Theory of soft solid electrolytes: Overall properties of composite electrolytes, effect of deformation and microstructural design for enhanced ionic conductivity

Re-chargeable batteries are an important element in the solution to the future of portable energy storage. In that context, electrolytes play a critical role in the adjudication of a battery’s capacity, efficiency and operation. In most current embodiments of rechargeable batteries, including the widely researched lithium-ion system, electrolytes are liquid. That said, the use 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 ideal candidates in the context of stretchable and flexible electronics. Unfortunately, most solid polymer electrolytes possess ionic conductivity that is orders of magnitude lower than typical liquid electrolytes. In this work, we explore the possibility of microstructure design to enhance the effective ionic conductivity of composite polymer electrolytes. We develop a theoretical framework, grounded in thermodynamics and principles of continuum mechanics, to model the coupled deformation, electrostatics and diffusion in heterogeneous electrolytes. Guided by numerical thought experiments, we establish a homogenization procedure that significantly reduces the complexity of the original non-linear problem and derive general analytical expressions for the effective behavior of electrolytes and closed-form solutions for specific microstructures. Using insights from our model, in addition to proposing suggestions for improving the ionic conductivity of solid electrolytes, we are also able to explain several perplexing experimental observations and address questions such as: (i) Why do some experiments show a dramatic improvement in the ionic conductivity of nanoparticle-impregnated polymers while others yield a decrease? (ii) What is the effect of deformation on ionic conductivity?