▎ 摘　　要

Layered carbon is a likely anode material for Na-ion batteries (NIBs). Graphitic carbon has a low capacity of approximately 35 (mA h)/g due to the formation of NaC64. Using first-principles methods including van der Waals interactions, we analyze the adsorption of Na ions and clusters on graphene in the context of anodes. The interaction between Na ions and graphene is found to be weak. Small Na clusters are not stable on the surface of pristine graphene in the electrochemical environment of NIBs. However, we find that Na ions and clusters can be stored effectively on defected graphene that has double vacancies. In addition, the adsorption energy of small Na clusters near a double vacancy is found to decrease with increasing cluster size. With high concentrations of vacancies the capacity of Na on defective graphene is found to be as much as 10-30 times higher than that of graphitic carbon.