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Implications from the ratio of surface tension to bulk modulus and nearest neighbour distance, for planar surfaces

The theory of impact between nano-sized particles leads to the important non-dimensional grouping γ/aB, where γ, a and B are the effective surface energy, effective near neighbour distance, and effective bulk modulus for the impacting surfaces. A general, though formal, expression for γ/aB is obtained for a planar surface, and a modified Lennard-Jones analysis suggests that this grouping is of the order of several per cent. Bounds are suggested on this ratio, which are verified for many of the elements about their melting points, for several liquids at 298 K, and for the liquified noble gases. It is suggested that, at the atomic scale, the ratio between yield stress and the bulk modulus is also approximately equal to this grouping, which would make impacts between nano-scaled surfaces very much harder than for macroscopic impacts. However, γ/aB is material dependent and can vary by a factor of two or more about its median value. Subject to such variation, it is suggested that, to leading order, collisions between pure nanoscale particles depend primarily on the number of atoms in the clusters, and on a non-dimensional velocity scale, for low-velocity impacts. The expression for γ/aB is evaluated approximately in planar geometry by assuming that interactions between surface atoms (or molecules) only involve radial pair surface interactions.