  Grain boundaries are topological defects that often have a disordered
character. Disorder implies that understanding general trends is more important
than accurate investigations of individual grain boundaries. Here we present
trends in the grain boundaries of graphene. We use density-functional
tight-binding method to calculate trends in energy, atomic structure (polygon
composition), chemical reactivity (dangling bond density), corrugation heights
(inflection angles), and dynamical properties (vibrations), as a function of
lattice orientation mismatch. The observed trends and their mutual
interrelations are plausibly explained by structure, and supported by past
experiments.
