The time lag in surface diffusion evaluated for the BET and BSB isotherms

One of the experimental methods to determine the coefficient of surface diffusion of species migrating in a porous material uses the measurement of the time lag. It represents the time required for the species to spend their life within the material when permeating through it. Describing the mass transport by a suitable transport model, the time lag can be expressed in terms of integrals whose evaluation depends on the adsorption isotherm of the studied species in the material. For porous building materials, the BET (Brunauer-Emmett-Teller) and BSB (Brunauer-Skalny-Bodor) model isotherms are usually very good approximations to the measured isotherms at low and medium concentrations. In this paper we derive a formula for the time lag for both these model isotherms. The formula can be readily applied in the analysis of experimental data, whereas the general expression involving integrals is much less straightforward to employ, being usually evaluated numerically for fixed values of parameters. The sensitivity of the time lag formula to the surface diffusivity is illustrated for an example of a porous brick with a water adsorption isotherm known from previous experiments.