Smectite molecular sieves. Part 3.—Theoretical considerations of sorption kinetics

Abstract

Early-time linear plots of uptake against t^1/2(t= time) are a feature of sorption kinetics, but the theoretical interpretation of their slopes, required to obtain diffusivities, has hitherto been restricted to sorption at constant pressure, or to sorption at constant volume for Henry's law isotherms. It is now shown, for constant diffusivities, that linear early-time plots of uptake against t^1/2 are to be expected for isotherms of any shape and for experimental conditions where both pressure and gas-phase volume vary simultaneously. Only the time over which the plot is linear will change with isotherm contour and experimental conditions. It is shown how these linear plots can give values of diffusivities for the above wholly general conditions.

For sorption under constant pressure into a bed of porous crystallites or particles of varying sizes, values of relaxation rate coefficients, D/(ā_z)², can be derived from plots of uptake against t^z . ā_z is a mean particle dimension which, for the method of moments, is shown to vary with z according to a particular formula. Its value increases with increasing z so that the relaxation rate coefficients then tend towards those of the larger particles. Particular attention has been given to the behaviour of ā_z for a Gaussian distribution of particle sizes. A procedure is indicated for obtaining from sorption kinetics that value of a which corresponds with the maximum in the Gaussian distribution, and hence a value of D/a² which is independent of z. The procedure also gives the standard deviation from the mean.