Collaborative Research: Field-Induced Mesophases

液晶因其在显示技术中的应用而广为人知，其中棒状分子通过电场排列和重新定向。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得寻找新材料成为该行业的焦点。弯核液晶不同于平板和便携式显示器中使用的标准材料，因为它们分子的特殊形状允许铁电行为和内在双稳定性，而制造成本较低。也就是说，它们在具有竞争力的生产成本下具有卓越的操作速度，分辨率和效率的潜力，以及更广泛的商业应用，包括空间光调制器（slm），光存储器，光学计算机和高分辨率微显示器。迄今为止，基于弯曲芯材料的器件的结构（中间相）的清晰描述尚未建立，并且需要克服许多技术困难。该项目关注这些应用密集型材料的数值和理论建模，并将填补理论和实验之间的现有空白。其结果将有助于验证和扩展现有模型，并将增加对相变性质，电学和光学性质的理解，最终有助于制造卓越的液晶器件。参与的研究生将在应用数学，计算数学和材料科学的跨学科领域进行培训。主要的研究目标将是电/磁光效应的分析，这将涉及材料缺陷及其相互作用的研究；层状结构铁电液晶模型的改进并且研究了一个新发现的相，在这个相中，弯曲的分子将自己排列成螺旋结构，绕着螺旋轴以纳米级的间距缠绕。研究人员将根据材料的各向异性光学特性来研究液晶对应用场的响应。主要的焦点将是弯曲核分子液晶中电光相互作用的建模和分析，重点是双稳/铁电性质和新发现的扭曲-弯曲向列相。还将考虑边界条件对Smectic A相中体积和受限样品形貌的影响。研究将基于广义单位向量和近序参数能量模型。研究人员将使用并推进非线性问题的数学工具的多样化集合，包括变分方法，渐近分析，以及非线性偏微分方程的分岔和正则理论。该项目的一个重要组成部分将是选择、改进和提出包含所研究现象的相关物理特征的模型。梯度流动的数值模拟以及与现有实验的比较将在研究方法中发挥重要作用。将讨论的具体问题包括通过对外加电场的双稳态响应来描述偏振调制的近晶a相中引入的缺陷，理解弯核材料的电自相互作用术语，以及探索扭弯弯核材料中的相变和磁场效应。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.