Case-II diffusion in polymers. II. Steady-state front motion

Abstract

We consider front formation and steady-state front motion in a one-dimensional polymer system undergoing case-II diffusion. The polymer system approximates a polymer sheet whose thickness is very small compared with its lateral dimensions. The osmotic pressure of Thomas and Windle (TW) is used in the theoretical analysis. The transient problem of front formation is formulated. It is found that the original coupled system of partial differential equations proposed by TW can be reduced to one equation. An exact solution of this equation for a diffusion front moving with a velocity V is presented. The solution allows us to predict the dependence of the steady-state velocity on material parameters and the equilibrium concentration of penetrant outside the sheet. The concentration and pressure profile ahead of the moving front is obtained. We also show that the TW Model predicts the existence of a Fickian tail ahead of the steadily moving front. Conditions for the dominance of the Fickian tail are determined. The predicitions of our theoretical analysis are then compared with concentration profiles of iodohexane diffusing into polystyrene determined from Rutherford backscattering spectrometry.

Reaction–diffusion model for the preparation of polymer gratings by patterned ultraviolet illumination

“…When, on the other hand, the polymer is glassy, the monomer first moves, creating a higher density, and swelling goes slowly. 30 However, at high conversions, the diffusion coefficients are very small anyway compared to ones during the early states of polymerization, and hardly any mass transport takes place. Therefore, since both phase separation of the polymer and case-II diffusion takes place at higher conversion, when most of the diffusion has already occurred, it is not considered to introduce large errors in the model.…”

A minimal model for solvent evaporation and absorption in thin films

“…Several models have been proposed which aim to couple the diffusion of absorbed solvent throughout the film with the elastic [40,41,42] or viscoelastic [43,44,45,46] response of the polymer network. Simplifications of these models that neglect the detailed mechanics of the polymer matrix have been proposed in the context of drug delivery [47,48,49].…”

A Spatially Nonlocal Model for Polymer Desorption

“…We make several additional physically reasonable simplifying assumptions so that the problem is more analytically tractable. As with β(C), the molecular diffusion coefficient D(C) also increases dramatically as the polymer goes from the glassy to rubbery state [37]. The true increase is continuous; some authors model it with an exponential [21,41].…”

“…Clearly these piecewise-constant functional forms are a simplification; the true dependence length is a smooth function ofC. Nevertheless, the use of such a simplified model has a long history of yielding analytically tractable results which match experiment well [12,[36][37][38][39][40]. With these piecewise-constant functional forms, our system becomes an MBVP for the glass-rubber interfaces(t), which separates thex-t plane into glassy and rubbery domains.…”

“…The true increase is continuous; some authors model it with an exponential [21,41]. However, in order to obtain analytic solutions, we follow the lead of [12,[36][37][38][39][40] and perform the same sort of averaging we use with β to obtain our functional form for D(C):…”