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

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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.