Sliding Friction of Amorphous Asperities on Crystalline Substrates: Scaling with Contact Radius and Substrate Thickness

Disorder in the contact between an amorphous slider and a crystalline substrate leads to a cancellation of lateral forces. Atomically flat, rigid surfaces exhibit structural superlubricity, with the frictional stress in circular contacts of radius a vanishing as 1/a. The inclusion of elasticity allows relative motion of domains on the surface in response to the random interfacial forces. The competition between disorder and elastic deformation is predicted to limit structural superlubricity and produce a constant frictional stress for a larger than a characteristic domain size lambda that depends on the ratio of the shear modulus G to the magnitude of interfacial shear stresses tau(0). Extensive simulations of a flat, amorphous punch sliding on a crystalline substrate with different system sizes and G/tau(0) are used to test scaling predictions and determine unknown prefactors that are needed for quantitative analysis. For bulk systems, we find an exponential decrease of the large a frictional stress and 1/lambda. with increasing G/tau(0). For thin free-standing films, the stress and 1/lambda. are inversely proportional to G/tau(0). These results may help explain the size-dependent friction of nanoparticles and plate-like materials used as solid lubricants.