Significance of concentration-dependent intracrystalline diffusion and surface permeation for overall mass transfer

The intracrystalline concentration profiles evolving during molecular uptake and release by nanoporous materials as accessible by interference microscopy contain a lot of hidden information. For concentration-independent transport parameter, the influence of surface resistances to overall mass transfer can be calculated by correlating the actual surface concentration with the overall uptake. By using a numerical solution of Fick’s 2nd law and considering a large variety of concentration dependencies of the transport diffusivity and the surface permeability, we show that the factor by which the transport process is retarded by the surface resistance may reasonably well be estimated by the type of correlation between the actual boundary concentration and the total uptake at a given time. In this way, a novel technique of uptake analysis which may analytically be shown to hold for constant diffusivities and surface permeabilities, is shown to be quite generally applicable