Ordering of two-dimensional crystals confined in strips of finite width.
Ordering of two-dimensional crystals confined in strips of finite width.
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二维晶体的有序化限制在有限宽度的条带中。
DOI：
10.1103/physreve.75.011405
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
K. Binder
中科院分区：
文献类型：
--
作者：
A. Ricci;P. Nielaba;S. Sengupta;K. Binder
蒙特卡罗模拟用于研究点粒子晶体与 d=2 维中的反幂律势正比，variantr;{-12} 相互作用的限制效应。该系统可以描述空气-水界面处的胶体颗粒，是二维熔融实验研究的模型系统。结果表明，系统的状态（宽度为 D 的条带）非常敏感地取决于提供限制的两个“壁”处的精确边界条件。如果使用与本体三角形晶体结构的顺序相称的波纹边界，则取向顺序和位置顺序都会增强，并且这种表面诱导的顺序在本体系统处于流体状态的温度下也持续存在于边界附近。然而，使用平滑的排斥边界作为提供限制的壁，仅增强了方向序，但位置（准）长程序被破坏：沿着壁在 y 方向上分开的两个粒子 n 晶格参数的均方位移然后从对数增加（d=2 的特征）跨越到随 n 的线性增加（d=1 的特征）。然后条带表现出消失的剪切模量。这些结果是用现象学调和理论来解释的。还讨论了条带宽度D与三角晶格结构不可通约性的影响，并与简单Ising和XY模型中相变的表面效应进行了比较。
Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential proportional, variantr;{-12} in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D ) depends very sensitively on the precise boundary conditions at the two "walls" providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y direction along the walls then crosses over from the logarithmic increase (characteristic for d=2 ) to a linear increase with n (characteristic for d=1 ). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and XY models is made.