Theory of Dilute Polymer Solution. III. Heterogeneous Polymer

The second virial coefficients of osmotic pressure and light scattering of heterogeneous chain polymer solutions are calculated to the double-contact approximation. Two types are assumed for the molecular weight distribution: the Schulz distribution, and the distribution with two deltalike peaks. Then, the heterogeneity corrections for intrinsic viscosity are evaluated on the assumption of the Schulz distribution. On the basis of the results obtained, a tentative attempt is made at interpreting the proportionality between the intrinsic viscosity at the Θ temperature and the square root of the molecular weight without discarding the hydrodynamic scheme, and the relation between the hydrodynamic and statistical radii of heterogeneous polymer coil is also examined. Finally, the relation between the second virial coefficient A2 and intrinsic viscosity [η] is discussed somewhat in detail. And it is shown that the initial curvature of the curve of [η]/[η]θ — 1 vs A2Mw/[η]θ is concave upward for ordinary fractionated samples, where [η]θ is the intrinsic viscosity at the Θ temperature, and Mw is the weight-average molecular weight. This statement is verified by comparison with experiment.