Sorption and desorption by ideal two-compartment systems: unusual behavior and data interpretation problems

This paper examines the current practices of fitting curves to sorption, desorption, and equilibrium data obtained from laboratory experiments. Systems of equations incorporating Freundlich isotherms and first-order kinetics for two different idealized sorbents, one “fast” and one “slow,” were solved numerically to produce “data”. Two-compartment curves were then fit to the data by nonlinear regression, and the parameters computed by the regression are compared with the original parameters used to produce the data. The results show that a sorbent with fast kinetics will not steadily accumulate sorbate until it reaches the equilibrium value but will overshoot equilibrium, accumulating an excess of sorbate. This overshoot will cause the sorption rates for both sorbents and the distribution between the fast and slow sorbents to be estimated incorrectly. The system may appear to be at equilibrium by external measures, but sorbate will slowly be redistributing from the fast to the slow sorbent. An isotherm constructed from data acquired during this process will have an incorrect coefficient and exponent. Consequently, the meaning of the results obtained by curve fitting may often be questionable and may say little about the phenomena occurring within the sorbate–sorbent–liquid system. Possible physical explanations for the effects observed are offered.