Elasticity of Particle Assemblies as a Measure of the Surface Energy of Solids

A theory is suggested to explain the elasticity of particle assemblies. It is shown that a regular cubic packing of spheres has an effective Young's modulus that depends on the contacts between individual particles. In particular, it is noted that the effective modulus depends on the interfacial attractive energy between the spheres, and thus provides a direct method for measuring the surface energy of solids. However, most particle assemblies are neither cubic nor regular. The problem is to describe the properties of these real systems in terms of the packing of the grains. Theoretically, it is shown that the modulus of a powder compact should vary as the fourth power of the particle packing fraction. This result has been verified experimentally and has been used to determine the surface energies of zirconia, titania, alumina, and silica powders. The measured values were sometimes much lower than expected from theoretical calculations of surface energy. Experiment has shown that such discrepancies result from contamination of the solid surfaces.