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

周DMS-0604912森林DMS-0604891这个合作项目的目标是一类具有重要技术意义的材料尺度聚合物纳米复合材料(PNC)的数学和计算。研究人员研究了两个主题：加工的流体动力学和有效的性能表征(例如，导电和机械性能)。PNC由细棒或薄片组成(数百万立方微米，产生与溶剂接触的足球场表面)，它们的取向分布和相对于基质的优异性能在测试系统中显示出材料性能的巨大增强。然而，纤维在自然界和工业上取得的成功在薄膜和模具中没有得到复制，因此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证明：剪切主导的、受限的稳定加工产生了复杂的动力学和棒状或血小板整体的异质性。所得薄膜的性质是高度各向异性、不均匀的，并且对纳米颗粒的几何形状、体积分数和工艺条件非常敏感。采用理论、模型、分析和数值算法来解释这些现象，探索最令人困惑的观测结果，绘制出胸膜流动的参数域，并表征导电性和机械有效性质张量。贯穿所有项目的关键对象是纳米粒子系综的取向概率分布函数(PDF)。PDF由DOI动力学理论描述，并将其推广到粘弹性溶剂中，研究人员和他们的合作者将其归结为均匀平均和渗流主导的有效性质表征。纳米复合材料的前景是深远的。纳米级的“设计者”分子被添加到传统材料中的比例非常低，结果是复合材料的性能相对于原始材料有了巨大的提高。纳米元素的强度要强得多，导电性或导热性明显更好，或者对污染传统材料的气体和液体是不透的。然而，这是有工程代价的，因为对传统复合材料有效执行的智能工程模型和数字代码根本不适用于纳米复合材料。每立方微米有数百万个纳米粒子，每一滴雨滴体积的足球场有新的表面积。因此，用现有的模拟工具无法模拟纳米复合材料的流动。主要研究人员正在设计新的数值模拟工具，基于新的理论模型，通过增加针对纳米复合材料的新物理特性，扩展了传统的流动过程模型和程序。这些预测与纳米工程实验者一起进行了测试。这项工作的目标是建立一个设计和控制纳米复合材料的平台，能够引导加工阶段实现目标性能规格。

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.