Rescaled Free-Volume Theory of Diffusivity of Polystyrene in Various Organic Solvents

It remains, as yet, far from satisfactory to account for the explicit role of the solvent effect on the transport behaviors of various polymer solutions, especially depending upon the polymer concentration. Here, we exploit the statistical mechanical free-volume theory to describe the diffusivity of polymer solutions in an analytical form in terms of the solvent-solvent, particle-particle, and solvent-particle pair correlation functions as a function of the polymer concentration. To be specific, we introduce a particle size scaling parameter as a measure of the effective polymer-solvent interaction that leads to different polymer globular states, depending on the embedding solvents. Upon applying the theory to the polystyrene (PS) in various organic solvents, the agreement between the theory and experiment is found to be very good over the entire PS volume fraction ϕ investigated by the experiment, i.e., up to ϕ ∼ 0.50. The scaling parameter determined is discussed in association with the Flory-Huggins polymer-solvent interaction parameter χ available in the literature.