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Modeling of Polymer Phase Equilibria Using Equations of State

  • Gabriele SadowskiEmail author
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 238)

Abstract

The most promising approach for the calculation of polymer phase equilibria today is the use of equations of state that are based on perturbation theories. These theories consider an appropriate reference system to describe the repulsive interactions of the molecules, whereas van der Waals attractions or the formation of hydrogen bonds are considered as perturbations of that reference system. Moreover, the chain-like structure of polymer molecules is explicitly taken into account. This work presents the basic ideas of these kinds of models. It will be shown that they (in particular SAFT and PC-SAFT) are able to describe and even to predict the phase behavior of polymer systems as functions of pressure, temperature, polymer concentration, polymer molecular weight, and polydispersity as well as – in case of copolymers – copolymer composition.

Keywords

Copolymers Equation of state Modeling Polymers Solubility Sorption Thermodynamics 

Symbols

A

Helmholtz energy

a

Parameter of the van der Waals equation

Bαβ

Fraction of bonds between segments α and β within a copolymer

b

Parameter of the van der Waals equation

d

Temperature-dependent segment diameter

g

Radial distribution function

g(d+)

Value of the radial distribution function at contact

k

Boltzmann constant

M

Molecular weight

M2p,j

Molecular weight of pseudocomponent j

Mn

Number average of molecular weight

Mw

Weight average of molecular weight

Mz

z-Average of molecular weight

\( \overline {{M^k}} \)

kth moment of the molecular weight distribution

m

Segment number

\( \bar{m} \)

Average segment number

N

Number of molecules

N*

Number of association sites per molecule or monomer unit

ni

Mole number

kij

Binary interaction parameter

p

Pressure

R

Ideal gas constant

T

Temperature

V

Volume

v

Molar volume

v00

Segment volume (parameter of SAFT)

xi

Mole fraction of component i (solvent or polymer)

x2p,j

Mole fraction of pseudocomponent j within polymer

W(M)

Continuous molecular weight distribution

wi

Weight fraction of component i

w2p,j

Weight fraction of pseudocomponent j in polymer

z

Compressibility factor

zα,zβ

Fraction of segments α or β in a copolymer

Abbreviations

HDPE

High-density polyethylene

L

Liquid

LL

Liquid–liquid

LDPE

Low-density polyethylene

MA

Methylacrylate

MWD

Molecular weight distribution

PA

Propylacrylate

PC-SAFT

Perturbed Chain Statistical-Associating-Fluid Theory

PR

Peng–Robinson

PHCT

Perturbed Hard-Chain Theory

PHSC

Perturbed Hard-Sphere-Chain Theory

PSCT

Perturbed Soft-Chain Theory

SAFT

Statistical-Associating-Fluid Theory

SAFT-VR

SAFT with Variable Range

SRK

Soave–Redlich–Kwong

Greek Letters

α,β

Segment type

ε

Dispersion energy parameter

εAA

Association-energy parameter

η

Reduced density

κAA

Association volume parameter

ρ

Number density (molecules per volume)

σ

Temperature-independent segment diameter

ϕi

Fugacity coefficient of component i in the mixture

ϕ2p,j

Fugacity coefficient of polymer pseudocomponent j in the mixture

Superscripts

assoc

Contribution due to association

chain

Contribution due to chain formation

disp

Dispersion (van der Waals attraction)

disp

Dispersion contribution according to the PC-SAFT model

hc

Hard-chain contribution

hs

Hard-sphere contribution

id

Ideal gas

pert

Perturbation

ref

Reference

res

Residual

I,II

Phases I and II

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Biochemical and Chemical Engineering, Laboratory for ThermodynamicsTU DortmundDortmundGermany

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