The diffusion of highly cross-linked, nearly monodisperse polystyrene latex spheres of 0.2-/tm radius in the presence of linear polystyrene as the matrix polymer in the moderately good solvent JV.1Vdimethylformamide at 25 °C was determined by quasi-elastic light scattering as a function of matrix concentration and molecular weight. This is the first report of a latex probe in trace amounts diffusing in an organic solvent, and with a matrix polymer chemically similar to the probe. The latex diffusion diminished monotonically with matrix concentration, which varied from moderately dilute solutions into the semidilute regime up to a matrix concentration of 8 times c*. Stokes-Einstein behavior was observed at all matrix concentrations and for both matrix molecular weights (2.15 x 10s and 1.1 X 106), within experimental error. In the semidilute region the entanglement relaxation was always much faster than probe motion. The diffusion data fit the scaling law D/D<¡ = exp(-ac'Af1'), with v equal to 0.99 and y equal to 0.49. Comparison is made to diffusion of latex probes in aqueous dispersants, and of silica probes in organic dispersants.

Dynamic light scattering has been used to study the diffusion of polystyrene (PS) latex spheres (≈0.2 μm radius) in poly(methyl methacrylate) (PMMA) solutions at 25 °C. The weight-average molecular weight of the PMMA was 350 000. The sign and magnitude of the deviations from the Stokes−Einstein (SE) equation varied dramatically with solvent quality. Positive deviations from SE behavior (ηD sphere/η0 D 0 > 1) were observed in good solvents for PMMA, such as dimethylformamide (DMF) and tetrahydrofuran (THF). We argue that these positive deviations are a result of a layer of solution locally surrounding the latex spheres that is rich in solvent and deficient in PMMA. This “depletion layer” is likely caused by a combination of entropic repulsion between the matrix PMMA and the latex spheres, and most importantly the immiscibility of PMMA and PS. A negative deviation (ηD sphere/η0 D 0 < 1) by almost of factor of 3 from the SE equation was observed in a dioxane−water mixed solvent, which is a ϑ-solvent for PMMA at 25 °C. PMMA adsorption onto the latex spheres is argued to occur under these unfavorable solvent conditions. At high matrix concentrations, entanglements of the adsorbed PMMA with free PMMA in solution likely occur. A very slow relaxation mode, in addition to the mode associated with sphere diffusion, was present in the CONTIN analyses of the PMMA/PS latex/dioxane−water system. It is possible that this mode is due to PMMA clusters, or less likely, bridged PS latex moieties.

The diffusion of highly cross-linked polystyrene latex spheres of radii 0.152 and 0.208 μm through solutions of poly(γ-benzyl-l- glutamate) (PBLG) has been studied by dynamic light scattering (DLS). The solvent used was dimethylformamide (DMF), in which PBLG adopts a rigid rodlike α-helical conformation. Tracer diffusion coefficients of the spheres in solutions of long rods (L ≈ 159 nm) were larger than predicted from the Stokes−Einstein equation. These positive deviations from the Stokes−Einstein equation are consistent with the theory of Auvray (J. Phys. 1981, 42, 79), which predicts the presence of a rod monomer depletion layer locally surrounding the spheres that extends a distance ≈ L from the surface of the sphere. The results are also consistent with the experimental work of others concerning depletion of stiff polymers near surfaces. Sphere tracer diffusion coefficients in solutions of smaller rods (L ≈ 48 nm) approximately follow the Stokes−Einstein equation. In this system, depletion effects are expected to be much smaller. Fits of the sphere diffusion data to the equation D/D 0 = exp(−αc υ) yielded values of υ = 1−1.1, which exceed those predicted by theory. We were also able to estimate translational diffusion coefficients of the PBLG in the ternary rod/sphere/solvent systems by employing very short sample times in the DLS experiment.

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