In contrast to the original assumption the Flory-Huggins interaction parameter c does not only depend on temperature and pressure but also on composition and - even in the region of high polymer concentrations - on the chain length of the polymer. Numerous attempts have been made to incorporate these features into the theory but despite partial advantages without veritable success. For this reason a paradigmatic change is proposed.
The theoretical analysis is performed by subdividing the dilution process (the physico- chemical basis of c) into two clearly separable states. It yields the following expression for c0, the c value in range of pair interaction: c0 = a - z l The parameter a measures the effect of contact formation between solvent molecules and polymer segments at fixed chain conformation, whereas the parameter z quantifies the contributions of the conformational changes taking place in response to dilution; z becomes zero for theta conditions. The influences of M are exclusively contained in the parameter l. The generalization of this approach to arbitrary polymer concentrations yields the relation c = a (1-nj)-2 -z(l+2(1-l)j). Only the additional parameter n is required to incorporate the composition dependence. Its employment to experimental data is very much facilitated by substituting for c0 (limiting value for j0); furthermore the expression can in good approximation be simplified to c (c0 + zl)(1- nj)-2 - zl(1+2j). This relation is capable of describing all types of composition dependencies reported in the literature, including the hitherto incomprehensible occurrence of pronounced minima in c (j ).
Other areas of theoretical know-how concern: (i) the applicability of the different corresponding state theories for the thermodynamic description of binary systems (ii) the modeling of multinary mixtures including the rationalization of special effects (like the expelling of the precipitant from mixed solvents, (iii) the role of ternary interaction parameters and, (iv) the use of acoustic measurements to obtain information on the interaction between polymers.
For more information, please see the following publications: 236, 237, 219, 218, 214, 212, 199, 162