Binary Mutual Diffusion Coefficients of Polymer/Solvent Systems Using Compressible Regular Solutions Theory and Free Volume Theory

Arsalan Farajnezhad; Orang Asef Afshar; Milad Asgarpour Khansary; Saeed Shirazian

doi:10.1515/jnet-2015-0036

Article

Binary Mutual Diffusion Coefficients of Polymer/Solvent Systems Using Compressible Regular Solutions Theory and Free Volume Theory

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Published/Copyright: February 5, 2016

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From the journal Journal of Non-Equilibrium Thermodynamics Volume 41 Issue 3

Abstract

The free volume theory has found practical application for prediction of diffusional behavior of polymer/solvent systems. In this paper, reviewing free volume theory, binary mutual diffusion coefficients in some polymer/solvent systems have been systematically presented through chemical thermodynamic modeling in terms of both activity coefficients and fugacity coefficients models. Here chemical thermodynamic model of compressible regular solution (CRS) was used for evaluation of diffusion coefficients calculations as the pure component properties would be required only. Four binary polymeric solutions of cyclohexane/polyisobutylene, n-pentane/polyisobutylene, toluene/polyisobutylene and chloroform/polyisobutylene were considered. The agreement between calculated data and the experimentally collected data was desirable and no considerable error propagation in approximating mutual diffusion coefficients has been observed.

Keywords: polymeric membrane; thermodynamic model; free volume; mutual diffusion coefficients; polymeric solutions

Appendix A

The first derivative (f′) of a given function (f) can be calculated at each point of interest (x0) using the central difference approximation [65]. However, to improve calculations accuracy and compensate the error of truncations, it is more precise to use a coupled central difference approximation formula of high and low accuracy as presented in eq. (18) [65], where s and t are two-step sizes around the point of interest, i. e. x0. It has been believed that this type of formulation approaches us as close as possible to the real value of derivative at the point of interest (x0) [65]. Therefore, using the explicit relationships of chemical potential and all aforementioned details of studied models (and any model of interest) and eq. (18), one could readily calculate the property of interest and establish a standalone computer routine for any future investigation:

(18)f′x0=1t2fx0+t−1s2fx0−s1t+1s−1t−1sfx0

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Received: 2015-6-22

Revised: 2015-10-29

Accepted: 2016-1-7

Published Online: 2016-2-5

Published in Print: 2016-7-1

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https://doi.org/10.1515/jnet-2015-0036

Keywords for this article

polymeric membrane; thermodynamic model; free volume; mutual diffusion coefficients; polymeric solutions