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 ≈ 200 nm) in dilute, semidilute, and entangled solutions of poly(vinyl methyl ether) (M_w = 1.3 × 10⁶). Over this range of matrix concentrations, 0 ≤ c[ƞ] ⩽ 36, the diffusivity drops by almost 5 orders of magnitude. Near c* (≈[ƞ]⁻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 “positive deviations” 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 for chain mobility in well-entangled systems. The behavior near c* is discussed in terms of the matrix correlation length, ξ, which has a maximum at ξ ≈ R_g for c ≈ c*. It is noted that the fluid layer within a distance ξ 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 ξ ≈ qR_g ≈ 1, rather than q ξ ≪ 1.