The Interaction of Nonlinear Deformation and Electrostatics with Applications for Designing New Materials and Explaining Natural Phenomena

The central theme of this dissertation is to examine the intricate manner in which nonlinear deformation is coupled with electrostatics and the myriad ways this coupling can be exploited to either design novel types of materials or explain natural phenomena. Indeed, the applications outlined in our work link together ostensibly three disparate topics: solid-state lithium-ion batteries, soft materials with giant electromechanical coupling, and insights into why some people hear the music better than others:

1. In most current embodiments of rechargeable batteries, 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, improved safety and 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 Chapter 2, 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 soft solid electrolytes.

2. Soft robotics requires materials that are capable of large deformation and amenable to actuation with external stimuli such as electric fields. Energy harvesting, biomedical devices, flexible electronics, and sensors are some other applications enabled by electroactive soft materials. The phenomenon of flexoelectricity is an enticing non-traditional mechanism that refers to the development of electric polarization in dielectrics when subjected to strain gradients. In Chapter 3, we present a statistical-mechanics theory for the emergent flexoelectricity of elastomers consisting of polar monomers. The theory leads to key insights regarding both giant flexoelectricity and material design.

3. Some people, entirely untrained in music, can listen to a song and replicate it on a piano with unnerving accuracy. What enables some to “hear” music so much better than others? Long-standing research confirms that part of the answer is undoubtedly neurological and can be improved with training. However, are there structural, physical, or engineering attributes of the human hearing mechanism apparatus~(i.e., the hair cells of the internal ear) that render one human innately superior to another in terms of propensity to listen to music? In Chapter 4, we investigate a physics-based model of the electromechanics of the hair cells in the inner ear to understand why a person might be physiologically better poised to distinguish musical sounds. A key feature of the model is that we avoid a “black-box" systems-type approach. All parameters are well-defined physical quantities, including membrane thickness, bending modulus, electromechanical properties, and geometrical features, among others. Using the two-tone interference problem as a proxy for musical perception, our model allows us to establish the basis for exploring the effect of external factors such as medicine or environment. As an example of the insights we obtain, we conclude that the reduction in bending modulus of the cell membranes (which for instance may be caused by usage of a certain class of analgesic drugs) or an increase in the flexoelectricity of the hair cell membrane, can interfere with the perception of two-tone excitation.

4. The mechanical response of nanostructures, or materials with characteristic features at the nanoscale, differs from their coarser counterparts. An important physical reason for this size-dependent phenomenology is that surface or interface properties are different than those of the bulk material and acquire significant prominence due to an increased surface to volume ratio at the nanoscale. In chapter 5, we provide an introductory tutorial on the continuum approach to incorporate the effect of surface energy, stress and elasticity and address the size-dependent elastic response at the nanoscale. We present some simple illustrative examples that underscore both the physics underpinning the capillary phenomenon in solids as well as a guide to the use of the continuum theory of surface energy.