Metropolis Monte Carlo Simulation of Two-Dimensional Small-Angle X-ray Scattering Patterns of Oriented Polymer Materials

The Metropolis Monte Carlo method has been applied to the simulation of two-dimensional (2D) small-angle X-ray scattering (SAXS) patterns observed for oriented crystalline polymer samples from which concrete aggregation structure models of stacked lamellae were derived. Two types of lamellar models were built here in this study: one was the aggregation model of rectangular lamellae of a fixed shape, and another was the coagulation model of small particles. In the first model, several thousands of rectangular lamellae of a fixed shape were arranged randomly in a large 2D cell, and their relative positions and orientations were modified stepwise so that the observed 2D SAXS pattern was reproduced best in a quantitative manner. In the second model, several tens of thousands of small and round particles were input randomly into the cell, and their positions were changed stepwise so that the observed SAXS pattern was reproduced well enough. In both cases, the stacked lamellar structure was derived concretely. The structure parameters were extracted from these models to describe the long period, lamellar thickness, lamellar orientations, and so on, including the calculation of the correlation functions for the lamellar stacking structure. The advantage of these two models has been discussed from various points of view.