A thermodynamically based method to quantify true sorption hysteresis

Sorption of organic chemicals to soils and sediments often shows true hysteresis (i.e., nonsingularity of the sorption-desorption isotherm not attributable to known experimental artifacts). Since true sorption hysteresis is fundamentally important to contaminant fate, a way to quantify it is desirable. Previously proposed indices of hysteresis are empirical and usually depend on the isotherm model. True sorption hysteresis to synthetic and natural organic solids has been attributed to irreversible alteration of the solid during the sorption-desorption cycle. Given this mechanism, we propose the Thermodynamic Index of Irreversibility (TII) for quantifying hysteresis in soils where natural organic matter dominates the sorption process. The TII is based on the difference in free energy between the real desorption state and the hypothetical fully reversible state. The index is 0 for completely reversible systems and approaches 1 as the process tends toward complete irreversibility. It does not require any assumptions about the physical properties or molecular composition of the solid, and it does not depend on a specific equilibrium model. A sensitivity analysis of measurement errors provides general recommendations for the setup of sorption-desorption experiments. The TII was applied to sorption of 1,4-dichlorobenzene (DCB) to two high-organic soils, Pahokee peat (PP) and Amherst soil (AS), and a low-rank coal reference material, Beulah-Zap lignite (BZL). Common artificial causes of hysteresis were eliminated. Hysteresis was significant in the peat and the coal. The TII was clearly concentration dependent for both solids; it decreased with concentration for the peat, but increased with concentration for the coal. The TII allows quantification of hysteresis as a function of sorbate-sorbent combination, concentration, time, and other variables.