Topological properties of polymer spherulitic grain patterns from simultaneous nucleation

Experimental and theoretical characterization of large-scale spherulitic grain patterns of isotactic polypropylene have been carried out under simultaneous nucleation conditions. Rigorous image analysis has been performed to characterize the topological correlation of grain-boundary shapes and grain sizes, as well as topological rearrangements during thermal activation experiments. The topological and geometrical aspects of the spherulitic grains are subjected to a comprehensive analysis, using the characterization methodology commonly employed in studies of random cellular patterns. A distinguishing feature of polymer grain patterns is the presence of topological defects. Topological defects have been identified by using standard computational geometry method such as the multigraphic construction of the grain-boundary network (GBN) and its relevant dual, the nearest-neighbour network. The topological defects are the mixed configurations of vertices containing three, four, five and six connectives, where the fraction of trivalent vertices is smaller than 1. It is found firstly that the two-cell correlation functions M-k(n) (the average number of k-sided grains adjoining an n-sided grain), are clearly highly non-linear with n, secondly that the common practice of plotting nm(n) versus n can conceal the non-linearity of the experimental data, where m(n) is the average sum of the number of sides of the grains immediately adjacent to an n-sided grain and thirdly that the plot of the relation of average area of grains to the number of sides is non-linear and S-shaped, owing to the polydisperse grain packing. These topological and geometrical characteristics indicate that the polymer GBN does not follow either the mathematical Voronoi diagram or the common random cellular structures displayed in many physical systems. Thermal activation experiments show that the polymer grain pattern is a topological unstable structure with very slow dynamics. Finally, these experimental observations are explained in relation to specific polymeric features.