NANOSTRUCTURED SURFACES AND EMERGENT PHYSICAL BEHAVIOR
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Due to larger surface to volume ratio, surfaces play a significant role at the nanoscale. Surface atoms have different coordination numbers, charge distribution and subsequently different physical, mechanical and chemical properties. These differences are interpreted phenomenologically by postulating the existence of surface energy and acknowledging that the various bulk properties such as elastic modulus, melting temperature, and electromagnetic properties are different for surfaces. In this dissertation, we consider two types of surfaces: those bounding a three-dimensional entity, and independent two-dimensional deformable surfaces that can be used to represent, for example, graphene sheets, thin films, and lipid bilayers among others. In this dissertation: (i) We develop a theoretical framework, complemented by atomistic calculations, that elucidates the effect of roughness on surface energy, stress and surface elasticity. We find that the residual surface stress is hardly affected by roughness while the superficial elastic properties are dramatically altered and, importantly, may also result in a change in its sign; this has significant ramifications in the interpretation of sensing based on frequency measurement changes. In particular, we also comment on the effect of roughness on the generally ignored term that represents the curvature dependence of surface energy, crystalline Tolman’s length. (ii) In the context of independent deformable surfaces, our focus is on electromechanical coupling; in particular, the rapidly emerging topic of flexoelectricity. Recent developments in flexoelectricity, especially in nanostructures, have lead to several interesting notions such as creating piezoelectric substances without using piezoelectric materials, enhanced energy harvesting at the nanoscale among others. In the biological context also, membrane flexoelectricity has been hypothesized to play an important role, e.g., biological mechano-transduction, hearing mechanisms. In this dissertation, we consider a heterogenous flexoelectric membrane, and derive the homogenized flexoelectric, dielectric and elastic response. In particular for purely fluid or lipid type membranes, we obtain exact results—one of very few in homogenization theory. Using quantum mechanical calculations, we also show that graphene can be designed to be pyroelectric, thus providing an avenue to create the thinnest possible thermo-electro-mechanical material.