Solvent-Induced Association of Polymers: Clustering and Network Formation
A thermodynamic treatment of a random, solvent-assisted association of polyfunctional macromolecules is developed. In the model proposed, a multiple association junction connecting m primary chains consists of m polymer functional groups with bm solvent molecules incorporated. Using Veytsman's procedure, basic thermodynamic functions and association equilibrium relations are derived. Different association characteristics are examined. When passing from a system with solvent-free junctions ( b = 0) to our model with b > 0, the shape of the calculated curves changes strikingly, e.g. the relative association degree α vanishes both in the neat solvent and neat polymer points, showing a maximum near the middle of the composition range. This results in the existence of two critical points of network formation (gel points), delimitating the compositional range of the coexistence of a network with finite clusters (gel region). Using extinction probability, the quantitative parameters characterizing the cluster-network relationships are calculated and analyzed. All of them display an extreme near the middle of the gel region, and various kinds of singularities appear in the two gel points. The effect of the stoichiometric ratio b on characteristic system parameters is discussed.