Modeling and analysis of nematic liquid crystals in thin geometries: Bistable configurations and free surface instabilities

薄几何形状向列液晶的建模和分析：双稳态配置和自由表面不稳定性

• 批准号: 0908158
• 负责人: Linda Cummings
• 金额: $ 39.93万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908158&HistoricalAwards=false
• 关键词: Modeling; analysis; nematic; liquid; crystals

CummingsDMS-0908158 This project centers on developing new analytical models fornematic liquid crystals (NLCs) in two basic configurations. Thefirst concerns NLCs "sandwiched" between two solid boundaries,subject to an applied electric field. This geometry is directlyrelevant to a number of liquid crystal display devices. Byinvestigating the response of the NLC layer to an externalelectric field, the investigator and her colleage develop newmodels relevant to the design of bistable LCD devices. Advanceshere could lead to the development of new, easily-manufactured,energy-saving technologies. The second configuration considersfree-surface dynamics of NLC films and drops, relevant tonumerous manufacturing processes. Mathematically, the problem iscomplicated by the need to model carefully the liquid crystalbehavior in the vicinity of any contact lines. This, in additionto the known unstable behavior, leads to a very complex problem,about which little is known theoretically. Systematic asymptoticreduction of the complex Ericksen-Leslie equations for nematicmedia, to the appropriate thin-film geometry, is made. Theformulation includes the effects of finite anchoring strength ofthe liquid crystal director field at the boundaries, and theeffects of liquid-solid interaction energy (via a disjoiningpressure). The theoretical investigations are augmented by anexperimental program, comprising simple table-top experimentscarried out by summer students at NJIT, and more sophisticatedinvestigations carried out by an experimental collaborator, PeterPalffy-Muhoray, at Kent State University. The project has two strands: A theoretical investigationinto optimal design of low-energy (so-called "bistable") LiquidCrystal Display (LCD) devices, for use in applications such ase-paper; and an investigation into the dynamics of nematic liquidcrystals spreading on surfaces, a process known to be unstable incertain situations. The development of a theoretical base for aworkable, easily-manufactured, low-energy LCD device would haveundeniable economic and environmental impact if it provedcompetitive, in terms of cost or performance, with the smallnumber of such low-energy LCD microtechnologies presentlyavailable. The investigations into free-surface spreading leadto a better understanding of coating processes and, particularlywith the inclusion of an electric field, offer potential for newways of controlling the evolution of spreading films inmanufacturing processes. This project is carried out incoordination with educational efforts that include invaluableresearch experiences for undergraduate students.

CummingsDMS-0908158 该项目的重点是开发两种基本配置的向列液晶 (NLC) 新分析模型。 第一个涉及“夹在”两个固体边界之间的 NLC，并受到施加的电场的影响。 该几何形状与许多液晶显示装置直接相关。 通过研究 NLC 层对外部电场的响应，研究人员和她的同事开发了与双稳态 LCD 设备设计相关的新模型。 这里的进步可能会导致新的、易于制造的节能技术的发展。 第二种配置考虑 NLC 薄膜和液滴的自由表面动力学以及相关的繁琐制造工艺。 从数学上讲，由于需要对任何接触线附近的液晶行为进行仔细建模，问题变得更加复杂。 除了已知的不稳定行为之外，这还导致了一个非常复杂的问题，而理论上对此知之甚少。 将向列介质的复杂 Ericksen-Leslie 方程系统地渐近简化为适当的薄膜几何形状。 该公式包括边界处液晶指向矢场的有限锚定强度的影响，以及液固相互作用能（通过分离压力）的影响。 实验计划增强了理论研究，包括新泽西理工学院暑期学生进行的简单桌面实验，以及肯特州立大学实验合作者 PeterPalffy-Muhoray 进行的更复杂的研究。 该项目有两个部分：对低能耗（所谓的“双稳态”）液晶显示（LCD）设备的优化设计进行理论研究，以用于自动纸张等应用；以及对向列液晶在表面上扩散的动力学的研究，已知这一过程在某些情况下是不稳定的。 如果在成本或性能方面证明与目前可用的少量此类低能耗 LCD 微技术相比具有竞争力，那么为可行的、易于制造的低能耗 LCD 设备开发理论基础将产生不可否认的经济和环境影响。 对自由表面铺展的研究使人们更好地了解涂层工艺，特别是在包含电场的情况下，为控制制造过程中铺展薄膜的演变提供了新方法的潜力。 该项目是与教育工作协调进行的，其中包括为本科生提供宝贵的研究经验。