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A Thermodynamically Based Method to Quantify True Sorption Hysteresis

^a Department of Chemical Engineering, Environmental Engineering Program, Yale University, 9 Hillhouse Avenue, P.O. Box 208286, New Haven, CT 06520-8286
^b Department of Soil and Water, Connecticut Agricultural Experiment Station, 123 Huntington Street, P.O. Box 1006, New Haven, CT 06504

View larger version (18K): [in a new window]   Fig. 1. Graphic and schematic representation of States S, D, , and for the calculation of the Thermodynamic Index of Irreversibility (TII). The identical sorbent particles are transferred from the sorption bath at solute concentration C = CS to one of the desorption baths at CD, C, or C. Irreversibility is symbolized by the distorted shape of the particle in State D. State S (CS/sorbed concentration q = qS) is the sorption state from which desorption is initiated. State D is the experimental desorption state (CD/qD). States (C/q) and (C/q) are hypothetical reversible desorption states.

View larger version (21K): [in a new window]   Fig. 2. Graphic representation of model calculations. Circles represent sorption points, triangles desorption points, and squares corresponding hysteresis indices. (a) Linear desorption with different irretrievable fractions b at C (CS)–1 = 0; (b) single desorption point (triangle) originating from different points (circles) along the sorption isotherm. The term C is the solute concentration, q is the sorbed concentration, and the superscript S represents the sorption state from which desorption is initiated.

View larger version (43K): [in a new window]   Fig. 3. (a) Calculated values of TII' for Freundlich sorption isotherm with Freundlich sorption isotherm exponent Nsorb = 0.8 and different preset Thermodynamic Index of Irreversibility (TII) values of 0.00, 0.25, 0.50, and 0.75. The fraction of solution displaced to initiate desorption is v/V = 0.9. The fractions of sorbate molecules sorbed in the sorbent in State S, fSsorb, are 0.1 (dash), 0.5 (solid), and 0.9 (dash dot dot). (b) Model Freundlich sorption–desorption systems with Nsorb = 0.8, and v/V = 0.9. Freundlich desorption isotherms are plotted for TII = 0.25 (long dash), TII = 0.50 (short dash), and TII = 0.75 (dash dot dot). Different fSsorb are represented by pointed lines and open symbols with inverse triangles , squares , and circles . (c) Absolute error in the TII, |TII – TII'|, over fSsorb for Nsorb = 0.8 and TII of 0.00 (solid), 0.25 (long dash), 0.50 (short dash), and 0.75 (dash dot dot). The fraction of solution displaced to initiate desorption is v/V = 0.9. (d) Calculated values of TII' for v/V ratios of 0.9 (dash), 0.5 (solid), and 0.3 (dash dot dot). The terms Nsorb and fSsorb are set to 0.8 and 0.5, respectively. The term v (L) is the volume removed to initiate desorption and V (L) is the total volume of solution.

View larger version (32K): [in a new window]   Fig. 4. Sorption–desorption data and Freundlich fits for 1,4-dichlorobenzene (DCB) on (a) Pahokee peat (PP) (KF = 91.6 ± 4.6 [g(1–N) kg–1 LN]; Nsorb = 0.79 ± 0.05; R2 = 0.995; standard error of estimates, SEE = 0.06; number of samples n = 40, 10 data points on which no desorption was initiated not shown); (b) Beulah-Zap lignite (BZL) (KF = 197.0 ± 9.3 [g(1–N) kg–1 LN]; Nsorb = 0.74 ± 0.05; R2 = 0.985; SEE = 0.115, n = 36, 10 data points on which no desorption was initiated not shown), and (c) Amherst soil (AS) (KF = 90.7 ± 5.2 [g(1–N) kg–1 LN]; Nsorb = 0.90 ± 0.07; R2 > 0.98; SEE = 0.109; n = 60, 40 data points at different particle concentrations not shown). (d) Corresponding Thermodynamic Indices of Irreversibility TII for PP (triangles), BZL (squares), and AS (circles, shown for all particle concentrations). Error bars represent standard deviations of three replicates for PP and BZL and four replicates for AS both in CD (concentration of the desorption point) and TII. DCB was determined by scintillation counting in (a) and (b) and gas chromatography in (c). The term C is the solute concentration; q is the sorbed concentration; KF is the Freundlich coefficient; Nsorb is the Freundlich exponent for the forward branch of the isotherm; and CD is the solute concentration at the experimental desorption point.

View larger version (18K): [in a new window]   Fig. 5. (a) Sorption isotherms of 1,4 dichlorobenzene (DCB) to Pahokee peat (PP) after 14 and 35 d equilibration and Beulah-Zap lignite (BZL) after 21 and 35 d equilibration. Regression lines represent Freundlich fits to the 35 d sorption data. DCB was determined by gas chromatography for the 14- and 21-d isotherms and by scintillation counting for all other experiments. (b) Desorption kinetics of DCB from PP and BZL. The term C* is the hypothetical concentration if all DCB mass was in solution, Ceq is the equilibrium concentration after desorption. Note that the data are plotted over the square root of time. The term C is the solute concentration, and q is the sorbed concentration.