Geigenfeind Thomas, de Las Heras Daniel
Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
J Chem Phys. 2019 May 14;150(18):184906. doi: 10.1063/1.5092865.
The excluded area between a pair of two-dimensional hard particles with given relative orientation is the region in which one particle cannot be located due to the presence of the other particle. The magnitude of the excluded area as a function of the relative particle orientation plays a major role in the determination of the bulk phase behavior of hard particles. We use principal component analysis (PCA) to identify the different types of excluded areas corresponding to randomly generated two-dimensional hard particles modeled as non-self-intersecting polygons and star lines (line segments radiating from a common origin). Only three principal components are required to have an excellent representation of the value of the excluded area as a function of the relative particle orientation for sufficiently anisotropic particles. Independent of the particle shape, the minimum value of the excluded area is always achieved when the particles are antiparallel to each other. The property that affects the value of the excluded area most strongly is the elongation of the particle shape. PCA identifies four limiting cases of excluded areas with one to four global minima at equispaced relative orientations. We study selected particle shapes using Monte Carlo simulations.
一对具有给定相对取向的二维硬粒子之间的排除区域是由于另一个粒子的存在而使一个粒子无法位于其中的区域。排除区域的大小作为相对粒子取向的函数，在确定硬粒子的体相行为中起着主要作用。我们使用主成分分析（PCA）来识别与建模为非自相交多边形和星形线（从共同原点辐射的线段）的随机生成的二维硬粒子相对应的不同类型的排除区域。对于足够各向异性的粒子，仅需要三个主成分就能很好地表示排除区域的值作为相对粒子取向的函数。与粒子形状无关，当粒子彼此反平行时，排除区域总是达到最小值。对排除区域值影响最强烈的性质是粒子形状的伸长率。PCA识别出排除区域的四种极限情况，在等间距的相对取向下具有一到四个全局最小值。我们使用蒙特卡罗模拟研究选定的粒子形状。
