First and Second Concentration-Dependent Coefficients of Translational Diffusion and Sedimentation for Poly(α-methylstyrene) in a Good Solvent

Abstract

The first and second concentration-dependent coefficients of translational diffusion, kD and kD2, and of sedimentation, ks and ks2, for poly(α-methylstyrene) fractions of high molecular weight in benzene at 30 °C were determined by dynamic light scattering and sedimentation velocity measurements. In the molecular weight, Mw, range of 3.76 × 105 ≤ Mw ≤ 6.85 × 106, the first coefficients are positive, as reported previously, but the second are negative, which has not been previously observed. These molecular weight dependences are described by power laws (k ∝ Mwa), but the exponents for kD (0.769) and ks (0.663) and for kD2 (1.54) and ks2 (1.48) are smaller than the predicted values in the good-solvent limit, 0.80 and 1.60, respectively. Expressed in the volume-fraction frame of reference, the coefficients are not constant, which contradicts the hard sphere approximation for swollen chains, and are represented well by universal functions of X, the ratio of the thermodynamic interaction radius derived from the second virial coefficient, A2, and the hydrodynamic chain radius derived from the diffusion coefficient; the functions are as predicted by Akcasu and Benmouna with a Mw-independent thermodynamic g factor (=A3/A22Mw) = 0.22−0.23. The hydrodynamic g factors defined by kD2/kD2 and ks2/ks2 are constant, −0.14 and −0.05, respectively, for higher Mw. The two- and three-body effective hydrodynamic interaction radii deduced from ks and ks2 are larger than those from kD and kD2, indicating the long-range nature of the purely hydrodynamic interactions. The swollen chain dynamics in good solvents cannot be described by the hard sphere approximation but require a more detailed treatment of hydrodynamic interactions.