Chain connectivity and conformational variability of polymers: Clues to an adequate thermodynamic description of their solutions, 2 - Composition dependence of flory-huggins interaction parameters

Full Paper: In Part 1 of this contribution we have reported how the Flory-Huggins interaction parameter chi can be <LF>modeled as a function of chain length within the composition range of pair interaction between the macromolecules by means of the three parameters alpha, zeta, <LF>and lambda. This contribution presents the extension of the <LF>approach to arbitrary volume fractions, phi, of the polymer and its application to published data on chi(phi). The resulting equation reads chi = alpha(1 - nuphi)(-2) - zeta(lambda + 2(1 - lambda)phi) and requires only the additional parameter nu to incorporate the composition dependence. Its employment to experimental data is very much facilitated by substituting for chi(o) (limiting value for phi --> 0); furthermore, the expression can in good approximation be simplified to chi approximate to (chi(o) + zetalambda)(1 - nu phi)(-2) - zetalambda(1 + 2phi). That is: only two parameters, nu and the product of zeta and lambda, need to be adjusted. This relation is capable of describing all types of composition dependencies reported in the literature, including the hitherto incomprehensible occurrence of pronounced minima in chi(phi). For a given system the evaluation of the chain length dependence of chi(o), reported in Part 1, and the present evaluation of the composition dependence of chi(o) yield the same data for the conformational response zeta. Similarly both types of measurements generate the same interdependence between zeta and alpha. The physical meaning of the different parameters and the reason for the observed correlations are discussed.