Phenomenological scaling laws for ‘‘semidilute’’ macromolecule solutions from light scattering by optical probe particles

Polymer solution dynamics may be inferred from light scattering spectra of dissolved optical probe particles. We compare a variety of probes in solutions of several polymers. In the ‘‘overlapping’’ concentration/molecular weight regime, the Stokes–Einstein equation fails by up to a factor of 2, while the probe diffusion coefficient D follows a scaling law D/D0=exp(−aMγcνRδ) (c, M, and R are the polymer concentration, molecular weight, and the probe radius, respectively). Experimentally, γ=0.8±0.1, ν=0.6–1.0, and δ=−0.1 to 0, contrary to the theoretical predictions γ=0 and δ=1. With very high molecular-weight polymers, we observe a further ‘‘entangled’’ regime, characterized by huge (104) failures of the Stokes–Einstein equation and the appearance of ‘‘fast’’ modes in the scattering spectrum.