A hybrid model for estimation of pore size from ortho-positronium lifetimes in porous materials

Abstract

The present paper proposes a novel model for estimating the free-volume size of porous materials based on the analysis of various experimental ortho-positronium ($o$-Ps) lifetime data. The model is derived by combining the semi-classical (SE) physics model, which works in the region of large pores (pore size $R >$ 1 nm), with the conventional Tao-Eldrup (TE) model, which is applicable only for the small-pore region ($R <$ 1 nm). Thus, the proposed model, called the hybrid (HYB) model, is able to smoothly connect the $o$-Ps lifetimes in the two regions of the pore. Moreover, by introducing the $o$-Ps diffusion probability parameter ($D$), the HYB model has reproduced quite well the experimental $o$-Ps lifetimes in the whole region of pore sizes. It is even in a better agreement with the experimental data than the most up-to-date rectangular TE (RTE) and Tokyo models. In particular, by adjusting the value of $D$, the HYB model can also describe very well the two defined sets of experimental $o$-Ps lifetimes in the pores with spherical and channel geometries. The merit of the present model, in comparison with the previously proposed ones, is that it is applicable for the pore size in the universal range of $0.2 - 400$ nm for most of porous materials with different geometries.