Kinetic Studies of Ni Organic Complexes Using Diffusive Gradients in

Nov 16, 2012 - In situ deployments of diffusive gradients in thin films (DGT) can provide direct information on complex .... Hao Zhang , William Davis...
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Kinetic Studies of Ni Organic Complexes Using Diffusive Gradients in Thin Films (DGT) with Double Binding Layers and a Dynamic Numerical Model M. R. Shafaei Arvajeh,† N. Lehto,† Ø. A. Garmo,‡ and H. Zhang*,† †

Lancaster Environment Centre, Lancaster University, Lancaster, LA1 4YQ, United Kingdom Norwegian Institute for Water Research, Sandvikaveien 59, N-2312 Ottestad, Norway

‡

S Supporting Information *

ABSTRACT: In situ deployments of diffusive gradients in thin films (DGT) can provide direct information on complex dissociation rates in natural waters. Recent advances in understanding the dynamics of the interactions of metal complexes within DGT devices have highlighted the characteristics of the binding layer, but there are few data to complement these theoretical developments. In this work the penetration into the Chelex binding layer of complexes of Ni with nitrilotriacetic (NTA) and Suwannee River fulvic and humic acids (FA and HA) in solution at pH 7 was investigated by deployment of DGT devices with two sequential binding layers, a “front” and a “back” layer. In Ni−NTA experiments, the masses of Ni bound by the front and back binding layers were similar, as predicted for slowly dissociating complexes. For Ni−FA/HA solutions, a higher mass of Ni was taken up by the front binding layer, consistent with fast dissociation from a high proportion of the binding sites. The ratio of Ni in the front to back binding layers was significantly lower (p < 0.05) for solutions of Ni−HA compared to those of Ni−FA, indicating that Ni−HA complexes are less labile than Ni−FA complexes in similar solutions (FA = 10 mg L−1 and HA = 8 mg L−1). A dynamic numerical model of the complexes in a DGT system was used to estimate the dissociation rate constants that provided the best agreement with the experimental data. Values obtained of 2 ± 0.5 × 10−4 s−1 for Ni−NTA and 2.5 × 10−3 s−1 for Ni−FA when FA = 20 mg L−1 and 3.42 × 10−4 s−1 for Ni− HA when HA = 8 mg L−1, could be rationalized with current knowledge of the dynamics of these systems. This approach can improve kinetic information obtainable using DGT and widen the range of considered complex labilities.

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INTRODUCTION Increasingly it is being recognized that the rate of dissociation of metal complexes in natural waters may be an important control in determining the behavior of metals, including their biological uptake.1,2 However, kinetic information relevant to natural waters is still quite scarce. Of the transition metals, complexes with Ni dissociate particularly slowly, which can be rationalized, according to the Eigen mechanism, by the relatively slow loss of water molecules from the hydrated cation.3 Competitive ligand exchange techniques have been used to obtain information on the rates of release of Ni from complexes with known ligands and in samples of natural waters.4−6 These approaches provide useful information, but cannot be used in situ.7 The technique of diffusive gradients in thin-films (DGT) has also been used to measure the rates of dissociation of Ni−NTA complexes.7 Subsequently in situ deployments of DGT were used to provide information on the rates of dissociation of metal complexes (including those of Ni) in natural waters.8 The mass of a metal accumulated by a DGT device during its deployment is affected by complex lability, which is a function of the rate at which the metal−ligand complex dissociates, and the mobility of different metal species in solution. Therefore, © 2012 American Chemical Society

physical, thermodynamic, and kinetic factors are all important in determining the amount of metal accumulated by a DGT binding layer.9,10 The first attempts to derive kinetic information were based on using a range of diffusion layer thicknesses, where the regulation of the diffusive flux provided a range of times available for metal dissociation.7,8 An implicit assumption of the interpretation was that metal complexes dissociate completely as soon as they encounter the resin. Work carried out subsequently has demonstrated that partially labile complexes can diffuse into the resin layer before appreciable dissociation occurs. The metal released from the complexes then binds with the resin at different penetration distances.9−11 This implies that the thickness of the resin layer will influence the amount of metal accumulated by the DGT device, as has been shown experimentally using lanthanide12 and cadmium−nitrilotriacetate complexes.13 Received: Revised: Accepted: Published: 463

April 8, 2012 November 8, 2012 November 16, 2012 November 16, 2012 dx.doi.org/10.1021/es301371b | Environ. Sci. Technol. 2013, 47, 463−470

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eluting the metal from the Chelex using 1 M HNO3 (Aristar) and analyzing the eluate using inductively coupled plasma mass spectrometry (ICP-MS, Thermo X-7, Thermo Fisher, Cheshire, U.K.). Rhodium was used as an internal standard. An elution factor (fe) of 0.85 was used to calculate the total accumulated mass on the resin.16 Model Concepts and Inputs. The dynamic numerical model used in this work is an extended version of the model presented by Lehto et al.9 compiled using a multiphysics package (COMSOL, UK). This multiphysics package provides a framework for obtaining numerical solutions using the finite element method. Its application to modeling metal and ligand interaction within a DGT-deployment solution system is described briefly here. A more detailed description and discussion of the model and the underlying assumptions can be found in Lehto et al.9 The extended numerical model simulates a metal and ligands within a DGT device with sequential binding layers as a one-dimensional system, where the model domain comprises three subdomains in continuity with each other: a DGT diffusive layer and the two sequential binding resin layers, one of which is in contact with the diffusive gel. The reacting species in the model are free metal, ligands that can react reversibly with the metal, and the complexes that arise from these reactions, as illustrated in eq 1. At equilibrium the concentrations of these species can be expressed using an equilibrium condition, such as the one shown in eq 2. The model assumes that the size of the diffusive boundary layer between the DGT device interface and the deployment solution is negligible and, therefore, the boundary of the diffusive layer that is not in contact with the front resin gel is modeled using a Dirichlet boundary condition where the initial concentrations of the species in the deployment solution are kept constant. The species in solution are thought to exist at equilibrium prior to their diffusion into the diffusive gel. The boundary condition at the opposite side of the domain (the far end of the back resin layer) is modeled using an insulating Neumann boundary condition. Transport of mobile species between the diffusive and the two resin gels occurs by molecular diffusion alone; this is modeled using Fick’s law of diffusion, where the rates of diffusion of the various mobile species are defined by their respective diffusion coefficients.9 The mobile species are free metal (M), free organic and inorganic ligands (OL and IL respectively: explained further below), and their metal−ligand complexes (MIL and MOL: explained further below). The stationary species are the resin binding sites (R) that are spatially fixed within the two resin gels and react with M to form highly stable metal−resin complexes (MR) in the resin gel that are also stationary. The reactions between the mobile and the stationary species are expressed in eqs 1−6, where the association (ka_O and ka_I)(L mol−1 s−1) and dissociation (kdiss_O and kdiss_I)(s−1) rate constants define the rate of interconversion among M, OL, IL, MOL, and MIL (eqs 1 and 3) and, therefore, the stability constants, KI and KO, (L mol−1) of the complexes MOL and MIL (eqs 2 and 4). Equation 5 describes the reaction between the metal (M) and the free resin binding sites (R) to form the complex (MR), where resin association (ka_res) and dissociation (kdiss_res) rate constants define the stability constant (Kres) of the complex MR (eq 6). This work follows the approach by Sékaly et al.17 and Lehto et al.9 in assuming that there is no significant dissociation of MR within the time scales involved in this work. This ostensibly irreversible reaction is represented in the model by a very low

This study exploits these new developments to investigate in greater detail the kinetics of dissociation of Ni complexed by nitrilotriacetic acid (NTA), fulvic acid (FA), and humic acid (HA). It investigates the use of two separate binding layers to obtain information on the penetration of the complexes prior to their dissociation. A dynamic numerical model was used to simulate the experiments and thereby estimate dissociation rates that fitted the experimental data.

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MATERIALS AND METHODS Experimental. The procedures for preparing and using DGT devices have been explained in detail by Zhang and Davison.14 DGT plastic holders with a sampling window area of 2.54 cm2 were supplied by DGT Research Limited, Lancaster, UK. A single diffusion gel layer thickness (0.8 mm) was used in all experiments. Two adjacent binding layers, each 0.4 mm thick, were used. They are referred to as “front layer” (in immediate contact with the diffusive gel) and “back layer” (between the DGT piston and the front layer), as shown in Figure 1 in the Supporting Information (SI). In standard DGT devices, less than half of the binding layer (∼0.18 mm) contains Chelex beads, as they settle by gravity on one side of the layer during casting.12 To achieve a more uniform distribution of Chelex beads in the resin layer, double the normal amount was used in the preparation of each binding layer. For each experiment, DGT devices were deployed in triplicate in a 5-L deployment solution, and at least two extra DGT devices were made to obtain blanks. The compositions of the deployment solutions are given in Table 1. Suwannee River Table 1. Composition of Solutions Used in the Experimentsa solution

Ni (μM)

NTA (μM)

A B C D E F

22.8 4.5 0.5 0.1 0.1 0.1

100 20 2

HS (mg/L)

pH

T (°C)

10 (FA) 20 (FA) 8 (HA)

7.08 7.05 7.03 7.02 7.00 6.93

19.3 18.8 19.1 22.2 22.7 20.0

a

HS: Humic substance; FA: fulvic acid; HA: humic acid. All solutions contained 0.01M NaNO3 and 0.01 M phosphate salts.

FA and HA (Humic Substances Society) and NTA were used as complexing agents. The pH was maintained at 7.02 ± 0.05 using a phosphate buffer and the ionic strength (I) was adjusted to 0.02 M using NaNO3. The solutions were equilibrated for 3 days prior to deployment. Concentrations of NTA were about 4 times higher than those of Ni and calculations using the Visual MINTEQ15 speciation program suggest that Ni−NTA complexes accounted for more than 99.99% of total Ni in the solution. DGT devices were deployed for 24 h in the Ni−NTA and Ni−FA solutions, and 142 h in the Ni−HA solution. The stirring rate was maintained constant at 700 rpm using a digital magnetic stirrer to minimize the thickness of the DBL and to ensure that it was the same in all deployments. Control measurements were made by deploying DGT devices with double binding layers for the same times in solutions containing only free metal ions and simple inorganic complexes. These inorganic solutions had the same pH, ionic strength, and metal concentration as the ones containing organic ligands. After deployments, the binding layers were removed and the accumulated mass of nickel on each layer was determined by 464

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Table 2. Input Data for Modelling Mass Uptake by Dual Binding Layer DGTs in the Presence of Different Organic and Inorganic Ligands reactant concentrations (mol L−1)

free organic ligand (OL)

free resin binding sites (R)

diffusion coefficients ( × 10−6 cm2 s−1)

metal− inorganic ligand (MIL)

metal− organic ligand (MOL)

solution

free metal (M)

free inorganic ligand (IL)

Σ metal

free metal (DM)

Ni− NTA (C) Ni−FA (E) Ni−HA (F)

2.55 × 10−10

9.94 × 10−3

1.28 × 10−12

0.2

1.87 × 10−10

5.77 × 10−7

5.78 × 10−7

4.90

4.21b

4.90

4.21

1.85 × 10−10

1.95 × 10−2

1.33 × 10−5a

0.2

1.85 × 10−10

9.96 × 10−8

1.00 × 10−7

5.42

1.65b

5.42

1.65

8.00 × 10−10

1.95 × 10−2

5.33 × 10−7a

0.2

8.00 × 10−10

1.22 × 10−7

1.24 × 10−7

5.02

0.57c

5.02

0.57

a

organic ligand (DOL)

metal− inorganic (DMIL)

metal− organic (DMOL)

Calculated based on the MW of fulvic (1500 Da) and humic (15000 Da) acids.21 bScally et al.7 cScally et al.31

Supporting Information. KI and kdissI are independent variables that can potentially influence the amount of Ni bound by the sequential resin layers. A sensitivity analysis was carried out to investigate the effect that different values of kdissI are likely to have on the modeled mass of Ni bound by R. The organic ligands are listed under the term OL, which is the sum of the available organic binding sites, i.e. [OL] = [OL1] + [OL2] + ...[ OLn]. This approach simplifies the modeling of the numerous binding sites present in natural organic matter. In the case of Ni−NTA, [OL] is considered to be the uncomplexed fraction of the ligand at equilibrium. In the case of Ni−FA and Ni−HA complexes, [OL] is considered to be effectively constant throughout the deployment. This approach was taken because the concentration of organic matter binding sites was considerably higher than the concentration of Ni. While we recognize that representing the binding to natural organic matter using a single binding constant can be considered a great oversimplification, it provides a simple first approximation that can aid understanding, provided the conditional nature of the values obtained is appreciated. The association rate constants (ka_I, ka_O, and ka_res) for Ni in the various scenarios were calculated under the assumption that the Eigen mechanism for complex formation applies (see Supporting Information). The ka values of various complexes were 2.5 × 108 (Ni−NTA), 1× 105 L mol−1 s−1 (Ni−IL, Ni− FA, Ni−HA, and Ni−Chelex100). The kdiss_res used in this modeling approach was 1 × 10−7 s−1. The concentrations of the various reactants (Table 1) and the geometries of the resin and diffusive gels were specified in the experimental setup. Literature values were used for the diffusion coefficients of the various Ni and ligand species; these input parameters are shown in Table 2. Therefore the only parameters involved in determining the amount of Ni bound by the two binding layers were kdiss for the dissolved complexes. A number of modeling scenarios were carried out where the kdiss for the complexes of interest, the conditional stability constants, K,and, by extension, the individual species’ concentrations in the bulk solutionwere varied. The modeled masses of Ni accumulated in the front and back layers were then compared to the experimentally determined masses for the same layers by calculating a percentage mean error (PME) of the modeled results to provide a numerical representation of the goodness of fit (see Supporting Information for calculation of PME).

kdiss_res (see Supporting Information for further details). We have assumed that there is no adsorption of ligand or complex to the hydrogel matrix or the Chelex resin7 and no formation of ternary complexes.18 ka I

M + IL XooooY MIL kdiss I

k [MIL] = KI = a I I kdiss I [M][ L]

(1)

(2)

ka O

M + OL XooooY MOL kdiss O

k [MOL] = KO = a O O kdiss O [M][ L]

(3)

(4)

ka res

M + R XoooooY MR kdiss res

k [MR] = K res = a res [M][R] kdiss res

(5)

(6)

At the start of a DGT deployment the concentration of all mobile species within the device is assumed to be zero. As the deployment proceeds, the mobile species diffuse into the diffusive and resin gels at their respective rates. R binds M, which results in a diffusive gradient of M from the solution into the resin gel. The depletion in the equilibrium concentration of M brings about the dissociation of MOL and MIL complexes and, hence, a further supply of M to bind with R; steady state diffusive gradients of complexes between the solution and the two resin gels are quickly established. The total amount of MR formed in each resin layer can be extracted from the model results by integrating the amount of MR formed throughout each resin gel subdomain. In this work, we model the uptake of nickel by DGT devices using sequential binding layers in the presence of inorganic and organic ligands. There are thought to be a number of inorganic and organic ligands that bind with Ni to form a range of complexes. For the purposes of this model, this has been simplified by representing all of the inorganic ligands under term, IL, i.e. [IL] = [IL1] + [IL2] + ...[ILn]; KI and kdissI are therefore conditional constants that reflect the cumulative influence that the various inorganic species have on the free metal ion concentration. The various inorganic species that are thought to form in the deployment solutions and KI and kdissI used to model them are listed in the

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RESULTS AND DISCUSSION Experimental Results. Measurements in Control Solutions. When DGT assemblies were deployed in inorganic 465

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solutions, where the dominating species were Ni2+ (>57%) and NiNO3+, Ni was accumulated mainly in the front binding layer. The mass in the back layer was generally less than 3% (2% ± 0.92%) of the total mass measured in both binding layers, and was considered negligible (data not shown). This observation, which suggests that the inorganic Ni species dissociate either prior to entering the binding layer, or immediately upon entering it, is consistent with the previous finding11 and the assumption that the inorganic Ni species considered here are very labile. When standard (single binding layer) DGT devices were deployed, the average ratio of the bulk solution concentration as measured by DGT (CDGT) (3 replicates) to the directly determined solution concentration (CSol) was 1.01 ± 2.4%. When the total mass of the two binding layers in the modified DGT samplers was considered the ratio of CDGT to CSol was 1.00 ± 3%; this demonstrates the good accuracy and precision of the technique. Measurements in Ni−NTA Solutions. The experimentally determined mass of Ni bound by the front and back layers of the modified DGT devices in solutions A, B, and C (Table 1) is shown in Figure 1a. For DGT devices deployed in the three Ni−NTA solutions, the total measured mass in both layers was less than predicted mass by eq 7.14

M=

C·D·t ·A Δg

(7)

The total concentration of Ni2+ is C, D is the diffusion coefficient, t is the deployment time, A is the exposure area, and Δg is the diffusion layer thickness. The diffusion coefficient of the Ni−NTA complexes was used in eq 7, as according to vMINTEQ, more than 99.99% of Ni2+ is bound to NTA3−. The percentage of Ni that was taken up by both layers of the DGT device was 20%, 26%, and 23% of the theoretical mass (when there is no kinetic limitation) for solutions A, B, and C, respectively. The result reflects the kinetic limitation of Ni availability to the two binding layers: approximately 74−80% of the total Ni in the solutions was not DGT labile in these deployments. Similar kinetic limitation has been observed previously.7 The ratio of metal accumulated by the front layer to the metal accumulated in the back layer was similar (1.2 ± 0.2) for the different solutions (Figure 1a). This shows that a proportion of the Ni−NTA complexes diffuse into the back binding layer before the Ni is released from the complex. Measurements in Ni−Humic Substances Solutions. The experimentally determined mass of Ni bound by the front and back layers of the modified DGT devices in solutions D, E, and F (Table 1) is shown in Figure 1b. The experimental results showed that most of the Ni was bound by the front binding layer of the DGT devices. The percentage of Ni that was taken up by both layers of the DGT device was between 83% and 89% of the theoretical mass This suggests that a significant proportion of the Ni complexed by the humic substances is DGT labile, consistent with previous observations.19,20 The Windermere Humic Acid Model VI (WHAM VI)21 models metal−humic complexation by considering a distribution of weak and strongly binding sites on the humic substance. HA is thought to have proportionally fewer carboxylic binding sites than FA.1 The binding sites demonstrate different affinities for metals: the carboxylic sites have weaker binding affinities than the phenolic sites.22 Kinetic limitation is likely to be observed when a large proportion of a metal is bound to the strongly binding sites.8 When the proportion of FA to Ni in the deployment solution was doubled by increasing the FA concentration from 10 (solution D) to 20 mg L−1 (solution E) the total mass of Ni taken up by the DGT devices decreased from 19.4 ± 0.7 (D) to 18.1 ± 0.7 ng (E). Although the reduction in the mass of Ni bound by the DGT device is not significant, it is consistent with more Ni−FA complexes being formed as the concentration of FA increases (eq 4). The ratio of mass of Ni bound by the front layer to the mass of Ni bound by the back layer was lower in the DGT devices deployed in solution E (4.2) when compared to the devices deployed in solution D (13.9) (Figure 1b). This indicates that when the ligand to metal ratio is increased, more Ni−FA complex is able to diffuse through the front layer and into the back layer before the Ni dissociates from the complex and is subsequently bound by the Chelex resin. This is again consistent with more partially labile Ni−FA complexes being formed. The ratio of mass of Ni bound by the front resin layer to the mass of Ni bound by the back layer in the DGT devices deployed in solution F (8 mg L−1 of HA) was 3.1. This is significantly lower (p < 0.05) than the ratio between the two layers in the DGT devices deployed in solution D (10 mg L−1 of FA), 13.9 (Figure 1b). For complexes with similar complexation kinetics a lower diffusion coefficient should

Figure 1. Mass of Ni accumulated on the front and back binding layers of DGT devices deployed in solutions with various compositions (Table 1). The error bars show the standard deviation of 3 replicates. The values in the boxes show the theoretical total mass (ng disc−1) when there is no kinetic limitation. The mass in the blank DGT sampler was 0.6 ± 0.2 ng. (a) Ni−NTA, t = 8 h in solution A, and 24 h in solutions B and C. (b) Ni−HS, t = 24 h in solutions D and E, and 72 h in solution F. 466

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result in a higher ratio. The low ratio for the slowly diffusing Ni−HA complexes (Table 2) is therefore attributed to slower rates of dissociation compared to the Ni−FA complexes when the ligands are present in similar concentrations. Rey-Castro et al.23 state that Ni2+ ions do not have any preference and are equally bound to the phenolic and carboxylic sites in humic substances. However, it has also been observed that as the ratio of metal to fulvic acid decreases, the proportion of strongly bound metal−FA complexes increases.4,6,8,17 The mass of Ni measured by DGT will be determined by the metal dissociating from both strong and weak binding sites, albeit at different rates. While it is difficult to determine the amounts of Ni released from each type of binding site using this experimental approach, it is reasonable to assume that there is a greater proportion of slowly dissociating metal complexes in solution E compared to solution D. Modeling Section. Control Solution. As mentioned earlier, Ni2+ is mainly accumulated in the front binding layer of the DGT device deployed in inorganic solutions. To simulate Ni accumulation in purely inorganic solutions, Ni2+ and NiNO3+ were considered to be the only significant inorganic species, as predicted by vMINTEQ. The default conditional stability constant of NiNO3+ used in vMINTEQ, (log K = 0.4) was applied and kdiss I was calculated with eq 2 assuming that the Eigen mechanism applied. The metal was accumulated almost exclusively (>99%) on the front binding layer of the simulated DGT consistent with results from the experiments (data not shown). This confirms that when metal is present only as free ions or fully labile inorganic complexes, metal uptake by DGT is controlled by the diffusion coefficient of the free metal ion in the diffusive gel and the labile compounds. Ni−NTA Solutions. We chose to simulate mass of Ni taken up by each binding layer using a range of possible values of kdiss O for Ni−NTA. According to eq 4, varying kdiss O is equivalent to varying the stability constant, KO, which in turn changes the equilibrium concentrations of the species [M], [IL], [OL], [MIL], and [MOL]. A sensitivity analysis where kdissI was modified (not shown) showed that the determination of a conditional kdissO for the organic species is not sensitive to variations in the concentrations of the inorganic ligand, its complexes, or kdissI. This is consistent with the inorganic complexes in this experimental system being highly labile and undergoing complete dissociation either before or immediately after their entry into the front resin layer, as reflected by the very high value of their conditional kdissI (see Supporting Information). Figure 2a shows the experimentally determined masses of Ni in each layer with the simulated accumulated mass in each layer as a function of pkdissO. As kdissO is increased, this in turn increases the rate of Ni−NTA complex dissociation and consequently it dissociates faster and more mass accumulates in the front binding layer when compared to the back layer. This is consistent with the qualitative interpretation of the previous section. The calculation of a PME value for each kdissO value modeled provided a systematic determination of the goodness of fit between experimental and modeled masses, where the lowest PME value was indicative of the best fit. The PME value expresses the average difference between the modeled and experimentally determined masses of Ni accumulated by front and the back layer as a percentage of the mass of Ni bound by the back layer and, therefore, quantifies the uncertainty in the kdissO value estimated using this method. The vertical dashed line in Figure 2 shows that the

Figure 2. Simulated accumulation of Ni in the front and back binding layer for a range of dissociation rate constants of Ni complexes. The dashed and solid horizontal lines are the mass of Ni in the back and front layers respectively, measured in the experiments. The vertical line indicates the best fit between modeled and experimental values. (a) Ni−NTA: the simulations are based on a ka_O of 2.5 × 108 L mol−1 s−1, where logKO = 12.25 (PME = 10.1%) gave the best fit, (b) Ni− FA: the simulations are based on a ka_O of 105 L mol−1 s−1, FA 20 mg L−1, Ni2+ 0.1 μM (PME = 6.7%), (c) Ni−HA: the simulations are based on a ka_O of 105 L mol−1 s−1, HA 8 mg L−1, Ni2+ 0.12 μM (PME = 13.3%).

best agreement to the experimental results, for both front and back resin layers, was obtained for pkdissO = 3.8 (kdissO = 1.4 × 10 −4 s−1), with a corresponding logKO = 12.25 (PME = 10.1%). This agrees very well with the accepted value of logKO value of 12.26 (adjusted using the Davies24 equation to I = 0.02 M). Simulation of all Ni−NTA experiments (Table 1) was undertaken (SI, Section S4, Table A, Figures II and III). The mean kdiss O value of 2 × 10−4 s−1 (standard deviation: 0.5 × 10−4 s−1) with the corresponding mean logKO value of 12.12 M−1 (standard deviation: 0.12 M−1) gave the best agreement with the experimental data. The mean kdiss O obtained here differs by a factor of about 6 from the previously reported value of 3.6 ± 0.5 × 10−5 s−1 when DGT samplers with a range of diffusion layer thicknesses were used.7 The discrepancy between the two results could be caused by the assumption made by Scally et al.7 that the complex does not penetrate into 467

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calculate conditional stability constants for solutions E (logKO = 6) and F (logKO = 6.2 M−1). The closest agreement between the experimental and the modeling results for the solution containing 8 mg L−1 of HA was found when kdissO = 3.42 × 10−4 s−1 (pkdissO = 3.47 (PME = 13.3%) (Figure 2c), corresponding to logKO = 8.47 M−1. The logKO predicted by WHAM VI was 7.3 M−1. These values of kdissO are much lower than those found for Ni−FA, indicative of strongly binding functional groups on HA. HA is thought to contain more carbon, nitrogen, hydrogen, and sulfur, but less oxygen, than FA, which could lead to the formation of less labile complexes.6 Most kinetic studies of Ni with natural organic matter have been done with FA and therefore, there is not much data available on binding of Ni by HA. Guthrie et al.6 used the competitive ligand exchange method (CLEM) with Chelex-100 resin as the competing ligand to determine values of kdiss O for HA. They found two kinetically distinguishable types of Ni−HA complexes which were “slowly labile” (kdissO ≈ 10−4) and “inert” (kdissO ≈ 10−6), a range which corresponds well to the average kdissO value obtained here. The conditional stability constants calculated from WHAM VI results are lower than the values determined using the approach presented here. Previous work has found that the DGT measured mass of Ni was lower than those predicted by WHAM VI when the dissolved organic carbon concentration was >3.4 mg L−1 (ca. >7 mg L−1 FA);30 the authors concluded that when using default binding parameters, WHAM VI underestimates Ni organic complexation. Interpretation of DGT measurements by employing the dynamic model provides a relatively simple and inexpensive method of estimating average dissociation rate coefficients of metal−organic complexes. As stated previously, humic substances are polyfunctional macromolecules with a wide spectrum of binding sites and binding strengths. Thus, using single association/dissociation rate constants is a simplification of the binding by these complexing ligands. The dissociation rate constants reported in the literature are known to be the average kdissO of metal−ligand complexes. The use of two binding layers has shown the potential ability of this type of DGT device to further discriminate between fast and slow dissociating metal complexes. The results here confirm that the metal uptake by DGT is not solely controlled by the diffusion coefficients of the species and that kinetic limitations may be considerable, such that they have to be taken into account in data interpretation. This is the first study that has considered the diffusion of metal−humic substance species within the binding layer and investigated its impact upon the kinetic measurements, by employing DGT devices with two binding layers. The different binding behavior observed between FA and HA warrants more studies on the dissociation rate characteristics of metal−humic acids complexes. This work has shown the potential of using the dual binding layer DGT device as an alternative approach to using different thicknesses of diffusion layers to obtain kinetic data. Further studies using DGT with multiple binding layers are needed to investigate the behavior of fast and slow dissociating complexes under various environmental conditions such as different temperature, pH, ionic strengths, ligand concentration and presence of other metals. Moreover, using various binding layers with different binding strengths, thicknesses and layer combinations would enable more accurate and precise determination of a wider spectrum of fast and slow dissociating

the binding layer. They assumed that the Ni−NTA complexes dissociate within the diffusion layer and the dissociation reaction can be classified as disjunctive. The results of this work have shown that the dissociation reactions of Ni−NTA can also occur within the binding layer. Therefore the kinetic supply of Ni from Ni−NTA complexes may not depend solely on the diffusion layer thickness, as it is likely to be influenced by the thickness of the binding layer. The approach taken here is believed to provide a superior estimate of the dissociation rate constant, owing to the numerical approach used, which avoids the assumption of instantaneous binding of metal to the resin. Solutions with Ni−Humic Substances. The conditional dissociation rate constant, pkdiss O, for Ni binding to FA and HA was varied, to investigate which value modeled the mass of Ni accumulated in the front and the back layer (Figure 2b and 2c). In solution E (20 mg L−1 FA), the best agreement between the modeled and measured mass of Ni in both the front and the back binding layer was found when kdiss O = 2.5 × 10−3 s−1 (logKO = 7.67 M−1) (PME = 6.7%). Simulations were also carried out for a solution with 10 mg L−1 FA (SI, Table A and Figure IV). The best agreement between the experimental data and predicted values was observed for kdiss O of 6.0 × 10−3 s−1 (logKO = 7.23 M−1) (PME = 4.1%). As noted before, it is possible that a greater proportion of strongly bound, slower dissociating, Ni−FA complexes are formed in the higher concentration Ni−FA solution. This would explain why a lower kdiss O valuewhich is an average value accounting for all Ni−FA complexesis observed.4,25,26 Humic substances are heterogeneous, polyfunctional macromolecules that carry a wide spectrum of binding sites with various binding strengths. As a result, their reactions with metals are medium specific and may show different dissociation rate constants depending on a number of variables, including metal and total ligand concentrations, pH, temperature, and the ionic strength of the medium.22 In obtaining rate data, researchers have employed various analytical techniques which have different kinetic windows. They have also used different approaches to measure M OL association rate constants, ka_O,1,3 or different ligand concentrations, OL,8,27 to obtain conditional stability constants for Ni−humic substances. Therefore, there is discrepancy among published data, which makes the comparison of the results difficult. Our kdissO values of 2.5−6.0 × 10−3 s−1 are in good agreement with Lam et al.4 who reported kdissO values of 5 −10 × 10−3 s−1, obtained for various Ni/FA ratios, using CLE/AdCV. Warnken et al.8 estimated the value of kdiss O for Ni−FA as 3.7 × 10−2 s−1 (logKO = 6.72 M−1) from in situ deployments of DGT in a fresh water with high dissolved organic carbon using a calculated value for ka_O. However, kdiss O decreased to 6.6 × 10−4 s−1 (logKO = 4.97 M−1) when a lower, experimentally determined, ka_O value was used. Moreover, these authors used the concentration of the phenolic sites as the [OL] in their calculations. Worms and Wilkinson27 used ion exchange techniques and the concentration of carboxylic sites as the [OL], to determine logKO values for Ni−FA that ranged from 4 to 4.6 M−1 in solutions where the ionic strength was 0.1 and 0, respectively. Zhang and Buffle28 used average values of the potential difference between the inside and the outside of fulvic macromolecules under various pH and ionic strength conditions to calculate Kos and, by extension ka_O; they reported a logKO value of 8.6 for Ni−FA complexes. Using [Ni2+] and [Ni−FA] predicted by the WHAM (VI) speciation program29 and the molar concentrations of FA, it is possible to 468

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binding sites on humic substances. Eventually, in situ application of DGT with multiple binding layers could reveal valuable kinetic information of metal organic complexes in natural media and improve our perception of metal lability and bioavailability.

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ASSOCIATED CONTENT

S Supporting Information *

Dimensions of DGT device used in the simulations; model input parameters for Ni inorganic solution, Ni−NTA solutions, Ni−FA solution (FA = 10 mg L−1), and calculation of association rate constants; calculation of percentage mean error (PME); graphs showing modeling results of Ni−NTA and Ni− FA. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Bill Davison and John Hamilton-Taylor for their advice. REFERENCES

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