Application of scaling concepts to sedimentation phenomena in semidilute macromolecular solutions

Abstract

AbstractSedimentation velocity data on polystyrene in a good solvent (toluene) and in a theta solvent (cyclopentane), over a large concentration range are reported. Under good‐solvent conditions the exponent β in the apparent scaling law describing the concentration dependence of the sedimentation coefficient (s ∝ cβ) in the semidiiute region is found to be concentration dependent. However, a power law fit to data for the highest molecular weight (M = 20.6 × 106) in the concentration region (c < 2 kg m−3) yields a value β = −0.59, somewhat smaller than that (−0.54) predicted theoretically. This discrepancy and the observed curvature in logs vs. logc at higher concentrations are discussed. Under theta‐solvent conditions, on the other hand, the concentration dependence of s in the semidilute regime can be represented by a simple power law, with β = −1.0, in excellent agreement with the theoretical prediction. The crossover concentration c*, separating the dilute and semidilute concentration regimes, was found to be well defined and located at c = 1/[η]. c* varies with molecular weight as M−0.73 and M−0.50 under good‐solvent and theta‐solvent conditions, respectively.