硬圆弧的相位行为
Phase behavior of hard circular arcs
摘要：
本文利用Monte Carlo数值模拟方法，研究了二维欧氏空间中从孔径角$θ\rightarrow 0$到孔径角$θ\rightarrow 2 π$的无限细硬圆弧系统的相位行为。除了在较低密度下的各向同性相和仅在足够小的$θ$值和中等密度值下形成的（准）双相之外，在形成的其他相（包括在较高密度下的各向同性相）中，硬的无限薄的圆弧自动组装形成簇。对于较小的$θ$值，这些簇是丝状的，或者对于较大的$θ$值，这些簇是圆形的。如果密度足够高，则细丝伸长、合并和拉直以最终产生无定形相，而圆粒压缩并将它们自身以它们的质心布置在三角形晶格的位置处以最终产生簇六方相。
英文摘要：
By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally-thin circular arcs, from an aperture angle $θ\rightarrow 0$ to an aperture angle $θ\rightarrow 2 π$, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase that solely forms for sufficiently small values of $θ$ and at intermediate values of density, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally-thin circular arcs auto-assemble to form clusters. These clusters are either filamentous, for smaller values of $θ$, or roundish, for larger values of $θ$. Provided density is sufficiently high, the filaments lengthen, merge and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.
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