Mathematics of Self-Assembled Materials

系统在没有直接控制或干预的情况下组装和组织的能力是生物和非生物系统的基础。诸如复杂聚合物的材料可以自组装成各种各样的形式，并且具有许多纳米技术和生物医学应用。该项目研究材料自组装模型，以发展理论洞察力和预测能力。公式的开发，连接微观分子特性的机械和形态学行为在更大的尺度。计算用于预测新的行为和定制输入工程纳米结构。该奖项为研究生和本科生提供研究和教育机会。该项目广泛研究聚合物，两亲性和基于颗粒的系统，以及创建纳米材料的基础工艺。描述形成的纳米粒子和两亲性结构的非均相聚合物系统的模型进行检查使用的分析和计算的方法，量化平衡，形态和动力学的混合物。结合这些模型，反问题的算法将开发的参数识别和工程设计的目的。在同一框架内研究了涉及大量相互作用粒子的自组装系统，从而预测了图案形成和集体行为。该研究的副产品包括数值和逆问题算法的开发。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The ability of systems to assemble and organize without direct control or intervention is fundamental to biological and non-biological systems. Materials such as complex polymers may self-assemble into a wide variety of forms, and have many nanotechnology and biomedical applications. This project studies models of material self-assembly to develop theoretical insight and predictive capabilities. Formulas are developed that connect microscopic molecular properties to mechanical and morphological behaviors at larger scales. Computations are employed for predicting novel behaviors and custom-tailoring inputs for engineered nanostructures. The award provides research and educational opportunities for both graduate and undergraduate students.This project broadly investigates polymer, amphiphilic, and particle-based systems, and processes fundamental to the creation of nanoscale materials. Models describing formation of nanoparticles and amphiphilic structures in heterogeneous polymer systems are examined using a mixture of analytical and computational approaches that quantify equilibria, morphology, and dynamics. In conjunction with these models, algorithms for inverse problems will be developed for purposes of parameter identification and engineering design. Self-assembled systems involving a large number of interacting particles are studied within the same framework, leading to predictions of pattern formation and collective behavior. Byproducts of the research include the development of numerical and inverse problem algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.