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

Abstract

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 to e[eta] less than or equal to 36, the diffusivity drops by almost 5 orders of magnitude. Near c(*) (approximate to[eta]-(1)) 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 &apos;&apos;positive deviations&apos;&apos; from Stokes-Einstein 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 fdr chain mobility in well-entangled systems. The behavior near c(*) is discussed,is terms of the matrix correlation length, xi, which has a maximum at xi approximate to R(g) for c approximate to c(*). It is noted that the fluid; layer within a distance w 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 xi approximate to qR(g) x 1, rather than q xi << 1.