Theory of Soft Solid Electrolytes

In batteries and other energy conversion and storage devices, the emergence of solid electrolytes in lieu of their liquid counterparts is being increasingly explored. Solid electrolytes offer increased stability and improved safety and, specifically polymers, are also useful in the context of stretchable and flexible electronics

Unfortunately, most solid polymer electrolytes possess ionic conductivity that is orders of magnitude lower than those of liquids. In this work, we explore the possibility of microstructure design to enhance the effective conductivity of composite polymer electrolytes. We develop a theoretical framework, to model the coupled deformation, electrostatics and diffusion in heterogeneous electrolytes. Using suitable scaling ansatz for homogenization, we find general expressions for the effective behavior of electrolytes and propose specific suggestions for improving their ionic conductivity.

Flexoelectricity and the Entropic Force between Fluctuating Fluid Membranes

Biological membranes undergo noticeable thermal fluctuations at physiological temperatures. When two membranes approach each other, they hinder the out of plane fluctuations of the other and thus this hindrance leads to an entropic repulsive force between membranes which, in an interplay with attractive and repulsive forces due to other sources, impact a range of biological functions: cell adhesion, membrane fusion, self-assembly, binding-unbinding transition among others. In this work, we take cognizance of the fact that biological membranes are not purely mechanical entities and, due to the phenomenon of flexoelectricity, exhibit a coupling between deformation and electric polarization. We use a variational perturbation method to analyze, in closed-form, the contribution of flexoelectricity to the entropic force between two fluctuating membranes and discuss its possible physical implications. We find that flexoelectricity leads to a correction that switches from an enhanced attraction at close membrane separations and an enhanced repulsion when the membranes are further apart.