Critical curvature localization in graphene. II. Non-local flexoelectricity-dielectricity coupling

As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474, 20180054), we present a general thermodynamic framework of flexoelectric constitutive laws for multi-layered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of highly oriented pyrolytic graphite (HOPG) surfaces. The thermodynamically consistent constitutive laws lead to a non-local interaction model of polarization induced by electromechanical deformation with flexoelectricity-dielectricity coupling. The non-local model predicts curvature and polarization localization along crinkle valleys and ridges very close to those calculated by density functional theory (DFT). Our analysis reveals that the non-local model can be reduced to a simplified uc-local or e-local model (Kothari et al. 2018 Proc. R. Soc. A 474, 20180054) only when the curvature distribution is uniform or highly localized. For the non-local 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. Our DFT analysis shows that polarization-induced adsorption of neutral molecules at crinkle ridges depends on the molecular weight of the molecule. Furthermore, our detailed study of polarization localization in graphene crinkles enables us to understand previously unexplained self-organized adsorption of C₆₀ buckyballs in a linear array on an HOPG surface.