Environ. Sci. Technol. 2007, 41, 843-849
On the Reversibility of Sorption to Black Carbon: Distinguishing True Hysteresis from Artificial Hysteresis Caused by Dilution of a Competing Adsorbate M I C H A E L S A N D E R †,§ A N D J O S E P H J . P I G N A T E L L O * ,†,‡ Department of Chemical Engineering, Environmental Engineering Program, Yale University, New Haven, Connecticut 06511, and Department of Soil and Water, The Connecticut Agricultural Experiment Station, New Haven, Connecticut 06511
Sorption hysteresis in environmental sorbents has important implications for pollutant transport and bioavailability. We examined the reversibility of sorption of benzene, toluene, and nitrobenzene, both singly and in pairs, by wood charcoal. A previous study showed that these compounds compete for the same set of adsorption sites on the char. Single-solute sorption was weakly hysteretic at high concentrations. The finding of comparable irreversibility for these compounds was taken as evidence that hysteresis is true and caused by pore elasticity. Hysteresis in the presence of a competitor was weak at low cosolute concentration but became stronger as the cosolute concentration increased. We attribute the growing hysteresis with cosolute concentration to a thermodynamic “competitor dilution effect”sa heretoforeunrecognized cause of hysteresis in multi-solute systems when the competing solute is simultaneously diluted with the target solute in the desorption step. It arises because the target solute re-equilibrates from a sorption point where competition is relatively high, to a desorption point where competition is relatively low. Simulations based on Ideal Adsorbed Solution Theory, a thermodynamic competition model, support the hypothesis. The cosolute also causes an increase in the linearity of the target solute isotherm, also attributable to competition thermodynamics. The competitive dilution effect can play a role in pollutant behavior in real systems if competing substances, natural or anthropogenic, are diluted or degraded making the target less accessible with time.
Introduction Environmental black carbon (BC) is the elemental carbonaceous residue of combustion (i.e., char and soot) that finds its way into the environment (1, 2). BC is a highly surface active material believed to play a role in the transport and * Corresponding author phone: 203-974-8518; fax: 203-974-8502; e-mail:
[email protected]. † Yale University. ‡ The Connecticut Agricultural Experiment Station. § Current address: Institute for Biogeochemistry and Pollutant Dynamics (IBP), Swiss Federal Institute of Technology ETH, Zurich, Switzerland. 10.1021/es061346y CCC: $37.00 Published on Web 12/14/2006
2007 American Chemical Society
bioavailability of hydrophobic organic compounds in soils, sediments, and aerosols that contain appreciable quantities of it (3-8). Much attention has focused on the factors controlling the magnitude of sorption by BCs in single-step uptake experiments, while little attention has been paid to the reversibility of sorption by including desorption steps. Sorption hysteresis is the non-coincidence of the sorption and desorption branches of the experimental isotherm. Both true and artificial causes are possible. True, as well as certain types of artificial hysteresis, can have important implications for both understanding mechanism and modeling pollutant behavior. Several decades ago Bailey et al. (9) observed hysteresis of nonpolar organic vapor sorption by activated carbon (AC), often considered analogous to BC in surface and pore structure. Terming it “low-pressure hysteresis” to distinguish it from capillary condensation hysteresis in mesopores at higher pressures, they attributed it to physical changes in the sorbent by “intercalation of molecules of adsorbate in narrow pore spaces leading to irreversible changes in the pore structure” (9). Later, a similar mechanism for true hysteresis was invoked for macromolecular sorbents. Initially applied to glassy synthetic and natural polymers (10-13), it has been extended to natural organic matter (NOM) (1419), and has come to be referred to as “pore deformation” hysteresis. According to this mechanism, incoming sorbate molecules exert pressure on internal pores or proto-pores smaller than the adsorbate molecular volume, causing their expansion or creation. At the same time the local matrix is softened (segment mobility increases) by interaction of permeant with segments. On desorption the matrix stiffens before relaxation of the expanded or created pores can be completed. The net increase in free volume of the solid during this cycle results in enhanced affinity for the sorbate during the desorption step that manifests as hysteresis. Pore deformation hysteresis does not occur in highly flexible solids whose segments can fully relax on desorption (i.e., rubbery polymers), nor in rigid, fixed-pore solids whose pores are not strained beyond their elastic limit (9). In addition to what may be inferred from Bailey’s work with AC (9), the deformability of BC pores is supported by evidence of swelling in BC samples (7, 20). Braida et al. (20) observed swelling of wood charcoal during benzene uptake from water. Jonker and Koelmans (7) offered swelling as an explanation for the different abilities of organic solvents to extract polycyclic aromatic hydrocarbons from BC samples. Braida et al. (20) attributed the strong hysteresis of benzene sorption by char to pore deformation on the basis of the swelling behavior, despite a counterintuitive solute concentration dependence in which hysteresis decreased with concentration. They reasoned that even at low solute concentrations, the local sorbed concentration in a narrow pore may be high enough to cause deformation. In addition, they proposed that collapse of the polyaromatic scaffold during desorption as swelling partially reversed could end up trapping some benzene molecules in the nascent closed sectors. This could contribute to the observed hysteresis if the release from the trapped state is sterically impaired or prevented. A similar “matrix trapping” mechanism was proposed by Weber et al. (21) to explain pronounced sorption hysteresis of phenanthrene in NOM of two soils and a shale in the presence of a dominant cosolute concentration of either trichloroethylene or 1,4-dichlorobenzene. In the absence of cosolute, phenanthrene sorption appeared reversible or slightly irreversible. They postulated that dominant concentrations of cosolute caused swelling during sorption VOL. 41, NO. 3, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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that was reversed during desorption, resulting in entrapment of a fraction of phenanthrene molecules. The present study was designed to clarify the mechanism of sorption hysteresis of aromatic compounds by the same wood char used to study benzene hysteresis (20). Since that study, we have shown by analysis of single-solute and bisolute isotherms that benzene (BEN), toluene (TOL), and nitrobenzene (NBZ) compete for an identical set of sites on the char (22). In this paper, we exploit this database to investigate the reversibility of sorption of these three compounds singly and in pairs. We rationalized that the matrix trapping mechanism should operate in both singleand multi-solute systems, given sufficiently high loadings for deformation to occur. Our objectives, therefore, were the following: to attempt to confirm single-solute hysteresis observed by Braida et al. for benzene (20); to assess whether hysteresis was dependent on the presence of a cosolute; and to determine whether hysteresis in the presence of a cosolute could be due to matrix entrapment or some other cause. As we will demonstrate, the interpretation of sorption-desorption hysteresis in multi-solute systems may lead to erroneous conclusions if thermodynamic competitive effects are not considered.
surface (23). The Freundlich equation for component i at equilibrium is as follows:
qi ) KF,i‚CiNi
where qi [mol kg-1] is sorbed concentration, Ci [mol L-1] is solute concentration, KF,i [mol1-N kg-1 LN] and Ni [unitless] are the Freundlich affinity and nonlinearity coefficients, respectively. The relevant single-solute coefficients have been reported (22). Sorption irreversibility is incorporated into IAST after assuming that BEN, TOL, and NBZ share the same sites (22); that hysteresis results from irreversible pore deformation; and that the three solutes deform pores roughly equally. Thus, the degree of deformation prior to desorption depends on total sorbed concentration, qtot [mol kg-1] ) q(target analyte) + q(competitor). Desorption of target i in a bi-solute system is modeled to occur from a hypothetical sorption state where q ) qtot and the equilibrium hypothetical solute concentration of i, C*(i) [mol L-1] is
C*(i) )
Experimental Section The char was prepared by atmospheric pyrolysis of maple wood shavings at 400 °C for 2 h (20, 22) and gently pulverized. It is highly carbonaceous (72% C; C/H atomic ratio, 2.1), contains only aromatic and carboxyl carbon by 13C-NMR, and is predominantly microporous (420 m2/g; porosity, ∼0.15; >80% porosity below 2 nm). Sorption-Desorption Experiments. Methodologies for single-solute and bi-solute batch sorption by char are given in detail elsewhere (22). Sorption was carried out in suspensions of char in 0.01 M CaCl2 and 200 mg L-1 NaN3 solution at 20 ( 1 °C for 35 d, which was longer than necessary to reach what appeared to be equilibrium (20). After centrifugation, ∼90% of the supernatant fluid was removed and immediately replaced by fresh solution to initiate desorption, which was then carried out in the same manner for 35 d. Supernatant samples were hexane extracted and analyzed by GC-FID. Sorbed concentrations were calculated by the difference in mass added (or mass remaining, in the case of desorption) and mass in solution, applying a correction for “bottle losses”. Quantification of Hysteresis. Hysteresis was calculated by the Thermodynamic Index of Irreversibility, TII (17):
TII )
lnCγ - lnCD lnCS - lnCD
(1)
where CS [mol L-1] and CD [mol L-1] are the solute concentrations at the sorption and desorption points and Cγ [mol L-1] is the hypothetical solute concentration corresponding to a reversible point on the sorption branch at the observed sorbed concentration of the desorption point. Provided sorbed- and solution-phase molecules are in thermodynamic contact and hysteresis is true, TII is a measure of the hysteresis loss of solute free energy in the cycle. TII ranges from 0 to 1, where a value of 1 represents complete irreversibility. Below ∼0.2 or above ∼0.8 in fractional uptake, TII is unreliable due to uncertainty in the denominator or numerator, respectively of eq 1 (17). Any interpretation of TII must consider that observed hysteresis may be a combination of true and artificial causes. Bi-Solute Competition Predicted by Ideal Adsorbed Solution Theory using Freundlich Isotherm Parameters. The IAST model assumes complete reversibility, perfectly shared sites, and ideal two-dimensional solutions on the 844
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(2)
( ) qtot
1/Nisorp
(3)
sorp KF,i
with the superscript (sorp) referring to the uptake stage. A Freundlich desorption isotherm that incorporates irreversibility with constant TII along the desorption branch has been derived (17). The coefficients are given by the following: sorp‚TII
KF,idesorp ) KF,isorp‚[C*(i)]Ni
Ndesorp ) Nsorp ‚(1 - TII) i i
(4) (5)
where (desorp) applies to desorption states that originate from desorp a solid with q ) qtot. The values of KF,i and Ndesorp are i determined separately for each experimental bi-solute sorption state at which desorption is initiated. Details on solving the IAST model are given in the Supporting Information.
Results and Discussion The single-solute sorption isotherms (22) and corresponding one-step desorption points are shown in Figure 1 for benzene (panel a), toluene (panel d), and nitrobenzene (panel i). Figure 1 also shows the bisolute sorption-desorption isotherms for benzene in the presence of toluene (panels b, c), for toluene in the presence of benzene (panels e, f) and nitrobenzene (panels g, h), and for nitrobenzene in the presence of toluene (panels j, k). Only those isotherms corresponding to the lowest and highest cosolute concentrations are shown; the complete set is available in the Supporting Information (Figures S1S4). Numbers adjacent to points in Figure 1 represent averaged fractional uptake for duplicate sorption data. Figure 2 shows plots of TII as a function of concentration for all single-solute and bisolute cases. The single-solute and low cosolute bi-solute data (i.e., cosolute concentration much lower than the principle solute concentration) are plotted together in the upper three graphs (panels a-c) for reasons that will become clear. TII was calculated only when the fractional uptake was within the range 0.20-0.8 as explained in the Experimental Section. Fractional uptake increases with decreasing solute concentration due to isotherm nonlinearity and the use of a constant sorbent-to-solution ratio. Thus, TII data are unfortunately restricted to the relatively high concentration end of the isotherms for the single solute isotherms and the bisolute isotherms at low competitor concentration. As the aqueous concentration declines, the solid-to-solution ratio that must be used to achieve a
FIGURE 1. Single-solute sorption isotherms and corresponding single step desorption points for benzene (BEN) (panel a); toluene (TOL) (panel d); and nitrobenzene (NBZ) (panel i). Competitive sorption isotherms and single step desorption points of target analytes at the lowest (panels b, e, g, j) and the highest (panels c, f, h, k) concentration of competitor. The numbers next to the points refer to the fractional uptakes at the sorption point. fractional uptake in the desired range becomes impractical for such a high-affinity adsorbent like charcoal. For example, 50% uptake of NBZ at C(NBZ) ) 10-6 mol L-1 requires a solid-to-solution ratio of approximately 2.3 × 10-5 (e.g., 25 mg : 1100 mL). Hysteresis in Single-Solute Systems and Bisolute Systems at Low Cosolute Concentration. Weak hysteresis (TII < ∼0.25) is observed for the single-solute isotherms of BEN and NBZ and all low-cosolute concentration bisolute isotherms of BEN, NBZ, and TOL (Figure 2, top row), with the exception of TOL in the presence of BEN. Values of TII are not greatly concentration-dependent. For BEN and NBZ, the single-solute TII nearly coincide with the low-concentration cosolute TII. The single-solute isotherm of TOL (Figure 1d) and the bisolute isotherm of TOL at low BEN cosolute concentration (Figure 1e) show much stronger hysteresis. These isotherms were set up and run at the same time, and for various reasons we believe that an undetermined experimental error led to artificially high values of TII. First, the weak hysteresis of TOL in the presence of NBZ is consistent with the other single-
solute systems and bisolute systems at low cosolute concentration. Second, it is not credible that a small concentration of NBZ would greatly reduce the hysteresis of TOL compared to TOL alone. Third, although possible, it is not likely that TOL has substantially greater hysteresis than BEN or NBZ in view of our finding in a previous study (22) that these three compounds share the same set of sorption sites on this char. Fourth, at the highest concentrations tested, the TOL isotherm curves upward in the TOL-low BEN case (Figure 1e) but downward in the TOL-low NBZ case (Figure 1 g). At these concentrations, TOL is about 103 more concentrated than the cosolute so its sorption should have been unaffected by the cosolute. The high TII samples of TOL in Figure 2b are framed to indicate that pronounced hysteresis likely resulted from undetermined experimental error. The finding of comparable hysteresis in single-solute and low cosolute bisolute systems (with the exception noted) confirms that competitor concentration in these cases is sufficiently dilute that it has little affect on sorption of the target analyte at concentrations where its irreversibility can be evaluated. Moreover, the finding is consistent with a VOL. 41, NO. 3, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Thermodynamic index of irreversibility, TII, for sorption of benzene (BEN), toluene (TOL), and nitrobenzene (NBZ) on char in selected systems. Top row: single-solute and low cosolute bisolute systems. Bottom row: high cosolute bisolute systems. The framed data in (b) are anomalous (see text). common mechanism for hysteresis, which we suggest to be pore deformation. The relatively low hysteresis of BEN reported here contrasts with the relatively high hysteresis of BEN sorption by this charcoal found in a previous study using similar equilibration time (20). However, due to a higher solid-to-liquid ratio used in that study (20), the fractional uptake of BEN exceeded 80% for almost all data, suggesting that the observed strong hysteresis may have been an artifact caused by the low degree of desorption achieved during single step dilution. Hysteresis in Bi-solute Systems with Increasing Cosolute Concentration. Figures 1 (panels c, f, g, and k) and 2 (panels d, e, and f) indicate that the isotherms of BEN, TOL, and NBZ are all strongly hysteretic at the two highest cosolute concentrations (TII > 0.6; and equal to 0.84 ( 0.12 average and standard deviation for all systems). These data, together with the full data in Figures S1-S4, show that sorption of the target analyte becomes increasingly hysteretic with increasing initial cosolute concentration. Clearly, the dramatic effect of cosolute concentration warrants explanation. The Competitor Dilution Effect Hypothesis. In this paper, we propose an artificial cause of hysteresis, referred to as the competitor dilution effect that applies to all systems containing more than one adsorbate. In our case, dilution is achieved by solution replacement, but in the general case, dilution may be achieved by supplementation of clean liquid or pressure decrease. Since dilution concomitantly reduces the external fluid concentration of the competing adsorbate(s) and the target adsorbate, it therefore alleviates competition for sorption sites from the viewpoint of the target adsorbate. If the target adsorbate re-equilibrates from a state at the sorption point where coadsorbate activity is relatively high (high degree of competition) to a state at the desorption point where coadsorbate activity is relatively low (low degree of competition), sorption of the target adsorbate may appear hysteretic as a result. The possibility of a competitor dilution effect was not discussed in a previous study (21). Such an effect is not just an experimental nuisance, it is clearly relevant to the field, since pollutant mixtures are the rule rather than the exception. IAST-Model Predictions. In this section, we use IAST to model the strictly thermodynamic effect of competitor 846
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dilution. The solid line in each panel of Figure 3 represents the Freundlich fit to the single-solute data (22). While the Freundlich model does not provide perfect fits (22), the fits are adequate for illustrative purposes here. This point is elaborated more in the Supporting Information. The graphs in Figure 3 depict IAST sorption-desorption cycles for the single-solute case and for the bi-solute case at the highest concentration of cosolute used. Sorption points (filled symbols) are based on actual added solute masses in the experiments; IAST-calculated desorption points (open symbols) are based on actual solution volume replacement values. In the bi-solute cases the desorption points are calculated by IAST either by assuming constant cosolute concentration (diamonds) or assuming dilution of the cosolute along with the principle solute (open triangles). For a full comparison of predicted and experimental bi-solute sorption data, the reader is referred to the Supporting Information (Figures S1-S4). The results of this exercise reveal two major trends. First, the IAST-predictions (Figure 3) are consistent with the observation of increasing linearity of the principle solute isotherm with increasing cosolute concentration (Figure 1 and Figures S1-S4). At the highest C0(competitor), the competitive isotherms are predicted to be almost linear: NBEN ) 0.98 (Figure 3a) and NTOL ) 0.91 (Figure 3b) in the BENTOL system, and NTOL ) 0.94 (Figure 3c) and NNBZ ) 0.92 (Figure 3d) for the TOL-NBZ system. The isotherms tend toward linearity because competition weakens as the concentration of the target solute increases relative to the fixed overall concentrationsand relatively constant solution-phase concentrationsof the cosolute. In IAST, effects on sorption are solely the result of inter-solute competition. The experimental increase in linearity of the target isotherm with increasing C0(competitor), therefore, does not necessarily signify a change in the overall mechanism of sorption from adsorption to absorption, as might be tempting to suggest. We came to the same conclusion previously (22) regarding the BEN-TOL system after finding superposition of singesolute isotherms and the isotherms corresponding to the sum q(BEN) + q(TOL) [mol kg-1] in bisolute experiments, all normalized for hydrophobic effects. The IAST model predictions, thus provide an alternative explanation for the increase
FIGURE 3. IAST-model predictions of competitive sorption isotherms and single step desorption points for the specified initial aqueous concentration of competitor, C0(competitor). Solid lines represent single-solute systems, dashed lines bisolute systems. Symbols represent calculated values. In the bi-solute systems, desorption points are predicted both when cosolute concentration is kept constant (diamonds) and when the cosolute is diluted along with the target analyte (open triangles).
FIGURE 4. Experimental (solid triangles; error bars represent standard deviations) and IAST-predicted thermodynamic indices of irreversibility (TII). C0(competitor) is the initial cosolute concentration. TIISS represents the intrinsic reversibility of the single solute. in isotherm linearity of phenanthrene in the presence of a dominant cosolute observed in (21); which those authors attributed to an increase in partition-type linear sorption due to cosolute swelling of the matrix. Although swelling is certainly possible, IAST predicts that competition alone increases linearity.
Secondsand most importantly with respect to the central theme of this papersthe IAST-model predictions in Figure 3 show apparent hysteresis resulting solely from diluting the competing cosolute along with the solute during the desorption step. Whereas the IAST assumption of reversibility is borne out in the single-solute cases (solid circles f open VOL. 41, NO. 3, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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circles) and in the bisolute cases when the cosolute concentration is kept constant (solid triangles f open diamonds), hysteresis is predicted at high cosolute concentration when the cosolute is allowed to dilute (solid triangles f open triangles). The cause of hysteresis is, therefore, “artificial”, i.e., it results from dilution of the cosolute. Figure 3 shows that the competitor dilution effect exists independently of any intrinsic irreversibility of target sorption, and suggests that experimental hysteresis found with increasing bisolute concentration (Figure 1 and Figures S1-S4) may alternatively be due in large part to a competitor dilution effect. An obvious experiment to test this would be to induce desorption of a target while maintaining constant cosolute concentration, whereupon the target should exhibit diminished hysteresis. While such an observation has actually been borne out (for phenanthrene in shale; (21)), it does not distinguish between the entrapment hypothesis invoked in (21) and the alternative explanation of a competitor dilution effect. The competitor dilution effect cannot, however, explain the finding of significant hysteresis in experimental singlesolute systems and in the bi-solute systems at low C0(competitor) (Figures 1, 2). It is, therefore, likely that part of the pronounced hysteresis at high C0(competitor) in the char system is, in fact, true. Such likelyhood is further evaluated in Figure 4, which compares experimental TII values for a given target analyte at the highest tested C0(competitor) to the curve corresponding to IAST-predicted TII values determined for different degrees of single-solute irreversibility, TIISS. Figure 4 shows the following. (a) For reversible single-solute sorption (i.e., TIISS ) 0.00), the predicted curve falls substantially below the experimental values. This finding strongly suggests that, at least at high sorbate loadings, true hysteresis operates in parallel with the competitor dilution effect. (b) When true hysteresis of single solute sorption is incorporated into IAST via eq 4 and 5, the predicted TII values increase as TIISS increases. The contributions of artificial hysteresis and true single solute hysteresis are not directly additive in terms of TII, however. (c) To approach experimental values, the predicted curves require TIISS values in excess of 0.25, a value we typically obtained for the single-solute and low cosolute bisolute systems in Figure 2. TOL in the TOL-BEN bi-solute systems (panel b) is predicted with a value of TIISS slightly greater than 0.25, while in all other cases data are still underestimated with TIISS ) 0.50. The discrepancy between predicted and experimental may be due to the imperfect fit of the Freundlich equation to the single-solute isotherms (22) (Figures S1-S4, Supporting Information), shortcomings of IAST, or nonuniform TII along the desorption branches of the isotherms. (d) Except for BEN in the BEN-TOL bi-solute system at TIISS > 0.00 (panel a), the IAST-model predicted TII-values show a maximum at intermediate target analyte concentrations. This effect has its origin in the nonlinearity of the target isotherm. For a constant volumetric dilution ratio and C0(competitor), it results from opposing effects: increasing absolute target solute concentration, which diminishes competition, and increasing fraction of target solute mass removed at the desorption step, which augments competition. Our findings clearly warrant further investigation on the mechanisms of true hysteresis in BC. The recent experimental technique using 14C-isotope exchange may prove helpful in this regard (18). Implications. This study has several important implications for the environmental behavior of hydrophobic organic compounds. (i) Sorption of low molecular weight aromatic compounds to BC materials may be irreversible; i.e., show true hysteresis. Comparable degrees of irreversibility for similarly sized molecules on a model char shown here are 848
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supportive of the irreversible deformation hypothesis as the cause of sorption irreversibility in BC, although it seems to be much smaller than we originally thought (20). (ii) The degree of nonlinearity of the isotherm for a given sorbate-sorbent pair may depend, not only on intrinsic effects, but also on competitive effects by cosolutes. Competitive sorption in natural solids by other contaminants, biomolecules (24), and dissolved humic substances (25) has been documented, and, in the case of contaminants and dissolved humic substances (25), has resulted in an increase in linearity of the target component’s isotherm. Moreover, an increase in sorption linearity with cosolute concentration does not necessarily mean a transition to partition-type sorption but instead could result from the purely thermodynamic effects of competition for sorption sites. The competitor dilution effect is reminiscent of the “implicit adsorbate” effect (26) proposed many years ago to address the observation of decreasing partition coefficient with increasing particle concentration and other behaviors. (iii) Sorption-desorption of a target analyte in multi-solute systems is susceptible to artificial hysteresis caused by competitor dilution. The relative contribution of this effect may be substantial. Its impact on total hysteresis requires quantification of sorption of all components singly and together. Recognition of the competitor dilution effect facilitates our understanding of the mechanisms of the hysteresis phenomenon. (iv) The competitor dilution effect may increase the affinity of a target analyte for the sorbent if the target and the cosolute are diluted simultaneously or if the cosolute is removed by biotic or abiotic processes. This can be important from both fate and remediation standpoints. If, for example, a cosolute is more volatile (or desorbs faster to an elution stream) than the target analyte, the target may show an apparent increase in sorption distribution ratio with time. Likewise, if a cosolute is biodegraded more readily than the target, the target may become progressively less bioaccessible with time.
Acknowledgments This study was funded by the National Science Foundation, Bioengineering Program (BES-0122761) with assistance from Federal Hatch funds administered by the U.S. Department of Agriculture. M.S. thanks the Environmental Research and Education Foundation (EREF) for support (Francois Fiessinger Scholarship 2003) and Pierro Santoro (Yale University) for support writing the FORTRAN code.
Supporting Information Available A comparison of the experimental and IAST-model predicted bi-solute sorption data and an evaluation of sorption hysteresis for all bi-solute systems at intermediate cosolute concentrations. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review June 6, 2006. Revised manuscript received November 1, 2006. Accepted November 2, 2006. ES061346Y
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