Diffusion of Polystyrene in Controlled Pore Glasses: Transition from the Dilute to the Semidilute Regime

The diffusion of polystyrene molecules inside controlled pore glasses with inert pore walls was investigated by the technique of dynamic light scattering over a wide range of concentrations of dissolved polystyrene in solutions in equilibrium with the porous glasses immersed in them. Index-matching of the solvent to the silica glasses effectively facilitates the acquisition of information on the dynamics of polymer chains inside the pore network without being compromised by multiple scattering of photons. When the solute concentration outside the pore is much smaller than the overlap concentration v*, the apparent diffusion coefficient of polymers within the D_pore shows little dependence on concentration, a result indicating the realization of a well-defined dilute regime inside the pore. As the outside concentration increases and approaches v*, D_pore rapidly increases. This tendency is more pronounced for polystyrene samples that have higher molecular weights and are predicted to have a lower partition coefficient and hence a lower concentration inside the pore. With further increases of concentration beyond v*, D_pore approaches the apparent diffusion coefficient outside the pore. Moreover, D_pore becomes almost the same for the three different molecular weights of polystyrene fractions studied and depends primarily on the weight concentration of the solute outside the pore. These features are typical of a semidilute solution regime for flexible polymers characterized by a correlation length ξ for monomer concentration fluctuations. The value of ξ calculated from is much smaller than the pore radius. The rapid increase in the diffusion coefficient is ascribed to a drastic increase of the polymer concentration inside the pore, which results from an equilibration of the chemical potential of the polymer molecule between the interior of the pore and the exterior. Thus, when the concentration exceeds v*, the osmotic pressure outside the pore increases rapidly and hence the chain tends to be squeezed into a pore even at the expense of reduced entropy. We present a quantitative analysis of this highly nonlinear partitioning of polymer molecules.