A universal exponential factor in the dimensional crossover from graphene to graphite

Abstract

A universal exponential factor, γc =π /2, is disclosed for the dimensional crossover of few-layer graphene (FLG) from two-dimensional graphene to three-dimensional graphite. γc is found by analyzing available experimental data on different properties of FLG with varying thickness. A theoretical study on the phonon spectrum of the vertical acoustic mode in FLG is carried out to further check this exponential factor γc. Interestingly, the same exponential factor appears in the dimensional crossover of the phonon mode. It turns out that the exponential factor γc is related to the homogeneous Helmholtz-like molal equation in the mass transfer with a first order chemical reaction. The finding should provide valuable information for experimentalists and theorists in the future investigation on thickness dependent properties of FLG. © 2010 American Institute of Physics.