An Isotope Exchange Technique to Assess Mechanisms of Sorption

The Connecticut Agricultural Experiment Station,. New Haven, Connecticut, 06511. The sorption of organic compounds to natural sorbents is often found ...
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Environ. Sci. Technol. 2005, 39, 7476-7484

An Isotope Exchange Technique to Assess Mechanisms of Sorption Hysteresis Applied to Naphthalene in Kerogenous Organic Matter MICHAEL SANDER† AND 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

The sorption of organic compounds to natural sorbents is often found to show hysteresis. The objective of this study was to develop an experimental technique based on the use of 14C isotopes to distinguish hysteresis due to experimental artifacts from true hysteresis due to thermodynamically irreversible processes. The study was also designed to investigate causation of true hysteresis (irreversible sorption). The technique determines the rates and the degree of isotope exchange (IE) on equilibrated sorption and desorption points at different constant bulk chemical concentrations. The technique was applied to the sorption of naphthalene (NAPH) on Beulah-Zap lignite, a low rank reference coal composed mainly of kerogen. Sorption of bulk was found to be reversible below 10-5 g L-1, but irreversible above 10-4 g L-1. Complete isotope exchange on sorption and desorption points that defined an irreversible cycle demonstrated that hysteresis was true. A comparison of normalized uptake and release kinetics of labeled and bulk NAPH at different concentrations revealed slow structural deformation processes of the sorbent during bulk sorption and desorption. This is taken as corroborating evidence for the pore deformation hypothesis of hysteresis in which incoming sorbate molecules induce quasi-reversible changes in the organic matter that lead to different pathways for sorption and desorption. Although unable to rule it out completely, the data demonstrate that physical entrapment of sorbate molecules plays a minor, if any, role to the observed hysteresis in this system.

Introduction The sorption of nonionic organic compounds to soils and sediments often shows hysteresis, or nonsingularity of the sorption and desorption branches of an isotherm. Hysteresis may be due to artificial causes (1-8), such as diffusion rate limitations, solute loss or decomposition, or solute association with a third phase undergoing change between the sorption and desorption steps. In some cases hysteresis is believed to be true (9-15) and to result from thermodynamically irreversible processes (16-20). True hysteresis is referred to * Corresponding author phone: (203)974-8518; fax: (203)974-8502; e-mail: [email protected]. † Yale University. ‡ The Connecticut Agricultural Experiment Station. 7476

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as “irreversible sorption”, a term used in the thermodynamic context that does not necessarily imply an irretrievably bound state. Confirmation of true hysteresis and understanding its underlying causes are crucial in view of the fundamental role sorption plays in the mobility and bioavailability of pollutants (21, 22). Notwithstanding claims of true hysteresis in soil systems, traditional batch sorption-desorption methods in common use for assessing reversibility are poorly suited for conclusively ruling out artifacts, particularly diffusion rate limitations, stemming from the imprecision of analytical measurements and the absence of independent verification of equilibrium. As a result, there is doubt and confusion in the literature about the origin of hysteresis. The same methodologies are even less suited for establishing causation when hysteresis is true. Clearly, alternative approaches are required. Since it is not possible at thermodynamic equilibrium for a given solute concentration to correspond to multiple sorbed concentrations, true hysteresis implies the formation of metastable states that lead to different microscopic pathways for sorption and desorption. The metastable entity can be sorbate, sorbent, or sorbate-sorbent complex, depending on the system. Capillary condensation hysteresis in rigid mesoporous solids occurs by formation of a metastable adsorbate film on the pore walls (23, 24). Metal ion adsorption on inorganic surfaces may involve metastable complexes with the surface that evolve into more stable complexes or precipitates over time (25, 26). Sorption hysteresis of gases, vapors, and solutes in glassy organic polymers is due to metastability in the sorbent itself (27-32). This mechanism is commonly referred to as “low-pressure” (10) or “poredeformation” hysteresis. The glassy organic solid state includes poorly interconnected pores (“holes”) that comprise the unrelaxed free volume of the solid. Pore-deformation hysteresis occurs by sorbate-induced alteration of the sorbent away from its thermodynamic state through an increase in the unrelaxed free volume. This may occur by two processes: dilation of existing holes as a result of thermal motions of sorbate molecules exerting pressure on the polymer strands lining the hole, and hole creation in which incoming sorbate molecules create new holes from proto-hole sites. This increase in internal volume during sorption is partially conserved during desorption because the structural rigidity of a glass impairs relaxation toward the thermodynamic state, resulting in the manifestation of hysteresis. Consistent with this mechanism is the “conditioning effect” in which a solid shows enhanced affinity for a sorbate in a second sorption cycle (29, 33). Nonionic organic compounds associate predominantly with the natural organic matter (NOM) fraction of soils in most cases. Given the physical similarity of macromolecular NOM (i.e., humic substances and kerogen) to organic polymers, the hole-deformation mechanism has also been postulated as the cause of irreversible sorption of organic compounds to macromolecular NOM, and considerable evidence has been published in support of this postulate (13, 15, 19, 20, 34). It has also been proposed that hysteresis may originate from physical entrapment of a fraction of sorbate in NOM accompanying a sorption-desorption cycle. Kan et al. (35) proposed “rearrangement” of the organic matter around some sorbate molecules during sorption that places them in a high-affinity local environment characterized by a far higher partition coefficient than the bulk of the sorbate. Braida et al. (12) showed that wood char particles swell when taking 10.1021/es050299r CCC: $30.25

 2005 American Chemical Society Published on Web 08/26/2005

up benzene from water and suggested that the swollen state collapses around some molecules during desorption, preventing their equilibration with solute molecules. This fraction would manifest itself in a nonzero intercept of the desorption branch of the isotherm. Physical entrapment may then logically be considered an extreme end-case of the pore deformation mechanism. Weber et al. (36) proposed a similar phenomenon occurring in soils and a shale. The main objective of this study was to develop a 14C isotope exchange method to validate true sorption hysteresis in natural particles and to probe its underlying cause. We applied the technique to the hysteresis of naphthalene (NAPH) on a low-rank coal reference standard, Beulah-Zap Lignite (BZL) that represents hard organic matter in soils and sediments. The degree of isotope exchange was evaluated in both directions after the sorption step (uptake and release of a minute mass of label to and from the solid), and in the reverse direction after the desorption step (release of a minute mass of label from the solid). Our results confirm concentration-dependent true hysteresis consistent with “pore deformation” as the mechanism, and reveal that sorbate entrapment plays only a minor, if any, role.

Experimental Section Materials. Naphthalene (99+%) (NAPH) was obtained from Aldrich (Milwaukee, WI). Naphthalene-UL-14C (31.3 mCi/ mmol; 99+% radiolabel purity), and sodium azide were from Sigma-Aldrich (St Louis, MO). Beulah-Zap lignite (BZL) was purchased from the Argonne National Laboratory (Argonne, IL) coal bank and is described elsewhere (37). Prior to use in all experiments, except the sorption-desorption batch equilibration, the coal was passed through a No. 140 mesh and a No. 325 mesh sieve to obtain the 0.045-0.105 mm fraction. Methodology. The technique forming the basis of this study comprises six separate experiments as follows. (i) Sorption kinetics of bulk contaminant (SKB): uptake rate of bulk contaminant at selected initial aqueous concentrations. For convenience we followed uptake of labeled contaminant. (ii) Desorption kinetics of bulk contaminant (DKB): release rate of equilibrated bulk contaminant at selected initial sorbed concentrations after dilution of the supernate with solutefree background liquid. For convenience, the bulk contaminant was in labeled form. (iii) Sorption-desorption isotherm construction: multipoint equilibrium sorption of bulk contaminant, followed by dilution of liquid phase with solutefree liquid and subsequent reequilibration to obtain the corresponding desorption data points. For convenience, the bulk contaminant was in labeled form. (iv) Forward isotope exchange at selected sorption points (FIES): uptake rate of a minute amount of label added after equilibration of bulk chemical containing no label. (v) Reverse isotope exchange at selected sorption points (RIES): release rate of label after equilibration with bulk chemical containing label by replacing the supernatant with a solution at the same bulk contaminant concentration containing only nonlabeled chemical. (vi) Reverse isotope exchange at the desorption point (RIED): same as RIES except done at the corresponding desorption point. Experiments iv-vi were carried out at constant C of the bulk chemical. The FIES, RIES, and RIED determine the degree to which sorbate molecules at the sorption and desorption point equilibrate with the bulk solution by comparing the apparent distribution coefficient (i.e., the concentration-dependent ratio of sorbed to solution concentration) of NAPH before the isotope exchange step at the sorption KSobs and desorption point KD obs, to the one observed after isotope exchange kIE obs. Complete reequilibration is

D,S -1 level off at unity following IE. given if the ratios kIE obs ‚ (Kobs) A mass balance was performed at each sampling time taking into account (i) cumulative removal of NAPH in previous sampling events, (ii) cumulative loss of NAPH determined by running blank controls, and (iii) decreasing solution volumes concurrent with increasing headspace volumes, into which NAPH is assumed to partition according to Henry’s Law. A detailed description of the underlying calculations is provided in the “Supporting Information” for this paper. The isotope exchange technique, in contrast to the traditional batch sorption-desorption method, discriminates between true and artificial hysteresis: (a) Nonattainment of diffusion equilibrium during sorption or desorption would show as a drift in bulk or label concentration during SKB, S -1 DKB, or IE experiments. (b) A ratio of kRIES obs ‚ (Kobs) > 1 would suggest either the “colloids effect” or loss of chemical unaccounted for by the controls. (c) If bulk sorption/ desorption is hysteretic in DKB, reequilibration after RIES to S -1 ) 1 on the same sorption point is direct kRIES obs ‚ (Kobs) evidence that bulk NAPH hysteresis is true, as the physical steps during solute replacement are identical for DKB and RIES. (d) Loss of chemical during batch equilibration or during initiation of desorption is further tested for by running control vials containing no solid that are handled identically to the test vials. Note that a technique similar to FIES and RIES has previously been used to characterize the sorption of pesticides and its metabolites to soils (38, 39). Compared to that technique, ours is advanced in that it (i) additionally determines bulk desorption kinetics as well as the degree of IE at the desorption point, (ii) is conducted at two different solute concentrations that are more than 2 orders of magnitude apart, and (iii) offers a much better defined profile of the rates of bulk and IE uptake and release. This study will demonstrate that only by combining the results from all six separate experiments is an unequivocal picture on the sorption-desorption characteristics for a given sorbatesorbent system obtainable. In all experiments, solid-to-liquid ratios were adjusted to obtain 40-60% equilibrium uptake of NAPH during sorption. The background solution was 0.01 M CaCl2 and 200 mg L-1 NaN3 to inhibit microbial activity. The sorbent was hydrated for more than 48 h prior to spiking of NAPH in methanol as a carrier (keeping methanol < 0.2 vol %). For IE experiments at high C, NAPH was added in the form of a saturated aqueous solution in 0.01 M CaCl2 and 200 mg L-1 NaN3 to eliminate transient precipitation of NAPH. All IE experiments and controls were run in triplicate. Sorption-desorption isotherms were constructed using 64-mL glass screw tubes topped with PTFE-lined caps. Samples received 8120 Bq of 14C-NAPH and enough nonlabeled NAPH to reach the target concentration. All other experiments were carried out in 160-mL glass flasks topped with PTFE-lined Mininert valves (Pierce Biotechnology, Rockford, IL). The use of 64-mL and 160-mL vessels gave equivalent results. The suspensions were amended with 5350 Bq labeled NAPH for SKB and FIES, 10 700 Bq for DKB and RIES, and 21 400 Bq for RIED. Additional nonlabeled NAPH was added to achieve final concentrations. All sample vials were mixed end-over-end at 20 ( 1 °C on Rugged Rotator shakers (Glas Col, Terre Haute, IN) operating at 15 rpm. For quantification (i.e., after 35 and 70 d for the sorptiondesorption isotherm and at time intervals for all other experiments) vials were centrifuged at 750g for 15 min at 20 ( 1 °C. A portion of supernatant was then removed and the radioactivity was measured by liquid scintillation counting in 15 mL of Optiflour (Packard Instrument Co.) on a Tri-Carb 2900TR liquid scintillation counter (Packard Bioscience Company). Desorption was initiated by removing 67% of

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FIGURE 1. Sorption kinetics of bulk (SKB) for naphthalene on Beulah-Zap lignite plotted as C(C0)-1 over the square root of time at two widely spaced final naphthalene concentrations indicated in the graphs. C is the measured concentration and C0 is the hypothetical solute concentration if all NAPH was in solution. The approximate final (equilibrium) concentrations CEq are indicated in the graphs. Different symbols represent replicate vessels.

FIGURE 2. Desorption kinetics of bulk (DKB) for naphthalene on Beulah-Zap lignite. C is the measured concentration at any time t, and C0 is the calculated initial concentration at t ) 0 following bulk dilution of NAPH (i.e., the theoretical concentration if no desorption from the solid were to occur). Initial aqueous concentrations before bulk dilution are (a) 5.41 × 10-5 g L-1 and (b) 1.41 × 10-2 g L-1. The approximate final (equilibrium) concentrations CEq are indicated in the graphs. Different symbols represent replicates.

solution for sorption-desorption isotherms and 77% for DKB, RIES, and RIED determined by vessel mass loss. Sorption hysteresis is quantified using the thermodynamic index of irreversibility (TII, 15)

TII )

lnCγ - lnCD lnCS - lnCD

(1)

where CS and CD are the aqueous concentrations of the sorption and desorption points, respectively, and Cγ is the concentration of the hypothetical reversible desorption state on the sorption isotherm with the same sorbed concentration as the desorption point. This index is a measure of molar free energy of sorption that goes into the creation of metastable sorbent states believed causative of hysteresis. The TII is 0 for the reversible case and approaches 1 as the degree of irreversibility increases.

Results SKB and DKB. Figure 1 shows the uptake (SKB) of NAPH at two widely spaced final (equilibrium) concentrations, CEq ) 5.58 × 10-5 g L-1 and CEq ) 1.34 × 10-2 g L-1. Uptake was normalized by C0, the hypothetical solute concentration if all NAPH was in solution. The uptake for both concentrations was followed for 140 d. The NAPH solute concentrations do not change after about 10 and 16 d for low (Figure 1a) and high (Figure 1b) CEq, respectively. The DKB are plotted in Figure 2 in the same manner as the SKB in Figure 1 except that C0 is the calculated initial concentration at t ) 0 following bulk dilution of NAPH. The final equilibrium concentrations CEq are 3.07 × 10-5 g L-1 and 7.07 × 10-3 g L-1 for Figure 2a and 2b, respectively. In both cases, C(C0)-1 level off after approximately 16 d and show no significant increase thereafter up to 105 d. Desorption kinetics at the high concentration are clearly bi7478

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phasic, as indicated by the “kink” in the curves at slightly less than 1 d. On the basis of SKB and DKB, the following equilibration times were employed for all subsequent experiments to rule out nonattainment of equilibrium as a result of slow diffusion: (i) isotherm data were obtained after 35 d equilibration in the sorption and 35 d in the desorption direction; (ii) FIES and RIES were initiated after 35 d equilibration of bulk NAPH; and (iii) RIED was initiated after 35 d for bulk sorption and another 35 d for bulk desorption equilibration. Sorption-Desorption Isotherms. The sorption isotherm and corresponding single-step desorption points of NAPH on BZL are shown in Figure 3a. The sorption isotherm was fit to the Freundlich equation: S ) KF‚CN , where S is the sorbed concentration [g (kg)-1], C is the solution concentration [g (L)-1], KF is the affinity coefficient [g(1-N)LNkg-1], and N is the Freundlich exponent. Doing so yields KF ) 297.1 (17.6) g(1-N)LNkg-1 and N ) 0.741 (0.007) with R2 ) 0.99 (standard errors of estimates in parentheses). The sorption data are in very close agreement with previous data obtained in our group (20). Figure 3a also shows that the sorption data points obtained by SKB, DKB, FIES, RIES, and RIED (pooled Freundlich fit: KF ) 226.0 (22.6) g(1-N)LNkg-1 and N ) 0.707 (0.012) with R2 ) 0.99) overlap with the isotherm. A linear depiction of the isotherm in Figure 3b and c clearly shows that sorption of NAPH to BZL is demonstrably hysteretic at higher C but not at lower C, where the desorption points x′ are indistinguishable from the sorption branch of the isotherm (Figure 3c). Figure 3d shows a plot of the thermodynamically based index of irreversibility (TII) (15) as a function of solute concentration at the desorption point. The TII reflects the molar free energy of sorption that goes into creation of metastable states during the sorption/ desorption cycle (15). The TII obtained over the whole isotherm ranges from ∼0 (i.e., return to the sorption curve)

FIGURE 3. (a) Log-scale sorption isotherm (filled circles) and single step desorption data (empty circles) of NAPH on Beulah-Zap lignite determined by batch equilibration. Pooled sorption data obtained by sorption and desorption kinetics of bulk, SKB and DKB, forward isotope exchange at the sorption point, FIES, and the reverse isotope exchange at the sorption and desorption points, RIES and RIED are represented by solid squares. (b) and (c) Sorption-desorption data plotted on linear scale for C < 1.2 × 10-2 g L-1 and C < 5.0 × 10-5 g L-1, respectively. (d) Concentration dependence of the thermodynamic index of irreversibility, TII. The TII is arbitrarily assigned to CD. Error bars in d represent standard deviations of replicates n (n ) 5 and n ) 6 at low and high CD, respectively).

FIGURE 4. Forward isotope exchange at the sorption point (FIES) for naphthalene sorption on Beulah-Zap lignite determined at the constant bulk concentrations CEq indicated in the graphs. Different symbols represent replicate vessels. below ∼2 × 10-5 g L-1 then increases, approaching a value of ∼0.45 above ∼2 × 10-4 g L-1. Values of TII calculated from data in DKB and RIED (squares in Figure 3d) are consistent with the trend exhibited by the whole isotherm. FIES. The results of forward isotope exchange at sorption at CEq ) 5.58 × 10-5 g L-1 and CEq ) 1.34 × 10-2 g L-1 are shown in Figure 4. Changes in C of label were monitored for 105 d after FIES, which corresponds to a total equilibration time of 140 d for bulk NAPH. Bulk NAPH concentrations were constant over this time period based on SKB data (Figure S -1 approached unity after about 1). The ratios of kFIES obs ‚(Kobs) 4 d at both concentrations and did not change appreciably over the following 12 weeks. This demonstrates that all sorbed NAPH molecules reequilibrated to the sorption point determined by the isotherm and SKB. RIES. Reverse isotope exchange at the sorption point at two widely spaced concentrations is shown in Figure 5. RIES was monitored for a total of 87 d. At both concentrations S -1 approaches a exchange occurs within 7 d and kRIES obs ‚(Kobs) value of 1.0. Thus, consistent with the findings of FIES, all sorbate molecules in the system are in free-exchange at the sorption point. Moreover, reequilibration of the Kd-ratio to unity following RIES indicates that bulk NAPH hysteresis in

Figure 3 is caused by the act of sorbate mass removal and its effect on the solid, and not by experimental artifacts. Had the “colloids effect” been the cause of hysteresis at high C, then the Kd-ratio would have equilibrated to a value close to S -1 ) 1.20(0.03. the one determined by DKB: KDKB obs ‚(Kobs) RIED. The results of the reverse isotope exchange at desorption at two widely spaced constant bulk NAPH concentrations are shown in Figure 6. Similarly to RIES, D -1 kRIED ratios leveled off rapidly after about 7 d and obs ‚(Kobs) approached unity. The latter result implies that NAPH reequilibrates to the original desorption point following RIED. This is not surprising at the low CEq where NAPH sorption is reversible (TII ) 0.002). However, at high CEq, where TII ) 0.359, the RIED also equilibrates back to the original desorption point and not to a point at or near the sorption branch of the isotherm. The hypothetical Kd-ratio to which RIED had equilibrated if bulk sorption was completely reversible is determined by mass-balanced projection of the experimental desorption point onto the forward branch of the sorption isotherm described by a local model fit around CD. This hypothetical reversible state is represented by the D -1 dashed-dotted line at kRIED ) 0.78 in Figure 6b. The obs ‚(Kobs) VOL. 39, NO. 19, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Reverse isotope exchange at the sorption point (RIES) for naphthalene on Beulah-Zap lignite determined at the constant bulk S -1 naphthalene concentration CEq indicated in the graphs. The calculated values of kRIES at time zero were around 4.84 and 4.86 for obs ‚(Kobs) low and high C, respectively. Different symbols represent replicate vessels.

FIGURE 6. Reverse isotope exchange at the desorption point (RIED) for NAPH sorption on BZL for bulk NAPH concentrations CEq indicated in the graphs. The dash-dot lines indicate the hypothetical plateau values corresponding to fully reversible bulk sorption. Different symbols represent replicate vessels. results clearly demonstrate that the RIED technique is sensitive enough to rule out slow sorption and/or desorption kinetics as the cause of hysteresis. We also examined the RIED data for indications that a fraction (F) of the excess sorbed concentration observed at the bulk desorption point at high concentration due to hysteresis may be attributed to entrapment of molecules initiated by the act of bulk desorption during the DKB. It may be assumed that, at equilibrium, freely exchangeable bulk chemical present after DKB will distribute between solid and solution phases at a ratio identical to that of the label after RIED, since bulk solute concentration was kept constant at CD obs. Since trapped chemical would not participate in this distribution, the calculated distribution coefficient of the label after RIED, kRIED calc (F), would exceed the observed distribution coefficient at the desorption point, KD obs, in relation to the value of F in excess of 1. An expression for kRIED calc (F) in terms of measured quantities is derived in the Supporting Information of this paper. Figure 7 shows the results for each of three replicate bottles. The circles represent the average of D -1 kRIED at 17 different times following apparent equiobs ‚(Kobs) librium and its standard deviation. For each replicate the D -1 hypothetical ratio of kRIED is marked correscalc (F)‚(Kobs) ponding to F ) 0.25, 0.5, 0.75, and 1. It can be seen that the data are not sufficiently precise to rule out entrapment of as much as 40%. However, it is much more likely that there is zero, or close to zero, entrapment, and the data clearly rule out a majority ending up in a trapped state.

Discussion

FIGURE 7. Evaluation of physical entrapment. The entrapped fraction is defined as F ) QDtrap‚(QDobs - QDrev)-1 where QDobs, QDtrap, and QDrev are, respectively, the observed, entrapped, and hypothetical reversible sorbed concentrations after bulk desorption at the same solution concentration, CDobs. QDrev is obtained by projecting QDobs onto the sorption branch of the isotherm using the Freundlich parameters. A value of F equal to 0 means all sorbed molecules are in free exchange with dissolved molecules, even though irreversible sorption has taken place. kRIED calc (F) is the calculated distribution coefficient of the label after RIED, and KDobs is the observed distribution coefficient of bulk chemical at the desorption point. D -1 The circles represent the average of kRIED obs (F)‚(Kobs) at 17 different times following apparent equilibrium and its standard deviation, where kRIED obs is the observed distribution coefficient of label after RIED.

The reversibility of NAPH sorption to BZL is concentration dependent: whereas sorption is indistinguishable from reversible below 10-5 g L-1, sorption is hysteretic above 10-4 g L-1 (TII = 0.4-0.5). The water solubility of NAPH at 25 °C is 3.22 × 10-2 g L-1 (40). On the basis of the isotope exchange technique, experimental artifacts such as rate-limiting diffusion, degradation, and the colloids effect can be ruled out as potential causes of hysteresis in the present system. In

fact, complete sorption reversibility at low C per se rules out artifacts because the experimental techniques were identical. Consequently, sorption hysteresis of NAPH at high C is the manifestation of a thermodynamically irreversible process in the solid taking place during the sorption-desorption cycle.

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FIGURE 8. Normalized uptake and release of naphthalene during (a) sorption of bulk (SKB), (b) desorption of bulk (DKB), (c) forward isotope exchange at the sorption point (FIES), (d) reverse isotope exchange at the sorption point (RIES), and (e) reverse isotope exchange at the desorption point (RIED). M is the cumulative mass of naphthalene taken up or released and MEq is the final mass taken up or released by the solid. Coals consist of alkyl chain-substituted aromatic macromolecular units linked by covalent and noncovalent bonds to form an internally microporous, three-dimensional network structure (41, 42). The viscoelastic character of coal decreases as a function of its aromatic content and the density of cross-links between coal macromolecules (43, 44). Being macromolecular in composition, coals structurally resemble glassy synthetic polymers. Glass transition temperatures above 300 °C have been reported for coals (45, 46). The sorption of organic compounds to coals and glassy polymers show many analogies (42-44, 47-55): (i) sorption isotherms on coals are often well described by polymer models, (ii) sorbate-induced structural deformation (i.e., swelling) occurs in both materials, and (iii) sorption irreversibility has been reported for both types of solids. Given the analogy between coals and glassy polymers, the most likely explanation for sorption hysteresis of NAPH above ∼10-5 g L-1 is irreversible deformation of micropores by the sorbate, such that sorption and desorption follow different pathways. Conversely, sorption reversibility observed below ∼10-5 g L-1 implies that deformation of BZL is negligible below that concentration. Pore deformation as the cause of hysteresis implies physical swelling of the solid. Swelling can be determined by gravimetric, volumetric, or optical methods (52-57). However, macroscopic swelling is not necessarily causative of hysteresis unless swelling itself is hysteretic (witness swelling in rubbery polymers where sorption is reversible) and tells little about processes occurring at the nanoscale (43). Positron annihilation lifetime spectroscopy (58, 59) has been used to

characterize nanoscale changes of polymers during a sorption-desorption cycle, but this technique is not widely available nor easily applied to environmental matrixes. In the following, we will present a novel means to test the pore deformation hypothesis for hysteresis of NAPH sorption to BZL. In this approach, the sorbate probes for molecularscale structural deformation and its reversibility. The concave down isotherm (Figure 3a) reflects decreasing affinity for NAPH with increasing C. According to the StefanMaxwell formalism for diffusion (60), the normalized rates of uptake or release, M (MEq)-1, where MEq is the mass finally taken up or released, is therefore expected to increase with absolute concentration C (61, 62). Figure 8 shows the fractional uptake rates for SKB, DKB, FIES, RIES, and RIED experiments in panels a-e, respectively. Increasing fractional uptake and release rates with C are observed during FIES (Figure 8c), RIES (Figure 8d), and RIED (Figure 8e). Thus, IE kinetics, determined at constant bulk NAPH concentrations, are consistent with the Stefan-Maxwell formalism. [Note that by adjusting the particle concentration in the present study to obtain approximately equal final uptake ratios (mass of NAPH taken up divided by total mass present in the system) throughout the isotherm we mitigate the so-called “shrinking gradient effect” (61, 62), which applies to nonlinear isotherms and acts to oppose the mentioned trend during uptake and reinforce it during release.] By contrast, the expected trend of increasing normalized rate with absolute concentration is not obeyed by bulk NAPH. Normalized uptake during SKB appears to show crossover VOL. 39, NO. 19, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 9. Comparison of normalized uptake of naphthalene during SKB and FIES or during DKB and RIES at low and high concentration indicated on the graphs. M is the cumulative mass of naphthalene taken up or released, and MEq is the final mass taken up or released by the solid. CEq is the final equilibrium concentration, and C0 is the initial concentration before initiation of DKB/RIED. behavior, with the rate becoming faster at the lower concentration at times longer than 0.25 d (Figure 8a). Normalized release during DKB is faster at the higher concentration (and thus consistent with theory) but it is indistinguishable at the two concentrations for times longer than 1 d. In addition, the DKB curve at the higher concentration shows biphasic (fast, slow) behavior. These findings, taken in combination with the IE data, strongly suggest that molecular diffusion of NAPH under changing bulk concentrations is coupled to a second, slow and concentrationdependent process; we take this process to be sorbateinduced deformation of the macromolecular backbone of BZL. A similar conclusion was drawn to explain prolonged (and biphasic) uptake of toluene to a pyridine-extracted coal (56). However, as uptake kinetics were measured at only one concentration, that study (56) lacked direct experimental evidence to rule out a bimodal distribution of diffusion path lengths as the cause. In contrast, by comparing the fractional rates during SKB and DKB at two concentrations in combination with IE rates determined under constant bulk NPAH concentrations, the IE technique presented herein unequivocally rules out path length effects as the cause of the trends exhibited by bulk NAPH in Figure 8a and b. On the basis of the results in Figure 8, we question an assumption inherent in typical diffusion models applied to natural particles that the sorbent structure is invarient during a sorption-desorption cycle. Slow structural changes have long been known to exist for polymer glasses and have been extensively studied in conditioning-annealing experiments (63, 64). For systems in which sorbate-induced structural changes take place, IE is a unique tool to determine the dependency of self-diffusivity on sorbate concentration, and thus, the degree of plasticization of the sorbent. The following conclusions on the reversibility of structural deformation can be drawn. (i) Since sorption exhibits true hysteresis at higher concentrations, structural relaxation of BZL upon bulk desorption has to be incomplete (i.e., partly irreversible). This is consonant with annealing experiments that generally show incomplete relaxation of glasses toward structural equilibrium below their glass transition temperatures (64). (ii) Deformation during uptake is not completely irreversible because otherwise release rate would have 7482

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increased with concentration, not only due to the StefanMaxwell predictions, but also due to enlargement of pore opening during the sorption step. (iii) The bi-phasic release pattern observed during DKB at higher concentration (Figure 8b) indicates that relaxation rates lag behind diffusion rates at some point. (iv) The lack of a parallel concentrationdependent behavior between the SKB and DKB rates, and between the respective bulk and IE rates, in and of themselves are indicative of irreversible changes in the solid during a bulk sorption-desorption cycle. Figure 9 compares the normalized rates of uptake (SKB vs FIES; panels a and b) and release (DKB vs RIES) (panels c and d) at both low (panels a and c) and high (panels b and d) concentration. In all cases, IE rates are faster than the corresponding bulk rates, especially at high concentration, due to the following. First, consistent with the StefanMaxwell prediction, diffusion is slowed by high energy sorption sites that need to be filled during SKB (but are occupied during FIES) and by high energy sites that are successively emptied during DKB (but remain occupied during RIES). Second, diffusion of the isotope takes place in or out of an already-filled solid that is more open and flexible than it is during diffusion in or out of the bulk. Third, sorption or desorption of the bulk is accompanied by matrix swelling or shrinking processes that prolong uptake or release; this is reflected in the biphasic shape of the curves for the bulk at high concentration (panels b and d). We summarize by illustrating the proposed mechanism for sorption irreversibility of NAPH to BZL in Figure 10. BZL is depicted as a particle of many macromolecules that form a microporous network. The dashed circle around the particle is drawn to help visualize particle swelling. At low concentration NAPH merely fills existing voids without inducing significant deformation (Figure 10a). Sorption, therefore, is reversible. As concentration increases, NAPH sorption becomes hysteretic due to irreversible deformation of the solid by NAPH during a sorption-desorption cycle (Figure 10b). Matrix relaxation occurs during bulk desorption but is incomplete: the solid after the sorption-desorption cycle, BZL*, is different from the original solid BZL. This is consistent with the results of a previous study in which BZL and humic acid were subjected to the conditioning effect using chlo-

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FIGURE 10. Proposed mechanism for naphthalene (NAPH) sorption to Beulah-Zap lignite (BZL). (a) Sorption is reversible at low NAPH concentrations (C < ∼10-5 g L-1). No significant deformation of BZL occurs. (b) Sorption is irreversible at high NAPH concentrations (C > ∼10-4 g L-1). NAPH-induced deformation of BZL is slow and partly irreversible upon desorption, which is symbolized by volumetric expansion beyond the dashed gray spheres around BZL. The solid obtained after complete desorption, BZL*, structurally differs from the starting material BZL. Sorbate entrapment does not explain observed hysteresis. rinated benzenes (20). The contribution of physical entrapment during desorption to hysteresis is likely minor, if not negligible. Isotope exchange techniquesssuch as the one described herestherefore show promise to unequivocally establish whether sorbate entrapment occurs during a sorption-desorption cycle. The use of isotopes overcomes ambiguities inherent to experimental techniques previously employed to establish sorbate entrapment as the cause of hysteresis. The present work has many important implications. (i) True hysteresis in natural organic matter solids can be demonstrated and results from irreversible deformation of the solid during a sorption desorption cycle. (ii) Hysteresis does not require the formation of an entrapped fraction during desorption. This allows the use of equilibrium expressions in contaminant-fate models as all chemicals in the solid are in free exchange with the bulk. (iii) Molecular diffusion and deformation are coupled for the NAPH-BZL system and lead to complex kinetics. Clearly, for systems such as this, coupled diffusion-relaxation models are needed. The present study demonstrates the unique potential of isotopes to establish the missing link between irreversibility and sorbent metastability.

Acknowledgments We thank the National Science Foundation, Bioengineering Program for funding (BES-0122761). Furthermore, M.S. thanks the Environmental Research and Education Foundation (EREF) for support (Francois Fiessinger Scholarship 2003).

Supporting Information Available Mathematical details involved in the isotope exchange experiments and the test for sorbate entrapment at the desorption point. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review February 14, 2005. Revised manuscript received July 22, 2005. Accepted July 26, 2005. ES050299R