Dynamic light scattering has been used to follow the tracer diffusion of polystyrene spheres (R % 200 nm) in dilute, semidilute, and entangled solutions of poly(viny1 methyl ether) ( M , = 1.3 x lo6). Over this range of matrix concentrations, 0 5 c[r]] 5 36, the diffusivity drops by almost 5 orders of magnitude. Near c* (=[r]]-') for the matrix, the diffusivity exceeds that estimated from the bulk solution viscosity via the Stokes-Einstein relation by a factor of about 3. Such "positive deviations" from StokesEinstein behavior have been reported previously in several systems. However, once the matrix concentration is sufficiently high for entanglements to be effective, Stokes-Einstein behavior is recovered. This new result was confirmed via forced Rayleigh scattering. In addition, these data can reconcile measurements of sphere diffusion with reptation-based models for chain mobility in well-entangled systems. The behavior near c* is discussed in terms of the matrix correlation length, E, which has a maximum at 6 = R, for c x c*. It is noted that the fluid layer within a distance 5 of the sphere surface will, in general, differ in composition from the bulk solution, and consequently the sphere mobility may well not sense the macroscopic solution viscosity, particularly near c*. As a corollary, for large matrix chains, dynamic light scattering may not monitor the long-time diffusion of the spheres near c*, because q t % qR, % 1, rather than q t << 1.
IntroductionThe tracer diffusion of spherical particles in polymer solutions has attracted a great deal of experimental a t t e n t i~n . l -~~ The principal motivation has been to understand diffusion in solutions containing mixtures of macromolecules of differing architectures, which might serve, for example, to test modern treatments of polymer solution dynamics or as models of important biological systems. It is probably fair to say, however, that these goals have not been completely attained; the results in the literature diverge in interesting ways. Our own focus has been on the possible applicability of the reptation hypothesis, and we have previously reported
