Gao Lianghui, Golubović Leonardo
Physics Department, West Virginia University, Morgantown, West Virginia 26506-6315, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 1):021708. doi: 10.1103/PhysRevE.67.021708. Epub 2003 Feb 27.
In this paper, we first elucidate the classical problem of the elastic free energy of a semi-infinite smectic-A liquid crystals, that fills the semispace above an interface (a boundary smectic layer) of a given shape. For the free energy of this interface, we obtain an effective interface Hamiltonian that takes into account the system discreteness introduced by the layered character of smectic-A liquid crystals. It is thus applicable to both short and long wavelength fluctuations of the interface shape. Next, we use our interface Hamiltonian to develop an efficient approach to the statistical mechanics of stacks of N semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. Within our approach, doing the practically interesting thermodynamic limit N--> infinity is reduced to considering a small stack, with just a few interacting manifolds, representing a subsystem of an infinite smectic. This dramatic reduction in the number of degrees of freedom is achieved by treating the first (the last) manifold of the small stack as an interface with the semi-infinite smectic medium below (above) the small stack. We illustrate our approach by considering in detail two-dimensional sterically stabilized smectic liquid crystals of long semiflexible polymers with hard-core repulsion. Smectic bulk (N= infinity ) equation of state and the universal constant characterizing entropic repulsion in these phases are obtained with a high accuracy from numerical simulations of small subsystems with just a few semiflexible polymers.
在本文中，我们首先阐明了半无限近晶 - A液晶弹性自由能的经典问题，该液晶填充了给定形状界面（边界近晶层）上方的半空间。对于该界面的自由能，我们得到了一个有效的界面哈密顿量，它考虑了由近晶 - A液晶的层状特性引入的系统离散性。因此，它适用于界面形状的短波和长波涨落。接下来，我们使用我们的界面哈密顿量来开发一种有效的方法，用于研究N个半柔性流形堆叠的统计力学，例如长半柔性聚合物的二维近晶相和三维层状流体膜相。在我们的方法中，进行实际有趣的热力学极限N→∞简化为考虑一个小堆叠，其中只有几个相互作用的流形，代表无限近晶的一个子系统。通过将小堆叠的第一个（最后一个）流形视为与小堆叠下方（上方）的半无限近晶介质的界面，实现了自由度数量的大幅减少。我们通过详细考虑具有硬核排斥的长半柔性聚合物的二维空间稳定近晶液晶来说明我们的方法。通过对只有几个半柔性聚合物的小子系统进行数值模拟，高精度地获得了近晶本体（N = ∞）的状态方程以及表征这些相中熵排斥的通用常数。
