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 flexoelectricitydielectricity 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 dielectri...