Coupling model analysis of polymer dynamics in solution: Probe diffusion and viscosity

The coupling model of Ngai et al. [K. L. Ngai, Disorder Effects in Relaxation Processes, edited by R. Richert and A. Blumen (Springer-Verlag, Berlin, 1994)] is applied to treat polymer dynamics in solution. Important dynamic quantities considered here include the zero-shear viscosity η and the light-scattering spectrum (field correlation function) g(1)(t) of optical probes suspended in solution. The coupling model describes systems in terms of two times, a basic relaxation time τ0 and a crossover time tc, and a coupling exponent n. Use of scaling arguments allows us to extract values for n from the concentration dependence of η and, by three separate paths, from the concentration, time, and scattering vector dependencies of g(1)(t). Values of n from these four distinct physical approaches are shown to be mutually consistent, especially in the higher-concentration, large-probe-particle regime in which the scaling arguments are most likely to be valid. The behavior of n above the solutionlike–meltlike viscosity transition, and the effect of probe size on n, are briefly discussed.