Chain Structure and Counterion Condensation in Solutions of Flexible Polyelectrolyte Chains

9619277刘在这个补助金的主要目标是发展的理论认识的聚电解质。 具体来说，这个项目有两个相关的组成部分：一个涉及进一步发展的变分形式主义，研究链结构的一个在任意浓度下的一个natural解决方案。 这与过去在无限稀释极限下对单链结构的研究相反。 第二部分是应用这一理论研究反凝聚。 这个理论的主要优点是，它可以处理波动，本质上灵活的链，它不需要限制到固定的模型几何形状，如线电荷和圆柱。 这项工作预计将解决一些最有争议的问题，在该领域的解决方案，也铺平了道路，甚至更复杂的系统，如带电的自组装表面活性剂系统，表面活性剂复合物，和表面活性剂/膜复合物的类似研究。 %在这个赠款给一个年轻的女性研究人员在理论聚合物科学，有支持研究性质的聚电解质。 这些是可溶于水的聚合物，通常在任何地方都可以找到，特别是与环境友好的加工有关。 该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，以及它们在相当高的水平上对进一步充电的响应。 这项工作使用复杂的，国家的最先进的，理论的机器，并建议进一步建立在PI的必要的数学技术的最新发展。 ***

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. ***