Geometric Analysis of Diffusion Pathways in Glassy and Melt Atactic Polypropylene

Michael L. Greenfield, University of California, Berkeley
Doros N. Theodorou, University of California, Berkeley


Glassy and melt atactic polypropylene microstructures obtained via energy minimization and Monte Carlo simulation are subjected to geometric analysis (Delaunay tessellation followed by volume and connectivity analysis) in order to determine the clusters of sites where a hard sphere penetrant of radius 0–2.5 Å can reside. A variety of cluster volumes are found for each penetrant radius, and typical clusters are visualized for methane, helium, and two hypothetical penetrants of smaller radius. Peaks are observed in the distribution of cluster volumes, representing characteristic hole sizes induced by local packing. The cluster root-mean-square radius of gyration and average accessible volume decrease monotonically for penetrants larger than helium. A hypothetical penetrant of radius ca. 0.9 Å can percolate the polymer structure, whereas the same size penetrant is trapped in a random close-packed (rcp) configuration of spheres with diameter commensurate with the polymer segments. Clusters accessible to small penetrants are used to isolate probable pathways for diffusion, and the connectivity of the network of clusters is quantified. Visualization of thermal fluctuations of clusters shows two kinds of mobility. In the melt, polymer fluctuations induce rapid cluster rearrangement. In the glass, clusters retain their identity, while thermal fluctuations infrequently open and close diffusion pathways between them. A methodology for applying this work to full energy-based calculations of diffusivity in the glass using multidimensional transition-state theory is introduced. © 1993, American Chemical Society. All rights reserved.