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.

本项目的重点是在两种基本构型下建立新的形式液晶（NLCs）分析模型。第一种是“夹在”两个固体边界之间的非晶状体，受外加电场的影响。这种几何形状与许多液晶显示设备直接相关。通过研究NLC层对外部电场的响应，研究者和她的同事开发了与双稳态LCD器件设计相关的新模型。这方面的进步可能会导致新的、易于制造的节能技术的发展。第二种结构考虑了NLC薄膜和液滴的自由表面动力学，与许多制造过程有关。在数学上，由于需要仔细模拟任何接触线附近的液晶行为，这个问题变得复杂了。除了已知的不稳定行为外，这导致了一个非常复杂的问题，而理论上对这个问题知之甚少。对向列介质的复杂Ericksen-Leslie方程进行了系统的渐近化简，得到了适当的薄膜几何形状。该公式包括边界处液晶导向场有限锚固强度的影响，以及液固相互作用能（通过分离压力）的影响。理论研究得到了实验项目的加强，包括由新泽西理工大学的暑期学生进行的简单的桌面实验，以及由肯特州立大学的实验合作者彼得·帕尔菲-穆霍雷进行的更复杂的研究。该项目分为两部分：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，用于电子纸张等应用；并对向列液晶在表面上扩散的动力学进行了研究，这一过程在某些情况下是不稳定的。一个可行的，易于制造的，低能耗的LCD设备的理论基础的发展，将有不可否认的经济和环境影响，如果它被证明具有竞争力，在成本或性能方面，与少量这样的低能耗LCD微技术目前可用。对自由表面扩散的研究有助于更好地理解涂层过程，特别是在电场的作用下，为控制制造过程中扩散膜的演变提供了新方法。该项目的实施与教育工作不协调，包括为本科生提供宝贵的研究经验。