Size dependence of static friction between solid clusters and substrates

The presence of static friction between two solids implies that they managed to interlock. In the absence of contamination, the degree of interlocking results from a competition between interfacial and elastic interactions. Here we include this competition into a theory describing the depinning of adsorbed clusters. We find that the friction force can decrease with their size and derive an expression for the critical radius below which interlocking is large. The theory is validated through simulations of krypton and silicon clusters adsorbed on a variety of substrates. Our study provides a quantitative explanation of why shear forces can be nonextensive at small scales, as it has often been observed experimentally.