Environ. Sci. Technol. 2004, 38, 5853-5862
History-Dependent Sorption in Humic Acids and a Lignite in the Context of a Polymer Model for Natural Organic Matter† YUEFENG LU AND JOSEPH J. PIGNATELLO* Department of Soil and Water, Connecticut Agricultural Experiment Station,123 Huntington Street, P.O Box 1106, New Haven, Connecticut 06504-1106
We examined sorption of two apolar compounds in three samples of macromolecular natural organic matter (NOM) in order to test whether history-dependent (“irreversible”) behaviors, including sorption hysteresis and the conditioning effect, agree with a pore deformation/creation hypothesis applicable to the glassy organic solid state as proposed in the polymer literature. The compounds are 1,2,4-trichlorobenzene (TCB) and naphthalene (Naph). The NOM samples are a soil humic acid (H-HA), an Al3+exchanged form of the same humic acid (Al-HA), and a lowrank coal (Beulah-Zap lignite, BZL). The HAs, at least, are believed free of environmental black carbon. The degree of nonlinearity in the isotherm and the ratio of hole-filling to solid-phase dissolution increased in the order of hardness (stiffness) of the solid: H-HA < Al-HA < BZL. Independent of solid, solutes show a 14-18 kJ/mol preference for hole “sites” as compared to dissolution “sites”, which we attribute to the free energy needed in the dissolution domain to create a cavity to accommodate the solute. All solids exhibited hysteresis and the conditioning effect, which refers to enhanced re-sorption after pretreatment with a conditioning agent (in this case, chlorobenzene). Conditioning the sample results in increased sorption and increased contribution of hole-filling relative to dissolution. The effects of original hole population, matrix stiffness, and solute concentration on the hysteresis index and on the magnitude of the conditioning effect are consistent with a poredeformation mechanism as the underlying cause of sorption irreversibility. This mechanism involves concurrent processes of irreversible hole expansion and the creation of new holes by the incoming sorbate (or conditioning agent). The results show that nonlinear and irreversible behavior may be expected for macromolecular forms of NOM that are in a glassy state and emphasize the case that NOM is not a passive sorbent but may be physically altered by the sorbate.
Introduction Sorption of hydrophobic organic compounds to soil or sediment natural organic matter (NOM) often shows nonlinear, competitive, and history-dependent (irreversible) behaviors (e.g., refs 1-10). A concept of sorption conforming * Corresponding author telephone: (203)974-8518; fax: (203)9748502; e-mail:
[email protected]. † This paper is part of the Walter J. Weber Jr. tribute issue. 10.1021/es049774w CCC: $27.50 Published on Web 09/25/2004
2004 American Chemical Society
to polymer theory has been advanced order to explain these behaviors (2, 3). NOM is conceived to be an amorphous, macromolecular solid that may exist in a rubbery (flexiblechain) state or glassy (rigid-chain) state depending on its physical-chemical structure, the concentration of sorbing molecules, and the temperature of the experiment. Recent thermal and thermomechanical measurements on terrestrialbased humic acids show transitions from more rigid glasslike regions to more fluid rubber-like regions at temperatures above room temperature up to over 70 °C (11-14). Additional works (15, 16) provide evidence for this behavior in whole soils. The glassy state can be idealized as having dual sorptive domains: a “hole-filling” domain consisting of molecularscale pores (holes) dispersed in a surrounding “dissolution” domain of a more fluid-like matrix that comprises the bulk of the solid phase. The presence of the holes reflects a persistent nonequilibrium state of the solid, which is due to the resistance of the matrix to achieving the thermodynamic fully relaxed state because of the stiffness of its macromolecules. Sorption to glassy solids is commonly approximated by the dual-mode model (DMM). The DMM contains a nonlinear term to describe hole-filling and a linear term to describe solid-phase dissolution. Nonlinear, competitive and irreversible sorption are associated with the hole domain. This paper deals chiefly with history-dependent behaviors including true hysteresis and the conditioning effect. True hysteresis, which has been observed in many studies of natural solids, refers to non-singularity of the sorption isotherm in the forward and reverse directions not caused by artifacts. The conditioning effect refers to enhanced re-sorption following initial sorption at relatively high concentrations (9, 17). Such behaviors are said to be “irreversible” in the thermodynamic sense because sorption follows different pathways on sorption and desorption or re-sorption. (The term irreversible here is not meant to imply permanent entrapment.) Establishing the bases for irreversibility contributes to an improved conception of sorption at the molecular level and may lead to advances in models to assess the transport, bioavailability, and risk of pollutants in the environment. The common underlying cause of true hysteresis and the conditioning effect in glassy synthetic polymers is pore expansion and pore creation by incoming sorbate molecules that is inelastic on the time scale of molecular diffusion (18-22). This inelasticity results in irreversibility because sorption and desorption take different pathways; that is, they occur to/from different physical states of the solid. We have suggested, on the basis of experiments with high-organic soils (9, 17), that a similar mechanism accounts for sorption irreversibility in NOM. In an experiment with a soil suspension in which the decay of the conditioning effect was monitored over time at 20 °C (17), we determined that relaxation of the matrix takes much longer than apparent distribution equilibrium. Alternatively, “matrix trapping” has been proposed as a cause of hysteresis in soil organic matter (23, 6) and in prepared chars (24). The premise of this mechanism is that sorption at relatively high concentration leads to a swollen (pore-opened) physical state of the solid that then collapses around some of the sorbate molecules when the external concentration is abruptly lowered, entrapping them. So far, no convincing evidence has been presented in favor of such a mechanism for soils in which sorption is dominated by macromolecular organic matter. In the present study, we examined sorption of two apolar compounds to three well-defined macromolecular NOM VOL. 38, NO. 22, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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samples. The purpose was to test whether sorption of these compounds was consistent with the glassy polymer model and whether history-dependent (irreversible) sorption behavior could be rationalized by the pore deformation/creation hypothesis. The weakly polar, weakly polarizable compounds 1,2,4-trichlorobenzene and naphthalene were selected to minimize specific interactions with sorbent functional groups that could complicate interpretation of the results and because each represents an important class of organic pollutants. The solids included the following: (i) a soilextracted humic acid in its H+-, metal ion-free form (H-HA); (ii) an Al3+-exchanged form of the same humic acid (Al-HA); and (iii) a low-rank coal, Beulah-Zap lignite (BZL). These solids span a wide range of “hardness” of macromolecular NOM. Hardness (as manifested by the glass transition temperature, Tg) is related to polymer chain and segmental mobilities, which decrease with increasing macromolecular weight, fraction of unsaturated bonds, and degree of crosslinking in the matrix (25). Indeed, higher temperature transitions were found for more aromatic, larger molecular weight humic materials (11-14). Humic acid is a relatively soft, yet still glassy form of SOM (11-14). BZL, on the other hand, is a geologically aged material that lies much higher on the scale of hardness than H-HA. Al-HA is more glassy than H-HA because of cross-linking by the aluminum ion, which makes the humic structure more rigid through its ability to coordinate to multiple functional groups (26).
Experimental Section Materials. 1,2,4-Trichlorobenzene (TCB) (99+%), naphthalene (Naph) (99+%), and chlorobenzene (CB) (99%, HPLC grade) were from Aldrich Chemical Co. The water solubility (Sw) of TCB is 30.1 mg/L, and the subcooled liquid water solubility of Naph is 106 mg/L at 25 °C (27). 1,3-Dibromopropane (98%) and 1,2-dichlorobenzene (99%, HPLC grade), also from Aldrich, were used as gas chromatographic internal standards. Humic acid was extracted from a peat soil (Terric Haplosaprist) collected in Amherst, MA, in May 2001. Procedures for preparation of H-HA and Al-HA are given in Lu and Pignatello (26). Briefly, H-HA was extracted with base by IHSS methods (28), passed through a cation-exchange resin to remove metal ions, and de-ashed with HCl/HF. The final product contained 6.18% w/w ash. Al-HA was obtained by Al3+ flocculation of re-dissolved H-HA according to a published method (29) that affords a material which was shown by Al nuclear magnetic resonance spectroscopy to contain Al ions coordinated to organic groups rather than incorporated in aluminum oxide polymers. The batch prepared for the present study had slightly different elemental composition than the one prepared previously (26). Using temperature-modulated differential scanning calorimetry (TMDSC), H-HA gave in duplicate measurements a glass transition at 56.0 and 61.2 °C and Al-HA at 58.9 and 62.3 °C. BZL is an Argonne premium coal sample (100 mesh, equivalent to 149 µm) obtained from Argonne National Laboratory (Argonne, IL). Properties of this material are available in Users Handbook for the Argonne Coal Sample Program (ANL/PSCP89/1, www.anl.gov/PCS/pcshome.html). There is yet no reliable published method for quantification of small amounts of black carbon in natural solids. The final product of H-HA was not completely soluble in 0.1 M NaOH. The insoluble residue (3% w/w) contained 18.8% organic carbon (OC). Sorption of TCB to this residue was comparable to the whole H-HA [Koc (OC normalized solidwater distribution coefficient) ) 6.21 × 103 L/kg OC at TCB solute concentration of 6.2 × 10-4 times its water solubility, Sw, compared to 2.85 × 103 L/kg OC for whole H-HA at 6.2 × 10-4 Sw] and more than 2 orders of magnitude weaker than sorption to a synthetic wood charcoal (24) (Koc ) 1.1 5854
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TABLE 1. Elemental Composition of the Solids sorbent H-HA Al-HA BZLa
non-conditioned conditioned non-conditioned conditioned non-conditioned
C (%)
H (%)
N (%)
Al (g/g)
53.56 53.49 21.14 20.86 65.85
4.40 4.40 3.68 3.71 4.36
2.95 2.91 1.25 1.24 1.04
0.003 0.13 -
a Elemental analysis data from The Users Handbook for the Argonne Coal Sample Program (ANL/PSCP-89/1, www.anl.gov/PCS/pcshome. html). Dash (-) indicates sample not analyzed.
× 106 L/kg OC at 6.2 × 10-4 Sw). Since black carbon particles, were they present, are expected to be enriched in the residues by virtue of their insolubility in base, these results point strongly against the presence of black carbon in H-HA in quantities high enough to contribute measurably to TCB sorption in the bulk sample. By inference Al-HA should be equally free of black carbon. BZL was reported (30) to contain negligible black carbon (ratio of black carbon to total OC, 0.0003) by a thermal oxidation technique. However, this technique was found to volatize prepared wood chars (31). Elemental composition of the three sorbents is given in Table 1. Solid Conditioning. Following the procedures in Lu and Pignatello (17), conditioned H-HA and Al-HA were prepared by mixing 1.5 g of H-HA or 2.5 g of Al-HA with 62 mL of 500 mg/L CB in water (Sw ) 503 mg/L). Conditioned BZL was prepared by mixing 2.5 g of BZL with 245 mL of 500 mg/L CB in water. No free-phase CB was present. The solid-towater ratios were chosen so that the equilibrium solute concentration of CB was approximately at 0.5Sw. The suspensions were equilibrated at 20 ( 1 °C for 6 d (H-HA and Al-HA) or 7 d (BZL), followed by N2 sparging for 5 d (H-HA and Al-HA) or 7 d (BZL) to quickly and completely remove the sorbed CB from the solids. The solids were then separated by centrifugation and air-dried. GC analyses indicated no detectable CB in the supernatant for each conditioned solid, and residual CB concentrations in the conditioned solids determined by a hot methanol extraction method followed by GC analysis (17) were less than the detection limit of 0.55 mg/kg, which is far below the lowest concentration in the subsequent sorption isotherms. Corresponding to each conditioned solid, a sample hereafter referred to as “nonconditioned” was prepared to rule out artifacts due to physical handling. Non-conditioned samples were handled identically in every respect to the conditioned samples except that the procedure omitted the CB. Conditioning had no effect on the CHN composition (Table 1). Sorption and Desorption. Sorption and desorption procedures were similar to those detailed in Lu and Pignatello (26). The liquid phase for H-HA and Al-HA was 0.001 M HCl solution including 200 mg/L NaN3 as bioinhibitor. The acidity kept the H-HA in particulate form. The liquid phase for BZL was 0.01 M NaCl and 200 mg/L NaN3 adjusted to pH 6.5. Sorption proceeded in parallel for the non-conditioned and conditioned solids as follows. About 40 mg of H-HA, 65 mg of Al-HA or 30-40 mg of BZL was added into 24-mL glass screw-cap vials with Teflon-silicone septa (65-mL vials for BZL), followed by addition of enough liquid phase to almost eliminate the headspace. After the sorbate was spiked in methanol carrier, the samples were rotated at 6 rpm at 20 ( 1 °C for 7-8 d for H-HA and Al-HA, which was more than adequate to reach apparent equilibrium (26). Contact time was 14 d for BZL, likewise adequate to reach apparent equilibrium (not shown). After equilibration, samples were centrifuged, and the analyte concentration in hexane extracts of the supernatant phase was determined by gas chromatography.
After completion of the sorption step, desorption from BZL was conducted in triplicate (TCB) or duplicate (Naph), using a single-step, centrifuge-withdraw-refill method (26). For TCB, 46%, 69%, or 91% of the supernatant was replaced with fresh liquid phase for the triplicate vials; for Naph, 69% or 91% of the supernatant was replaced for the duplicate vials. Equilibration time was the same as for sorption. Desorption from H-HA and Al-HA was reported earlier (26). Sorption Modeling. Sorption isotherms were fitted by both the Freundlich model and the simple dual-mode model (DMM) using weighted (by 1/q2) nonlinear regression. The Freundlich model is given by
q ) K FC n
(1)
where q (mg/kg) is the equilibrium sorbed concentration, C (mg/L) is the equilibrium solution phase concentration, KF [(mg/kg)/(mg/L)n] is the affinity coefficient, and n is an exponential constant that may be taken as an index of linearity (n ) 1 is linear). The simple DMM includes solid-phase dissolution described by a linear term and hole filling described by a Langmuir term and is given by
q ) KDC +
S0bC 1 + bC
(2)
where KD (L/kg) is the dissolution domain partition coefficient, and S0 (mg/kg) and b (L/mg) are the capacity and affinity coefficient, respectively, of the hole-filling domain. For purposes of this study, the solid is considered uniformly glassy; if, however, the solid is a composite of rubbery and glassy phases, KD represents a lumped parameter incorporating the (linear) partition coefficient for the rubbery phase(s) and the dissolution domain partition coefficient for the glassy phase(s). Equation 2 draws a sharp distinction between hole sites and dissolution sites, an assumption that we point out later is a simplification. The ratio (S0b/KD) in eq 2 reflects the contribution of hole-filling relative to dissolution in the Henry’s law (i.e., low concentration) region of the isotherm (17). Since hole-filling is responsible for nonlinear behavior, (S0b/KD) is thus an alternative index of nonlinearity.
Results and Discussion Sorption to Non-Conditioned and Conditioned Solids. The sorption isotherms of TCB and Naph in the three nonconditioned and conditioned sorbents (H-HA, Al-HA, and BZL) are shown in Figure 1. Each was fitted to the Freundlich model and the DMM, and the parameters are in Table 2. To facilitate discussion, the isotherms are re-plotted in Figure 2 as the logarithm of the solid-to-water distribution ratio (Kd ) q/C) versus reduced solute concentration (C/Sw). Both the Freundlich model and the DMM give acceptable fits (cf., SEE, Table 2); however, the Freundlich model fails to capture the log-scale curvature of the isotherms, which was evident in most cases. To quantify the conditioning effect, we employed the ratio of (dq/dC) of the conditioned to the non-conditioned solids at constant C, expressed as follows:
R)
dq(C)/dC(conditioned) dq(C)/dC(non-conditioned)
|
(3)
C
where dq(C)/dC is an indicator of sorption affinity at a given C. A semilog plot of R as a function of C/Sw for each system is shown in the graph in Figure 3. Bar graphs comparing model parameters of the non-conditioned and conditioned systems are in Figure 4a,b. Plots showing the contribution in non-conditioned solids of hole filling to total sorption (mass sorbed in hole domain divided by total mass sorbed)
as a function of reduced solute concentration appear in Figure 4c. Observations from Figures 1-4 and Table 2 produce the following conclusions: (i) Nonlinearity (i.e., concentration-dependent Kd, Figure 2) characterizes sorption in all cases. The Freundlich n ranged from 0.669 (Naph in BZL) to 0.932 (Naph in non-conditioned H-HA). For H-HA, n was as low as 0.776 (TCB in conditioned H-HA). Since the tested HA solids are free of black carbon, these results indicate that nonlinear sorption observed in soils is not exclusively linked to the presence of small amounts of thermally altered carbonaceous materials (environmental black carbon) as suggested by some investigators (e.g., refs 32-36) but can also be linked to glassy forms of macromolecular NOM. (ii) The solutes have a stronger affinity for BZL than for H-HA or Al-HA, especially at low concentration. Present knowledge of coal structure indicates that it has both elastic and viscoelastic macromolecular substance, which includes a large population of holes of a size comparable to the sorbing molecules (37, 38). The abundance of molecular-scale holes in BZL structure, as supported by DMM analysis of the isotherms here, is believed to account for its high apparent sorption affinity. In addition, BZL may be more “hydrophobic” than H-HA and Al-HA (BZL has a slightly higher C/H ratio), and so this could be of secondary importance. (iii) For the non-conditioned solids, n decreases in the order H-HA > Al-HA > BZL (Figure 4a, black bars), indicating that nonlinearity increases with the hardness of the solids (H-HA < Al-HA < lignite). The ratio (S0b/KD), which represents the ratio of the contribution of hole-filling to that of dissolution at low concentration, follows the same order (Figure 4b). Thus, hole-filling is comparatively weak for the soft H-HA (S0b/KD is 1.10 for TCB and 0.46 for Naph), becomes more important for the Al-cross-linked HA (1.91 and 1.76, respectively), and dominates sorption for the lignite (6.42 and 5.36, respectively). Figure 4c shows how the contribution of hole-filling to total sorption for the non-conditioned samples diminishing as C approaches Sw. Similar trends exist for the conditioned solids (not shown) except that each curve is displaced upward relative to the curve for the respective non-conditioned solid. (iv) Hole sites, although relatively sparse, have a much higher affinity for solute than dissolution sites. At infinite dilution, the density of hole sites seen by the solute is S0, whereas the density of total “sites” seen by the solute is the hypothetical capacity of the solid at the water solubility limit (eq 2, C ) Sw). This capacity is hypothetical because it excludes swelling or softening effects at high concentration. The fraction fH of hole sites relative to total sites is thus:
fH )
S0
(4)
S0bSw KDSw + 1 + bSw
The values of fH for the non-conditioned solids, listed in Table 3, range from 0.00044 to 0.013. They follow the expected order H-HA < Al-HA < BZL. TCB has a greater fH accessible to it than Naph in H-HA and BZL but a smaller fH than Naph in Al-HA. As Figure 4c shows, hole-filling contributes about 35-85% of total sorption to the solid in the limit of infinite dilution. However, the intrinsic affinity of solute for holes compared to dissolution sites is comparatively much greater than that range in contribution would suggest, as shown by the following analysis. Consider the hole domain to consist of a set of volume elements of the solid each containing one hole site and its surrounding matrix. Consider the dissolution domain likewise. Let us assume that the mass fraction of volume elements VOL. 38, NO. 22, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Sorption isotherms of (a) 1,2,4-trichlorobenzene (TCB) and (b) naphthalene (Naph) to conditioned and non-conditioned H-HA, Al-HA, and BZL together with Freundlich model and dual-mode model (DMM) fitted curves. making up the hole domain relative to total sorbent mass is approximately equal to fH. If we regard the hole and dissolution domains both as phases into which partitioning occurs, then the following equilibria can be written for a given compound i:
iw ) (i)H
xH hH S0bFHV ) -RT ln xw fHV hw
∆GH-w ) -RT ln
(i)D ) iw -∆GD-w ) RT ln
(i)D ) (i)H
hD xD K DF D V ) RT ln xw (1 - fH)V hw
∆GH-D ) -RT ln
[
]
S0b (1 - fH) KD
fH
9
(6)
V h H FH
RT ln 5856
(5)
V h DF D
(7)
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 22, 2004
where the subscripts H, D, and w represent hole domain, dissolution domain, and aqueous phase, respectively; x is the mole fraction of i present in the indicated phase; ∆G is the change in Gibbs free energy of partitioning of i between the indicated phases; V h is the molar volume of the phase; F is the density of the phase; R is the gas constant; and T is the temperature. The sum of the hole-dissolution domain free energy of partitioning (∆GH-D) and the term RT ln(V h HFH/V h DFD) may thereby be calculated from eq 7 and are listed in Table 3 for each solute-(unconditioned) sorbent combination. They range from -14 to -18 kJ/mol. The ratios V h H/V h D and FH/FD are unknown. However, if we assume hole and dissolution volume elements in a given solid are of similar molecular composition, just different in configuration and flexibility, it is unlikely either ratio falls outside the range 0.5-2. This makes RT ln(V h HFH/V h DFD) within ( 3.4 kJ/mol (possibly close to 0) and hence negligible. By this analysis, hole-filling is intrinsically about 14-18 kJ/mol more favorable than dis-
TABLE 2. Freundlich Model and Dual-Mode Model Parameters for Sorption of TCB and Naph on H-HA, Al-HA, and BZLa Freundlich
sorbate on sorbent TCB on H-HA
NCb
C TCB on Al-HA NC C Naph on H-HA NC C Naph on Al-HA NC C TCB on BZL Naph on BZL
NC C NC C
dual-mode model
KF
n
R2
SEE*c
S0 (mg/kg)
b (mg/L)
KD (L/kg)
R2
SEE*
991 ( 49 1498 ( 76 307 ( 14 439 ( 21 692 ( 34 1024 ( 57 151.7 ( 6.2 210.8 ( 9.1
0.884 ( 0.013 0.776 ( 0.011 0.839 ( 0.013 0.753 ( 0.011 0.932 ( 0.023 0.796 ( 0.022 0.809 ( 0.022 0.713 ( 0.021
0.9978 0.9917 0.9956 0.9934 0.9893 0.9759 0.9966 0.9962
0.0405 0.0776 0.0560 0.0694 0.0798 0.1185 0.0439 0.0446
21.1 ( 8.8 91.2 ( 18.6 10.9 ( 3.0 22.9 ( 3.9 30.4 ( 39.9 62.8 ( 22.1 61.8 ( 29.0 60.0 ( 14.7
52.8 ( 26.2 57.7 ( 13.9 52.7 ( 18.9 84.2 ( 19.1 9.91 ( 16.48 41.8 ( 25.6 2.89 ( 1.51 9.01 ( 3.18
1016 ( 59 1442 ( 99 302 ( 17 435 ( 25 659 ( 60 1022 ( 78 101.7 ( 13.8 141.8 ( 14.2
0.9959 0.9914 0.9931 0.9885 0.9905 0.9923 0.9989 0.9991
0.0573 0.0826 0.0734 0.0955 0.0806 0.0716 0.0264 0.0230
1.10 3.65 1.91 4.44 0.457 2.57 1.76 3.82
4726 ( 145 5795 ( 187 2136 ( 74 2620 ( 97
0.731 ( 0.007 0.738 ( 0.007 0.669 ( 0.016 0.669 ( 0.015
0.9676 0.9574 0.9979 0.9968
0.1493 1165 ( 141 16.6 ( 2.3 0.1716 1404 ( 178 17.2 ( 2.5 0.0346 799 ( 148 8.67 ( 2.14 0.0433 828 ( 150 11.4 ( 2.7
3016 ( 190 3685 ( 255 1295 ( 125 1715 ( 162
0.9984 0.9975 0.9944 0.9954
0.0332 0.0418 0.0567 0.0519
6.42 6.54 5.36 5.52
(S0b)/KD ratio 3.33 2.33 5.64 2.17 1.02 1.03
a Obtained by weighted (w ) 1/q2) nonlinear regression. Abbreviations are in Table 1. b NC ) non-conditioned; C ) conditioned. c Standard error of estimates, which is the square root of the average weighted squared error from the regression line.
FIGURE 2. Comparison of apparent solid-to-water distribution coefficients (Kd) as a function of reduced concentration (C/Sw) for sorption in conditioned and non-conditioned H-HA, Al-HA, and BZL. (a) TCB and (b) Naph. Lines represent dual-model model fits. Sw is the water solubility (subcooled solubility for Naph). solution, with little variation among the solids and between the two compounds. This is equivalent saying that, at infinite dilution, a molecule such as TCB or Naph is on the order of 3 × 102 to 4 × 103 times [i.e., exp(-∆GH-D/RT)] more likely to occupy a hole than a dissolution site. As stated earlier (Experimental Section), the DMM is a simplification; ∆GH-D should be regarded as the difference in free energy between the highest energy hole sites and the lowest energy dissolution sites. Since there is no reason to expect that the composition of hole walls is much different chemically than the composition of the bulk solid, we propose that the strong preference for hole sites is due to the prior existence of a cavity in the NOM phase to accommodate the incoming sorbate. For a dissolution site, the NOM strands have to move apart to create a cavity, and that costs free energy. This idea is illustrated in eqs 8 and 9.
(v) All three solids showed the conditioning effect. If the analogy between NOM and glassy polymers can be made
(18, 19, 21, 22), this history-dependent behavior means that the NOM matrix is deformed irreversibly by the incoming sorbate. The magnitude of the conditioning effect follows the order H-HA > Al-HA . BZL for reasons which will be discussed later in the paper. (vi) For H-HA and Al-HA, the magnitude of the conditioning effect (R) diminishes with C, approaching 1 as C approaches Sw (Figure 3). This may be explained by assuming that as concentration increases holes become filled and dissolution becomes correspondingly more important. The trend for BZL, which gives the smallest conditioning effect, is less apparent. (vii) The conditioning effect for the two probes TCB and Naph in a given solid and for a given conditioning agent are quite similar, both in terms of magnitude and concentration dependence (Figure 3). This suggests that SOM experiences nonspecific physical changes during conditioning that are not very sensitive to sorbate structure, at least for molecules of comparable size. (viii) Conditioning creates new hole domain in the solids, as evidenced by the tendency of S0b/KD to increase and n to decrease with conditioning (Figure 4a,b). These changes are greatest for the softer NOM of H-HA, intermediate for the cross-linked NOM of Al-HA, and close to zero for the harder VOL. 38, NO. 22, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Comparison of magnitudes of the conditioning effect in three solids as a function of C/Sw. Sw is the water solubility (subcooled solubility for Naph). NOM of BZL. (Even though the changes for BZL are small, there is no question conditioning takes place; see Figures 1 and 2.) (ix) Both S0b and KD increase with conditioning, although increases in KD are relatively small as compared to increases in S0b. Under the two-site simplifying assumption of the DMM we would expect all the changes to occur in the hole domain. It may thus be concluded that there is probably a gradual transition from sites of hole character to sites of dissolution character. Sorption-Desorption Hysteresis. Sorption hysteresis of TCB and Naph in BZL (Figure S1 in Supporting Information) was much more pronounced than hysteresis of the same compounds in H-HA and Al-HA observed in a previous study (26). The degree of hysteresis between a given point of origin on the sorption branch (Cs, qs) and its corresponding desorption point (Cd, qd) can be quantified by the Thermodynamic Index of Irreversibility (TII) derived in Sander et al. (39):
TII )
ln Cγ - ln Cd ln Cs - ln Cd
(10)
where Cγ corresponds to the point (Cγ, qd) projected onto the sorption branch at qd using an appropriate model, in this case the DMM. The TII is a fundamental advance over a previous method for quantifying hysteresis (24, 26). TII may range from 0 (fully reversible) to 1 (no desorption at all). Figure 5 shows a plot of TII as a function of Cs for each compound in each solid. The TII for both TCB and Naph increases in the order H-HA < Al-HA < BZL. H-HA gave essentially reversible sorption of TCB except at high concentration. Thus, TII correlates with the glassy character of the solid and the contribution of the hole domain relative to dissolution domain in that solid (H-HA f Al-HA f BZL). These trends are consistent with the pore deformation hypothesis (1719, 21, 22), which posits that desorption takes a different pathway than sorption. The greater reversibility of sorption in H-HA can be attributed to (i) the higher proportion of dissolution type sorption, which is reversible, and (ii) H-HA’s more elastic structure in response to the entering and leaving of molecules. The TII for both compounds in BZL tends to 5858
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decrease as the concentration increases. Also, there seems to be some dependence on sorbate structure (TCB shows greater hysteresis), but further work is necessary to elucidate the cause. Irreversible Effects in the Context of a Paradigm for Sorption to Macromolecular NOM. True hysteresis and the conditioning effect are fundamentally related (17-19, 21, 22), as they both involve inelastic matrix changes upon sorption. These changes, which take place concurrently, include (i) irreversible expansion of existing holes and (ii) creation of new holes. The flexibility of NOM during a sorption/desorption cycle can be illustrated with a rheological model (40). To accommodate a penetrant molecule entering a local region, the matrix may need to part to form a cavity or enlarge an existing cavity. In response to the leaving of the penetrant, the physical relaxation of the deformed matrix has a time evolution nature. The matrix can be modeled to include two compartments: a fast-relaxing (elastic) compartment (VE), which may be associated with the dissolution domain, and a slow-relaxing (viscoelastic) compartment (VV), which may be associated with the stiffer hole domain. The time evolution of matrix relaxation is approximated by
dVE ) -λE(T, q, λE0)(VE,∞ - VE) dt
(11)
dVV ) -λV(T, q, λV0)(VV,∞ - VV) dt
(12)
where λE and λV are the elastic and viscoelastic compartment relaxation rate constants (time-1), which are functions of T, q, and the intrinsic relaxation rate constant (λE0 and λV0, respectively) in the absence of penetrant at reference temperature T0. For a given glassy solid, λE0 . λV0; therefore λE . λV. According to polymer theory, solid-phase dissolution is analogous to solvation. Upon desorption of a molecule from a dissolution site cavity, the deformed local matrix relaxes relatively quickly (elastic term, eq 11), so that the process of matrix expansion and relaxation is essentially reversible. In the case of hole-filling, sorbate molecules preferentially fill
FIGURE 4. Comparison of conditioned and non-conditioned H-HA, Al-HA, and BZL: (a) Freundlich n. (b) DMM (S0b/KD). (c) Contribution of hole-filling relative to overall sorption (mass sorbed in hole domain divided by total mass sorbed) as a function of C/Sw (non-conditioned solids only), calculated from the DMM parameters (solid lines represent experimental concentration ranges, and dashed lines represent extrapolation based on the estimated parameters). small, high affinity holes that best fit the molecule. Holes that are comparable in size or smaller than the penetrant must expand. Relaxation of a deformed hole upon penetrant removal depends on the value of λV but is generally much slower than relaxation of a deformed dissolution site. Although full relaxation of a hole can be expected eventually, the time scale is typically much longer than that of a practical desorption experiment (17); hence, it can be considered irreversible. The left molecule has a higher affinity for the
expanded hole than for the original hole because the work of expansion has already occurred and the surface area is greater. Such higher affinity contributes to true hysteresis in the isotherm. Hole creation occurs when a molecule penetrates a local site previously fully occupied by matrix segments; when it later leaves that site, the matrix does not relax fully to fill the void. Figure 6 represents schematically how irreversible expansion of existing holes and creation of new holes are affected VOL. 38, NO. 22, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 5. Comparison of sorption-desorption hysteresis (Thermodynamic Index of Irreversibility, TII) of TCB and Naph in H-HA, Al-HA, and BZL. For TCB in H-HA, the negative TII value at the lowest concentration was truncated to zero, and the arrow indicates the calculated value was out of range.
FIGURE 6. Schematic graphs illustrating the major factors leading to increasing hysteresis as a function of sorbate concentration and sorbent hardness: (a) irreversibility of hole expansion, (b) new hole creation, and (c) hole-filling contribution to sorption. Sg denotes glass transition concentration of sorbate. by matrix stiffness and sorbate concentration. The value of λV varies inversely with matrix stiffness, while for a given solid, λV increases with q due to plasticization of the solid. Hence, the irreversibility of expansion (Figure 6a) increases with matrix stiffness and decreases with sorbate concentration, approaching nil at the Sg where the solid is converted 5860
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to the rubbery state. Hole creation (Figure 6b) becomes more difficult the stiffer the solid; on the other hand, the newly created holes have a longer lifetime (i.e., 1/λV). For a given solid, hole creation becomes progressively easier as concentration increases, reaching a maximum at Sg (18, 19). When the Sg is exceeded during sorption, on desorption as the solid
TABLE 3. Values of the Fraction of Total “Sites” Making Up the Hole Domain (fH) and the Maximum Value of the Hole-Dissolution Domain Free Energy of Partitioning (∆GH-D) at Infinite Dilution
TCB on H-HA TCB on Al-HA TCB on BZL Naph on H-HA Naph on Al-HA Naph on BZL a
fH
∆GH - D + RT ln(V h HGH/V h DGD) (kJ/mol)
0.00069 0.0012 0.013 0.00044 0.0057 0.0059
-18a -18 -15 -17 -14 -17
Uncertainty, about (2 kJ/mol.
passes back through the Sg new holes become “frozen” in the matrix around sorbate molecules, which serve as templates. A final consideration is the hole population in the original solid (Figure 6c). Hole population is positively correlated with matrix stiffness (Table 3). The fewer the original holes, the less the effects of irreversible hole expansion will be manifested. Also, since for any solid the holes fill up with concentration, it follows that hysteresis due to irreversible expansion will decrease with concentration. On the other hand, the fewer the original holes, the more impact hole creation will have on enhanced re-sorption. A combination of the trends represented in Figure 6 can explain the results we obtained. Hence, the observed order in conditioning effect (BZL < Al-HA < H-HA) is evident when one realizes that along this series (i) the original hole population decreases, so the production of new holes becomes more and more noticeable in subsequent behavior; and (ii) the conditioning agent, CB, becomes more effective at softening the solid. The observed order in hysteresis (H-HA < Al-HA < BZL) follows the order in predominance of hole-filling sorption and the (expected) reverse order in λV in the original solid. The concentration dependence of hysteresis is also explainable on the basis of sorbent properties. For BZL, hysteresis is dominated by irreversible expansion of existing holes, while new hole creation is relatively unimportant (i.e., BZL shows a small conditioning effect). Accordingly, BZL hysteresis is seen to decrease with concentration. Conversely, for H-HA, irreversible expansion of existing holes is relatively unimportant while hole creation is relatively important. Hence, hysteresis in H-HA is negligible at low concentrations but begins to appear at high concentrations as a result of self-conditioning. The implications of the results of this study are as follows: (i) Nonlinear and history-dependent behavior are characteristic of glassy macromolecular NOM and not exclusively linked to thermally altered carbonaceous materials. The facts that nonlinearity, bi-solute competitive effect and hysteresis in the soil humic acid H-HA can be enhanced by Al3+ crosslinking of the humic acid (26) and that the nonlinearity of sorption in both humic acids can be enhanced by conditioning provide compelling evidence for this argument. (ii) NOM is not a passive sorbent but responds to the presence of the sorbate, depending on sorbate structure and concentration and the properties of the solid. (iii) The free energy of sorption to NOM includes formation of a cavity in the solid to accommodate the sorbate molecule, if one does not already exist. This suggests that the extraordinarily high affinity of organic molecules for some carbonaceous materials, like black carbons and coals, is partly due to the fact that a high population of molecular-size cavities already exists.
Acknowledgments The authors are grateful for support by grants from the U.S. Department of Agriculture CSREES NRICGP 2001-35107-
10053 and the National Science Foundation BES-0122761. We thank Eugene LeBoeuf for TMDSC analysis of the humic acid samples.
Supporting Information Available One figure demonstrating hysteretic sorption-desorption of 1,2,4-trichlorobenzene (TCB) and naphthalene (Naph) in the non-conditioned Beulah-Zap lignite (BZL), plotted as log Kd vs log(C/Sw). This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review February 13, 2004. Revised manuscript received August 5, 2004. Accepted August 17, 2004. ES049774W
