On the Pace–Datyner theory of diffusion of small molecules through polymers

Abstract

SynopsisThe 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

Strains in an Inflated Rubber Sheet

“…23,24,[31][32][33] Better accuracy can be realized using a general form of the strain energy function suggested by Rivlin. 22 The curvature in the stress-strain response is captured to some extent by molecular theories of rubber deformation, such as the constraint models, [34][35][36][37][38][39][40] which include the effect of topological interactions on the microscopic deformation. However, these models still tend to overestimate the stress for compression.…”

Birefringence of Rubber during Creep and Recovery

“…According to constraint models of rubber elasticity, C has a weak dependence on stress; [4][5][6] however, the quantitative accuracy of these models is limited. 7 Experiments indicate the stress optical law to remain valid up through at least moderate extensions (e.g., 50%) for a wide variety of neat rubbers in mechanical equilibrium.…”

Optical Birefringence of Polyisobutylene during Creep and Recovery

“…15 It is also similar to an analysis of the residual (zerostress) birefringence of double-network rubbers. 3 An explanation for the birefringence of double networks is predicated on the idea that the strain dependence of the stress optical coefficient is different for extension and compression, as known from rubber elasticity theory 24 as well as experimentally. 25,26 As we have discussed previously, 12 the change in sign of ∆n upon recovery, as observed herein, may reflect a delicate balance within the distribution of chain orientations during creep flow, prior to attainment of steady state.…”