Birdi Nishant, Underwood Tom L, Wilding Nigel B, Puri Sanjay, Banerjee Varsha
School of Interdisciplinary Research, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India.
Department of Chemistry, University of Bath, Bath BA2 7AY, United Kingdom.
Phys Rev E. 2022 Feb;105(2-1):024706. doi: 10.1103/PhysRevE.105.024706.
The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.
棒状液晶（LC）颗粒的各向异性形状导致当向列相分子并排或首尾相连排列时具有不同的能量值。这种由参数κ′控制的能量各向异性对平衡和非平衡性质有着深远影响。使用盖伊 - 伯恩（GB）模型，该模型展现出向列相（Nm）以及低温近晶相（Sm）有序性，我们进行了大规模蒙特卡罗和分子动力学模拟，以探究κ′对平衡相图以及温度T猝灭或粗化后的非平衡畴生长的影响。GB模型中有两个转变：（i）在T₁ₑ时从各向同性转变为Nm，以及（ii）在T₂ₑ < T₁ₑ时从Nm转变为Sm。κ′显著降低T₁ₑ，但对T₂ₑ的影响相对较小。Nm相中的畴生长遵循著名的利夫希茨 - 艾伦 - 卡恩（LAC）定律，L(t) ∼ t¹/²，并且演化是通过弦缺陷的湮灭进行的。该系统表现出动力学标度，并且对于κ′而言也是稳健的。我们发现，在我们所考虑的猝灭温度T（T > T₁ₑ → T < T₂ₑ）下的Sm相具有SmB有序性，层内的LC分子呈六方排列（SmB - H相）。该相中的粗化表现出一种显著的双时间尺度情形：首先，LC分子排列并发展出取向有序（或向列性），随后出现特征性的分层（或近晶性）以及层内的六方键取向有序。因此，生长在早期遵循LAC定律L(t) ∼ t¹/²，然后在后期急剧转变为较慢的生长 regime。我们的观察强烈表明，在该 regime 中L(t) ∼ t¹/⁴。有趣的是，关联函数在两个 regime 中都表现出动力学标度，并且标度函数是通用的。动力学对于κ′的变化也是稳健的，但在较大值时近晶性更为明显。此外，早期动力学由弦缺陷控制，而后期演化由界面缺陷决定。我们认为，即使Sm层内存在其他种类的局部有序，这种情形对于Sm相也是通用的。
