncertainty: u(pKa) = 0.02; u(T) = 0.01 K with the level of confidence at 0.95.

28

From Table 2.6 to 2.8, it could be observed that basicity of amines was sensitive

to temperature and pKa values of protonated amines decreased with a temperature

increase. ln(Ka) versus 1/T was plotted in Figure 2.3 to calculate the standard state

enthalpy change and standard state entropy change by using Van’t Hoff equation, and

results were listed in Table 2.9 to 2.11. The high heat duty is a most challenge in CO2

capture application, therefore, the heat of absorption/regeneration plays an important role

in evaluation of the amine systems performance [13, 26, 27]. In general, tertiary amines

have lower enthalpy change than primary and secondary amines, which suggests lower

heat requirements in the regeneration process of amines.

Meanwhile, the basicity of amines can also be compared apparently through

Figure 2.3 and 2.4. As defined in previous section, pKa is the minus logarithm of Ka,

therefore, ln(Ka) will be negative for compounds. As a consequence, ln(Ka) value will be

lower when an amine has a higher pKa value, in another word, an amine has a stronger

basicity when its ln(Ka) value is lower. Figure 2.3 compared the basicity of primary

amines with MEA, secondary amine with DEA and tertiary amines with MDEA. It can be

noticed that every target amine has a stronger basicity than the commercial amine in the

same amine category, which was desirable. And for polyamines, their second and third

dissociation abilities were also compared in Figure 2.4(b) and 2.4(c), respectively.

29

(a)

(b)

30

(c)

Figure 2. 3 ln(Ka1) vs 1/T for amines (a) primary amines; (b) secondary amines; and (c)

tertiary amines

31

(a)

(b)

32

(c)

Figure 2. 4 ln(Ka) vs 1/T for studied amines. (a) ln(Ka1) for all studied amines (b) ln(Ka2)

for diamines and triamines (3) ln(Ka3) of triamines.

33

Table 2. 9 Thermodynamic quantities for first dissociation of amines in aqueous solutiona

Solvent -∆𝑟𝐺𝑚0 (kJ∙ mol-1) ∆𝑟H𝑚

0 (kJ∙ mol-1) ∆𝑆0 (kJ∙mol-1∙K-1)

MDEA 49.73 34.85 -0.05

n-2AOE13PDA 55.04 49.08 -0.02

2DMAOEE 53.90 27.07 -0.09

2-MPMDA 65.25 62.27 -0.01

DMAPAPA 60.48 45.57 -0.05

DAOMDPA 53.19 44.25 -0.03

DMAOEOE 52.76 37.85 -0.05

DBEA 58.55 37.68 -0.07

PEA 56.43 47.49 -0.03

Table 2. 10 Thermodynamic quantities for second dissociation of amines in aqueous

solutiona

Solvent -∆𝑟𝐺𝑚0 (kJ∙ mol-1) ∆𝑟H𝑚

0 (kJ∙ mol-1) ∆𝑆0 (kJ∙mol-1∙K-1)

n-2AOE13PDA 48.66 54.62 0.02

2DMAOEE 46.04 25.17 -0.07

2-MPMDA 52.82 61.76 0.03

DMAPAPA 51.11 45.15 -0.02

DAOMDPA 52.97 44.03 -0.03

34

Table 2. 11 Thermodynamic quantities for third dissociation of amines in aqueous

solutiona

Solvent -∆𝑟𝐺𝑚0 (kJ∙ mol-1) ∆𝑟H𝑚

0 (kJ∙ mol-1) ∆𝑆0 (kJ∙mol-1∙K-1)

n-2AOE13PDA 31.80 37.76 0.02

DMAPAPA 37.40 43.36 0.02

DAOMDPA 35.78 20.87 -0.05

aStandard uncertainties: u(-∆𝑟𝐺𝑚0 )=0.05; u(∆𝑟H𝑚

0 ) = 0.05; u(∆𝑆0 ) = 0.05 with the level

of confidence at 0.95.

2.5 PDS prediction of pKa values of protonated amines and related updates

Perrin, Dempsey and Serjeant established a computer-free group addition method

(the PDS method) for pKa values prediction of acids and bases in 1981, which only

applied a table of fixed pKa base values depending on types of amino groups and ∆pKa

linearly additive functional-group corrections [21]. Unlike computational methods, the

PDS method is very simple to use and can obtain results with an acceptable accuracy.

The PDS prediction was based on linear free energy relationships through analogy,

extrapolation and interpolation from existing experimental data within particular classes

of substances [21]. Sumon et al. updated parameter values (new PDS method) through a

least-squares fits to experimental pKa values of 32 amine-training set [33]. Qian et al.

updated parameters (QSSG method) by taking additional factors into consideration,

including steric hindrance, solvent, intramolecular hydrogen bonding and δ-p

hyperconjugation [34]. Table 2.12 listed parameters used for original PDS, new PDS and

QSSG method, and their difference among them can be observed directly [34]. The

predicted pKa values of 8 target amines along with MDEA were summarized in Table

35

2.13 to 2.15, using PDS, new PDS and the QSSG method. The root-mean-square (rms)

errors for 9 amines were 0.29, 0.24, and 0.24, respectively. It can be found that both new

PDS and QSSG reduced rms error as compared with original PDS method. In addition,

QSSG did not have further improvement about these 9 amines as compared with new

PDS method, because studied amines did not have those functional groups that were

taken into consideration for updated parameters in the QSSG method, in another word,

new added factors were calculated as 0 during the pKa prediction.

36

Table 2. 12 Parameters for pKa prediction using PDS, new PDS and QSSG methods.

Taken from [34]

Terms Functional group PDS

values

New PDS

values

QSSG

values

Base value Primary amino NH2R 10.77 10.60 10.60

Secondary amino NHR2 11.15 11.10 10.80

Tertiary amino NR3 10.50 10.60 10.60

∆pKa shifts each CH3 on tertiary N -0.2 -0.2 -0.2

each CH3 on primary and

secondary N

-0.2 -0.2 0

each β OR -1.2 -1.4 -1.3

each β NH2 -0.8 -0.9 -0.9

each β NHR -0.9 -1.0 -0.8

each β NR2 -0.9 -1.0 -1.0

each β OH -1.1 -1.0 -1.0

each γ group +0.4Δβ +0.4Δβ +0.6Δβ

each δ group +0.4Δγ +0.4Δγ +0.6Δγ

each ε OH group 0 0 +0.6Δγ

ring effect +0.2 0 +0.2

if two equivalent N sites +0.3 +0.3 +0.3

β- CH(CH3)2 - - -0.3

β-C(CH3)3 -0.45

37

Terms Functional group PDS

values

New PDS

values

QSSG

values

∆pKa shifts solvent effects (CH2CH2OH)2 +0.3

solvent effects (CH2CH2OH)3 +0.6

steric effects of cyclic tertiary

amine

-0.5

intramolecular H bonding +0.2

Table 2. 13 Base weakening effect according to the PDS method

Chemical Amine

type

Base

value

N-Me β-OR β-OH γ -

group

PDS error

MDEA 3 10.50 -0.2 0 -2.2 0 8.1 0.44

n-2AOE13PDA 1 10.77 0 0 0 -0.36 10.41 -0.16

2DMAOEE 3 10.50 -0.4 -1.2 0 0 9.20 0.40

2-MPMDA 1 10.77 0 0 0 0 10.77 -0.15

DMAPAPA 1 10.77 0 0 0 -0.36 10.41 -0.03

DAOMDPA 1 10.77 0 0 0 -0.36 10.71 -0.26

DMAOEOE 3 10.50 -0.4 -1.2 0 0 8.90 0.15

DBEA 3 10.50 0 0 -1.1 0 9.40 0.47

PEA 2 11.15 0 0 -1.1 0 10.05 -0.22

rms error 0.29

38

Table 2. 14 Base weakening effect according to new PDS method

Chemical Amine

type

Base

value

N-Me β-OR β-OH γ -

group

New

PDS

error

MDEA 3 10.60 -0.2 0 -2.0 0 8.40 0.15

n-2AOE13PDA 1 10.60 0 0 0 -0.40 10.20 0.05

2DMAOEE 3 10.60 -0.4 -1.4 0 0 9.10 0.50

2-MPMDA 1 10.60 0 0 0 0 10.60 0.02

DMAPAPA 1 10.60 0 0 0 -0.40 10.20 0.18

DAOMDPA 1 10.60 0 0 0 -0.40 10.50 -0.05

DMAOEOE 3 10.60 -0.4 -1.4 0 0 8.80 0.25

DBEA 3 10.60 0 0 -1.0 0 9.60 0.27

PEA 2 11.10 0 0 -1.0 0 10.10 -0.27

rms error 0.24

Table 2. 15 Base weakening effect according to the QSSG method

Chemical Amine

type

Base

value

N-

Me

β-

OR

β-

OH

γ-

group

ε-

OH

QSSG error

MDEA 3 10.60 -0.2 0 -2.0 0 0 8.70 -0.15

n-2AOE13PDA 1 10.60 0 0 0 -0.48 0 10.12 0.13

2DMAOEE 3 10.60 -0.4 -1.3 0 0 0 9.20 0.40

2-MPMDA 1 10.60 0 0 0 0 0 10.60 0.02

DMAPAPA 1 10.60 0 0 0 -0.48 0 10.12 0.26

DAOMDPA 1 10.60 0 0 0 -0.60 0 10.30 0.15

DMAOEOE 3 10.60 -0.4 -1.3 0 0 -0.22 8.68 0.37

DBEA 3 10.60 0 0 -1.0 0 0 9.60 0.27

PEA 2 10.80 0 0 -1.0 0 0 9.80 0.03

rms error 0.24

39

Chapter 3: Artificial Neural Network Application in pKa Predictions of Amines

3.1 Soft modeling

Even though pKa values can be measured experimentally in most cases, it does

cost and is time consuming. Especially researchers often have interest in the pKa values

of compounds that have not been synthesized yet. Therefore, there is a need to predict

pKa in advance to save effort, and numerous studies took attempts and focused on

improvements of prediction accuracy within recent decades.

Computational chemistry is most widely used for developments of pKa

calculation. Four factors play key roles in calculations, including a thermodynamic cycle

that relates the gas phase to the solution phase, relevant experimental values, and accurate

calculations for both gas-phase and solvation [35]. The pKa of a base is related to the

overall Gibbs free energy change (∆Gaq) of the proton-transfer reaction in aqueous

solution (equation 3.1), and the relation is written as equation 3.2 [35]. The key point of

pKa prediction is to predict ∆Gaq with high accuracy.

BH+(aq) + H2O ⇋ B(aq) + H3O

+ Eqn. 3.1

pKa = ∆Gaq

RTln10 Eqn. 3.2

Where R is gas constant and T is temperature in K.

Khalili et al. predicted the pKa values of 17 amines with an assist of Gaussian 03

software [36]. The B3LYP and MP2 levels of theory with 6-311++G** basis set were

used for geometry optimization and energy calculations [36]. Solvent effects were

computed using the IEFPCM method. In their recommendation for pKa values prediction

of amines, one explicit water molecule was added into the continuum cavity of the solute

40

molecule [36]. It introduced hydrogen bonding effects in the PCM model, and deviation

of pKa prediction could reach 0.68 pKa unit [36].

Sumon et al. simplified the procedure for both Gaussian 03 and Gaussian 09 users

based on the method established by Khalili et al. (the KHE method) as follows [37]: a)

Instead fitting parameter of G(aq)(H+) in the KHE method, they used a constant of -270.3

kcal/mol by adopting the sum of G(g)(H+, 1 atm) = -6.3 kcal/mol with ∆solvG(H+, 1 atm

gas→1 M aqueous solution) = -264.0 kcal/mol; b) they reduced the basis set from triple

to double zeta to compromise the accuracy and calculation speed; c) they neglected

effects of the statistical entropy which was less thn 1 kcal/mol and replaced ΔhEnuc,int with

the constant -9.4 kcal mol/L to eliminate the need for gas-phase opt+freq calculations. In

summary, the new method, SHE method, is to compute equation 3.3, and it had an rms

error of 0.28 for a training set of 32 amines [37].

pKa = (1/1.3643) [ –270.3 + Eel(B·H2O) – Eel(BH+·OH2) – 9.4] + C Eqn. 3.3

Where the Eel(B.H2O) and Eel(BH+·OH2) are MP2 energies, converted to kcal

mol/L (times 627.50955), from the bottom of Gaussian logfiles (“MP2=”) of SCRF=

(PCM, Gaussian 03 Defaults) MP2/6-31G(d) geometry optimizations of maximally trans

conformers. The C value was -1.7 for cyclic amines and -0.7 for acyclic amines,

respectively.

However, it still has limits and is challenging to predict pKa values of larger

molecules, since it requires the high level of calculation in order to obtain accurate

results. For instance, the Gibbs energy change for the solution dissociation equilibrium

needs to be determined within ±1.36 kcal/mol so that a pKa value accurate to ±1 pKa unit

41

could be derived [35]. PDS method and related updates which were discussed in chapter

2 were all based on the mathematical relation that is called a quantitative structure-

property relationship (QSPR). Regarding the molecular structure, the variation of pKa

values could be tied numerically to the behavior of a molecule dissociation [35]. The

descriptors (numerically encode electronic effects and contributions of different

substituents) were usually obtained through multiple linear regression (MLR) or least-

squares fit based on intensive experimental database [35].

ANN is one of artificial intelligence, which is inspired by human brain and aim to

process information in a ‘soft’ modeling way without the need to establish a

mathematical model [38, 39]. Therefore, the advantage of ANN over traditional fitting

models is its flexibility and ability to recognize nonlinear relationship in complicated

systems without prior knowledge of an existing model, and it becomes more and more

popular in solving scientific and engineering problems [38-43].

Habibi-Yangjeh et al. combined QSPR with ANN and successfully predicted pKa

values of various benzoic acids and phenols at 25 oC [41]. A three-layer feed forward

ANN with back-propagation algorithm was established. Input layer included six

molecular descriptors appearing in the MLR model: the polarizability term (πI), most

positive charge of acidic hydrogen atom (q+), molecular weight (MW), most negative

charge of the acidic oxygen atom (q−), the hydrogen-bond accepting ability (εB) and

partial charge weighted topological electronic (PCWTE) descriptors [41]. And the output

was pKa value. The architecture of ANN was optimized to 6-24 (number of neurons in

the hidden layer)-1 [41]. Finally total squared correlation coefficient (R2) was 0.9931

with individual R2 for training, validation and prediction set were 0.9926, 0.9943 and

42

0.9939, respectively [41]. Total rms error was 0.2648, and individual rms error for

training, validation and prediction set were 0.2700, 0.2479 and 0.2575, respectively [41].

However, published work had limitations of models that they only had ability to

predict pKa values at 25 oC. Due to the temperature dependency of pKa, this work focused

on the model development to achieve the pKa prediction of amines at different

temperature by using ANN.

3.2 Artificial Neural Network Overview

ANN mimics the human brain, detecting the patterns and relations in supplied

data and is trained to acquire their knowledge through experience. McCulloch and Pitts

introduced a model with two inputs and one output in 1943 [38]. Soon Hebb outlined a

law for synaptic neuron learning in 1949, which was later known as Hebbian Learning

[38]. This idea inspired the development of computational deep learning. In 1986, the

backpropagation algorithm became popular after Rumelhart and McClelland rediscovered

the applications of connectionism (parallel distributed processing) for neural simulation,

which was originally described by Werbos [38].

3.2.1 Feed-forward Neural Network

There are various neural network architectures, one of the most widely used in

chemical applications among them is the feed-forward network [38-43]. As its name

shows, it contains only forward paths, where the information flows in from input towards

output. It means that there is no feedback and signals from one layer are not transmitted

to a previous layer.

43

ANN has highly interconnected structures consisting of an input layer, an output

layer and at least one hidden layer. A simplest feed-forward ANN with single hidden

layer was demonstrated in Figure 3.1. The input layer contains data collected from the

outside world and passes them to the hidden layer. Then the hidden layer detects the

patterns from input, and obtained knowledge through training process is expressed by

weights and bias. Weights show the strength of the connection between input and output

data. Bias represent the difference between predicted results and real values. Finally

output layer receives signals from hidden layer and provides information to the outside

world.

Figure 3. 1 A basic structure of an ANN model

The basic model of ANN can be descried as a series of functional transformations

as shown in equation 3.4 [38].

ym = 𝜌m(wmxm+bm) Eqn. 3.4

44

Where vector xm represents the input signal from layer m-1 to m (m=1, 2 … n).

Matrix wm are weights from each neuron in layer m-1 to neurons in the layer m. In this

matrix, each element in a row corresponds to a neuron in layer m-1, and each element in a

column corresponds to a neuron in layer m. Vector bm is bias, and 𝜌m is a vector of

activation functions [σ1 σ2… σn]. ym is the total output of layer m.

Activation functions are used to achieve data transformation and it plays the

important role in an ANN model. Without applying an activation function, a model

would simply be a linear regression model, which limits its power in solving complicated

problems [38]. There are a number of activation functions and sigmoid activation

function, which is defined in equation 3.5, is one of the most popular activation functions

and was chosen in this work [39-43].

σ(a) = 1

1+exp(−a) Eqn. 3.5

3.2.2 Backpropagation algorithm

Error-correction learning is a technique to determine the offset (error) of a system

output with a desired value, and obtained error is used to improve the training step [38,

39]. The backpropagation algorithm is one of the most robust and widely used tools in the

training, and it helps to update weights of the network by passing error signals backwards

[38, 39]. Backpropagation training follows three steps [38]:

1) Input data selected for training are fed in a forward direction to hidden layer,

and hidden neurons compute activation and producing results, which are received by

output layer. For a single hidden layer ANN, this process can be expressed

mathematically through equation 3.6 to 3.9:

45

For the hidden layer: 𝑛𝑒𝑡𝑗 = Σ𝑖=0𝑁𝑖𝑛

𝑉𝑗𝑖𝑋𝑖 Eqn. 3.6

𝐻𝑗 = 𝜎(𝑛𝑒𝑡𝑗) Eqn. 3.7

For the output layer: 𝑛𝑒𝑡𝑘 = Σ𝑗=0𝑁ℎ𝑖𝑑𝑑𝑒𝑛

𝑊𝑘𝑗𝐻𝑗 Eqn. 3.8

𝑂𝑘 = 𝜎(𝑛𝑒𝑡𝑘) Eqn. 3.9

Where 𝑋𝑖 is the output of the ith neuron in the input layer; 𝑉𝑗𝑖 is the weight from

the ith neuron in the input layer to the jth neuron in the hidden layer; 𝑁𝑖𝑛 is the total

number of neurons in the input layer; 𝑛𝑒𝑡𝑗 is the input of the jth neuron in the hidden

layer; 𝜎 is the activation function; 𝐻𝑗 is the output of jth neuron in the hidden layer; 𝑊𝑘𝑗 is

the weight from the jth neuron in the hidden layer to the kth neuron in the output layer;

𝑁ℎ𝑖𝑑𝑑𝑒𝑛 is the total number of neurons in the hidden layer; 𝑛𝑒𝑡𝑘 is the input of the kth

neuron in the output layer, and 𝑂𝑘 is the output of the kth neuron in the output layer. For

the convenience of explanation, biases for the hidden layer and the output layer are both

assigned as 1 and associated weights are written as 𝑉𝑗0 and 𝑊𝑘0, respectively.

2) Errors are calculated according to target data, and necessary changes to weights

are done, which can be expressed as equation 3.10 to 3.11:

𝑊𝑘𝑗(𝑛𝑒𝑤) = 𝑊𝑘𝑗(𝑜𝑙𝑑) + 𝛥𝑊𝑘𝑗 Eqn. 3.10

𝑉𝑗𝑖(𝑛𝑒𝑤) = 𝑉𝑗𝑖(𝑜𝑙𝑑) + 𝛥𝑉𝑗𝑖 Eqn. 3.11

The derivation is explained as follows:

Cost function: 𝐸 = 1

2Σ𝑘=1

𝑁𝑜𝑢𝑡(𝑌𝑘 − 𝑂𝑘)2 Eqn. 3.12

46

Where 𝑌𝑘 is the output of the kth neuron in the output layer; 𝑁𝑜𝑢𝑡 is the total

number of neurons in the output layer, and 𝑂𝑘 is the desired value of the kth neuron in the

output layer.

Changes of weights are defined in equation 3.13 and 3.14:

Δ𝑊𝑘𝑗 = −𝜂𝜕𝐸

𝜕𝑊𝑘𝑗= −𝜂

𝜕𝐸

𝜕𝑛𝑒𝑡𝑘∙

𝜕𝑛𝑒𝑡𝑘

𝜕𝑊𝑘𝑗 Eqn. 3.13

Δ𝑉𝑗𝑖 = −𝜂𝜕𝐸

𝜕𝑉𝑗𝑖= −𝜂

𝜕𝐸

𝜕𝑛𝑒𝑡𝑗∙

𝜕𝑛𝑒𝑡𝑗

𝜕𝑉𝑗𝑖 Eqn. 3.14

Where 𝜂 is the step size.

It is convenient to introduce error functions (𝛿) and define them in equation 3.15

and 3.16:

𝛿𝑘𝑂 = −

𝜕𝐸

𝜕𝑛𝑒𝑡𝑘 Eqn. 3.15

𝛿𝑗𝐻 = −

𝜕𝐸

𝜕𝑛𝑒𝑡𝑗 Eqn. 3.16

The partial derivatives can also be calculated through equation 3.17 to 3.20:

𝜕𝑛𝑒𝑡𝑘

𝜕𝑊𝑘𝑗=

𝜕

𝜕𝑊𝑘𝑗𝛴𝑗=0

𝑁ℎ𝑖𝑑𝑑𝑒𝑛𝑊𝑘𝑗𝐻𝑗 = 𝐻𝑗 Eqn. 3.17

𝜕𝑛𝑒𝑡𝑗

𝜕𝑉𝑗𝑖=

𝜕

𝜕𝑉𝑗𝑖𝛴𝑖=0

𝑁𝑖𝑛𝑉𝑗𝑖𝑋𝑖 = 𝑋𝑖 Eqn. 3.18

𝛿𝑘𝑂 = −

𝜕𝐸

𝜕𝑛𝑒𝑡𝑘= (𝑌𝑘 − 𝑂𝑘)𝜎′(𝑛𝑒𝑡𝑘) Eqn. 3.19

𝛿𝑗𝐻 = −

𝜕𝐸

𝜕𝑛𝑒𝑡𝑗= Σ𝑘=1

𝑁𝑜𝑢𝑡𝛿𝑘

𝑂𝑊𝑘𝑗𝜎′(𝑛𝑒𝑡𝑗) Eqn. 3.20

47

Equation 3.13 and 3.14 can be recalculated by substituting equation 3.19 and

3.20, respectively:

𝛥𝑊𝑘𝑗 = η𝛿𝑘𝑂𝐻𝑗 Eqn. 3.21

𝛥𝑉𝑗𝑖 = η𝛿𝑗𝐻𝑋𝑖 Eqn. 3.22

𝛿 is the function that makes back propagation process can be achieved and the

function for each layer depends on the function from the previous layer.

3) The same procedure is repeated until the minimum error is approached.

3.3 Parameter selection and data collection

Most research used neural network to predict pKa values combined with QSPR

method, however, the challenge was to convert structural information of compounds into

numerical inputs acceptable to ANN. In order to improve the accuracy of prediction, the

molecular descriptor must describe the structural features as distinctly as possible. In

general, researchers need generate the descriptors firstly by constructing and optimizing

the molecular models with the aid of some software, such as HyperChem and MOPAC

program [40-43]. This process takes time and needs lots of efforts. In addition, developed

ANN models based QSPR were limited at 25 oC. And thus, there is a need to develop a

more flexible model that is able to achieve pKa predictions at different temperature.

Meanwhile, there are also some developments of modeling about physical properties

based on QSPR with aid of ANN, and it was found that their descriptors acted as ANN

inputs had overlaps with those inputs that were used for pKa predictions. Therefore, it

became possible to predict pKa of a compound with its physical properties as ANN

inputs.

48

Kauffman et al. predicted surface tension and viscosity for common organic

solvents by ANN and they generated descriptors which embodied structural information

about topological, geometric and electronic features in intermolecular interactions,

including charge of most positive atom, surface area of donatable hydrogen atoms, partial

positively charged atoms, and partial negative charged atoms [42]. For prediction of

surface tension, the architecture was optimized to 8-6-1 with individual regression

coefficient of 0.965, 0.960 and 0.976 for training, validation and prediction set,

respectively [42]. The relevant rms error of each set was 2.22, 2.22 and 2.76, respectively

[42]. For prediction of viscosity, an 8-7-1 architecture ANN was optimized and obtained

rms error of training, validation and prediction set as 0.147, 0.148 and 0.242, respectively

[42]. The individual regression coefficient was 0.974, 0.965 and 0.887 for each set,

respectively [42].

Artemenko et al. used valence, hybridization type and atomic charge as inputs to

predict density and viscosity of organic compounds [40]. For prediction of density, the

overall regression coefficient was 0.9935, and individual rms error was 0.020, 0.026, and

0.038 for training, validation and prediction set, respectively [40]. For viscosity, the

overall regression coefficient was 0.9885, and individual rms error was 0.084, 0.104, and

0.141 for training, validation and prediction set, respectively [40].

Zhang et al. applied ANN for density and refractive index predictions of alkenes

and inputs included the polarity number and other structural features relevant to double

bonding [43]. Finally, they explored a 5-5-3 architecture and obtained the relative

standard deviation of 0.44% and 0.11% for density and refractive index, respectively

[43].

49

Collecting a wide range of experimental data was an important step to create the

appropriate modeling. Most data were collected from literatures and some of non-found

data were experimentally measured in this work. Finally, 568 data points of 25 sets of

amines relevant to CO2 capture were used as listed in Table 3.1, and these data can be

divided into three categories: (a) molecular weight, critical pressure and critical pressure

as inputs that were used to identify the compound; (b) temperature and physical

properties as inputs including density, viscosity, surface tension and refractive index that

were used to correlate pKa values; (c) pKa values as outputs. The critical temperature (Tc)

and critical pressure (Pc) are listed in Table 3.2.

50

Table 3. 1 Collected data information

Amine CAS

number

Temp Range

(K)

No. of

Data

Reference

Methyldiethanolamine

(MDEA)

105-59-9 298.15 – 313.15 28 [44, 45]

Monoethanolamine (MEA) 141-43-5 298.15 – 313.15 28 [26, 46-49]

1-amino-2-propanol

(MIPA)

78-96-6 298.15 – 313.15 24 [36, 50]

Dimethylpropanolamine

(DMPA)

3179-63-3 298.15 – 313.15 24 [26, 51]

2-(Methylamino)ethanol

(MAE)

109-83-1 298.15 – 313.15 24 [52, 53]

2-amino-2-methyl-1-propanol

(AMP)

124-68-5 298.15 – 313.15 24 [49, 53-55]

Diethanolamine (DEA) 111-42-2 298.15 – 313.15 28 [46, 56-59]

Triethanolamine (TEA) 102-71-6 298.15 – 313.15 24 [12,16, 23-

25]

3-amino-1-propanol

(3AP)

105-87-6 298.15 – 313.15 24 [36, 60, 61]

N,N-Dimethylethanolamine

(DMEA)

108-01-0 298.15 – 308.15 16 [53, 62-64]

51

Amine CAS

number

Temp Range

(K)

No. of

Data

Reference

Ethyldiethanolamine

(EDEA)

139-87-7 298.15 8 [26, 64]

Piperidine (PD) 110-89-4 298.15 8 [37, 65, 66]

2-(Ethylamino)ethanol

(EMEA)

110-73-6 298.15 8 [26, 67, 68]

Diethylethanolamine

(DEEA)

100-37-8 298.15 8 [26, 48, 69]

Butylamine (BA) 109-73-9 298.15 8 [70-72]

Tert-butylamine

(tert-BA)

75-64-9 298.15 8 [37-39]

3-(Dimethylamino)-1-

propylamine

(DMAPA)

109-55-7 298.15 8 [51, 73, 74]

N-(2-Aminoethyl)-1,3-

propanediamine

(n-2AOE13PDA)

13531-52-7 298.15 – 313.15 28

This Worka

Bis[2-(N,N-

dimethylamino)ethyl] ether

(2DMAOEE)

3033-62-3 298.15 – 313.15 28

52

aDetailed information was explained in Appendix A

Amine CAS

number

Temp Range

(K)

No. of

Data

Reference

N,N-

Dimethyldipropylenetriamine

(DMAPAPA)

10563-29-8 298.15 – 313.15 28

This Worka

3,3′-Diamino-N-

methyldipropylamine

(DAOMDPA)

105-83-9 298.15 – 313.15 28

2-[2-

(Dimethylamino)ethoxy]ethan

ol

(DMAOEOE)

1704-62-7 298.15 – 313.15 28

2-(Dibutylamino)ethanol

(DBEA)

102-81-8 298.15 – 313.15 28

N-Propylethanolamine

(PEA)

16369-21-4 298.15 – 313.15 28

53

Table 3. 2 Critical properties of amine used in modeling

No. Amine CAS

number

Tc (K) Pc (kPa) Reference

1 MDEA 105-59-9 741.9 4160

APV88.PURE32a

2 MEA 141-43-5 678.2 7124

3 MIPA 78-96-6 614 5670

4 DMPA 3179-63-3 605 3873.31

5 MAE 109-83-1 630 5220

6 AMP 124-68-5 619.8 3862.1

7 DEA 111-42-2 736.6 4650.82

8 TEA 102-71-6 772.1 2743

9 3AP 105-87-6 649 5500

10 DMEA 108-01-0 571.82 4140

11 EDEA 139-87-7 728 3738.11

NISTV88.NIST-TRCb

12 PD 110-89-4 594.05 4650.82

13 EMEA 110-73-6 671 5342.64

14 DEEA 100-37-8 592 3180

15 BA 109-73-9 531.9 4200

16 tert-BA 75-64-9 483.9 3840

17 DMAPA 109-55-7 593.3 3586

18 n-2AOE13PDA 13531-52-7 478.86 4051.8 Jobackc

54

a APV88.PURE32: Pure Component Databank of Aspen Properties

bNISTV88.NIST-TRC: Standard Reference Subscription Database

cJoback: Detailed information available in Appendix B

3.4 Modeling and Results

3.4.1 Modeling with all input parameter

To introduce inputs, the critical properties (Tc and Pc) were used to identify the

specific amine in the modeling, temperature and physical properties (density, viscosity,

surface tension and refractive index) were chosen as variables of modeling.

During the modeling, a default setting of data division for training, validation and

testing were applied. 70% of data from the database were randomly selected and used for

training the network, and the rest 15% of data were chosen for validation and the other

15% were used for testing the modeled network.

The optimization of ANN plays a crucial role in network training, including the

optimization of the hidden layer number and neuron number in each hidden layer.

No. Amine CAS

number

Tc (K) Pc (kPa) Reference

19 2DMAOEE 3033-62-3 591.22 2482.59

NISTV88.NIST-TRCb

20 2-MPMDA 15520-10-2 654 3430.89

21 DMAPAPA 10563-29-8 457.31 2718.33 Jobackc

22 DAOMDPA 105-83-9 695 2799.88

NISTV88.NIST-TRCb

23 DMAOEOE 1704-62-7 662 9307.52

24 DBEA 102-81-8 720 2508.8

25 PPEA 16369-21-4 648 4105.5

55

Theoretically, there is no particular systematic methods for calculating optimal number of

hidden layer and its neurons. Therefore, the program was executed with one layer and

with number of neurons in the range of 5 to 15 firstly to compare their performance.

Figure 3.2 showed the performance with comparison of R and mean squared error

(MSE), and it can be found that single hidden layer with 5 neurons had the best

performance (Roverll = 0.97598, MSEtrain = 0.0062, MSEval = 0.0094 and MSEtest =

0.0244). In order to obtain a better modeling result, a program with two hidden layers

was further executed. The first layer was fixed with 5 neurons according to the

optimization at the first step, and then second layer with number of neurons in the range

of 4 to 15 was tested. The comparison of performance of ANN models with the

architecture of 8-5-X-1 (X = 4, 5 … 15) was shown in Figure 3.3. According to the

performance that R and MSE were the considered parameters to select the optimal model,

the architecture of 8-5-7-1 was chosen as best ANN model (Roverall = 0.99424, MSEtrain =

2.20E-05, MSEval = 0.0094 and MSEtest = 0.0078). The weights and bias values for the

generated ANN network were listed in Table 3.3 to 3.5.

56

(a)

(b)

Figure 3. 2 Performance of ANN model with a single hidden layer of different number of

neurons. (a) R; (b) MSE.

57

(a)

(b)

Figure 3. 3 Performance of ANN model with different number of neurons in the second

hidden layer. (a) R; (b) MSE.

58

Table 3. 3 Weights and biases for the first hidden layer

5

4

3

2

1

Neu

ron

Tab

le 3.3

Weig

hts an

d b

iases for th

e first hid

den

layer

0.5

6587

-0.1

1131

0.0

0200

-0.1

0165

-0.9

0140

Tem

p

-0.2

5096

0.4

5404

0.1

7377

0.2

3167

1.2

6728

MW

0.0

4946

-0.0

5187

0.3

6082

0.7

8441

0.1

7801

Tc

0.5

3460

-0.3

4300

0.2

9879

0.7

9700

-0.2

6354

Pc

-0.1

3470

-1.1

0700

-0.0

4112

0.9

1007

0.2

3100

n

0.6

5300

0.1

8501

1.3

9244

-1.0

4270

-0.2

2393

γ

-0.0

3420

1.2

8922

-1.0

9232

1.7

3399

0.5

1943

𝜌

0.8

4495

-0.1

4319

0.7

4701

0.7

9946

0.8

2292

𝜂

1.9

0616

-1.3

9991

0.7

3443

1.0

9392

1.9

8977

bias

59

Second hidden layer

Tab

le 3.4

Weig

hts an

d b

iases for th

e second

hid

den

layer

7

6

5

4

3

2

1

Neu

ron

-0.0

3291

1.1

3384

-0.1

3183

0.0

1209

0.4

6478

-0.5

8823

-0.4

5948

1

First h

idden

layer

1.2

5251

0.3

7617

-0.6

6514

0.4

4161

1.5

4465

2.1

8967

0.5

6265

2

1.2

9429

1.7

7381

2.0

2062

0.0

5459

-1.2

7009

1.2

0782

0.0

1276

3

-1.1

0049

0.6

8016

-0.9

3698

2.0

5884

-0.6

9490

0.6

8793

1.5

3071

4

-0.4

2144

-1.3

7880

0.3

6172

0.7

1506

-0.1

6672

1.0

9309

0.3

6629

5

2.0

5962

1.0

16166

1.5

6382

-0.2

9219

-1.4

3382

0.8

1502

1.8

4972

bias

60

Table 3. 4 Weights and biases for the second hidden

layer

Table 3. 5 Weights and bias for the output layer

Weig

hts

Tab

le 3.5

Weig

hts an

d b

ias for th

e outp

ut lay

er

-1.8

1776

1

Seco

nd h

idden

layer n

euro

n

0.4

3961

2

-0.4

6271

3

-0.7

0389

4

-0.8

0258

5

-0.1

8706

6

-0.4

3720

7

1.2

4658

bias

61

The final architectural diagram of selected ANN model was shown in Figure 3.4.

Performance improvements during training, validation and testing process were

illustrated in Figure 3.5. It can be found that best validation performance was reached at

epoch 19 while training performance still kept improving with the increase of the epoch

number.

Figure 3. 4 pKa function fitting neural network

Figure 3. 5 Performance improvement

62

The figure below displays the plots of the outputs with respect to targets for

training, validation, and test process. The broken line was the ideal trendline which meant

network outputs were equal to the desired values. It can be found that Roverall was above

0.99, therefore, the predicted outputs were in a good agreement with target pKa values.

Figure 3. 6 Regression plot for pKa prediction

The error histogram was shown in Figure 3.7, which gave an indication of

outliers. It can be seen that most errors fell in -0.00746, while the maximum absolute

value of the error was 0.4056 from the test part. None of data was slipped because there

was no evidence suggesting the outliers came from experimental errors.

63

Figure 3. 7 Error histogram

3.4.2 Modeling with reduced input parameter

Although a satisfied ANN model has been obtained as mentioned in section 3.4.1,

there was an idea to develop a model with reduced types of input parameter. Because of

the limitation of literature sources for collecting every physical properties, the ANN

model would become more flexible to use if it was possible to use fewer types of input

parameter. This section focused on improvements of the modeling based on the

optimized architecture of the ANN model.

Three types of input parameters (MW, Tc and Pc) used for identification of the

compound were remained due to their availability. Temperature as an input parameter

64

was also remained according to the temperature dependency of pKa values. For physical

properties (n, γ, ρ and η), there were three stages in optimization based on types of

remaining input parameter. Firstly, only one of them was removed and rest data were

treated as inputs for modeling. Secondly, two of them were removed from the list of input

parameter. Finally, only one of them was kept for modeling. Performance of ANN

models was listed in Table 3.6. It can be found that the performance had a tendency to

become worse with reduced inputs according to decreased Roverall and increased MSE for

training, validation and test process except the model with both surface tension and

refractive index remained as the input parameter.

Table 3. 6 Performance of ANN models

Input physical properties Roverall MSEtrain MSEval MSEtest

Without density 0.99166 5.7158E-4 0.0024 0.0473

Without surface tension 0.99072 5.9412E-5 0.0031 0.0517

Without viscosity 0.99332 3.4927E-5 0.0058 0.0538

Without refractive index 0.98861 5.6525E-4 0.0013 0.0644

Density & viscosity 0.97433 4.9624E-5 0.0126 0.1914

Density & surface tension 0.97124 1.0526E-5 0.0231 0.0958

Density & refractive index 0.97976 1.3896E-4 0.0353 0.0479

Viscosity & surface tension 0.97322 2.8415E-4 0.0019 0.0490

Surface tension & refractive

index

0.99216 4.40E-5 0.0045 0.0203

65

Input physical properties Roverall MSEtrain MSEval MSEtest

Viscosity & refractive index 0.96910 1.5689E-4 0.0405 0.0772

Density 0.91996 0.0012 0.0041 0.1431

Viscosity 0.92769 0.0241 0.0448 0.3153

Refractive index 0.92286 0.0691 0.1315 0.0605

Surface tension 0.91592 0.0767 0.0334 0.1705

Even though the new ANN model had a bit weaker performance as compared

with the model obtained in section 3.4.1, its predicted values were still in a good

agreement with targets and this model was more flexible for application as a result of

fewer inputs. Figure 3.8 illustrated performance improvement during training, validation

and testing process. The best validation performance was reached at epoch 76, and

performance for three process became stable with the increase of the epoch number.

Regression plot showed the model outputs had a good agreement with desired pKa values

as shown in Figure 3.9. In Figure 3.10, it can be found that most errors fell in -0.00136,

but the maximum absolute value of the error as 0.4263 was bigger than 0.4056 of the

previous model. Weights and biases generated from the new selected model were

summarized in Table 3.7.

66

Figure 3. 8 Performance improvement of the new selected ANN model

Figure 3. 9 Regression plot of the new selected ANN model

67

Figure 3. 10 Error histogram of the new selected ANN model

68

Table 3. 7 Weights and

biases for the first hidden

layer of the new model

5

4

3

2

1

Neu

ron

Tab

le 3.7

Weig

hts an

d b

iases for th

e first hid

den

layer o

f the n

ew m

odel

0.4

1621

-0.1

3677

0.9

9251

-0.2

6552

-0.2

4583

Tem

p

-1.2

9392

-1.1

4074

1.6

44345

-2.4

5499

-0.5

3796

MW

-2.4

4923

-1.0

7368

1.1

9356

-0.2

7215

0.3

4906

Tc

-0.4

6173

-2.2

6976

0.9

6452

-0.6

2048

-1.4

0387

Pc

-0.0

2108

-0.3

4010

-0.3

3267

0.5

2218

2.0

6833

n

0.4

4231

-0.1

0590

-0.4

3248

-1.6

3970

-0.7

7081

γ

-1.1

06

78

-0.6

49

54

-0.8

19

73

-2.1

75

58

-1.4

04

91

bias

69

Table 3. 8 Weights and biases for the second hidden layer of the new model

Second hidden layer

Tab

le 3.8

Weig

hts an

d b

iases for th

e second

hid

den

layer o

f the n

ew m

odel

7

6

5

4

3

2

1

Neu

ron

0.9

4147

0.7

8894

2.0

1430

0.6

1351

1.0

9133

1.4

15478

0.8

0230

1

First h

idden

layer

2.0

1779

-1.3

6249

-0.2

9533

-1.6

3782

0.3

5854

0.4

3758

-0.0

4456

2

0.7

2308

0.8

9407

0.5

79025

-0.5

2673

0.3

6101

0.3

0487

-1.8

7507

3

1.0

4200

-0.3

1867

0.1

5001

0.8

6454

0.4

3377

-1.5

5243

0.7

9456

4

1.0

4200

1.2

4849

0.8

1178

-0.4

3624

-1.5

1654

0.5

3265

0.1

5055

5

1.0

7317

1.8

8289

-0.1

9128

0.4

0227

-1.0

5016

-0.7

0657

-2.2

3222

bias

70

Table 3. 9 Weights and bias for the output layer of the

new model

Weig

hts

Tab

le 3.9

Weig

hts an

d b

ias for th

e outp

ut lay

er of th

e new

model

-0.0

3506

1

Seco

nd h

idden

layer n

euro

n

-1.4

0955

2

-0.0

6625

3

-0.5

4109

4

0.7

8760

5

-0.5

5320

6

-0.5

2638

7

-0.1

8994

bias

71

Chapter 4: Conclusion and Recommendations

In this study, the pKa values of eight amines [N-(2-Aminoethyl)-1,3-

propanediamine, Bis[2-(N,N-dimethylamino)ethyl] ether, 2-Methylpentamethylene

diamine, N,N-Dimethyldipropylenetriamine, 3,3’-Diamino-N-methyldipropylamine, 2-

[2-(Dimethylamino)ethoxy]ethanol, 2-(Dibutylamino)ethanol, and N-

Propylethanolamine] have been determined experimentally within a temperature range of

298.15K – 313.15K by using the potentiometric titration method.

It was observed that the basicity of amines was sensitive to temperature changes

and pKa values of amines decreased with the increase of the temperature. Meanwhile, the

predicted pKa values of eight target amines along with MDEA were calculated using

PDS, new PDS and the QSSG method. The root-mean-square (rms) errors for 9 amines

were 0.29, 0.24, and 0.24 for three methods, respectively. It can be found that both new

PDS and QSSG reduced rms error as compared with original PDS method. In addition,

QSSG did not have further improvement about these 9 amines as compared with new

PDS method, because the updated factors did not apply to studied amines in terms of

their chemical structures. The thermodynamic quantities including the standard state

enthalpy change (∆H0) and the standard state entropy change (∆S0) for the dissociation

process were determined via Van’t Hoff equation.

To establish a new model for pKa prediction at different temperature, some data

of amines (25 compounds) relevant to CO2 capture were collected and used based on the

feedforward artificial neuron network (ANN) with the backpropagation algorithm.

Additionally, some physical properties (density, viscosity, surface tension and refractive

72

index) of eight studied amines were measured experimentally at a temperature range of

298.15K – 313.15K. Eight parameters were used as the input data, and these parameters

were divided into two categories: (a) molecular weight, critical pressure and critical

pressure as inputs that were used to identify the compound; (b) temperature and physical

properties as inputs including density, viscosity, surface tension and refractive index that

were used to correlate pKa values. An optimized architecture of 8-5-7-1 was selected and

predicted outputs were in a good agreement with targets, whose regression coefficient

was 0.99424 and mean squared error for training, validation and test process was 2.20E-

05, 0.0094 and 0.0078, respectively.

To compromise the flexibility of the ANN model, the other architecture of 6-5-7-

1 which reduced density and viscosity as inputs was selected, and it had a regression

coefficient was 0.99216 and mean squared error for training, validation and test process

was 4.40E-05, 0.0045 and 0.0203, respectively.

The pKa values reflected the basicity of amines and experimental results showed

that all studied novel amines had stronger basicity than MEA, DEA or MDEA depending

on the amine type. Moreover, measured viscosities of 8 amines were much lower as

compared with MEA, DEA and MDEA. It was desirable in industrial application because

less viscous liquids required less energy duty of pumps, resulting in the reduced expense

of equipment and operation. To summarize, 8 novel amines can be strong candidates of

importance in CO2 capture on the low values of their viscosities and high values of their

pKa. It was recommended to do more research work on their kinetics, solubility, heat

73

capacity, amine degradation, foaming and equipment corrosion with respect to solvents

with stronger basicity.

74

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80

Appendix A: Experimental Determination of Physical Properties of Amines

Appendix A-1: Density Measurement

Densities of studied were automatically measured and recorded by an Anton Paar

DMA-4500 density meter. Air check and deionized water check were done to calibrate

the density meter at an ambient temperature. The checks can be passed unless the results

were within 5E-05 g/cm3 of the desired values. The uncertainty of the density data was

estimated to be ± 5E-05 g/cm3 and the reproducibility was ±3E-05 g/cm3. The density of

pure MDEA were compared with the experimental values from Muhammad and Mandal,

and AAD% was 0.08 and 0.09, respectively. The experimental results were listed in

Table A-1.1.

Table A-1. 1 Densities of studied amines

Solvent

Density(g/mL)

298.15K 303.15K 308.15K 313.15K

n-2AOE13PDA 0.933641 0.929476 0.925310 0.921140

2DMAOEE 0.845511 0.841305 0.837086 0.832864

2-MPMDA 0.861528 0.857520 0.853504 0.849480

DMAPAPA 0.870757 0.866710 0.862665 0.858626

DAOMDPA 0.898479 0.894457 0.890431 0.886410

DMAOEE 0.951487 0.947464 0.943422 0.939368

DBEA 0.856270 0.852195 0.848113 0.844024

PPEA 0.898967 0.895062 0.891138 0.887190

81

Appendix A-2: Viscosity Measurement

Viscosities were measured by using a U-tube glass Cannon-Ubbelohde

viscometers (Cole-Parmer). A water bath (model CT500, Cannon Instrument Company,

USA) was used to maintain required temperatures. The uncertainty of the temperature

was 0.01K as measured by a Cole-Parmer resistance thermometer (model H-01158-65,

Anjou, Quebec, Canada). The efflux time was read from a digital stopwatch with the

uncertainty of the time as 0.01 s and the reproducibility was ±0.55 s. According to

Poiseuile’s law as written in equation A-2.1, the kinematic viscosity can be obtained.

Finally the dynamic viscosity can be calculated by multiplying the kinematic viscosity by

the corresponding density.

𝜈 = 𝑘1𝑡 − 𝑘2/𝑡 Eqn. A-2.1

Where v was kinematic viscosity in mm2/s, t was the efflux time in second, k1 and

k2 were both viscometer constants in mm2/s2. In general, k2 represented the correction

which could be negligible.

Validation was done by comparing measured dynamic viscosities of deionized

water and MDEA with literatures. Uncertainty of dynamic viscosity was ±0.05 mPa∙s.

For water, AAD% was 0.26 and 0.30 with experimental values from Muhammad and

Mandal, respectively. For MDEA, AAD% was 0.26 and 0.30 with experimental values

from Muhammad and Mandal, respectively.

The experimental results were listed in Table A-2.1.

82

Table A-2. 1 Viscosities of studied amines

Solvent

Dynamic viscosity (mPa∙s)

298.15K 303.15K 308.15K 313.15K

n-2AOE13PDA 7.26 6.05 5.01 4.33

2DMAOEE 1.17 1.07 1.00 0.92

2-MPMDA 2.65 2.20 1.93 1.74

DMAPAPA 4.26 3.61 3.11 2.74

DAOMDPA 5.17 4.40 3.84 3.29

DMAOEE 7.49 6.38 5.46 4.74

DBEA 6.80 5.57 4.57 3.89

PPEA 14.68 11.75 9.32 7.79

83

Appendix A-3: Refractive Index Measurement

The refractive indices of amines were measured by using an Atago RX-5000-α

refractometer. To validate the refractometer, refractive indices of MDEA were measured

and compared with literature data. It was found the uncertainty was ±0.00001. AAD%

was 0.15 and 0.22 as compared with data from Muhammad [45] and Razavizadeh [75],

respectively. The experimental results were listed in Table A-3.1.

Table A-3. 1 Refractive indices of studied amines

Solvent

Refractive index

298.15K 303.15K 308.15K 313.15K

n-2AOE13PDA 1.48025 1.47802 1.47569 1.47337

2DMAOEE 1.42785 1.42575 1.42351 1.42124

2-MPMDA 1.45685 1.45491 1.45235 1.45027

DMAPAPA 1.46085 1.45853 1.45623 1.45397

DAOMDPA 1.47108 1.46908 1.46701 1.46495

DMAOEE 1.43887 1.43663 1.43468 1.43305

DBEA 1.44212 1.43988 1.43766 1.43543

PPEA 1.44037 1.43788 1.43577 1.43423

84

Appendix A-4: Surface Tension Measurement

A K100 Tensiometer (Kruss, USA) was used to measure surface tensions of

amines by using a platinum plate-detachment method under 1 atm. The platinum plate

was thoroughly cleaned and dried by the flame to avoid any residue before each

measurement. The uncertainty of the surface tension was ±0.005 mN/m. The surface

tensions of deionized water and MDEA were measured and compared with literature

data. It was found AAD% was 0.10 and 0.12 with Vargaftik [76] and Vazquez [77] for

water. For MDEA, AAD% was 1.06 and 0.98 with Muhammad [45] and Alvarez [78].

The experimental results were listed in Table A-4.1.

Table A-4. 1 Surface tensions of studied amines

Solvent

Surface Tension (mN/m)

298.15K 303.15K 308.15K 313.15K

n-2AOE13PDA 42.509 41.979 41.655 41.089

2DMAOEE 25.996 25.382 24.933 24.458

2-MPMDA 35.355 34.667 34.365 33.923

DMAPAPA 31.073 30.494 29.918 29.251

DAOMDPA 36.516 36.037 35.585 35.093

DMAOEE 31.527 30.886 30.556 30.091

DBEA 26.243 25.565 24.94 24.507

PPEA 29.716 29.355 29.063 28.668

85

Appendix B: Estimation of Critical Properties of Amines

The Joback method was commonly used to predict the critical properties of

compounds from their molecular structures. The equations B-1, B-2 showed the way to

calculate the critical temperature and the critical pressure, respectively.

Tc = Tb[0.584 + 0.965∑Tc,i – (∑Tc,i)2]-1 Eqn. B-1

Pc = 100[0.113 + 0.00332NA - ∑Pc,i]-2 Eqn. B-2

Where Tc was critical temperature in K; Tb was normal boiling point in K; Tc,i

was group contribution of temperature in K; Pc was critical pressure in kPa; NA was the

number of atoms in the molecular structure; Pc,i was group contribution of pressure in bar.

Table B.1 listed the group contribution and calculated critical temperature was 478.86K

and 457.31K for n-2AOE13PDA and DMAPAPA, respectively. Calculated critical

pressure was 4051.80 kPa and 2718.33 kPa for n-2AOE13PDA and DMAPAPA,

respectively.

Table B. 1 Group contribution of critical properties

Group Tc (K) Pc (bar)

-CH3 0.0141 -0.0012

-CH2- 0.0189 0

-NH2 0.0243 0.0109

>NH (non-ring) 0.0295 0.0077

>NH (ring) 0.013 0.0114

>N-(nonring) 0.0169 0.0074