Concentration-dependent kinetics of pollutant desorption from soils

Materials

The soils and their organic carbon (OC) contents (g/100 g dry wt basis) were Cheshire (CT, USA) fine sandy loam (1.4), Pahokee (FL, USA) (43.9), Seal Beach (CA, USA) (1.5), Mount Pleasant silt loam (NY, USA) (4.5), and Port Hueneme (CA, USA) (0.62). The source and additional physical properties of each soil are given elsewhere [3, 8, 12, 13]. Because Seal Beach soil was known to be heavily contaminated with Bunker C oil, a modified Seal Beach soil was prepared by extracting Seal Beach soil with pentane [8] to address the potential effects of this oil contamination. Modified Seal Beach soil has 0.74 g of OC per 100 g soil. All soils were air dried, sieved through a 0.5- or 2-mm sieve, and sterilized by gamma irradiation [14]. [9-¹⁴C]Phenanthrene (>98%, 46.9 mCi/mmol) and unlabeled phenanthrene were purchased from Sigma Chemical (St. Louis, MO, USA). The aqueous phase for all experiments was an inorganic salts solution at pH 7.1 [14] containing NaN₃ (0.2 g/L) to inhibit aerobic degradation.

Desorption kinetics

Uptake curves of phenanthrene in the listed soils have been given elsewhere [8]. After 180 d of sorption, sample vials were centrifuged as described in that study [8] and 60 to 90% of the supernatant liquid was discarded. The remaining suspension was transferred to a 30-ml crimp-cap separatory funnel with a Teflonr̀ stopcock (Fisher Scientific, Pittsburgh, PA, USA) or a 60-ml vial with Teflon-lined closure (Fisher Scientific), and the discarded supernatant was replaced. The replacement fluid consisted of the supernatant from a PAH-free soil suspension prepared at the same soil to water ratio as used in the individual sorption experiments and equilibrated for 60 to 90 d. This was done to ensure continuity in water chemistry (colloids, ions, pH, and so on) between the sorption and desorption stages of the experiment. Each vessel was amended with 200 mg of Tenax (20/35 mesh), which serves as an infinite sink for phenanthrene [15, 16]. This amount of Tenax corresponded to 15 to 80 times the mass of soil organic matter (SOM). Kinetic studies (D. Zhao, J.J. Pignatello, unpublished data) have confirmed that phenanthrene concentrations reach and are maintained at undetectable levels within minutes at the employed Tenax to water ratios.

The vessels were mixed end-over-end at 21 ± 0.2°C. At timed intervals, the soil was transferred to new vessels containing fresh Tenax and desorption was continued. Acetonitrile was used to rinse the previous portion of Tenax into a vial, which was placed on a rotary shaker at 21°C for 16 h. An aliquot of the extract was then assayed for radioactivity. For desorption experiments conducted in 60-ml vials, the vials were centrifuged at 1,350 to 2,200 rpm, depending on the soil, and the Tenax (which floats) was removed with a spatula. Fresh Tenax was added to each vial and shaking was continued. The Tenax was extracted as above. The amount desorbed from the soil at each time was calculated from the initial amount sorbed and the cumulative amount taken up by the Tenax.

At the end of desorption, selected samples were separated from the final Tenax portion and extracted with methanol at 70°C for 4 h. The total ¹⁴C recovery from the soil and all Tenax portions was 96 ± 8 % (average of 18 vials). For 8 of the 18 methanol extracts, phenanthrene was phase-transferred to hexane containing naphthalene as internal standard and its concentration was determined by gas chromatography with a Supelco PTE 5™ column and a flame ionization detector. The resistant fraction calculated on the basis of gas chromatography analysis was always higher than that calculated on the basis of scintillation counting (by a factor ranging from 1.1 to 2.8). Although the reason for the disagreement is unclear, the conclusion can be made that the resistant fraction is phenanthrene itself and not degradation products.

Isotherms

Representative examples of 180-d phenanthrene sorption isotherms are shown in Figure 1. These data were obtained in a previous study [8]. The concentration-dependence of desorption should be related to a parameter that expresses the degree of linearity of the isotherm. The uptake data for the isotherms previously obtained were fit in this study to two models from which indices of linearity can be obtained. Fits to these models are included in Figure 1 and model parameters for all soils are listed in Table 1.

The first model is the Freundlich model, which is given by

(1)

where the subscript (_OC) refers to the value normalized to OC content, q_OC is the equilibrium sorbate concentration, C is the equilibrium solute concentration, and K_F,OC and N are the Freundlich affinity and exponent parameters, respectively. A value of N equal to 1 indicates a linear isotherm.

The second model is the simple dual-mode model (DMM), which has been used to model sorption of hydrophobic compounds in organic matter [13, 17-19]. This model includes a linear term to account for ordinary partitioning in a dissolution domain, and a Langmuir term to account for a site-specific, adsorptionlike mechanism taking place in hydrophobic nanovoids (holes) comprising a hole domain

(2)

where K_D,OC is the OC-based partition coefficient of the dissolution domain, and Q_OC and b are the OC-based capacity and affinity coefficients, respectively, of the hole domain.

In the limit of infinite dilution, the fractions of equilibrium sorption in the dissolution domain (f) and hole domain (f) are

(3)

Because the dissolution domain is associated with linear sorption and the hole domain is associated with nonlinear sorption, it follows that f, ranging from 0 to 1, may be taken as an index of linearity. Values of f are included in Table 1.

One can see that f and N correlate. This correlation is evaluated later. Regardless of which index is used, the degree of linearity of phenanthrene sorption in soils follows the order Pahokee ∼ Mount Pleasant < Cheshire < modified Seal Beach ∼ Port Hueneme < Seal Beach (linear). Because Mount Pleasant has much less OC than Pahokee, one can see that nonlinearity is not necessarily related to OC content.

Kinetics

Desorption of phenanthrene in the presence of Tenax was followed in each of the soils at selected high and low initial absolute sorbed concentrations after the 180-d sorption period. The desorption curves are plotted in Figure 2. Sorbed concentrations are normalized to the initial value, q0.

Empirical analysis of concentration-dependent rates. The first objective was to evaluate concentration-dependent kinetics empirically to avoid bias that might occur through the choice of a kinetic model based on a particular mechanism. A consensus on the most appropriate model for uptake of contaminants by soils and sediments has so far been lacking.

Accordingly, the desorption curves in Figure 2 were each fit to an arbitrary logarithmic expression of the form

(4)

where a, b, and c are the regression coefficients, which are obviously meaningless from a physical standpoint. The fractional rate is just the first derivative of Equation 4

(5)

The standard error in the rate(t), S_rate, is given by

(6)

where S_b and S_c are the standard errors in the coefficients. Equation 4 was fitted to the desorption of each soil (all replicate data points included) by stepwise linear regression (Systat5, SPSS, Chicago, IL, USA). The linear term in ln(t) was significant in all cases (p < 0.05). The second quadratic term was dropped if p > 0.15.

Table Table 1.. Freundlich^a and dual-mode sorption isotherm parameters of phenanthrene in six soils; see text for explanation of symbols

Soil	Solute concn. range (μg/ml	n	log KF,OC (μg/g OC)-(μg/ml)−n	KD,OC (ml/g OC)	QOC (μg/g OC)	b (ml/μg)	f
Pahokee (FL, USA)	0.0003–0.181	0.72	4.3	26,788	617	179	0.196
Mt. Pleasant (NY, USA)	0.001–0.686	0.73	3.9	9,689	564	65.9	0.209
Cheshire (CT, USA)	0.002–0.769	0.79	4.2	16,786	736	55	0.293
Port Hueneme (CA, USA)	0.001–0.455	0.91	4.7	52,903	226	218	0.518
Modified Seal Beach (CA, USA)	0.001–0.290	0.92	4.9	95,270	216	378	0.538
Seal Beach (CA, USA)	0.002–0.312	1.0	4.9b	73,133b	∼0	∼0	∼1

• ^a Data from Braida et al. [8].
• ^b Values are based on organic carbon (OC) content from both natural organic matter and Bunker C oil.

The fitted curves according to Equation 4 are displayed in Figure 2, where it can be seen that the fits in most cases are good; this is indicated by the high r² values and low standard errors (legend to Fig. 2). A notable exception is Seal Beach at 25,000 μg/g OC, where replicate data inexplicably showed wide variation. The time-zero datum and final datum in each data set were not included in the regression; therefore, the interpretation of the results is limited to the range of included data.

The fractional rates as a function of percent remaining sorbed, together with error bars at selected points representing ±S_rate(t), are presented in Figure 3. Examination of the results shows that the effect of initial absolute phenanthrene concentration on fractional desorption rate is inversely related to the degree of linearity in the isotherm. For soils in which the isotherm is nonlinear (Pahokee, Mount Pleasant, and Cheshire), desorption at the highest concentration is relatively faster than desorption at the lowest concentration. For two of the three soils in which the isotherm is linear or nearly linear (modified Seal Beach and Port Hueneme), desorption is significantly unaffected by concentration, even for very high differences in the initial phenanthrene loading. For the third soil in which the isotherm is linear (Seal Beach), the results are inconclusive principally because of the large errors in the rate for the high concentration case (see the high degree of scatter in those data, Fig. 2). Cheshire soil, with intermediate indices of linearity, shows a significant difference in fractional rate between 160 and 2,000 or 13,000 μg/g OC, but no significant difference in fractional rate between the two higher concentrations.

Resistant fraction. With only one exception, a substantial fraction of phenanthrene (4–31% of initial) strongly resisted desorption in the presence of the infinite sink by the end of the desorption period, which lasted up to 606 d (Fig. 4, which replots data from Fig. 2). The exception is Mount Pleasant soil; in this soil, desorption appeared to be complete after 30 d at the higher of the two concentrations, whereas a 4% resistant fraction remained after 566 d at the lower concentration. As will be discussed later, this may be due to the modification of the SOM by high concentrations of sorbate. Calculations based on the isotherm of phenanthrene in Tenax (D. Zhao, J.J. Pignatello, unpublished data) show that in the last desorption step, the hypothetical soil concentrations in equilibrium with the Tenax and the aqueous phase is three orders of magnitude or more smaller than the actual soil concentrations. This clearly indicates that the resistant fraction arises from a rate limitation.

Previous studies have shown that the fraction resistant to exhaustive aqueous extraction is inversely concentration-dependent. An inverse relationship between initial or applied concentration and resistant fraction was found for tetrachloroethene, trichloroethene, and 1,2-dibromo-3-chloropropane in the Cheshire soil [12] and for trichloroethene in various model and natural porous materials [20]. In the latter cases [20], the authors concluded that the resistant fraction is related qualitatively to the inverse value of the Freundlich N.

The results of the present study confirm the trend toward decreasing resistant fraction with increasing initial sorbed concentration for nonlinear cases, but indicate that as the isotherm tends toward linearity, this concentration dependence may even reverse. For soils in which isotherm nonlinearity is relatively high (Pahokee and Mount Pleasant) the resistant fraction is inversely related to initial sorbed concentration. For soils in which nonlinearity is relatively low (Seal Beach, modified Seal Beach, and Port Hueneme), the relationship does not vanish but rather is reversed and the resistant fraction is greater for the higher concentration. Cheshire soil, with an intermediate degree of nonlinearity, shows decreasing resistant fraction between 160 and 2,000 μg/g OC, then increasing resistant fraction between 2,000 and 13,000 μg/g OC.

Application of a nonlinear mechanistic kinetic model. Having demonstrated concentration-dependent desorption kinetics empirically, we now wish to test the applicability of a nonlinear radial diffusion model based on the DMM that was developed earlier [19]. The dual-mode diffusion model (DMDM) assumes Fickian diffusion of molecules in the dis-solution domain and immobilization of molecules in the holes of natural organic matter.

The governing equation is given by

(7)

where q_D and q_H represent sorbed concentrations in the dissolution and hole domains, respectively, of organic matter as a function of the radial coordinate r and time t; and D_D is the self-diffusivity in the dissolution domain. For a given chemical, soil, and temperature, D_D is considered concentration-independent.

The apparent diffusivity (D_app) thus has concentration-independent and concentration-dependent components

where

(8)

The DMDM was solved numerically by using the same algorithms as used by Zhao et al. [19] except for the following modifications. The boundary condition was modified to accommodate the presence of the infinite sink Tenax by assuming zero solution-phase phenanthrene at all times. A desorption-resistant fraction, F_r, was introduced to account for the amount of phenanthrene that remains sorbed after several months of desorption. The assumption was made that F_r is governed by a different diffusivity or a different rate law. The value of F_r, which for each soil was chosen as the concentration remaining at the last experimental point, was subtracted from all data before application of the model. Fits of the data by the DMDM without subtracting F_r (not shown) were poor.

The sole fitting parameter of the DMDM is the diffusion rate parameter, D_D/r, where r0 represents a characteristic diffusion length, which is unknown. Each set of desorption data was fitted separately to obtain the best D_D/r. The best-fit curves were obtained by minimizing the mean weighted square error as described by Zhao et al. [19] and they are shown in Figure 4. Values of D_D/r for all soils and concentrations are given in Table 2. The DMDM could not be used for Seal Beach soil because the isotherm is linear.

The fits tend to slightly underpredict desorption at very early times and slightly overpredict desorption at intermediate times. The values of D_D/r for two of the soils agree well with those published earlier (1.6 × 10⁻³/h for Cheshire, and 1.5 × 10⁻⁴/h for Pahokee [19]) where phenanthrene desorption was performed by using a sequential dilution technique (desorption to a finite bath) rather than the present technique (desorption to an infinite bath). The DMDM predicts D_D/r to be independent of initial sorbed concentration provided the sorbed concentration is below the amount that would soften (plasticize) the SOM. This expectation is met for most soils. The ratio between D_D/r at low and high concentration ranges between 0.81 and 0.9; the exception is Mount Pleasant silt loam for which D_D/r increases significantly (a factor of three) with concentration. Plasticization, which is well known for polymers [21], can result in faster diffusion within the solid. Hence, the concentration dependence of D_D/r for Mount Pleasant may be due to plasticization at high concentrations.

As the instantaneous local dissolution-domain concentration q_D increases, g(q_D)⁻¹, and therefore D_app, increases (Fig. 5a). As q_D reaches very high values, the holes become saturated and g(q_D)⁻¹ approaches unity. As q_D approaches zero, g(q_D)⁻¹ approaches K_D/(K_D + Qb), which is just the local fraction of dissolution-type sorption and is equal to f. Figure 5b shows that lim_qD.0 g(q_D)⁻¹ (hence, f) correlates with the Freundlich N. In other words, D_app for desorption is concentration-dependent to the degree that the isotherm is nonlinear. The data for Cheshire soil (Fig. 3) reflect the sigmoidal shape of g(q_D)⁻¹ versus q_D curve, in that a strong concentration effect is found between 160 and 2,000 μg/g OC but little concentration effect is found between 2,000 and 13,000 μg/g OC.

Implications

We have demonstrated that normalized desorption rates are dependent on the absolute concentration when the isotherm is nonlinear. The magnitude of the concentration effect is inversely related to the degree of linearity as represented by f of the DMM (Eqn. 3) or by N of the Freundlich model. Nonlinearity is a function of the quality of the organic matter. Concentration-dependent kinetics arises from the heterogeneity of natural organic matter as a sorbent. Heterogeneous models for organic matter that have been proposed include rubbery/glassy polymer models such as the DMM [1, 13, 17], hard carbon/soft carbon models [22, 23], and models based on the assumption of fixed, activated carbonlike pores present in materials such as soot and charcoal [22-27]. Variations in the character of organic matter phases, the size of organic matter particles or coatings, and different accessibility of organic particles or coatings within the interstices of inorganic aggregates all may play a role in determining soil-specific rates [1]. The present desorption study and the earlier uptake study [8] indicate a consequence of nonideal sorption behavior in the kinetic realm, and suggest that concentration effects should be taken into account whenever sorption and desorption rates are a consideration. The DMDM ascribes the increase in apparent diffusivity with concentration in terms of progressive population of the dissolution domain at the expense of the hole domain, that is, as immobile sites (holes) become filled up.

The magnitude of the concentration effect can be expected to vary with experimental conditions and whether sorption or desorption is being observed. Uptake from an infinite bath (i.e., at constant solute concentration) or release to infinite dilution (i.e., in the presence of an infinite sink such as Tenax) will be subject to an intrinsic concentration effect on the apparent diffusivity, if one exists. Uptake from a finite bath where the soil to water ratio is held constant will be subject additionally to the shrinking gradient effect [8], which, when the isotherm is concave-down, will oppose the intrinsic concentration dependence of the apparent diffusivity and reduce the observed concentration effect. For the sequential-dilution batch method of measuring desorption rates, in which the supernatant liquid is repeatedly diluted with clean liquid to achieve desorption, the shrinking gradient effect reinforces the intrinsic concentration effect on diffusivity, rather than opposing it as in uptake in a finite bath. This was illustrated by White and Pignatello [28] and also by Zhao et al. [19] in their study of batch uptake and batch sequential dilution desorption of phenanthrene in the presence of a competing cosolute, pyrene. There, increasing the concentration of a competing cosolute was regarded as fulfilling a similar function as increasing the solute concentration.

Table Table 2.. Dual-mode diffusion model parameters for phenanthrene desorption from soils at different initial sorbed concentrations; see text for explanation of symbols^a

Soil	q0 (μg/gOC)	Resistant fraction Fr	DD/r (h−1)	MWSEb
Pahokee (FL, USA)	250 ± 25	0.38 ± 0.06	3.8 × 10−4	0.00217
	4,100 ± 25	0.25 ± 0.05	4.2 × 10−4	0.0114
Mt. Pleasant (NY, USA)	280 ± 31	0.10 ± 0.03	1.3 × 10−3	0.0530
	4,900 ± 270	0.01 ± 0.08	4.0 × 10−3	0.1230
Cheshire (CT, USA)	160 ± 28	0.36 ± 0.03	1.3 × 10−3	0.00978
	2,000 ± 250	0.26 ± 0.08	1.6 × 10−3	0.0192
	13,000 ± 930	0.29 ± 0.03	1.4 × 10−3	0.0201
Port Hueneme (CA, USA)	980 ± 73	0.19 ± 0.03	5.1 × 10−4	0.0265
	21,000 ± 65	0.26 ± 0.02	5.8 × 10−4	0.0182
Modified Seal Beach (CA, USA)	530 ± 74	0.09 ± 0.01	1.8 × 10−3	0.0956
	25,000 ± 130	0.16 ± 0.04	2.0 × 10−3	0.0907
Seal Beach (CA, USA)	240 ± 67	0.13 ± 0.04	NA	NA
	25,000 ± 1,900	0.17 ± 0.11	NA	NA

• ^a OC = organic carbon. NA = not applicable. Values are standard deviations with 95% confidence limits.
• ^b Mean weighted square error, MWSE = 1/M ∑ (C - C/C)² where C and C are experimental and calculated aqueous phase concentrations of the ith point of M total points.

In many cases, natural solids may harbor a fraction of the originally sorbed chemical in a highly resistant state [1, 12, 20, 28, 29]. All soils in the present study displayed such a fraction. This fraction can be very large. In the Pahokee soil at the lower concentration, about 31% of the initial phenanthrene was still sorbed after 20 months of continuous desorption at the maximum possible rate (i.e., to a zero-concentration bath). In contrast to the results of others [20], the highly resistant fraction in the samples in the present study was not necessarily related to the degree of isotherm linearity, because all three of the cases showing linear or nearly linear isotherms (Seal Beach, modified Seal Beach, and Port Hueneme) gave substantial resistant fractions. The existence of a highly resistant fraction in such cases is remarkable because hysteresis is not characteristic of a partitionlike, homogeneous-potential sorbent, as SOM is often regarded to be, and is implied by the linearity. The identity, or identities, of microscopic soil structures responsible for highly hindered diffusion occurring on net desorption are still a matter of debate [1, 13, 22-27, 30, 31]. Xia and Pignatello [13] have given evidence for irreversible deformation of pores, presumably located in organic matter, during net sorption that gives rise to hysteresis. Thus, structural relaxation of the solid, in addition to molecular diffusion, may regulate desorption rates.

Sorbed molecules have been demonstrated [13] to be able to plasticize SOM at sufficiently high concentrations, just as they can synthetic and natural polymers [21]. This can result in faster sorbate diffusion within the solid phase. Consistent with this, Mount Pleasant soil gives a higher D_D/r² at the higher of the two initial sorbed concentrations.

The modified Seal Beach soil behaves as if the removed Bunker C oil, which comprises about one half of the OC in the parent soil, was an additional partition medium for phenanthrene. Because the isotherm parameters based on total OC content (from natural organic matter and oil) are nearly the same for Seal Beach as for Modified Seal Beach, removal of the oil lowers the amount sorbed per gram of whole soil by about one half. Removal of the oil also decreases the linearity consistent with the oil acting like a partition domain.