Thickness dependent adhesion force and its correlation to surface roughness in multilayered graphene

In this paper adhesion force of multi-layered graphene films with different thickness is experimentally determined and studied for the first time. In thin graphene layers, the adhesion force increases with decreasing thickness and approaches that of substrate which is correlated to Van Der Waals force transparency of mono-layer graphene. In very thick graphene layers, a rise in adhesion force is seen which we correlate to surface roughness changes of the substrate. Simple models for measuring adhesion force for a flat surface with sub-nanometer roughness and tip-radius scale roughness are proposed. Based on these models we understand that small surface roughness decreases adhesion force while large roughness will increase the adhesion force. This deduction is corroborated by the experimental data obtained from adhesion force measurements. It is also shown that roughness in the scale of AFM tip-radius can double the adhesion force easily and surface roughness plays an important role in the adhesion force measurements.