Mehri Saeed, Dyre Jeppe C, Ingebrigtsen Trond S
Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
Phys Rev E. 2022 Jun;105(6-1):064703. doi: 10.1103/PhysRevE.105.064703.
This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.
本文对Gay-Berne液晶模型进行了数值研究，其参数对应于棒状分子。重点关注温度高于1时的各向同性相和向列相，我们发现维里热涨落和势能热涨落之间存在强关联，这反映了隐藏的标度不变性对称性。这意味着同构体的存在，它们是热力学相图中具有近似不变物理性质的曲线。我们在数值上研究了各向同性相中的一条同构曲线和向列相中的一条同构曲线。在这两种情况下，通过均方位移以及速度、角速度、力、扭矩和一阶及二阶勒让德多项式取向序参量的约化单位时间自相关函数的数据，证明了动力学具有良好的不变性。对于取向时间自相关函数，在短时间内观察到与同构不变性的偏差，这反映了转动惯量被假定为常数，因此在约化单位中不是同构不变的这一事实。从分子的径向分布函数及其取向的数据中证明了结构同构不变性。为作比较，还沿着具有相似温度变化的等容线对所有量进行了模拟，在这种情况下未观察到不变性。我们得出结论，如同构理论所预测的，在所研究的区域中棒状Gay-Berne模型的热力学相图本质上是一维的，这一事实可能允许简化未来的理论和数值研究。
