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

CummingsDMS-0908158这个项目的中心是开发两种基本构型的向列相液晶(NLC)的新分析模型。第一种是关于“夹在”两个固体边界之间的NLC，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层对外电场的响应，研究人员和她的同事开发了与双稳态LCD器件设计相关的新模型。这些进步可能会导致新的、易于制造的节能技术的发展。第二种构型考虑了NLC膜和液滴的自由表面动力学，以及相关的大量制造工艺。从数学上讲，这个问题很复杂，因为需要仔细地模拟任何接触线附近的液晶行为。这一点，加上已知的不稳定行为，导致了一个非常复杂的问题，理论上对此知之甚少。对向列型介质的复Ericksen-Leslie方程进行了系统的渐近约化，得到了适当的薄膜几何形状。该公式包括液晶指向矢场在边界处的有限锚定强度的影响，以及液-固相互作用能的影响(通过分离压力)。NJIT的暑期学生进行了简单的桌面实验，肯特州立大学的实验合作者PeterPalffy-Muhoray进行了更复杂的研究，实验项目对理论研究进行了补充。该项目有两个方面：一是用于电子纸等应用的低能量(所谓的“双稳”)液晶显示(LCD)器件的优化设计的理论研究；二是向列相液体晶体在表面扩散的动力学研究，这一过程在某些情况下是不稳定的。开发一种可行、易于制造的低能耗LCD器件的理论基础，如果在目前可用的此类低能耗LCD微技术很少的情况下，在成本或性能方面具有竞争力，将对经济和环境产生不可否认的影响。对自由表面铺展的研究有助于更好地了解涂层过程，特别是在电场的作用下，为控制制造过程中铺展薄膜的演变提供了新的方法。该项目的实施与教育工作不协调，其中包括为本科生提供宝贵的研究经验。

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.