Nascimento E S, Henriques E F, Vieira A P, Salinas S R
Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil.
Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, 96010-900 Pelotas, RS, Brasil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062503. doi: 10.1103/PhysRevE.92.062503. Epub 2015 Dec 1.
We introduce shape variations in a liquid-crystalline system by considering an elementary Maier-Saupe lattice model for a mixture of uniaxial and biaxial molecules. Shape variables are treated in the annealed (thermalized) limit. We analyze the thermodynamic properties of this system in terms of temperature T, concentration c of intrinsically biaxial molecules, and a parameter Δ associated with the degree of biaxiality of the molecules. At the mean-field level, we use standard techniques of statistical mechanics to draw global phase diagrams, which are shown to display a rich structure, including uniaxial and biaxial nematic phases, a reentrant ordered region, and many distinct multicritical points. Also, we use the formalism to write an expansion of the free energy in order to make contact with the Landau-de Gennes theory of nematic phase transitions.
我们通过考虑单轴和双轴分子混合物的基本迈尔 - 绍佩晶格模型，在液晶系统中引入形状变化。形状变量在退火（热化）极限下进行处理。我们根据温度T、本征双轴分子的浓度c以及与分子双轴度相关的参数Δ来分析该系统的热力学性质。在平均场水平上，我们使用统计力学的标准技术绘制全局相图，结果表明该相图呈现出丰富的结构，包括单轴向列相和双轴向列相、一个折返有序区域以及许多不同的多临界点。此外，我们使用形式体系来写出自由能的展开式，以便与向列相转变的朗道 - 德热纳理论建立联系。
