Modelling the phase behaviour of polymer-solvent mixtures

and surfactant systems with the SAFT-γ Mie EoS

Mariana Leitão da Silva Santos

Thesis to obtain the Master of Science Degree in

Chemical Engineering

Supervisors: Dr. Thomas Lafitte, Prof. Dr. Eduardo Morilla Filipe

Examination Committee

Chairperson: Prof. Dr. Carlos Henriques

Supervisor: Prof. Dr. Eduardo Morilla Filipe

Member of the committee: Dr. Pedro Morgado

20th October 2016

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Acknowledgements

I cannot find words to express my gratitude to my Supervisor Dr. Thomas Lafitte for his support and

valuable knowledge – it has truly been an honour to work with you. I would also like to thank Dr. Vasileios

Papaioannou, for his (much needed) help and availability.

This thesis would not have been possible without my Professor (and also Supervisor) Dr. Eduardo Filipe

– I am forever indebted for your support and for giving me this chance. I also owe my deepest gratitude

to Process Systems Enterprise Ltd., in particular to Dr. Costas Pantelides, for the opportunity to enrol in

this Internship.

A very special thank you to all my journey companions and colleagues, who enriched this experience:

Tom, Su, Alhandra, Eleni, Matteo, Federico, Renato,Artur, Mariana, Francisco, Maria, Pierre, Sancho,

and Leonor. To my shorter-term buddies – Alex, Luisa, and Josh –, I am grateful for the thoughts and

experiences we shared.

To my parents: no words can describe how much I appreciate you unconditional love and support, I love

you both very much. I would also like to thank my little brother, for looking up to me – you made me try

harder, even without knowing. To the rest of my family: thank you for being there; particularly to my

grandma, for sheltering me and for her endless patience (and comfort food), and to my grandparents

for their love and support.

Last but far from least, to my fiancé João: I will be forever grateful for the lovely years we shared so far,

and for the amazing last few months that made me certain this is only the beginning of something great!

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Resumo

A capacidade preditiva é uma das características mais procuradas nas ferramentas de modelação de

propriedades termodinâmicas, sendo estas continuamente desenvolvidas no sentido de diminuir a

necessidade de incluir dados experimentais na determinação dos parametros moleculares dos

modelos.

Aplicando o software gSAFT® na plataforma gPROMS®, foi avaliada a capacidade predictiva da

equação de estado SAFT-γ Mie (contribuição de grupos, GC) na descrição do equilíbrio de fases em

sistemas complexos, como polímero-solvente (poliestireno, poli(acetato de vinilo), polietileno,entre

outros) e misturas do surfactante não-iónico n-alkyl polyoxyethylene ether (CiEj).

Um dos maiores desafios na modelação destes sistemas consiste na escassez de dados experimentais

de equilíbrio líquido-vapor (ELV) para componentes puros, visto estes serem normalmente utilizados

na determinação dos parametros moleculares do modelo. Esta situação tende a ser contornada usando

dados experimentais relativos a misturas binárias e/ou multicomponente. A contribuição de grupos

permite caracterizar sistemas-objectivo após a determinação dos parâmetros relativos aos seus grupos

funcionais (podento resultar do estudo de dados experimentais de componentes mais simples e

facilmente disponíveis, incluindo ELV de compostos puros).

A maioria dos sistemas polímero-solvente estudados foram previstos correctamente, dispensando a

implementação de dados experimentais de polímeros na estimação de parametros. O ELV de

surfactantes puros e de misturas binárias surfactante-água é facilmente reproduzido pelos modelos

desenvolvidos (e frequentemente tranferíveis para sistemas semelhantes). Misturas binárias CiEj -

alcanos são muito difícies de modelar e misturas ternárias água- CiEj -alcano, impossíveis de prever.

A concentração micelar crítica (CMC) dos sistemas água- CiEj foi também modelada, e a dependência

desta em relação ao comprimento da molecula de surfactante foi bem reproduzida.

Palavras-chave: equação de estado, SAFT-γ Mie, polímeros, surfactantes, equilíbrio de fases,

imiscibilidade líquido-líquido

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Abstract

One of the most desired features in thermodynamic tools is a predictive capability, hence

thermodynamic modelling frameworks have been developed towards decreasing the need for

experimental data for the determination of molecular model parameters.

Using gSAFT® software within gPROMS® platform, an assessment of the predictive capability of the

SAFT-γ Mie EoS (a group contribution (GC) approach) is carried regarding the phase equilibrium of

complex materials. In this project are studied: polymer-solvent systems (PS, PVAc, PVME, PE, among

others) and non-ionic (n-alkyl polyoxyethylene ether, CiEj) surfactant mixtures.

The paucity of pure-component vapour-liquid experimental (VLE) data poses a challenge in the

modelling of these systems, as these are typically used to develop the required model parameters. This

is usually tackled by using experimental data for fluid-phase behaviour of binary and/or multi-component

mixtures. The GC formalism advantageously allows the characterisation of target systems once the

parameters for the functional groups that describe them have been obtained (e.g. by studying simpler

data typically available, including pure-component VLE).

The modelling of polymer-solvent systems was very successful - nearly all polymer systems studied

were accurately predicted without using binary polymer data to adjust the interaction parameters. Pure-

surfactant VLE and CiEj-water binary mixtures are easily correlated to by the developed models, and

sometimes even transferable to similar systems, but CiEj-alkane binaries are very difficult to reproduce,

and ternary water-CiEj-alkane mixtures are non-replicable. The critical micellar concentration (CMC) of

CiEj-water systems was also modelled, and the dependency of the CMC on surfactant chain length was

well captured.

Keywords: equation of state, SAFT-γ Mie, polymers, surfactants, phase behaviour, closed-loop

immiscibility.

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Contents

Acknowledgements ................................................................................................................................. 2

Resumo ................................................................................................................................................... 3

Abstract.................................................................................................................................................... 4

List of Tables ........................................................................................................................................... 7

List of Figures .......................................................................................................................................... 9

Nomenclature ........................................................................................................................................ 14

Introduction .................................................................................................................................... 17

1.1 Motivation .............................................................................................................................. 17

1.2 State of the art ....................................................................................................................... 18

1.2.1 Polymer-solvent systems ............................................................................................... 18

1.2.2 Surfactant mixtures ........................................................................................................ 20

Theoretical Background ................................................................................................................. 21

2.1 Intermolecular interactions .......................................................................................................... 21

2.2 Evolution of Equations of State (EoS) ................................................................................... 22

2.2.1 Ideal Gas Law ................................................................................................................ 23

2.2.2 Van der Waals and Cubic EoS ...................................................................................... 23

2.2.3 Statistical associating fluid theory (SAFT) ..................................................................... 24

Modelling of phase behaviour of polymer-solvent mixtures and surfactant systems using gSAFT

………………………………………………………………………………………………………………35

3.1 gSAFT .................................................................................................................................... 35

3.2 Polymer-sol