Graphene has been widely investigated in many areas of research. Some
studies even explored the applicability of graphene as separation molecular membranes.
The structure of the perfect graphene is composed of hexagonal honeycombs and reminds
of a perforated structure that could have the potential to separate very small molecules.
We have shown that this is not the case, because the barriers for diffusion through an ideal
graphene layer are extremely high even for the smallest atoms in nature. To utilize graphene
as separation membranes, defects need to be introduced into graphene structure. The
role of intrinsic defects in graphene for the diffusion of molecules through the graphene
sheets has not been fully explained yet, so we have primarly investigated vacancy point
defects. By calculations based on the density functional theory (DFT), we modeled the
diffusion of H2 and O2 through vacancies of different sizes in graphene sheet. Our DFT
calculations clearly revealed that non-passivated vacancy defects of pure graphene are
so reactive as to dissociate molecules, such as H2 , O2 , and H2O. In particular, calculated dissociation barriers are low enough for the vacancy defects to quickly get passivated; O2 even dissociates without a barrier at non-passivated vacancy defects. For this reason, we also considered vacancies, passivated with dissociated O2 and H2O molecules. Diffusion
barriers, calculated for various types of vacancies were then compared with respect to each
other on the basis of their numerically calculated van der Waals vacancy areas. Finally,
we also considered a special type of line defects, named as side slits. Here, we have
estimated the diffusion barriers based on the experience gained from the time consuming
transition-state nudged-elastic-band (NEB) calculations of diffusion barriers for molecular
diffusion through vacancy defects in graphene sheet. The gained experience allowed us
to estimate the diffusion barriers for the diffusion through the side slits by using the
simplified constrained relaxation calculations. We have then compared the so calculated
diffusion barriers with respect to the relative size of the molecules, whereby we made
the comparision for H2 , O2 and H2O molecules. As to better appreciate the calculated
diffusion barriers, we also performed an analysis on the basis of energy distribution of
gas phase molecules that is based on the Maxwell-Boltzmann velocity distribution of
gas-phase molecules. In this way, we calculated the fraction of molecules that have kinetic
energy high enough to overcome the diffusion barrier for several characteristic diffusion
barriers.
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