Mathematics of Anisotropic Electrical and Dielectric Properties of Nanocomposites

ZhengDMS-08-7954 本论文主要研究了纳米复合材料的两个重要方面：（1）纳米复合材料的均匀化有效介电常数;（2）纳米复合材料的电导率以介电常数为主。 该项目的重点是各向异性系统与取向有序的纳米粒子，是基于一个准确的描述nanoparticleorientational概率分布函数从流处理数据库，然后我们映射到effectiveproperties通过体积平均和渗滤现象。在第一部分中，有效介电张量被认为是在两个明确的系统目前的利益：高介电常数纳米粒子分散在聚合物中，和conductingnanoparticles分散在聚合物。 这两种体系都能提高有效介电性能。 这需要仔细的准备，因为这些特性对成分和加工的细节非常敏感。 在第二部分中，我们考虑了突出的电性能的关键方面，如渗流阈值的机械加载的修改，多尺度均匀化方法，和非分子尺度的电子跳跃模型。 为了应对这些挑战，需要开发数值和数学的均匀化和非平衡化技术。 拟议的项目修改，应用，测试和扩展现有的数学理论和两相（或三相，如果考虑界面）复合材料的数值方法，其中粒子和新的表面积的数量只是简单地取代现有的工具。 通过将设计的纳米颗粒混合到传统材料中来实现极端性能增强的愿望是基于原型实验的。 然而，纳米复合材料面临着新的挑战，因为没有预测性的数学或计算工具。 该项目是对这些需求的回应，通过物理分析和科学计算的协调结合，从单个颗粒到整体性质。 今天，粒子数的限制只允许测量纳米粒子分布的低矩，而实验中发现的分布细节的固有材料敏感性是未知的。 该项目提供了深入了解的机制，潜在的极端财产收益，从而提供了关键的输入到设计和控制策略。

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.