Application of genetic algorithm in calculation of the phase behavior of binary and ternary polymer solutions

Abstract

A genetic algorithm as an optimization procedure has been developed to predict the phase behavior of polymer solutions. The phase equilibrium diagrams of binary and ternary polymer solutions have been determined using the appropriate form of Flory–Huggins free-energy function for polymer solutions. A concentration and temperature dependent form of the interaction parameter has been used to reflect the effect of temperature and polymer properties in the free-energy form. The proposed genetic algorithm is applied to compare the phase behavior results of some typical polymer solutions with the results of the classical determination methods and then applied to some conventional ternary polymer solutions as polymer–solvent–nonsolvent systems. The proposed algorithm use a set of individual states as the initial chromosomes and uses the general rules as crossover, mutation, and with use of a fractional objective function determines the binodal points or the phase diagram boundaries of polymer solutions. The properties of an industrially relevant polymer solution, a polystyrene–cyclohexane solution, have been used to emphasize on the industrial application of the proposed algorithm. The algorithm has been used to predict the phase behavior of the two polymer–solvent–nonsolvent systems as polystyrene-butanone-methanol and polystyrene-butanone-propanol at three different temperatures and results show good agreement with the experimental observations. The algorithm also has the capability to predict both the concentration-independent and concentration-dependent interaction parameters among the different components. The genetic algorithm is an easy-to-use, state-of-art, and very fast optimization tool, and has very strong capability to solve nonlinear systems in chemical and polymer engineering topics.