On the Pace–Datyner theory of diffusion of small molecules through polymers (original) (raw)

The Pace-Datyner theory for diffusion of penetrant molecules in polymers has been analyzed. I t has been found that the correct solution of the problem they pose is possible only at 0 K, since then the separation of two chains at x = m is equal to the minimum of the DiBenedetto potential for their interaction. Otherwise the energy of symmetrical separation is infinite. By using the linearization method to solve the differential equation, Pace and Datyner neglected the problem of unnatural boundary conditions at x = 00 for temperatures above 0 K. The exact numerical solutions of differential equations at temperature 0 K were therefore compared with the results of the Pace-Datyner linear approximation. For temperatures different from 0 K the solution of the problem is possible only when the proper cutoff is imposed. The analytical expression for the coefficients in the DiBenedetto potential has been found, and the potential can be written as