Modeling & analysis of nematic films: Flow-substrate interactions

该奖项将支持在两种具有广泛工业和基础科学兴趣的情况下分析和模拟控制向列型液晶（NLCs）的新数学模型：(1)自由表面扩散，(2)NLC薄膜（有或没有外加电场）在两个紧密间隔的表面之间的行为，其性质可能通过与NLC的相互作用而改变。每个问题都与基于NLC的显示器的制造、设计和使用中的应用有关，其中板材之间的NLC薄夹层受到应用场的影响，以控制NLC的分子取向，从而控制光学特性。在刚性衬底上的NLC薄膜的自由表面铺展中，已知在某些情况下，不稳定性可以自发地表现出来。已经确定了这些不稳定的机制，但仍有几个问题有待解决。(i)在基材表面和自由表面上对导向器具有强锚定条件的任何模型都需要在接近表观接触线时进行正则化。研究人员将研究可能的正则化机制，包括弛豫到各向同性状态，以及分子尺度的范德瓦尔斯（vdW）相互作用（必须在明显接触线附近相关）。（ii）将详细考虑不同缺陷/斜纹类型对扩散和稳定性的作用。对二维薄膜中理想化缺陷的初步研究表明，它们对整体动力学没有显著影响。然而，需要更一般的模型来得出确切的结论。将各种拓扑类型的三维缺陷纳入我们的扩散模型，并分析它们对扩散特性和可能的不稳定性的影响。（iii）这些模型将扩展到在软聚合物基板上扩散的情况。在具有柔性软边界面的新一代液晶显示器（LCD）器件中，约束聚合物板之间的NLC行为与应用相关。这些表面如何影响设备行为将被研究，特别关注“导向滑动”的影响，当NLC在表面施加应力时，聚合物界面的锚定特性会在长时间尺度上发生变化。这些模型将用于研究合适的LCD器件设计。该奖项将支持与向列液晶（NLC）微显示器的制造、设计和使用直接相关的问题的研究。这种显示器的基本操作单元（像素）是透明板之间的一个简单的NLC三明治，可以在其上施加电场来有效地控制层的光学特性。研究人员将研究NLC薄膜如何在两个紧密间隔的聚合物表面之间表现的基本问题。这种聚合物表面作为新一代柔性电子显示器的基础具有经济潜力。该奖项将支持理论研究，从而发展强大的预测模型，以补充实验研究。该项目将产生重大的教育影响，为应用数学顶点课程的高级本科培训提供实验和理论模块。博士生将接受研究方面的培训，同时还将担任顶点课程的实验室助理，获得宝贵的指导经验并发展他/她的实验技能。

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.