DIFFUSION OF SPHERES IN ENTANGLED POLYMER-SOLUTIONS - A RETURN TO STOKES-EINSTEIN BEHAVIOR

Dynamic light scattering has been used to follow the tracer diffusion of polystyrene spheres (R approximate to 200 nm) in dilute, semidilute , and entangled solutions of poly(vinyl methyl ether) (M(w) = 1.3 x 10 (6)). Over this range of matrix concentrations, 0 less than or equal t o e[eta] less than or equal to 36, the diffusivity drops by almost 5 o rders of magnitude. Near c() (approximate to[eta]-(1)) for the matrix , the diffusivity exceeds that estimated from the bulk solution viscos ity via the Stokes-Einstein relation by a factor of about 3. Such ''po sitive deviations'' from Stokes-Einstein behavior have been reported p reviously in several systems. However, once the matrix concentration i s sufficiently high for entanglements to be effective, Stokes-Einstein behavior is recovered. This new result was. confirmed via forced Rayl eigh scattering. In-addition, these data can reconcile measurements of sphere diffusion with reptation-based models fdr chain mobility in we ll-entangled systems. The behavior near c() is discussed,is terms of the matrix correlation length, xi, which has a maximum at xi approxima te to R(g) for c approximate to c(). It is noted that the fluid; laye r within a distance w of the sphere surface will, in general, differ i n composition from the bulk solution, and consequently the sphere mobi lity may well not sense the macroscopic solution viscosity, particular ly near c(). As a corollary, for large matrix chains, dynamic light s cattering may not monitor the long-time diffusion of the spheres near c(), because q xi approximate to qR(g) x 1, rather than q xi << 1.