A Study of Curvature Localization in Multilayer GrapheneKothari, MrityunjaycreatorKim, Kyung-SukAdvisorGao, HuajianReaderHenann, DavidReaderStein, DerekReaderBrown University. Engineering: Mechanics of Solidssponsor2019xviii, 86 p.born digitalThesis (Ph. D.)--Brown University, 2019thesesWe discover a new, curvature-localizing, subcritical buckling mode that produces a shallow-kink configuration in multi-layer graphene. Our density functional theory (DFT) analysis reveals the mode configuration - an approximately 2 nm wide boundary layer of localized curvature that connects two regions of uniformly but oppositely sheared stacks of flat atomic sheets. The kink angle between the two regions is limited to a few degrees ensuring elastic deformation. By contrast, a purely mechanical model of sandwich structures shows progressive supercritical curvature localization spread over a 50-100 nm wide boundary layer. We propose an effective-locality model of electromechanics, which reveals that the coupling between atomic-layer curvature and electric charge polarization, i.e. quantum flexoelectricity, leads to the emergence of a boundary layer. Within this boundary layer, the curvature is focused primarily within a 0.86 nm fixed band width. Both DFT and the model analyses show focused distribution of the curvature and polarization exhibiting oscillating decay with the boundary layer. The interactions between flexoelectrically generated dipoles lower the potential energy and also switch the stability from supercritical for a mechanical sandwich structure to subcritical for a flexoelectric crinkle. In additional to the structural and stability characterization of crinkles, a general thermodynamic framework of flexoelectric constitutive laws for multilayered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of HOPG surfaces. Our analysis reveals that the nonlocal model can be reduced to a simplified uc-local or e-local model only when the curvature distribution is uniform or highly localized. For the nonlocal model, we calibrated and formulated the layer-number dependent dielectric and intrinsic flexoelectric coefficients of MLGs. In addition, we also obtained layer-number dependent flexoelectric coefficients for uc-local and e-local models. A peak polarization of 0.12 e/nm is predicted for a 3 ◦ end angle and is concentrated in the boundary layer. The charge distribution in agreement with DFT and is significant enough to adsorb charged and polarizable molecules on the surface. This charge segregation is controllable by macroscopic deformation and is expected to be useful in studies of selective graphene-surface functionalization for various applications. Bifurcation analysis of a bilayer graphene on softer substrates shows the existence of crinkle bifurcation and is capable of generating periodic crinkle patterns.Applied mathematicsSolid Mechanics2D MaterialsEnglishRPB2019060310.26300/mtbw-qg51In CopyrightCollection is open for research.dissertations