Collaborative Research: Collaborative Proposal for Mathematics & Computation of Nano-Composite Flows & Properties

ZhouDMS-0604912森林DMS-0604891 这个合作项目的目标是数学和计算的一个技术上重要的一类材料称为聚合物纳米复合材料（PNC）。 研究人员研究两个主题：加工的流体动力学和有效特性表征（例如，导电和机械性能）。 PNC由一系列细棒或薄片组成（每立方微米有数百万个，与溶剂表面接触形成足球场），它们的定向分布和相对于基体的上级性质在测试系统中表现出极大的材料性能增强。 然而，在自然界和工业中使用纤维的成功，其均匀地对齐承载或传导纳米元件，尚未被复制用于膜和模具，从而极大地限制了应用范围。 这些困难在基准实验中得到了广泛的记录：剪切主导，受限的稳定加工产生了复杂的动力学和杆或血小板合奏的异质性。所得膜的性质是高度各向异性的、不均匀的，并且对纳米颗粒的几何形状、体积分数和加工条件敏感。 理论，模型，分析和numericalalgorithms进行解释这些现象，探索最令人困惑的意见，映射出参数域的强大的薄膜流，并表征导电性和机械有效属性张量。 纳米粒子系综的取向概率分布函数（PDF）是所有项目的核心目标。 PDF由Doi动力学理论及其对粘弹性溶剂的扩展来描述，研究人员及其合作者将其合并为均匀化平均和分散主导的有效性质表征。 纳米复合材料的前景是深远的。纳米尺度的“设计师”分子以非常低的成本添加到传统材料中，结果是复合材料的性能相对于原始材料有了巨大的提高。 纳米元件更坚固，导电性或热性能更好，或者不渗透污染传统材料的气体和液体。 然而，这是有工程代价的，因为智能工程模型和数字代码在传统复合材料中表现得很有效，但在纳米复合材料中却不适用。每立方微米有数百万个纳米颗粒，每一滴雨滴的体积相当于一个足球场的新表面积。因此，纳米复合材料流不能用现有的模拟工具进行模拟。 主要研究人员正在设计新的数值模拟工具，新的理论模型的基础上，通过增加新的物理特定的纳米复合材料，扩展了传统的流动处理模型和代码。 预测测试与nano-engineering experimentalists。 这项工作的目标是为纳米复合材料的设计和控制提供一个平台，能够控制加工阶段以实现目标性能规格。

ZhouDMS-0604912ForestDMS-0604891 This collaborative project targets mathematics andcomputation for a technologically important class of materialscalled polymer nano-composites (PNCs). The investigators studytwo topics: the hydrodynamics of processing, and effectiveproperty characterization (e.g., conductive and mechanicalproperties). PNCs consist of ensembles of thin rods orplatelets (millions in a cubic micron, generating football fieldsof surface contact with the solvent), whose orientationaldistribution and superior properties relative to the matrix haveexhibited huge enhancements of materials properties in testsystems. However, success in Nature and industry with fibers,which uniformly align the load bearing or conductingnano-elements, has not been duplicated for films and molds,thereby dramatically limiting the range of applications. Thedifficulties are widely documented in benchmark experiments: shear dominated, confined steady processing yields complexdynamics and heterogeneity in the rod or platelet ensemble. Resultant film properties are highly anisotropic, non-uniform,and sensitive to nano-particle geometry, volume fraction, andprocessing conditions. Theory, models, analysis, and numericalalgorithms are undertaken to explain these phenomena, to explorethe most perplexing observations, to map out parameter domains ofrobust film flows, and to characterize the conductivity andmechanical effective property tensors. The key object acrossall projects is the orientational probability distributionfunction (PDF) of the nano-particle ensemble. The PDF isdescribed by the Doi kinetic theory and its extension toviscoelastic solvents, which the investigators and theircollaborators merge into homogenized averaging andpercolation-dominated effective property characterization. The promises of nano-composite materials are profound. Nano-scale "designer" molecules are added at very low percentagesto traditional materials, with the result of huge gains inperformance properties of the composite relative to the originalmaterial. The nano-elements are much stronger, conductelectricity or heat significantly better, or are impermeable togases and liquids that contaminate traditional materials. Thereis an engineering price, however, in that the smart engineeringmodels and numerical codes that perform effectively fortraditional composites simply do not apply to nano-composites. There are millions of nano-particles per cubic micron, withfootball fields of new surface area per raindrop of volume. Thus, nano-composite flows cannot be simulated with existingsimulation tools. The principal investigators are designing newnumerical simulation tools, based on new theoretical models,which extend the traditional flow processing models and codes byaddition of new physics specific to nano-composites. Thepredictions are tested in conjunction with nano-engineeringexperimentalists. The goal of this effort is a platform fordesign and control of nano-composite materials, with the abilityto steer the processing phase to achieve targeted propertyspecifications.