Investigations of Liquid Crystalline Mesophase Transitions via Landau-de Gennes Phenomenological Models

Giorgi DMS-1108992主要研究员考虑与描述液晶相变的非线性问题相关的分析问题，重点是基于复杂序参数的模型。主要研究近晶材料中磁场和电场诱导的相变，特别是手性倾斜近晶体系。该方法是研究近晶液晶所描述的广义唯象Landau-de Gennes能量，其中考虑到完整的机电耦合，有限的表面锚定和增加的相互作用耦合条款。研究人员研究实验中观察到的影响：电场下的折返相，近晶层的收缩导致近晶C* 转变时的折叠不稳定性，由外加场引起的波动，场致相变，以及由非手性分子组成的液晶中宏观手性性质的紧急显示。这些效应在考虑液晶的行为和与制造近晶液晶器件相关的问题时出现。 该方法使用了来自非线性偏微分方程的各种数学工具，包括变分方法，渐近分析和偏微分方程正则性理论。工作的一部分是验证和完善包含所研究现象的基本特征的模型。近晶型液晶的研究比非晶型液晶少。在近晶液晶中，长分子指向近似相同的方向，称为指向矢;与近晶液晶不同，近晶液晶的长分子也近似排列在平面层中。指向矢和层法线之间的倾斜，以及这种倾斜在层间移动时的旋转，都涉及近晶液晶的切换特性。 液晶以其在液晶显示技术中的应用而闻名，目前的设备大多基于介晶相，并且非常接近物理极限。这一重要应用的未来在于倾斜手性近晶中间相，由于其铁电或反铁电性质，具有上级操作速度和分辨率。铁电液晶的商业应用包括空间光调制器、光存储器、光计算机和高分辨率微显示器。由于近晶材料的当前和未来应用的重要性，有必要通过数学分析来验证和扩展现有的理论模型。通过理论研究所提出的模型的解决方案的属性，并将其与实验结果进行比较，该项目增加了对液晶相变的性质以及软凝聚态物质的电学和光学性质的理解。这反过来又导致更好的方式来构建基于液晶的设备。

Giorgi DMS-1108992 The principal investigator considers analytical questions related to nonlinear problems describing liquid crystalline phase transitions, with an emphasis on models based on complex order parameters. The main focus is the study of magnetic- and electric-field-induced phase transitions in smectic materials in general, and chiral tilted smectic systems in particular. The approach is to study smectic liquid crystals as described by generalized phenomenological Landau-de Gennes energies, which take into account the complete electromechanical coupling, finite surface anchoring and added interaction coupling terms. The investigator studies effects observed in experiments: reentrant phases under electric fields, shrinkage of smectic layers that lead to folding instabilities at smectic C* transitions, undulation induced by applied fields, field-induced phase transformations, and the emergent display of macroscopic chiral properties in liquid crystals that are composed of achiral molecules. These effects arise in considering both the behavior of liquid crystals and issues associated with manufacturing smectic liquid crystal devices. The approach uses a diverse collection of mathematical tools coming from nonlinear partial differential equations, including variational methods, asymptotic analysis and partial differential equation regularity theory. Part of the effort is to validate and refine the models that contain the essential features of the examined phenomena. Smectic liquid crystals are less studied than nematic liquid crystals. As in nematic liquid crystals, the long molecules in smectic liquid crystals point in approximately the same direction, called the director; unlike nematic liquid crystals, the long molecules of smectic liquid crystals also are arranged approximately in planar layers. The tilt between the director and the normal to the layer, and the rotation of this tilt as one moves between layers, are involved in the switching properties of smectic liquid crystals. Liquid crystals are well-known for their use in liquid crystal display technology, where devices at the moment are mostly based on nematic mesophases and operate very close to physical limits. The future of this important application resides in tilted chiral smectic mesophases, which due to their ferroelectric or antiferroelectric properties have superior operational speed and resolution. Commercial applications of ferroelectric liquid crystals include spatial light modulators, optical memory, optical computers and high-resolution microdisplays. Due to the importance of current and future applications of smectic materials, there is a need for validation and extension of the available theoretical models through mathematical analysis. By theoretically studying the properties of the solutions of the proposed models, and comparing them to experimental results, the project adds to the understanding of the nature of the liquid crystalline phase transitions, and the electrical and optical properties of soft condensed matter. This in turn leads to better ways of building liquid crystal based devices.