Mathematics of Anisotropic Electrical and Dielectric Properties of Nanocomposites

研究者研究了纳米复合材料的两个重要领域：(1)纳米复合材料的有效介电常数均质化；(2)纳米复合材料的渗透导电性。该项目侧重于具有定向有序纳米颗粒的各向异性体系，并基于对流动处理数据库中纳米颗粒定向概率分布函数的准确描述，然后我们通过体积平均和渗透现象将其映射到有效性质。在第一部分，有效介电张量被考虑在两个明确的系统当前的兴趣：高介电常数纳米粒子分散在聚合物和导电纳米粒子分散在聚合物。这两种体系都被观察到导致有效介电性能的增强。这需要仔细准备，因为这些特性对成分和加工的细节非常敏感。第二部分讨论了突出电学性质的关键方面，如通过机械载荷改变渗透阈值、多尺度均质化方法和分子尺度电子跳变模型。需要发展数值和数学均质和非平衡渗透技术来应对这些挑战。拟议的项目修改、应用、测试和扩展了现有的两相（或三相，如果考虑相间）复合材料的数学理论和数值方法，其中颗粒数量和新表面积完全压倒了现有的工具。通过将设计好的纳米颗粒混合到传统材料中来实现性能的极大提高是基于原型实验的。然而，纳米复合材料面临着新的挑战，目前还没有预测的数学或计算工具。这个项目是对这些需求的回应，通过数学分析和科学计算的协调结合，范围从单个颗粒到整体性质。今天，由于粒子数的限制，只能测量纳米粒子分布的低矩，而在实验中观察到的分布细节的固有材料灵敏度是未知的。该项目深入了解了极端财产收益背后的机制，从而为设计和控制策略提供了关键输入。

ZhengDMS-08-7954 The investigator studies two important areas innanocomposites: (1) homogenized effective dielectric constant ofnanocomposites; and (2) percolation-dominated electricalconductivity of nanocomposites. This project is focused onanisotropic systems with orientationally ordered nanoparticles,and is based on an accurate description of the nanoparticleorientational probability distribution function fromflow-processing databases, which we then map to effectiveproperties through volume averaging and percolation phenomena. In the first part, the effective dielectric tensor is consideredin two explicit systems of current interests: high dielectricconstant nanoparticles dispersed in polymers, and conductingnanoparticles dispersed in polymers. Both systems are observedto lead to enhanced effective dielectric properties. Thisrequires careful preparation, because the properties areextremely sensitive to details of composition and processing. Inthe second part, key aspects of salient electric properties areconsidered, such as percolation threshold modification bymechanical loading, multiscale homogenization method, and amolecular-scale electron hopping model. Numerical andmathematical homogenization and non-equilibrium percolationtechniques need to be developed to address these challenges. Theproposed projects modify, apply, test, and extend existingmathematical theory and numerical approaches for two-phase (orthree phase, if interphase is considered) composites, where thenumber of particles and new surface area simply overwhelmexisting tools. The aspirations for extreme property enhancements throughdesigner nanoparticles mixed into traditional materials are basedon prototype experiments. However, there are new challengesunique to nanocomposites for which there are no predictivemathematical or computational tools. This project is a responseto these needs, through a coordinated combination of mathematicalanalysis and scientific computation, ranging in scale fromindividual particles to bulk properties. Today, limitationsimposed by particle numbers only allow low moments of thenanoparticle distributions to be measured, and the inherentmaterial sensitivity to the details of the distribution observedin experiments is unknown. This project gives insight into themechanism underlying extreme property gains, and thus provideskey input into design and control strategies.