Mean interparticle distances between hard particles in one to three dimensions

Formulas for correlating morphological parameters in mixtures containing polydisperse hard particles are important for investigating the relationships of the properties of these mixtures with morphological parameters. Two simple new formulas are derived, respectively for relating the number averaged surface to surface or center to center interparticle distances between impenetrable particles with average particle diameter, volume fraction of particles, particle spatial distribution parameter and dimensional number. The geometrical importance of particle spatial distribution parameter is given. The two formulas are generally applicable to a system filled with hard particles obeying any particle size distribution and occupying any lattice in one to three dimensions.