Analytical expressions for electrostatics of graphene structures

• An atomistic moment method is applied for the estimation of graphene structures electrostatics.
• New analytical equations are obtained for the prediction of total charge or capacitance of graphene structures.
• The lowest point charges are found at the center of a graphene structure, while the maximum charges are found at its corners.
• The maximal charge enhancement increases as the size of the graphene structure is increased as well.

This study focuses on electrostatics of various graphene structures as graphene monolayer, graphene nanoribbons, as well as multi-layer graphene or graphene flakes. An atomistic moment method based on classical electrostatics is utilized in order to evaluate the charge distribution in each nanostructure. Assuming a freestanding graphene structure in an infinite or in a semi-infinite space limited by a grounded infinite plane, the effect of the length, width, number of layers and position of the nanostructure on its electrostatic charge distributions and total charge and capacitance is examined through a parametric analysis. The results of the present show good agreement with corresponding available data in the literature, obtained from different theoretical approaches. Performing nonlinear regression analysis on the numerical results, where it is possible, simple analytical expressions are proposed for the total charge and charge distribution prediction based on structure geometry.