Occupied and accessible volumes in glassy polymers and their relationship with gas permeation parameters

In order to relate the microstructure of polymer chains to the gas permeation properties, a novel method is proposed for the calculation of the van der Waals (V-W), occupied ((occ)), and accessible (V-acc) volumes of polymers, using polyimides as examples. In this approach, V-occ and V-acc values are obtained as characteristics of polyer-gas systems. Correlations between V-occ and the gas permeability (P) and diffusion (D) coefficients are demonstrated. Accessible volume, V-acc, determined experimental densities, and V-occ calculated using a Monte Carlo technique, as well as the fractional accessible volume (FAV) (V-acc/V-sp), where V-sp is the specific volume of polymers, also correlate well with the P and D values. The slopes of these correlations increase with increasing molecular size of the diffusing molecules. In addition, the parameters of the equations for D(FAV) and P(FAV) strongly depend on conformation rigidity (Kuhn segment) of the polyimides. An interpretation of the results obtained is presented.