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Polymer Thermodynamics pp 389–418Cite as

Modeling of Polymer Phase Equilibria Using Equations of State

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Part of the book series: Advances in Polymer Science ((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.

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Abbreviations

A :

Helmholtz energy

a :

Parameter of the van der Waals equation

B αβ :

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

M 2p,j :

Molecular weight of pseudocomponent j

M n :

Number average of molecular weight

M w :

Weight average of molecular weight

M z :

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

n i :

Mole number

k ij :

Binary interaction parameter

p :

Pressure

R :

Ideal gas constant

T :

Temperature

V :

Volume

v :

Molar volume

v 00 :

Segment volume (parameter of SAFT)

x i :

Mole fraction of component i (solvent or polymer)

x 2p,j :

Mole fraction of pseudocomponent j within polymer

W(M):

Continuous molecular weight distribution

w i :

Weight fraction of component i

w 2p,j :

Weight fraction of pseudocomponent j in polymer

z:

Compressibility factor

z α,z β :

Fraction of segments α or β in a copolymer

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

α,β:

Segment type

ε :

Dispersion energy parameter

ε AA :

Association-energy parameter

η :

Reduced density

κ AA :

Association volume parameter

ρ :

Number density (molecules per volume)

σ:

Temperature-independent segment diameter

ϕ i :

Fugacity coefficient of component i in the mixture

ϕ 2p,j :

Fugacity coefficient of polymer pseudocomponent j in the mixture

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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Authors and Affiliations

  1. Department of Biochemical and Chemical Engineering, Laboratory for Thermodynamics, TU Dortmund, Emil-Figge-Strasse 70, 44227, Dortmund, Germany

    Gabriele Sadowski

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  1. Gabriele Sadowski
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Correspondence to Gabriele Sadowski .

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Editors and Affiliations

  1. Inst. Physikalische Chemie, Universität Mainz, Jakob-Welder-Weg 13, Mainz, 55099, Germany

    Bernhard A. Wolf

  2. Sekr. TK7, TU Berlin, Straße des 17. Juni 135, Berlin, 10623, Germany

    Sabine Enders

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Sadowski, G. (2010). Modeling of Polymer Phase Equilibria Using Equations of State. In: Wolf, B., Enders, S. (eds) Polymer Thermodynamics. Advances in Polymer Science, vol 238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/12_2010_94

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