Linear Viscoelastic Diffusion in the Poly(styrene)-Ethylbenzene System: Comparison between Theory and Experiment

Abstract

We compare mutual diffusion data in the poly(styrene)-ethylbenzene system with theory. The experiments were differential vapor sorptions carried out at 40°C on a thin film over a range of compositions spanning the system's glass transition. Under these conditions, viscoelastic relaxation strongly influences mutual diffusion, so that non-Fickian sorption data are seen. The theories considered account for the influence of relaxation by including fading memory in the mixture's free energy density. By fitting the data with the theory, we extracted as a function of ethylbenzene weight fraction, ω 1 , the mutual binary diffusion coefficient, D 12 , relaxation times, τ 1 and τ 2 (> τ 1 ), and the ratio of the high-frequency mechanical modulus to the osmotic modulus, k 0 . In the glassy state, D 12 and τ 1 remain nearly constant, while in the liquid state they change rapidly with ω 1 (D 12 increases; τ 1 decreases). The Vrentas-Duda free volume theory, 4,5 modified to account for the influence of the glass transition can account for the trends. The shorter relaxation time, τ 1 , agrees with mechanically measured relaxation times in the transition zone. The longer time, τ 1 , shows rough agreement with the terminal time, although the comparison is not definitive. The ratio k 0 is found to be constant, at ∼O(10) over the entire concentration range, whereas the Flory-Huggins theory predicts that it should slowly increase with ω 1 ; the reasons for the discrepancy are not clear