A General Free Volume Based Theory for the Diffusion of Large Molecules in Amorphous Polymers Above T_g. 3. Theoretical Conformational Analysis of Molecular Shape

Mauritz and Storey have advanced a free volume theory for the above-T_g diffusion, in amorphous polymers, of molecules that are large in relation to the size of the dynamic chain segments of the host polymer. This theory has been favorably evaluated in general terms against experimental evidence for plasticizer-in-PVC diffusion while utilizing somewhat crude estimates of the requisite sizes and shapes of the penetrant molecules. In this work, the actual atomic-level structures of these complex molecules are theoretically determined by an energetics-based conformational analysis. The diffusion theory, in its most general form, requires the values of the penetrant's maximum cross sectional areas that are perpendicular to the three principal axes that pass through the molecular center of gravity. We have developed numerical methods for evaluating these irregular areas for the intrinsically complex structures predicted by the theoretical conformational analyses, and the resultant diffusion coefficients for di-n-alkyl phthalates in rubbery PVC are in reasonable agreement with available experimental data.