Packing efficiency and accessible surface area of crumpled graphene

Abstract

Graphene holds promise as an ultracapacitor due to its high specific surface area and intrinsic capacitance. To exploit both, a maximum surface area must be accessible while the two-dimensional (2D) graphene is deformed to fill volume. Here, we study stable crumpled graphene sheets of different lengths, $L$, using full atomistic molecular dynamics (MD) and determine a fractal dimension of $D\ensuremath{\cong}2.36\ifmmode\pm\else\textpm\fi{}0.12$, indicating efficient spatial packing. Introduction of defects inducing a transition from membrane-like to amorphous carbon further enhances packing efficiency. Further, variation of self-adhesion energy indicates a predominant role in randomly folded graphene. We determine that approximately 60% of the specific surface area of graphene is solvent accessible once crumpled and can be tuned with applied compression and crumpling. We analyze the solvent accessible surface area (SASA) and approximate the upper bound of free crumpled graphene capacitance to \ensuremath{\approx}329 F/g. Once crumpled, the achievable capacitance is highly dependent on the confined volume.