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This paper reports the results of a theoretical investigation of the effect of a sorbent size distribution on the zero length column (ZLC) method for measuring intracrystalline diffusion. A new model incorporating a continuous log-normal distribution of crystal size is introduced. It is shown that such a distribution introduces tailing into the normally linear long time region of the desorption curve, although this curvature is not obvious when the initial concentration drop is fast. Analysing such a curve with the standard ZLC model causes the diffusional time constant to be underpredicted, whereas the adsorption related parameter L is overpredicted. The error increases with increasing distribution width. It is shown that the curve may be well approximated by summing the desorption curves of the individual, discrete size fractions, weighted by their volume fraction. The systematic error introduced into the measured diffusion coefficient when analysing data for sorbent samples with a size distribution with the standard model may be reduced if the mean particle size is defined as the ratio of the sample's volume to its surface area. |
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