CHAIN INTERACTIONS IN POOR-SOLVENT POLYMER-SOLUTIONS - EQUILIBRIUM AND NONEQUILIBRIUM ASPECTS

In this paper, we compute the interaction free energy between two poly mer chains as a function of their separation R, in the poor-solvent re gime below the ideal Theta temperature. We present both conventional ' 'equilibrium'' and ''frozen-chain'' nonequilibrium interaction free en ergies: in the latter case, the conformational state of the chains is not allowed to relax as they approach. The two types of calculation co rrespond to two distinct limits for the relative magnitudes of the ''d iffusion time'' and the ''conformational relaxation time'' of the chai ns and give qualitatively different results below the collapse tempera ture. Both times scale as eta N, eta being the solvent viscosity and N the chain length. Hence the true chain interaction free energy corres ponds neither to the equilibrium nor to the frozen-chain one, but to s ome 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 c ontraction ratio of the chain radii of gyration over the unperturbed s tate. The second virial coefficient A(2) is computed from the cluster integral of the chain interaction free energy: below the collapse temp erature, the equilibrium and the frozen-chain values of A(2) can diffe r by up to 3 orders of magnitude. We prove that a mean-field expressio n 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 k inetics of chain collapse and aggregation.