Chain Structure and Counterion Condensation in Solutions of Flexible Polyelectrolyte Chains

9619277刘这笔赠款的主要目的是从理论上加深对聚电解质的理解。具体地说，这个项目有两个相关的部分：一个是进一步发展变分形式，研究任意浓度下聚电解质溶液的链结构。这与过去关于聚电解质链结构的工作形成对比，后者被限制在无限稀释极限下的单链。第二部分是该形式主义在反离子凝聚研究中的应用。这个理论的主要优点是它可以处理波动的、本质上是柔性的链，并且它不需要限制固定的模型几何形状，如线电荷和圆柱体。这项工作有望解决聚电解质溶液领域中一些最具争议性的问题，并为更复杂的体系的类似研究铺平道路，如带电自组装表面活性剂体系、聚电解质络合物和聚电解质/膜络合物。%在这笔资助中，一位年轻的理论聚合物科学女研究人员获得了研究聚电解质性质的支持。这些聚合物可溶于水，随处可见，尤其与环境友好的加工有关。这个项目的工作解决了带电聚合物结构中的一些长期存在的问题，以及它们对相当高水平的进一步充电的响应。这项工作使用了复杂的、最先进的理论机器，并建议进一步建立在PI最近必要的数学技术发展的基础上。***

9619277 Liu The principal objective in this grant is to develop theoretical understanding of polyelectrolytes. Specifically there are two related components of this project: One involves further development of a variational formalism to study the chain structure of a polyelectrolyte solution at arbitrary concentrations. This is in contrast to past work on the polyelectrolyte chain structure which has been limited to a single chain, in the infinite dilution limit. The second part is an application of this formalism to study counterion condensation. The principal advantage of this theory is that it can treat fluctuating, intrinsically flexible chains and it does not require restriction to fixed model geometries such as line charges and cylinders. This work is expected to resolve some of the most controversial questions in the field of polyelectrolyte solutions and also pave the way for similar studies of even more complex systems such as charged self-assembled surfactant systems, polyelectrolyte complexes, and polyelectrolyte/membrane complexes. %%% In this grant to a young female researcher in theoretical polymer science, there is support to study properties of polyelectrolytes. These are the polymers that are soluble in water, generally found everywhere and especially relevant to environmentally-benign processing. The work in this project addresses some long standing questions in the structure of charged polymers and their response to further charging at fairly high levels. This work uses sophisticated, state-of-the-art, theoretical machinery and proposes to further build on the PI's recent development of necessary mathematical techniques. ***