Statistical mechanical model of diffusion of complex penetrants in polymers. I. Theory

A previously developed model of simple penetrant diffusion is extended to encompass complex penetrants of idealized molecular shape, characterized by dimensions of length, width, and thickness. Expressions are obtained for D(0,T), the diffusion coefficient at zero penetrant concentration (c), and the fractional increase in D(0,T) as a function of c and temperature (T). The model predicts that D(0,T) will exhibit Arrhenius behavior at temperatures well above T_g and gives the limiting activation energy as a function of penetrant thickness and the polymer energy/distance constants used previously. For T_g < T ? T_g + 150 K the model requires two new disposable parameters, in addition to the jump-length parameter of the simple penetrant theory. These parameters, however, have precise physical meanings (all are lengths) and together with the penetrant dimensions and polymer constants determine the absolute magnitude of the diffusion coefficient as well as its relative dependence on c and T. For T ? T_g + 40 the relative concentration dependence may be calculated in terms of the penetrant dimensions and polymer constants only.