Organization of charged molecules in heterogeneous media

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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.