Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911, Leganés, Madrid, Spain.
Phys Chem Chem Phys. 2011 Aug 7;13(29):13247-54. doi: 10.1039/c1cp20698b. Epub 2011 Jun 24.
We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes σ(1) > σ(2) > σ(3). A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio κ(1) = σ(1)/σ(2) while keeping κ(2) = σ(2)/σ(3), we predict phase diagrams for various values of κ(2) which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid types are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for κ(2)≳ 2.5. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxiality centred at κ(1)≈κ(2) which widens as κ(2) increases. For κ(2)≳ 5 the region κ(2)≈κ(1) of the packing-fraction vs. κ(1) phase diagrams exhibits interesting topologies which change qualitatively with κ(2). We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric in the neighbourhood of κ(1)≈κ(2) is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.
我们使用基于基本测度的密度泛函理论，研究了各向同性、单轴棒状和板状向列相以及双轴向列相等均匀相之间的相对稳定性，其中所研究的流体由尺寸大小为 σ(1) > σ(2) > σ(3) 的硬板状粒子组成。我们采用受限取向（Zwanzig）近似。通过改变比 κ(1) = σ(1)/σ(2)，同时保持 κ(2) = σ(2)/σ(3)，我们预测了不同 κ(2)值的相图，其中包括所有均匀相：各向同性相、单轴棒状和板状向列相以及双轴向列相。此外，我们还获得了各向同性相相对于向列相、柱状相和塑性固体相的涨落的旋节线不稳定性。与最近的实验结果一致，我们发现双轴向列相在 κ(2)≳ 2.5 时开始稳定。此外，正如先前关于双轴硬粒子的理论和模拟预测的那样，我们得到了一个以 κ(1)≈κ(2)为中心的双轴性区域，该区域随着 κ(2)的增加而变宽。对于 κ(2)≳ 5，在 κ(2)≈κ(1)处的填充率与 κ(1)相图的区域表现出有趣的拓扑结构，这些拓扑结构随着 κ(2)的增加而发生定性变化。我们发现，双轴形状各向异性的增加有利于双轴向列相的形成。我们的研究首次将 FMT 理论应用于双轴粒子，因此超越了二阶维里近似。我们预测相图在 κ(1)≈κ(2)附近必须是不对称的，这是本方法的一个真正结果，而以前基于二阶理论的研究并未考虑到这一点。
