Thermodynamjc Interactions in Dilute Polymer Solutions: the Virial Coefficients

The statistical thermodynamics of dilute polymer solutions is reviewed from the point of view of the continuum theory based on molecular distribution functions. The comparatively rigorous perturbation treatment of the second and third virial coefficients, and various approximate theories derived from it to give closed-form expressions useful for good-solvent systems. are outlined. Indications from theory and representative experimental data are discussed for linear chains, branched chains, and binary solutes comprising polymers alike chemically but different in molecular weight and/or branched structure. It is suggested that apparently anomalous thermodynamic and conformational behaviour observed with branched chains reveals a basic inadequacy in the so called 'two-parameter' class of statistical theories. INTRODUCTION: HISTORICAL One of the most striking properties of long-chain polymers is the extreme departure of their solutions from Raoult's law. This behaviour attracted early attention in physicochemical studies of polymers and conceptual understanding of the basis for it was one of the important milestones in the progressive application of physical principles to macromolecular systems. Two rather distinct formalisms, one based on lattice models and the other on molecular distribution functions, have been applied in studying the thermodynamics of polymer solutions. First, the development of lattice or cell theories for simple liquid mixtures1 and, in particular, efforts to extend them to mixtures of molecules of disparate size2 inspired application of similar ideas to polymer solutions. The result was the celebrated theory presented independently by Huggins3 and by Flory4'5 in 1942. Despite innumerable variations and extensions of the lattice treatment—and a glance at the program of this Microsymposium indicates clearly enough that after thirty years the lattice method is still far from a dead issue—the essence of it can be expressed very simply. One imagines the solution volume to be divided into cells in each of which one can place either a segment of a polymer chain or a solvent molecule. The numbers of distinguishable configurations