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

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Abstract
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 α S 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 α S and Ψ , and (2) linearity between z and the square root of the molecular weight. It was found that the Yamakawa–Tanaka theory of α S 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 α η indicated no existence of the draining effect, and there was no satisfactory theory of α η . An empirical relation between α η and z was obtained, where values of z were calculated from observed values of α S using the Yamakawa–Tanaka equation. It was found that at small z, α η 3 = 1 + C 1 z + ··· , with 1.05 < C 1 < 1.55 . This is a theoretical problem to be solved. Based on the empirical relation between α η 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.

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