Experimental Test of the Two-Parameter Theory of Dilute Polymer Solutions: Poly-p-methylstyrene

In order to test the two-parameter theory of dilute polymer solutions, light-scattering and intrinsic-viscosity measurements were carried out on fractions of poly-p-methylstyrene in toluene, dichloroethane, cyclohexane, and methyl ethyl ketone at 30°C, and in diethyl succinate at temperatures ranging from 16 to 60°C. The theta temperature for this polymer in diethyl succinate was found to be 16.4°C. With the data for the statistical-radius expansion factor αS and the interpenetration function Ψ appearing in the second virial coefficient, validity of a theory of these quantities was examined using the two criteria introduced previously: (1) consistency in the values of the excluded-volume parameter z determined from αS and Ψ, and (2) linearity between z and the square root of the molecular weight. It was found that the Yamakawa–Tanaka theory of αS and the Kurata–Yamakawa theory of Ψ were a self-consistent pair of intramolecular and intermolecular theories of interaction which satisfied both of the two criteria. The data for the viscosity-radius expansion factor αη indicated no existence of the draining effect, and there was no satisfactory theory of αη. An empirical relation between αη and z was obtained, where values of z were calculated from observed values of αS using the Yamakawa–Tanaka equation. It was found that at small z, αη3 = 1 + C1z + ···, with 1.05 < C1 < 1.55. This is a theoretical problem to be solved. Based on the empirical relation between αη and z, the equation for the Stockmayer–Fixman viscosity plot was revised. Values of the polymer–solvent interaction parameter B determined from viscosity plots using the revised equations were in good agreement with those from mean-square radii and also from second virial coefficients.