Organization of charged molecules in heterogeneous media

技术概述：该奖项支持对凝胶弹性和静电耦合的理论和数值研究。静电在现代材料的发展中起着至关重要的作用，包括用于水过滤的膜、用于诊断的功能化纳米颗粒、用于基因治疗的多电解质复合物、用于药物输送的纳米凝胶、锂离子电池和新型设备。这些系统通常需要非均质弹性介质的支持，其中可以传递信息，例如双连续膜或凝胶。这些材料以及生物凝胶的许多功能都是由电荷和组成的非均质性造成的。在求解任意形状的非均质介质中的静电和弹性问题方面都存在很大的挑战。该项目旨在开发确定非均相凝胶性质的方法，包括经典平均场模型中忽略的效应，如离子的硬核、介电失配和弹性能。更具体地说，PI将：(i)通过非线性密度泛函理论研究致密离子凝胶中硬核相互作用的影响，该理论适当地解释了长期和短程相互作用，并将通过计算机模拟测试结果；（ii）通过能量变分原理分析二价离子或吸收分子存在时局部介电异质性的影响，该原理使人们能够在相同的模拟时间步长中更新电荷和介质的响应；（ii）利用连续弹性模型描述局部非均质引起的凝胶形状变化，建立局部非均质耦合的凝胶弹性效应公式。在研究中将使用各种技术，包括密度泛函方法、粗粒度分子动力学模拟和有限元方法。对静电的理解将有助于凝胶自组装和合成材料设计的研究。PI与墨西哥复杂电解质领域的专家合作。PI和她的墨西哥合作者的共同努力将有助于设计清洁水的智能凝胶，这在墨西哥和美国都是一个重要的社会问题。此外，PI致力于通过监督来自代表性不足的少数民族的学生和博士后，继续增加科学领域的多样性。她还致力于教育公众，并通过参加西北大学的外展项目，让中学生和高中生参与科学研究。该奖项支持对凝胶的弹性和静电耦合的理论和数值研究。凝胶是由稀交联的聚合物分子组成的网络，悬浮在液体中，但表现出固体的一些机械特性。分子的某些部分通常携带电荷，电荷之间的相互作用既决定了分子在凝胶中的组装，也决定了凝胶的性质。该奖项资助研究如何正确描述凝胶中的静电相互作用及其与材料弹性特性的相互作用。凝胶用于各种各样的应用。本研究也将适用于其他软材料和系统。对非均质软材料中结合弹性效应的静电相互作用进行适当的理论描述对于设计新材料（如过滤水以使其安全饮用的膜）将是重要的。这项研究将与墨西哥的专家合作进行。PI参与了她所在大学的外联工作，并致力于扩大代表性不足群体的代表性。

TECHNICAL SUMMARYThis award supports theoretical and numerical research on the coupling of elasticity and electrostatics of gels. Electrostatics plays a critical role in the development of modern materials including membranes for water filtration, functionalized nanoparticles for diagnostics, polyelectrolyte complexes for gene therapy, nanogels for drug delivery, lithium-ion batteries and novel devices. These systems often require the support of a heterogeneous elastic medium where the information can be transferred such as a bicontinuous membrane or a gel. Many of the functions of these materials, as well as of biological gels, result from charge and composition heterogeneities. There are great challenges in both, solving electrostatics and elasticity problems in heterogeneous media of arbitrary shapes. The PI aims to develop ways to determine the properties of heterogeneous gels including effects neglected in classical mean field models such as the hard core of the ions, the dielectric mismatch and the elastic energy. More specifically, the PI will: (i) study the effect of hard-core interactions in dense ionic gels via a non-linear density-functional theory that accounts properly for long- and short-range interactions and will test the results via computer simulations;(ii) analyze the effect of local dielectric heterogeneities in the presence of divalent ions or absorbing molecules via an energy variational principle that enables one to update charges and the medium's response in the same simulation time step; and(ii) develop a formulation of elasticity effects in gels coupled to local heterogeneities using a continuum elasticity model to describe the gel-shape changes induced by local heterogeneities.A variety of techniques will be used in the research including a density-functional approach, coarse-grained molecular-dynamics simulation, and finite-elements methods. The understanding of electrostatics will inform research on self-assembly of gels and the design of synthetic materials. The PI collaborates with experts in complex electrolytes in Mexico. The combined efforts of the PI and her Mexican collaborators will aid the design of smart gels for cleaning water, which is an important societal problem in both Mexico and the US. Moreover, the PI is committed to continue increasing diversity in science by supervising students and postdocs from underrepresented ethnic groups. She is also committed to educate the public and engage middle and high school students in scientific research by participating in outreach programs at Northwestern University.NONTECHNICAL SUMMARYThis award supports theoretical and numerical research on the coupling of elasticity and electrostatics of gels. A gel is a network of dilutely cross-linked polymer molecules suspended in liquid but exhibiting some of the mechanical properties of a solid. Parts of the molecules generally carry electric charges, and the interactions of the charges govern both the assembly of the molecules into a gel and the gel's properties. This award funds research on how to properly describe electrostatic interactions in gels and their interplay with the elastic properties of the material. Gels are used in a wide variety of applications. This research will also be applicable to other soft materials and systems. A proper theoretical description of electrostatic interactions combined with elastic effects in heterogeneous soft materials will be important for the design of new materials, such as membranes for filtering water to make it safe for drinking. The research will be carried out in collaboration with experts in Mexico. The PI is involved in outreach efforts at her university and is committed to broadening representation from underrepresented groups.