A new sorption model with a dynamic correction for the determination of diffusion coefficients

This paper describes an improvement to the method used for the calculation of diffusion coefficients from data obtained by the measurement of vapor sorption kinetics in a flat, non-porous polymeric membrane. The advantage of our corrected model is that it can be applied to systems displaying both fast and slow sorption kinetics, as is demonstrated using cellulose myristate – hexane and cellulose acetovalerate – ethanol systems at a temperature of 298 K. Experiments were conducted on a specially developed sorption apparatus equipped with McBain’s spiral quartz balances. Sorption kinetics are generally described by the solution of Fick’s second law, the solution of which assumes relative pressure in the form of the unit step function. Our correction involves modifying this solution so that a more realistic relative pressure increase is assumed in terms of the Laplace transform.