A simple genetic algorithm for the numerical evaluation of binodal curves in ternary systems polymer-liquid (1)-liquid (2) and polymer (1)-polymer (2)-solvent is presented. The technique exploits a specifically developed restarting technique based on a combined elitist and zooming strategy on the last population at each iteration. The objective function (fitness) is represented by the weighted sum of the squared differences of chemical potentials of the two phases of each component, obtained evaluating first derivatives of Gibbs free energy of the mixture with respect to the number of moles of the components. The method proposed (a) is numerically stable since it does not require the evaluation of first derivatives of the objective function and (b) can be applied in a wide range of cases changing the equation of state. Several comparisons with simplified iterative procedures presented in the past in the technical literature both for mixtures of two polymers with identical characteristics in a solvent and for mixtures of solvent-nonsolvent-polymer with solvent-polymer interaction parameter equal to zero are reported. Finally, a comparison between present results and the alternating tangent approach is reported for two technically meaningful binary systems, when a simplified PC-SAFT equation of state is adopted. The comparisons show that reliable results can be obtained by means of the algorithm proposed and suggest that the procedure presented can be used for practical purposes
Genetic Algorithm for the determination of binodal curves in ternary systems Polymer / Liquid(1) / Liquid(2) and Polymer(1) / Polymer(2) / Solvent
MILANI, Gabriele;
2007
Abstract
A simple genetic algorithm for the numerical evaluation of binodal curves in ternary systems polymer-liquid (1)-liquid (2) and polymer (1)-polymer (2)-solvent is presented. The technique exploits a specifically developed restarting technique based on a combined elitist and zooming strategy on the last population at each iteration. The objective function (fitness) is represented by the weighted sum of the squared differences of chemical potentials of the two phases of each component, obtained evaluating first derivatives of Gibbs free energy of the mixture with respect to the number of moles of the components. The method proposed (a) is numerically stable since it does not require the evaluation of first derivatives of the objective function and (b) can be applied in a wide range of cases changing the equation of state. Several comparisons with simplified iterative procedures presented in the past in the technical literature both for mixtures of two polymers with identical characteristics in a solvent and for mixtures of solvent-nonsolvent-polymer with solvent-polymer interaction parameter equal to zero are reported. Finally, a comparison between present results and the alternating tangent approach is reported for two technically meaningful binary systems, when a simplified PC-SAFT equation of state is adopted. The comparisons show that reliable results can be obtained by means of the algorithm proposed and suggest that the procedure presented can be used for practical purposesI documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
