Multi-scale Phenomena in Macromolecular Fluids and Nano-Composite Materials

这项研究的目标是发展一种数学理论、模型和计算工具，以支持高分子材料和纳米复合材料的设计和开发。这些材料是由各向异性分子(向列型聚合物)组成的，它们在临界浓度以上经历自发的无序-有序转变。由向列型聚合物制成的材料通过集体分子排列结构实现其性质。特定的分子聚合物产生各种性能增强，从强度(杜邦产品芳纶和蜘蛛丝)到导电性(碳管和导电聚合物)，再到屏障穿透性能(盘状粘土小板材)。主要的技术挑战是将光纤的结果扩展到其他几何形状，如薄膜和模具。然而，在典型的层流处理流程中，分子响应对流动类型和强度以及分子特性(如形状和浓度)高度敏感。除了复杂的动力学外，在流动过程中，内部流动响应和固体边界上的分子锚定条件之间存在空间冲突。结果是，与纤维加工流动中的均匀分子取向分布不同，薄膜和模具流动总是在分子和加工设备之间产生长度尺度上的形态。这些普遍存在的结构无论是从理论上还是从实验上都没有被理解，但它们决定了最终用途材料的有效性质。由该奖项支持的研究将有助于理解典型的线状聚合物层流中发生的动力学和结构。现代高性能材料和纳米复合材料主要是用简单的元素设计的，从棒状分子到片状分子。到目前为止，在实验室规模的实验中已经实现了可标记的性能增强，提高了强度和耐用性，屏蔽了热或气体，并调节了电磁波的传输。技术上的挑战是将这些实验结果应用于工业上可行的过程和材料。数学和计算科学面临的挑战是建立坚实的理论、建模和模拟工具的基础，从这些基础上设计和控制过程和最终材料的性质。受限空间中流动分子的理论仍然无法预测和控制流动过程中产生的分子结构。然而，在纳米复合材料的加工薄膜和模具中，往往会出现微米级的分子结构。此外，块体材料的性能以及它们的失效和破坏模式是由在加工过程中产生的分子结构决定的。该奖项将支持一项研究计划，该计划结合了向列型聚合物材料和纳米复合材料在加工流程中的动力学和结构特性方面的理论、建模、模拟和与实验室数据的比较。这些结果将为下一阶段的材料管道奠定基础，在下一阶段，材料的整体性质将从分子性质中推断出来。

The goal of this research is the development of a mathematicaltheory, models, and computational tools which underpin the design andof macromolecular materials and nano-composites. These materials arecomprised of anisotropic molecules (nematic polymers), which undergo aspontaneous disorder-order transition above a critical concentration.Materials made from nematic polymers achieve their properties throughthe collective molecular alignment structure. Specific molecularelements yield diverse property enhancements, from strength (theDupont product Kevlar and spider silk), to electrical conductivity(carbon tubes and conducting polymers), to barrier penetrationproperties (discotic clay platelets). The major technologicalchallenge is to extend results with fibers to other geometries such asfilms and molds. However, in typical laminar processing flows, themolecular response is highly sensitive to flow type and strength, andto molecular properties such as shape and concentration. In additionto complex dynamics, during flow processing there is a spatialconflict between interior flow response and molecular anchoringconditions at solid boundaries. The result is that instead of auniform molecular orientational distribution, as in fiber processingflows, film and mold flows always generate morphology on length scalesbetween the molecules and the processing devices. These ubiquitousstructures are not understood, either theoretically or experimentally,yet they dictate the effective properties of the end-use materials.The research supported by this award will help to understand the dynamicsand structures that occur in typical laminar flows of nematicpolymers.Modern high-performance materials and nano-composites are primarilydesigned with simple elements, from rod-like to platelet molecules.Remarkable property enhancements have been achieved thus far inlaboratory-scale experiments, with increased strength and durability,the ability to shield heat or gases, and to tune electromagnetic wavetransmission. The technological challenge is to scale theseexperimental results to industrially viable processes and materials.The challenge to mathematics and computational science is to build asolid foundation of theory, modeling, and simulation tools from whichto design and control the processes and final material properties.The theory of flowing molecules in confined spaces is still unable topredict and control the molecular structure created during flowprocessing. Yet micron-scale molecular structures always occur inprocessed films and molds of nano-composites. Furthermore, the bulkmaterial performance properties as well as their failure and damagemodes are dominated by the molecular structures generated inprocessing. The award will support a research program combiningtheory, modeling, simulations, and comparisons with laboratory data inthe dynamics and structure properties of nematic polymer materials andnano-composites in processing flows. These results will be the basis for the next phase of the materials pipeline, where bulk materialproperties are deduced from the molecule properties.