Spinodal equation for polydisperse polymer solutions

Abstract
In this paper polydisperse polymer solutions are considered to be described by a class of free-energy functions generalizing the classical Flory-Huggins relation by replacing Huggins’ X -term by a function which is assumed to depend on a finite number of moments of the molar mass distribution. Most free-energy functions used in practice obey this condition. For this class of free-energy functions a spinodal theorem is proved; if the phase considered lies on the spinodal, then a matrix Q is positive semidefinite and its determinant, det Q , equals zero. The calcu­lation of the matrix Q is relatively simple. M. Gordon, P. Irvine & J. W. Kennedy ( J. Polymer Sci . 61, 199 (1977)) and P. Irvine & M. Gordon ( Proc. R. Soc. Lond. A 375, 397 (1981)) showed that the spinodal problem considered may be simplified by replacing the given distribution by a spinodal equivalent distribution consisting of a number of discrete polymer species. For this reason a finite moment problem has to be solved. The theorem proved in this paper results in avoiding the solution of this moment problem and, furthermore, guaran­tees the stability matrix to possess the minimal order.

This publication has 10 references indexed in Scilit: