Anisotropic rheology and friction of suspended graphene

Graphene is a powerful membrane prototype for both applications and fundamental research. Rheological phenomena including indentation, twisting, and wrinkling in deposited and suspended graphene are actively investigated to unravel the mechanical laws at the nanoscale. Most studies focused on isotropic setups, while realistic graphene membranes are often subject to strongly anisotropic constraints, with important consequences for the rheology, strain, indentation, and friction in engineering conditions. Graphene in particular is recognized as the thinnest solid lubricant material and a large amount of work has been dedicated to understanding the fundamentals mechanisms of this effect and to unravel parameters relevant to its technological development. Here, we experimentally show how graphene's frictional response to an external indenter is severely altered by conditions of anisotropic suspension, specifically when graphene is clamped across a long and narrow groove. Results show that the friction coefficient is significant when the tip is sliding parallel to the groove while becoming ultralow in the orthogonal direction. While the experimental data suggest that-rather unexpectedly-prestrain of the graphene sheet as a result of clamping is negligible, the key to understanding the underlying mechanism is provided by simulations. The paramount mechanism is provided by the extra anisotropic strain induced from indentation under anisotropic constraints, which in turn produces an anisotropic stiffening of the graphene. While the focus of this work is on graphene, we believe our experimental protocol and the physical mechanism uncovered by our model can be applicable to other 2D membranelike materials.