Modeling & Analysis Of Nematic Films: Flow-Substrate Interactions

This award will support analysis and simulation of new mathematical models governing nematic liquid crystals (NLCs) in two situations of widespread industrial and basic scientific interest: (1) free surface spreading, and (2) behavior of a film of NLC (with and without an applied electric field) between two closely-spaced surfaces whose properties may be modified by interaction with the NLC. Each problem is relevant to applications in the manufacture, design and use of NLC-based displays, where a thin sandwich of NLC between plates is subjected to an applied field, to control the molecular orientation of the NLC, which in turn controls the optical properties. In free-surface spreading of a film of NLC over a rigid substrate, it is known that instabilities can manifest spontaneously under certain circumstances. A mechanism for these instabilities has been identified, but several issues remain to be resolved. (i) Any model with strong anchoring conditions on the director at both substrate and free surface requires regularization as an apparent contact line is approached. The investigators will study possible regularizing mechanisms, including relaxation to the isotropic state, and molecular scale van der Waals' (vdW) interactions (which must be relevant in the vicinity of an apparent contact line). (ii) The role of different defect/disclination types on spreading and stability will be considered in detail. Preliminary study of idealized defects within 2D films suggests that they do not significantly affect global dynamics. However, more general models are needed to draw firm conclusions. 3D defects of various topological types will be incorporated into our spreading model and their influence on spreading properties and on possible instabilities will be analyzed. (iii) The models will be extended to the case of spreading over soft polymer substrates. The behavior of NLC between confining polymeric plates is relevant for applications related to a new generation of Liquid Crystal Display (LCD) devices with soft flexible bounding surfaces. How such surfaces affect device behavior will be studied, with a particular focus on the effect of 'director gliding', where anchoring properties at a polymer interface can change over long timescales when the NLC exerts a stress on the surface. These models will be used to investigate suitable LCD device designs.

The award will support the study of problems that are directly relevant to the manufacture, design and use of Nematic Liquid Crystal (NLC)-based microdisplays. The basic operating unit of such displays (a pixel) is a simple sandwich of NLC between transparent plates, across which an electric field can be applied to effectively control the optical properties of the layer. The investigators will study basic problems of how NLC films behave between two closely-spaced polymeric surfaces. Such polymeric surfaces have economic potential as the basis for a new generation of flexible electronic displays. The award will support theoretical investigations, leading to the development of robust predictive models, that complement experimental investigations. The project will have significant educational impact, providing experimental and theoretical modules for advanced undergraduate training in a capstone course in applied mathematics. A Ph.D. student will be trained in research and will also serve as laboratory assistant for the capstone course, gaining valuable mentoring experience and developing his/her experimental skills.