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.

中文翻译：

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高分子聚合物二维小角X射线散射图案的Metropolis Monte Carlo模拟

Metropolis Monte Carlo方法已应用于模拟二维（2D）小角度X射线散射（SAXS）图样，该图样是针对定向结晶聚合物样品观察到的，由此得出了叠层薄板的混凝土聚集结构模型。在此研究中，建立了两种类型的层状模型：一种是固定形状的矩形薄片的聚集模型，另一种是小颗粒的凝结模型。在第一个模型中，将数千个固定形状的矩形薄片随机排列在一个大型2D单元中，并逐步修改它们的相对位置和方向，以便以定量方式最好地复制观察到的2D SAXS模式。在第二个模型中，数以万计的小而圆形的颗粒被随机输入到细胞中，并逐步改变它们的位置，以使观察到的SAXS模式足够好地重现。在这两种情况下，堆叠的层状结构都是具体产生的。从这些模型中提取结构参数，以描述长周期，层状厚度，层状取向等，包括计算层状堆叠结构的相关函数。从不同的角度讨论了这两种模型的优点。包括层状堆叠结构相关函数的计算。从不同的角度讨论了这两种模型的优点。包括层状堆叠结构相关函数的计算。从不同的角度讨论了这两种模型的优点。