▎ 摘　　要

A simplified model is proposed to calculate reduced self-attractive energy of a free monolayer graphene sheet due to ripples. The model admits stable periodic ripple mode of a free-standing graphene ribbon in the absence of a substrate or mechanical stress, and the predicted wavelengths are in robust agreement with observed values. The predicted minimum value of tensile force for eliminating ripples is consistent with related data reported in literature. These results suggest that even the self-attractive energy alone could be strong enough to drive ripple formation. This gives an alternative explanation for ripple formation of free graphene sheets. (C) 2013 AIP Publishing LLC.