Collaborative Research: Field-Induced Mesophases

液晶因其在显示技术中的应用而广为人知，在显示技术中，棒状分子通过电场排列并重新定向。大多数可用的显示器都接近物理极限，对更快、更高效设备的持续需求使寻找新材料成为行业的焦点。弯芯液晶与平板和便携式显示器中使用的标准材料的不同之处在于，其分子的特殊形状允许以较低的制造成本实现铁电行为和固有的双稳态。也就是说，它们有潜力以具有竞争力的生产成本实现卓越的操作速度、分辨率和效率，以及更广泛的商业应用，包括空间光调制器(SLM)、光学存储器、光学计算机和高分辨率微显示器。到目前为止，基于弯芯材料的器件的结构(中间相)还没有得到明确的描述，需要克服许多技术困难。该项目涉及这些应用密集型材料的数值和理论模型，并将填补理论和实验之间的现有空白。其结果将有助于对现有模型的验证和扩展，并将有助于理解相变的性质以及电学和光学性质，最终有助于制造基于液晶的优秀器件。参与培训的研究生将接受应用数学、计算数学和材料科学等跨学科领域的培训。主要的研究目标将是电磁/磁光效应的分析，这将涉及到对材料缺陷及其相互作用的研究；对具有层状结构的铁电液晶的现有模型的改进；以及对新发现的相的研究，在该相中，弯曲分子以螺旋形结构排列，绕着具有纳米级间距的螺旋轴缠绕。研究人员将基于材料的各向异性光学特性来研究液晶显示出的外加磁场的响应。主要的重点将是弯曲核心分子液晶中电光相互作用的模拟和分析，重点是双稳/铁电性质和新发现的扭曲-弯曲向列相。边界条件对近晶A相中大块和受限样品的形态的影响也将被考虑。这些研究将基于广义的单位矢量和近晶有序参数能量模型。研究人员将使用和推进各种数学工具来解决非线性问题，包括变分方法、渐近分析以及非线性偏微分方程的分叉和正则性理论。该项目的一个基本组成部分将是选择、改进和提出包含所研究现象的相关物理特征的模型。梯度流的数值模拟和与已有实验的比较将在研究方法中发挥重要作用。将解决的具体问题包括描述通过对外加磁场的双稳态响应在偏振调制近晶A相中引入的缺陷，理解弯芯材料的电自相互作用术语，以及探索扭曲弯曲弯芯材料中的相变和磁场效应。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Liquid crystals are widely known for their use in display technology, where rod-like molecules are aligned and reoriented via electric fields. Most of the available displays operate close to physical limits, and the constant demand for faster and more efficient devices has made the search for new materials the focus of the industry. Bent-core liquid crystals differ from the standard materials used in flat panels and portable displays in that the special shape of their molecules allows for ferroelectric behavior and intrinsic bistability at a lower manufacturing cost. That is, they have potential for superior operational speed, resolution, and efficiency at a competitive production cost as well as a wider spectrum of commercial applications which include spatial light modulators (SLMs), optical memories, optical computers and high-resolution microdisplays. To date, a clear description of the configurations (mesophases) of the devices based on bent-core materials has not been established, and many technical difficulties need to be overcome. This project is concerned with the numerical and theoretical modelling of these application-intensive materials and will fill an existing gap between theory and experiments. Its outcome will contribute to the validation and extension of the available models and will add to the understanding of the nature of phase transitions, and of electrical and optical properties, ultimately contributing to the manufacturing of superior liquid crystals-based devices. The graduate students involved will be trained in the interdisciplinary areas of applied mathematics, computational mathematics, and materials science. The main research objective will be in the analysis of electro/magneto optic effects, which will involve the study of materials' defects and their interactions; the refinement of existing models for ferroelectric liquid crystals with layered structures; and the study of a newly discovered phase, where the bent molecules arrange themselves in an heliconical structure, winding about a helical axis with nanoscale pitches. The investigators will examine the response to applied fields exhibited by a liquid crystal based on the materials' anisotropic optical properties. The main focus will be on the modelling and analysis of electro-optic interactions in bent-core molecule liquid crystals with an emphasis on bistable/ferroelectric properties and on the newly discovered twist-bend nematic phase. The effects of boundary conditions on the morphology of bulk and confined samples in Smectic A phases will also be considered. The studies will be based on generalized unit vectors and smectic order parameter energy models. The investigators will use and advance a diverse collection of mathematical tools for nonlinear problems, including variational methods, asymptotic analysis, and bifurcation and regularity theories for nonlinear partial differential equations. An essential component of the project will be to select, refine, and propose models that contains the relevant physical features of the examined phenomena. Numerical simulations of gradient flows and comparison with available experiments will play an important role in the research approach. Specific issues that will be addressed include a description of defects introduced in the polarization modulated smectic A phase by the bistable response to an applied field, understanding the electric self-interaction terms for bent-core materials, and exploring phase transitions and magnetic field effects in twist-bend bent-core materials.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.