Macromolecules, Vol.29, No.20, 6663-6670, 1996
Chain Interactions in Poor-Solvent Polymer-Solutions - Equilibrium and Nonequilibrium Aspects
In this paper, we compute the interaction free energy between two polymer chains as a function of their separation R, in the poor-solvent regime below the ideal Theta temperature. We present both conventional "equilibrium" and "frozen-chain" nonequilibrium interaction free energies : in the latter case, the conformational state of the chains is not allowed to relax as they approach. The two types of calculation correspond to two distinct limits for the relative magnitudes of the "diffusion time" and the "conformational relaxation time" of the chains and give qualitatively different results below the collapse temperature. Both times scale as eta N, eta being the solvent viscosity and N the chain length. Hence the true chain interaction free energy corresponds neither to the equilibrium nor to the frozen-chain one, but to some kind of interpolation of the two whose form remains to be examined. The role of the chain entanglements is also briefly discussed : their relaxation time scales as eta N(7/3)alpha(s)(-4), alpha s being the contraction ratio of the chain radii of gyration over the unperturbed state. The second virial coefficient A(2) is computed from the cluster integral of the chain interaction free energy : below the collapse temperature, the equilibrium and the frozen-chain values of A(2) can differ by up to 3 orders of magnitude. We prove that a mean-field expression for A(2) derived by us in a previous paper is the first term in the series expansion of the frozen-chain coefficient. Finally, we discuss the implications of our findings for the shape of the polymer-solvent phase diagram and for the interpretation of Chu’s experiments on the kinetics of chain collapse and aggregation.