Macromolecular clusters in poor-solvent polymer solutions

Abstract

We apply our previously proposed “Gaussian cluster” model [J. Chem. Phys. 104, 1626 (1996)] to the study of macromolecular association and aggregation, under poor-solvent conditions (T<Θ). The properties of the macromolecular clusters are studied as a function of the number of chains ν=2,3,4,…, of the attractive two-body excluded-volume parameter z and of the repulsive three-body parameter K1. In the temperature window between its upper stability temperature and the coil-globule transition temperature for the single chains, a cluster of 2÷10 chains can have a smaller radius of gyration than an isolated polymer chain, provided K1 is sufficiently small. We suggest that this parameter may be estimated by considering the relative separations between the Θ, the critical and the collapse temperatures. We compute the equilibrium distribution of the chains in a dilute solution among all possible cluster sizes (including ν=1, the isolated chains); population of the clusters ν⩾2 increases with K1, but is generally rather small. Below the coil–globule transition temperature, anywhere on the dilute side of the two-phase region of the phase diagram, there is no free-energy barrier to polymer aggregation and precipitation: a single collapsed chain is a “critical nucleus” and the spinodal practically coincides with the binodal.