An Algorithm for Calculation of Phase Equilibria in Polydisperse Polymer Solutions Using the SAFT Equation of State

Abstract

We propose an algorithm for calculating phase equilibria of polydisperse polymer systems using the SAFT equation of state. The algorithm is formally exact and the computation time is independent of the number of pseudocomponents used to represent the polymer molecular weight distribution. The algorithm is based on the assumptions that the discrete pseudocomponents have the same segment size, the chain length is directly proportional to the molecular weight, and the binary interaction parameter kij between the discrete pseudocomponents is zero. The basic version of the algorithm assumes that the dispersion energy parameter (u0/k) is the same for all the pseudocomponents and the binary interaction parameter kij is the same between all the pseudocomponents and the solvent. The algorithm is then generalized to the case where the dispersion energy parameter (u0/k) is different for each pseudocomponent and the polymer/solvent binary interaction parameter is different for each pseudocomponent. Distinctive features of the phase diagrams of polydisperse systems are illustrated by calculating the cloud point and shadow point curves of polyethylene solutions in ethylene using the algorithm proposed in this work.