Surface area and volume fraction of random open-pore systems

For the first time, explicit approximate formulas are presented for the volume fraction and specific surface area of random open-pore systems with poly-disperse pore size distributions. It is shown that the formulas are valid for broad classes of models for porous media characterized by tunable pore size distributions and a variable degree of inter-penetrability of pores. The formulas for the poly-disperse case are based on expressions derived previously for mono-disperse penetrable-sphere models. The results are obtained by analysis of a series of open-pore models, which are prepared by computer simulation of systems of randomly packed partially penetrable spheres with various poly-disperse size distributions such as gamma, lognormal, and Gaussian. The formulas are applied in a study of atomic layer deposition processes on open-pore systems, and the effective Young's modulus and the effective thermal conductivity of Al2O3 coated porous polypropylene electrodes for lithium ion batteries are predicted.