The Helfrich-Hurault (HH) elastic instability is a well-known mechanism behind patterns that form as a result of strain upon liquid crystal systems with periodic ground states. In the HH model, layered structures undulate and buckle in response to local, geometric incompatibilities in order to maintain the preferred layer spacing. Classic HH systems include cholesteric liquid crystals under electromagnetic field distortions and smectic liquid crystals under mechanical strains, where both materials are confined between rigid substrates. However, richer phenomena are observed when undulation instabilities occur in the presence of deformable interfaces and variable boundary conditions. Understanding how the HH instability is affected by deformable surfaces is imperative for applying the instability to a broader range of materials. In this review, the HH mechanism is reexamined and special focus is given to how the boundary conditions influence the response of lamellar systems to geometrical frustration. Lamellar liquid crystals confined within a spherical shell geometry are used as the model system. Made possible by the relatively recent advances in microfluidics within the past 15 years, liquid crystal shells are composed entirely of fluid interfaces and have boundary conditions that can be dynamically controlled at will. Past and recent work that exemplifies how topological constraints, molecular anchoring conditions, and boundary curvature can trigger the HH mechanism in liquid crystals with periodic ground states is examined. The review ends by identifying similar phenomena across a wide variety of materials, both biological and synthetic. The fact that the HH mechanism is a generic and often overlooked response of periodic materials to geometrical frustration is highlighted.

中文翻译：

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由几何挫败驱动的 Helfrich-Hurault 弹性不稳定性

Helfrich-Hurault (HH) 弹性不稳定性是由于具有周期性基态的液晶系统上的应变而形成的图案背后的众所周知的机制。在 HH 模型中，分层结构会响应局部几何不兼容性而波动和弯曲，以保持首选的层间距。经典的 HH 系统包括电磁场畸变下的胆甾型液晶和机械应变下的近晶液晶，这两种材料都被限制在刚性基板之间。然而，当存在可变形界面和可变边界条件时出现波动不稳定性时，会观察到更丰富的现象。了解 HH 不稳定性如何受到可变形表面的影响对于将不稳定性应用于更广泛的材料至关重要。在这篇综述中，重新审视了 HH 机制，并特别关注边界条件如何影响层状系统对几何挫败的响应。限制在球壳几何形状内的层状液晶被用作模型系统。由于过去 15 年来微流体技术的相对较新的进展，液晶壳完全由流体界面组成，并且具有可以随意动态控制的边界条件。过去和最近的工作举例说明了拓扑约束、分子锚定条件和边界曲率如何触发具有周期性基态的液晶中的 HH 机制。审查最终确定了各种生物材料和合成材料中的类似现象。强调了 HH 机制是周期性材料对几何挫败的通用且经常被忽视的响应这一事实。