Strong strain dependence of friction in graphene kirigami allows engineering a negative coefficient of friction

The friction force typically increases linearly with normal load with a constant of proportionality called the coefficient of friction. Most materials exhibit a positive friction coefficient, so that an increase in the normal load leads to an increase in the friction force. Recently, materials with negative friction coefficients have been observed at meticulously constructed interfaces due to an interplay between superstructures at heterojunctions, out-of-plane buckling, or the ordering of thin water films. However, the magnitude of the negative friction coefficient is typically much less than 10⁻², the geometries are highly restrictive, and the mechanisms are difficult to scale to larger systems. Here, we show that a friction coefficient of −0.08 can be obtained for a graphene sheet modified with kirigami-inspired cuts when inducing sheet tension through a normal load coupling. We use molecular dynamics simulations to show that the frictional behavior of kirigami cut sheets exhibits a strong nonmonotonic dependence on in-plane strain, while only weakly influenced by normal loading. We argue that the strong influence of strain arises from changes in commensurability between the graphene sheet and the substrate when the sheet deforms and buckles out of plane. We propose a simple nanomachine design that couples normal loading and sheet tension which enables the realization of different frictional laws, including a negative coefficient of friction. This represents a unique approach to creating tunable frictional surfaces and opens up applications in sheet-like systems across scales.