Surface area and pore volume of a system of particles as a function of their size and packing

Size-dependent properties of colloidal and nanoscale systems could be evaluated in only two limiting approximations: supposing particles to be free or employing random dense packing models and their quantitative versions. However, real colloidal and nanoscale systems are formed by neither free nor densely packed particles, and the methods enabling one to calculate their properties at intermediate densities remain unknown. In this paper, simple relations between the particle radius R, surface area As, pore volume Vp, and packing fraction ρ are constructed in terms of the gapped gapless packing model. Calculations using recent data on As and Vp reveal that the particle radii predicted by the model are in good agreement with experimental measurements, and the ρ values evaluated for the first time depend on the pre-history of the system studied. Finally, conclusions are drawn that any dispersed solid of the specific surface area exceeding 30 m2/g must be constituted of nano-sized particles, and that assemblages of nano-sized particles of R > 2.6 nm are inevitably mesoporous.