Environ. Sci. Technol. 2000, 34, 2215-2223
Modeling Cd and Zn Sorption to Hydrous Metal Oxides P. TRIVEDI AND L. AXE* Department of Civil and Environmental Engineering, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102
The mobility and bioavailability of Cd and Zn in soils and sediments are affected by contaminant distribution mechanisms. One important process is sorption to hydrous aluminum, iron, and manganese oxides, which are ubiquitous in soils and sediments as both discrete particles and coatings and exhibit a high affinity for these metals. Mechanistic models are required for accurately assessing risks to populations and in the long-term management of contaminated soils and sediments. This research demonstrates intraparticle diffusion is the rate-limiting step in the sorption of Cd and Zn to microporous oxides. Furthermore, as much as 90% of the total sorption sites on the oxides reside on the micropore walls. Because longterm experiments require a lengthy period of time, predictive methods would be useful for determining surface diffusivities. Theoretically, surface diffusivities can be predicted from site activation theory, which is based on the random walk model where atoms or molecules vibrate at localized sites along the surface. Once the vibrating ion has sufficient energy, it will jump to a neighboring site. For a given metal, the associated activation energy was observed to be equivalent for all three oxides; in an effort to predict this energy, a correlation is presented between the adsorption enthalpy and the adsorbate hydrated radius. For each oxide, the Polanyi constant (R) that relates adsorption enthalpy and activation energy was equivalent for the transition metals studied.
Introduction Heavy metals such as cadmium and zinc are released into aquatic and soil environments largely from various anthropogenic activities and pose a serious threat to plants, animals, and humans because of their toxicity and persistence (1-4). Extensive research (5-9) has demonstrated that the mobility and bioavailability of these metals are impacted by sorption to hydrous oxides of aluminum (HAO), iron (HFO), and manganese (HMO), which are ubiquitous in soils and sediments. To assess risks to the surrounding environment and manage remedial activities requires accurate models and well-defined transport parameters. Although limited, studies have shown that sorption of heavy metals to hydrous oxides is a two-step process (10-16): a rapid adsorption of metal ions to the external surface is followed by slow intraparticle diffusion along the oxide micropore walls. This intraparticle diffusion is the rate-limiting mechanism in the sorption process. Studies including the present one demonstrate that * To whom correspondence should be addressed. Phone: (973) 596-2477. Fax: (973) 596-5790. E-mail:
[email protected]. 10.1021/es991110c CCC: $19.00 Published on Web 04/25/2000
2000 American Chemical Society
FIGURE 1. Adsorption edges of Cd and Zn adsorption to hydrous metal oxides at 25 °C and as a function of ionic strength (µ). For all Cd studies, the initial concentration was 5 × 10-5 M [except for Cd adsorption to HFO, 2 × 10-7 M (15)] and for all Zn studies the initial concentration was 5 × 10-5 M. HAO and HFO concentrations were 1 g L-1, and HMO was 0.1 g L-1. the long-term experiments used to observe and model diffusion require lengthy periods of time and therefore methods to predict diffusivities are needed. Axe and coworkers (15, 16) have estimated surface diffusivities using site activation theory and assuming a sinusoidal potential field along the pore surface (17):
Ds ) λ[Ea/2m]1/2 exp[-Ea/(RT)]
(1)
where λ is the mean distance between sites, m is the molecular weight of the diffusing species, Ea is the activation energy required for a sorbed ion to jump to the neighboring site, and exp[-Ea/(RT)] is the Boltzmann factor. The adsorption enthalpy (∆H°) is related to Ea through the Polanyi relation Ea ) R (∆H°), where R is the Polanyi constant (17, 18). In this paper, experimental surface diffusivities are determined, and theoretical ones are estimated. With the objective of developing a predictive method, two hypotheses are tested. (1) For a specific metal ion, EA is equivalent for all hydrous oxides. (2) For a specific hydrous oxide, metals from the one group of the Periodic Table form similar sorption complexes with the hydrous oxide surface and hence have the same R. Several studies have revealed the adsorption affinity for metal ions to oxides follows the order of Pb > Cu > Zn > Cd > Co > Mn > Sr > Ca (5-8, 19-25). Gray (26) compared VOL. 34, NO. 11, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Isotherms of Cd and Zn adsorption to hydrous metal oxides at 25 °C and different pH values. Solid lines represent the linear distribution model; Kd (L g-1) represents the distribution coefficient. HAO and HFO (15) concentrations were 1 g L-1, and HMO was 0.1 g L-1. the trends of cation adsorption to manganese dioxide with Hofmeister series and showed that the adsorption sequence for alkaline earth metals and certain heavy metals follows the reverse order of their hydrated radii. Pan and Liss (27) proposed that Zn, a much harder Lewis acid than Cd2+, binds more strongly to goethite. In efforts to predict adsorption, Morgan and Stumm (5) and others (24, 27-31) have correlated the adsorption equilibrium constant to the first hydrolysis constant of the metal. Wehrli et al. (32) developed a linear relation between the rate constant for water exchange and the intrinsic adsorption rate constants. For the most part, correlations developed in previous studies (33-38) were based on one temperature; hence, the relations cannot be used for other conditions. In a number of studies (5, 27-29), however, adsorption of metal ions to oxides has been modeled 2216
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as a function of temperature to obtain the adsorption enthalpies. From the van’t Hoff equation, adsorption enthalpy is related to the adsorption affinity or equilibrium constant (39). Adsorption enthalpy represents the bonding energy between the adsorbate ion and the sorbent; it is primarily a function of the intermolecular forces of attraction (40, 41) and when electrostatic ones dominate:
∆H° ) f(Z2/RH)
(2)
where Z is valence charge of a metal ion and RH is its hydrated radius. In this paper, in an effort to predict enthalpies and activation energies, two correlations are presented with one relating adsorption enthalpies and hydrated cationic radii
and the other relating enthalpies and activation energies. These correlations can be used to help predict sorption behavior.
Materials and Methods All sorption studies were conducted with freshly precipitated oxides. HAO and HMO were synthesized according to the methods detailed previously (16). HFO was precipitated as described by Dzombak and Morel (42). These porous amorphous oxides have been characterized in earlier works (11, 16). Solutions were prepared with reagent-grade chemicals and Millipore-Q water following standard methods (43). Stock solutions were tagged with 109Cd and 65Zn; their activities in the samples of suspension and filtrate were measured with a Beckmann LS6000SE liquid scintillation counter (16). Two types of sorption experiments were conducted: (i) short-term (i.e., 4 h contact time) and (ii) long-term ones that were designed to evaluate diffusivities. Turbulent hydraulic conditions (Re g 2.5 × 105 with respect to the reactor diameter) were maintained in all experiments to minimize the external mass-transfer resistance (44, 45). Procedures for short-term studies of adsorption edges and isotherms are conventional and described elsewhere (11, 15, 16). In earlier short-term studies (11, 15, 16), a contact time of 4 h demonstrated equilibrium (or pseudo-equilibrium) was reached between the bulk aqueous phase and that sorbed to the external surface. For each system, adsorption edges were studied at 25 °C and two ionic strengths. Isotherm studies of Cd and of Zn were conducted at 4, 14, and 25 °C and at multiple pHs to evaluate equilibrium constants, site densities, and adsorption enthalpies. In addition, for select systems, a Phillips X’Pert X-ray diffractometer (XRD) with Ni-filtered CuKR radiation was employed to study Zn sorption to HMO and Cd sorption to HAO and to determine whether in the sorption process there were any detectable variations in the XRD patterns. The long-term or constant boundary condition (CBC) experiments were used to study the slow sorption process of intraparticle surface diffusion. In these studies, the metal ion concentration in the bulk aqueous phase was maintained approximately constant by continuously monitoring its concentration and adding adsorbate as needed (11, 15, 16). Therefore, the adsorbate concentration on the external surface of the particle was maintained constant, Cs. Under the Results and Discussion, the analytical solution (46) to the mass balance given the initial and boundary conditions is integrated over the volume of the spherical aggregated particles. For these experimental studies, surface diffusivity is the only fitting parameter in the model. By using the three ubiquitous amorphous oxides and two metals from the same group in the Periodic Table, this research involved testing the hypothesis that, in surface diffusion and based on site activation theory, the activation energy required to jump to the neighboring site is a function of the metal type and that this type behaves similarly with a specific oxide.
Results and Discussion X-ray diffraction profiles of hydrous metal oxides revealed that these oxides remain amorphous when Cd or Zn was sorbed to their surfaces. There was no evidence of a surface precipitate or solid solution formation in metal sorption to the hydrous oxides. The diffraction studies showed that HAO and HMO aged 6 months with and without the adsorbate remained amorphous. Many other studies (11, 47-49) have found that sorption may inhibit oxide crystallization; however, for the duration of our studies, we did not observe crystallization with or without contaminant sorbed. Adsorption edges for Cd and Zn adsorption to hydrous metal oxides (Figure 1) illustrate the sigmoid curve charac-
FIGURE 3. Effect of temperature on Cd and Zn adsorption to hydrous oxides. Solid lines represent Van’t Hoff model, and the data points represent adsorption equilibrium constant (K) evaluated from the isotherm studies. Reported values are adsorption enthalpies (kcal mol-1). teristic of transition metals; these results are consistent with others (7, 13, 15, 19, 50-54). The affinity of Cd and Zn ions for the hydrous oxide surfaces follows the order of HMO > HFO > HAO; this result is in agreement with others (13, 19, 51, 54). Comparing these results with earlier ones of strontium (16, 22), the affinity of cations to hydrous metal oxides follows the trend of Zn > Cd > Sr and is consistent with the cation affinity order discussed earlier. For all systems, the amount of Cd2+ and Zn2+ sorbed decreased with increase in ionic strength, which suggests that metal ions retain their waters of hydration upon sorption to amorphous oxides (55). Many other studies have found similar results (15, 16, 29, 56). Conversely, many others observed no significant effects of ionic strengths on cation adsorption to metal oxides (28, 55, 57-59); however, most of these studies were conducted with crystalline oxides (28, 55, 59). Krapiel et al. (29) attributed the decrease in adsorption of Zn and Ni to montmorillonite with increase in ionic strength to an electrostatic cation exchange process. Misak et al. (13) demonstrated that the decrease in the activity coefficient with increase in ionic strength could explain the adsorption edge shift to the right. Applying activity coefficients to the present studies could not explain the decrease in sorption with increasing ionic strength; one probable reason is different electrolytes. Misak et al. (13) used NaCl when studying Co and Zn sorption to ferric and stannic oxides, where metal-complexation increases with increasing electrolyte concentration. However, NO3- does not form metal complexes, and its contribution is limited to the suppression of the diffuse layer with increase in ionic strength. To study the effect of concentration on adsorption, isotherms for cadmium and zinc adsorption to hydrous oxides (Figure 2) demonstrated a linear relationship (R2 g 0.96) between the sorbed and the bulk aqueous concentrations. VOL. 34, NO. 11, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. CBC studies with 1 g L-1 HAO at pH 7 and 25 °C: (a) experimental data of Cd sorption [Cd]bulk ) 1.5 × 10-8 M, (b) internal sorption modeled for Cd, (c) experimental data of Zn sorption [Zn]bulk ) 1.3 × 10-9 M, and (d) internal sorption modeled for Zn. Dashed lines determined from the propagation of errors (POE) method provide the error or standard deviation (SD).
TABLE 1. Cd and Zn Sorption Parameters at pH 7 parametersa
HAO-Cdb
HAO-Znb
HFO-Cdc,d
HFO-Znc
HMO-Cdc
HMO-Znc
Ct (mol of Sr/g) K ∆G° (kcal/mol) ∆S° (kcal/mol K)e ∆H° (kcal/mol) Ea (kcal/mol) R (Polanyi relation constant) theor. Ds (cm2/s) expt. Ds (cm2/s)
0.011 5011 -5.03 0.07 15.98 13.10 0.82 2.51 × 10-13 2.5 × 10-13
0.011 5364 -5.07 0.08 18.80 14.50 0.77 5.41 × 10-14 5.4 × 10-14
0.025 2600 -4.64 0.09 21.50 13.30 0.62 1.2 × 10-14 1.0 × 10-14
0.025 4000 -4.90 0.09 22.70 15.70 0.69 8.53 × 10-16 8.49 × 10-16
0.034 134 653 -6.97 0.10 23.10 13.35 0.58 1.19 × 10-13 1.14 × 10-13
0.034 234 529 -7.30 0.11 24.99 15.20 0.61 9.65 × 10-15 9.5 × 10-15
a All parameters are based on 25 °C except the enthalpy. b (8% error. c (10% error. is calculated from the thermodynamic relation (39), ∆G° ) ∆H° - T ∆S°.
This relationship suggests one average type of adsorption site present on the oxide surface. During these studies, no significant change in pH was observed, however, the oxide 2218
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d
Data for Cd sorption to HFO obtained from ref 15. e ∆S°
may act as a buffer. In a number of studies, the Langmuir model has been employed to describe metal sorption to oxides: Zn and Pb adsorption to goethite (33, 34); Zn
FIGURE 5. CBC studies and modeling results at pH 7 and 25 °C, where the externally sorbed contribution has been subtracted: (a) Cd internal sorption to 1 g L-1 HFO with [Cd]bulk ) 1.0 × 10-8 M (two studies conducted)(15), (b) Zn internal sorption to 1 g L-1 HFO with [Zn]bulk ) 1.5 × 10-8 M, (c) Cd internal sorption to 0.1 g L-1 HMO with [Cd]bulk ) 1.5 × 10-9 M, and (d) Zn internal sorption to 0.1 g L-1 HMO with [Zn]bulk ) 1.2 × 10-9 M. Dashed lines determined from the propagation of errors (POE) method provide the error or standard deviation (SD). adsorption to Al and Fe hydrous oxides (50); Cd adsorption to hydrous manganese oxides (60); Pb adsorption to hydrous ferric oxide (61); Cr(III) sorption to hydrous Fe oxides (62); Sr sorption to ferrihydrite (63); iron-cyanide adsorption onto γ-Al2O3 (64); Cu, Cd, and Pb adsorption on red mud (mixed Al, Fe, Si, and Ti oxides) (65); and Pb sorption to biogenic Mn oxides (66). Because the site densities (Ct in moles per gram) of HAO, HFO, and HMO are approximately equivalent to the total number of available sites (Cv in moles per gram) (15, 16), the Langmuir isotherm reduces to the linear distribution model. The distribution coefficient Kd (L g-1) is then simply the product of the equilibrium constant and site density (11, 15, 16, 44). Similar results were observed at 4 and 11 °C with R2 g 0.94. Metal adsorption to the hydrous oxides increased with increasing temperature, indicating an endothermic adsorption reaction (Figure 3). This phenomenon has been
observed by many others: Sr and Cd sorption to hydrous manganese oxide (36, 38); Sr and Cd sorption to HFO (15); Cd, Pb, and Zn sorption to goethite (33-35); and Sr sorption to HAO and HMO (16). Typically, most hydrogen bonds range between 2 and 12 kcal mol-1, covalent or chemical bonds are greater than 50 kcal mol-1, and physical types of bonds are much less than chemical ones (40, 67). Because adsorption enthalpies in the present studies do not exceed 25 kcal mol-1, adsorption is a physical type of reaction where the cations do not lose their waters of hydration upon sorption (40, 41). In the slow sorption process, where a CBC was maintained, the initial amount of metal sorbed corresponded to the isotherm results representing adsorption to the external surface (Figure 4, panels a and c). With time, the amount of metal ion sorbed to the oxide gradually increased due to intraparticle surface diffusion. From our isotherms, we found VOL. 34, NO. 11, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 6. Predicting equilibrium at pH 7 and 25 °C for Sr, Cd, and Zn sorption to hydrous metal oxides given their respective particle size distributions. no evidence of more than one average type of site. Assuming that there is no difference between the type of sites located externally and internally and given the particle geometry and boundary conditions, the solution to the partial differential equation from the mass balance is integrated over the volume of the spherical aggregated particles resulting in the mass sorbed per particle at a given time (11, 15, 16, 46):
M ) 4πCs
[
(
)]
-Dn2π2t 6 ∞ 1 1exp 3 π2n)1n2 R2
R3
∑
(3)
where 2220
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D)
Ds
[ ( )] 1+
FKi
(4)
where Ds is the surface diffusivity and fitting parameter in the model, is the oxide porosity, F is the bulk density, and Ki is the distribution coefficient representing the equilibrium constant times the internal site density. As mentioned above, the oxides have been characterized in previous work (11, 16). The amount sorbed to the internal surface of a single particle times the number of particles present for given radius (R) was summed over the entire particle size distribution to obtain the concentration sorbed internally. The particle size
FIGURE 7. (a) Correlation of adsorption enthalpy with the inverse of the hydrated radius [RH (71)], and (b) correlation between activation energy and adsorption enthalpy based on Polanyi relation. distributions used have been characterized for all three oxides in situ (11, 16). This total plus that sorbed to the external surface found from the short-term sorption studies (Kd) provides the theoretical concentration. By minimizing the variance, the only fitting parameter is surface diffusivity; modeling results are shown in Figures 4 and 5 (and Table 1) and include Cd sorption to HFO (15). Errors associated with the model from the propagation of errors (POE) statistical method (68) are also included in Figures 4 and 5. The POE accounted for the standard deviations (SD) in the number of particles for the 32 different sizes as well as the error in the distribution coefficient describing the mass adsorbed to the external surface. All data fall within 1 or 2 standard deviations of the model. Best-fit surface diffusivities ranged from 10-16 to 10-12 cm2 s-1. Barrow et al. (56) estimated diffusion parameters for Zn and Cd in goethite to be 6.5 × 10-19 cm2 s-1 and 3 × 10-20 cm2 s-1, respectively. Fuller et al. (10) evaluated effective
diffusivities for As(V) in HFO, which were in the order of 10-11 cm2 s-1. Papelis et al. (12) found Cd and Se(IV) diffusivities in porous aluminas ranged between 10-12 and 10-10 cm2 s-1. Axe and Anderson (11, 15) evaluated Cd and Sr surface diffusivities in HFO that ranged from 10-14 to 10-13 cm2 s-1. Misak et al. (13) reported self-diffusion coefficients of Co and Zn in hydrous Fe(III) and Sn(IV) oxides to be in the order of 10-11 cm2 s-1. In a more recent work, diffusivities for Sr in HAO and HMO ranged from 10-12 to 10-11 cm2 s-1 (16). Furthermore, in the research presented here along with previous work (15, 16), of the total adsorption sites, internal ones constitute as much as 50% in HAO, 40% in HFO, and 90% in HMO. These site densities are based on modeling the systems studied here and are in agreement with those observed when studying Sr sorption and assessing site densities as detailed by Trivedi and Axe (16). For each oxide and its associated particle size distribution, Figure 6 illustrates internal sorption or intraparticle surface diffusion (at pH 7) VOL. 34, NO. 11, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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as a function of the square root of time, where sorption reaches equilibrium in approximately 3-4 months for Sr and 2-5 years for Cd. Interestingly, Zn, which has the greatest affinity for these oxides, requires approximately 5-10 years to reach equilibrium. Thus, in aquatic environments where the oxides are present as discrete particles and coatings, amorphous aluminum, iron, and manganese oxides act as a sink for trace metal contaminants. Conversely, during desorption, these amorphous oxide particles act as longterm source for contaminants in ecosystems. Most transport models that employ distribution coefficients and retardation factors are inadequate for describing metal and radionuclide mobility in subsurface environments (69, 70). Because the internal sites account for as much as 90% of the total, accurate modeling requires inclusion of this contribution. However, long-term studies require a lengthy period of time, and therefore predictive methods would be useful for determining surface diffusivities. In earlier studies (15, 16), surface diffusivities decreased with an increase in pH, demonstrating that they are a function of site density, which is consistent with site activation theory (15-17). In sorption studies with strontium (16), Ea was approximately equivalent for all three oxides. In this research, the activation energy for a given metal was found again to be equivalent [within the error (68)] for all oxides as well. On the basis of the experimental surface diffusivity, the best-fit activation energy for each system was evaluated using eq 1. As a result, for a given oxide, R was approximately equivalent for the transition metals Cd and Zn (Table 1). In an effort to predict the activation energies, adsorption enthalpies were correlated with the inverse of the hydrated radius (RH) of the adsorbate (Figure 7a) (71). The linear correlation suggests that metal adsorption to hydrous oxides is dominated by Coulombic forces, as in physical interactions the hydrated sheath would be retained. The correlation presented potentially allows for predicting adsorption enthalpy (and hence the equilibrium constant) for any metal sorbed to hydrous Al, Fe, and Mn oxides. This correlation and recent spectroscopic studies of Sr sorption to HFO (72) and HMO (73) suggest that metals such as Sr, Cd, and Zn are electrostatically complexed with 1-2 oxygens on the oxide surface. In Figure 7b, the relationship between activation energy and enthalpy is presented for Cd and Zn adsorption to each oxide. Interestingly, as shown in the figure, the activation energy for a metal is equivalent for all three oxides. Furthermore, for each oxide, R is approximately equivalent (given the error) for Cd and Zn, which suggests that for a particular oxide, R is constant for metals of the same group from the Periodic Table. Therefore, the activation energy can be estimated from the ∆H° - RH-1 correlation. Theoretical surface diffusivities presented in Table 1 suggest that the slow sorption process can be modeled using site activation theory to predict diffusivities. These surface diffusivities reveal that the slow sorption process may require anywhere from a few months to several years to reach equilibrium. The contribution of this slow intraparticle sorption accounts for as much as 90% of the adsorption sites.
Acknowledgments This research was supported through start-up funds granted to L. Axe from New Jersey Institute of Technology.
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Received for review September 28, 1999. Revised manuscript received March 13, 2000. Accepted March 15, 2000. ES991110C
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