Adsorption of Diffusing Tracers, Apparent Tortuosity, and Application to Mesoporous Silica

The apparent tortuosity due to adsorption of diffusing tracers in a porous material is determined by a scaling approach and is used to analyze recent data on LiCl and alkane diffusion in mesoporous silica. The slope of the adsorption isotherm at small loadings is written as β = q A /q G , where q A is the adsorption–desorption ratio and q G = ϵ/(as) – 1 is a geometrical factor depending on the range a of the tracer-wall interaction, the porosity ϵ, and the specific surface area s. The adsorption leads to a decrease of effective diffusion coefficient, which is quantified by multiplying the geometrical tortuosity factor τ geom by an apparent tortuosity factor τ app . In wide pores or when the adsorption barrier is high, τ app = β + 1, as obtained in previous works, but in narrow pores there is an additional contribution from frequent adsorption–desorption transitions. These results are obtained in media with parallel pores of constant cross sections, where the ratio between the effective pore width ϵ/s and the actual width is ≈0.25. Applications to mesoporous silica samples are justified by the small deviations from this ideal ratio. In the analysis of alkane self-diffusion data, the fractions of adsorbed molecules predicted in a recent theoretical work are used to estimate τ geom of the silica samples, which is ≫1 only in the sample with the narrowest pores (nominal 3 nm). The application of the model to Li+ ion diffusion leads to similar values of τ geom and to a difference of energy barriers of desorption and adsorption for those ions of ∼0.06 eV. Comparatively, alkane self-diffusion provides the correct order of magnitude of τ geom , with adsorption playing a less important role, whereas adsorption effects on Li+ diffusion are much more important.