Environ. Sci. Technol. 2003, 37, 1379-1384
In Situ Measurements of Dissociation Kinetics and Labilities of Metal Complexes in Solution Using DGT SHAUN SCALLY, WILLIAM DAVISON, AND HAO ZHANG* Department of Environmental Sciences, Lancaster University, Lancaster, LA1 4YQ, United Kingdom
The technique of diffusive gradients in thin films (DGT) binds metal ions to a resin after they have diffused through a well-defined layer of gel. If metal complexes dissociate in this diffusion layer, they will in principle be measured. By varying the thickness of the layer the extent of metal dissociation can be controlled. These principles were used to examine the lability of metal complexes, and, where possible, to determine the dissociation rate constant. DGT measurements were made using devices with a range of diffusive layer thicknesses (0.16-2.0 mm) in solutions containing copper or nickel in the absence and presence of nitrilotriacetic acid (NTA). Rate expressions were derived to relate the transfer kinetics to the effective measurement time of DGT. The dependence of DGT measurements on diffusion layer thickness can be modeled assuming a dissociation rate constant, k-1, of 3.6 ( 0.5 × 10-5s-1 for NiNTA-. CuNTA- was found to be fully labile, with k-1 > 0.012 s-1. The results agreed well with the limited rate data available in the literature. This work has demonstrated, for the first time, the validity of the assumption that only the free metal ion and not the metal complex, reacts with the binding resin of the DGT device. DGT therefore has the potential to distinguish between adjunctive and disjunctive mechanisms of complex dissociation. Because DGT can be readily deployed in situ, in natural waters, soils, and sediments, it opens up the possibility of directly obtaining kinetic information in natural or contaminated environmental systems.
Introduction Equilibrium models are sufficiently well established and parametrized that they are used routinely for describing the distribution of chemical species in waters (1). They are essential to understanding and predicting solubility and sorption processes. They also form the basis for the free ion activity model (FIAM) and biotic ligand model (BLM) approaches to predicting uptake of metals by biota (2, 3). However, this equilibrium condition is often not achieved in nature and the rate of dissociation of metal complexes may be important. For example, if membrane uptake of metal is fast, biological uptake will not depend simply on the free ion activity (2), as demonstrated by Hudson and Morel (4) and Mirimanoff and Wilkinson (5). The free metal ion is still presumed to be transferred across the membrane and there * Corresponding author phone: 44-1524-593899; fax: 44-1524593985; e-mail:
[email protected]. 10.1021/es0202006 CCC: $25.00 Published on Web 02/27/2003
2003 American Chemical Society
is a dynamic equilibration with the complexes, with association and dissociation continually occurring. However, depletion of the concentration of the free ion at the membrane surface diminishes the rate of complex association, resulting in a net dissociation of free metal ions from complexes. This component of complexed metal also contributes to the accumulated metal. To appreciate fully the uptake of metals in natural waters it is necessary to have information on the kinetics of dissociation of the metal complexes present. Kinetic information has been obtained from the rate of reaction of metals with resins (6, 7) or competing ligands (8). During voltammetry, metal ions are removed at a surface (analogous to membrane uptake) and a net dissociation of metal complexes is induced within the diffusion layer. Anodic stripping voltammetry can therefore be used to obtain information on the rate of dissociation of metal complexes (9, 10). In situ electrochemical measurements are possible, but their calibration and use in natural waters is not easy. Consequently, any kinetic information has been obtained from laboratory measurements on samples that have usually been chemically modified. The newly developed technique of DGT (diffusive gradients in thin films) can be readily used in situ (11). During deployment, metals bind to a Chelex resin after they have diffused through a layer of hydrogel. Metal complexes that dissociate in the diffusion zone of the hydrogel will be measured according to the proposed theory of the technique (12). In principle the kinetic window can be adjusted by varying the thickness of the diffusion layer, allowing estimation of kinetic constants. In this work, this previously untested theory is examined by performing systematic DGT measurements on solutions containing Cu or Ni in the presence of the complexing ligand nitrilotriacetic acid (NTA). Simple equations are developed, based on the previous outlined concepts, that allow derivation of kinetic dissociation constants from the DGT measurements. Kinetic Information from DGT. If there are only simple metal ions in solution, their steady state transport through a DGT device can be represented by the profile shown in Figure 1. After deployment, metals are eluted from the resin, and the accumulated mass, Ma, can be measured by any suitable analytical technique. As the deployment time, t, and the exposed surface area, A, are known, the flux, F, can be easily calculated (eq 1).
F ) Ma/At
(1)
During deployment the flux is simply given by Fick’s Law (eq 2)
F ) CD/∆g
(2)
where C is the concentration of metal in the solution, D is the diffusion coefficient of the metal ion through the gel, and ∆g is the thickness of the diffusion layer. The measured mass is therefore inversely proportional to ∆g (eq 3).
Ma ) CDAt/∆g
(3)
When there is also a metal ligand complex, ML, in the solution, it will contribute to the measured mass if it dissociates during transport through the diffusion layer.
ML S M + L
(4)
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FIGURE 1. Representation of concentration profiles of a metal, M, and its complex, ML, through a DGT device. Two profiles for ML are shown, representing the cases when exchange between M and ML is slow (solid line) and fast (dashed line). from both free metal ions in solution, M, and free metal ions dissociated from ML, M′ (eq 5)
Ma ) (CMDM + CM′DML)At/∆g
(5)
where CM is the concentration of free metal ion in the solution and DM is the diffusion coefficient of the free metal ion. CM′ is the concentration of metal dissociated from ML so that it is available for measurement by DGT, and DML is the diffusion coefficient of the metal complex, ML. The first-order dissociation of ML (of concentration CML) to M is given by eq 6, where k-1 is the dissociation rate constant and τ is the time available for the dissociation.
CM′ ) CML(1 - exp[-k-1τ])
(6)
This reaction can occur while ML is transported through the diffusion layer, as the concentration of M is lowered in this zone (Figure 1). As M is efficiently consumed at the resin, it is assumed that this reaction is effectively irreversible. The characteristic time for transport of the complex through a diffusion layer of thickness ∆g, td, is given by eq 7 (9), where DML is the diffusion coefficient for the complex ML.
td ) (∆g)2/(2DML)
(7)
As ML can only be measured if it dissociates during time td, it is a reasonable approximation to set τ ) td. Combining eqs 5, 6, and 7 gives the full equation for predicting the measured accumulated mass of metal (eq 8).
Ma ) (CMLDML(1 - exp[-k-1(∆g)2/2DML]) + CMDM)At/∆g (8) Figure 2 shows a plot of mass versus ∆g using eq 8. When the exponential term that represents the kinetic limitation is negligibly small, expressed by exp[-k-1(∆g)2/2DML] 9.2DML/(∆g)2 and ML can be considered to be fully labile (9). The measurement of M and ML by DGT is then controlled solely by diffusion (curve a in Figure 2; eq 9).
Ma ) (CMLDML+ CMDM)At/∆g
(9)
When the kinetic term dominates, expressed by exp[-k-1(∆g)2/2DML] > 0.99, k-1 < 0.02DML/(∆g)2 and ML can be considered to be inert (9). The DGT measurement is 1380
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FIGURE 2. Plot showing DGT measured mass of metal (ng) versus gel thickness (cm). (a) Complex is fully labile with respect to DGT. Uptake is governed solely by transport through the diffusive layer. (b) Complex dissociation limits the uptake of metal, which becomes kinetically rather than diffusion controlled. For this example, k-1 ) 0.005 s-1, the deployment time was 6 h and M/ML ) 0.01. effectively only determined by the diffusion of M (eq 10).
Ma ) CMDMAt/∆g
(10)
There is an intermediate zone where ML is partially labile (0.02DML/(∆g)2 < k-1 < 9.2DML/(∆g)2). In this case the DGT measurement is controlled by the dissociation kinetics of ML (eq 8). When ∆g is very small, there is insufficient time for the complex to dissociate, and the contribution from ML is close to zero. The contribution from M dominates (far left part of curve b in Figure 2) as the exponential term in eq 8 is close to 1. As ∆g increases the exponential term becomes smaller and the measured mass increases, consistent with there being more time for the complex to dissociate due to the reaction time increasing as the square of ∆g (eq 7). With further increasing ∆g, there is little kinetic limitation to the supply of M from ML. The measured mass reaches a maximum and declines (middle part of curve b in Figure 2) as the mass eventually becomes controlled by diffusion and therefore inversely proportional to ∆g (far right part of curve b in Figure 2).
Materials and Experimental Methods Preparation of Gels and DGT Device. Details of diffusive and resin gel preparation have been outlined previously (12). A polyacrylamide hydrogel, 15 vol % acrylamide (BDH Chemicals) and 0.3 vol % agarose cross-linker (DGT Research Ltd), was used as the gel solution in this preparation. To prepare the diffusive gel, 70 µL of ammonium persulfate initiator (10%) and 20 µL of TEMED catalyst were added to 10 mL of the gel solution. This solution was cast between two glass plates and allowed to set at 42-45 °C for 1 h. By using spacers of different thickness, diffusive gels of thickness 0.162.0 mm were produced. All gels were hydrated in MilliQ purified water for at least 24 h, to allow them to establish a new stable dimension. The water was changed several times to remove any impurities and unreacted reagents by diffusion. Gels were then conditioned and stored in 0.1 M NaNO3 solution. The resin gel was prepared by adding 3-4 g of MQ washed ion-exchange resin (Chelex-100, Na form, 200-400 wet mesh) in 10 mL of gel solution. Ammonium persulfate (50 µL) and 15 µL of TEMED were added, and the solution was cast in the same manner as the diffusive gel to produce a resin gel 0.4 mm thick. The gel holder used was a simple piston design (12) with a 2-cm-diameter window (DGT Research Ltd). The resin gel layer was placed on top of the
TABLE 1. Solution Conditions Used in Experiments metal
concn. [NaNO3] [NTA] mM µM µM
Cu Ni Ni Cua Cub Nib
1.74 7.1 25.1 235.5 1.56 6.8
10 10 10 100 10 10
20 80 80 1000 0 0
pH 5.09 7.04 7.02 6.3 5.3 7.06
buffer nM
MNTA%
T °C
acetate (1.8) phosphate (3.0) phosphate (6.0)
99.9 99.7 99.8 99.9 0 0
22.0 26.8 22.8 17.0 25.1 27.5
acetate (1.3) MOPS (1.0)
a Concentration used in diffusion cell experiment for determining Cu-NTA diffusion coefficient. b Concentrations used in control deployments.
piston, and then it was overlain by the diffusive gel. The front cap was then pressed down to form a seal between the cap and the gel surface. Diffusion Coefficient Measurements. The diffusion coefficients of simple metal ions through the diffusive gel layer have been reported previously (13). As the experiments discussed here involve the diffusion of M-NTA complexes, it was necessary to measure the diffusion coefficient of these metal complexes in the diffusive gel. The cell used comprised two 70-mL Perspex compartments, each with an interconnecting 1.5-cm-diameter opening. A 2.5-cm-diameter disk of gel was placed between the openings, and the whole assembly was clamped together. Carrier solution (50 mL) containing the metal complex (>99.9% complexed) was introduced into one compartment, and 50 mL of carrier solution without the metal complex was introduced into the other. Both compartments were stirred continuously using an overhead stirrer. Sub samples of 0.2 mL were taken from each compartment at 5-min intervals and analyzed for metal by electrothermal atomic absorption spectroscopy (AAS) (Perkin-Elmer 4100). DGT Experiments Nitrilotriacetic acid (NTA) (Sigma Chemicals) was used as the ligand in this study. All chemicals and buffer solutions were treated with Chelex-100 before use to remove metal impurities. To demonstrate the effect of metal complex dissociation, experiments were performed on solutions where metals were >99% complexed. The speciation program MINEQL+(Version 4.5) was used with constants from the IUPAC Stability Constants Database (14) to calculate solution composition (Table 1). As the dominant complex was always either CuNTA- or NiNTA-, the charge is not usually shown in the subsequent text. The acetate and phosphate buffers used would be involved in the reaction, as their complexes with the metal ion in the gel layer would differ from those in bulk solution, due to the changing ratio of free metal to complexes. They were assumed to be sufficiently labile to not contribute to the measured kinetics (15). For each experiment, DGT assemblies were deployed in 4 L of solution which was well stirred. The deployment times were either 4 or 6 h and the temperature was constant to within ( 1 °C. After deployment, the resin gel was removed and placed in 1 mL of 1 M HNO3 for 24 h to elute the metal. The metal concentration in the eluent was then analyzed by electrothermal atomic absorption spectroscopy (AAS) (Perkin-Elmer 4100). The mass of metal accumulated by DGT was calculated from the concentration in the eluent, Ce, using eq 11 (12).
Mass ) Ce(Vgel + Vacid)/0.8
(11)
Vgel is the volume of the resin gel and Vacid is the volume of HNO3 added for elution. The accepted elution efficiency of 0.8 was used (12). DGT Control Measurements. Control deployments were carried out for solutions containing Cu and Ni in the absence of the NTA complexing reagent. The mass of metal ac-
FIGURE 3. Plots of measured mass of Cu versus time for diffusion cell experiments with solutions of Cu in NaNO3 and Cu in NTA. cumulated was measured in the same way, and the plots of measured mass vs ∆g were obtained. The compositions of the solutions are shown in Table 1. Simultaneous deployment of replicate devices with different gel layer thicknesses necessitated use of a higher volume of solution (4 L) and a larger container than used in previous studies (12, 16). Stirring was consequently less efficient, resulting in a significant diffusive boundary layer (DBL) at the surface of the device. Control experiments were used to estimate this DBL. The reciprocal of the measured mass was plotted against ∆g, and the slope and intercept of the line was used to estimate the DBL, according to the method described by Zhang et al. (16). The value obtained was taken into account in calculations for all experiments, including those with ligands. As all experiments were performed in the same way (the same container, solution volume, and stirring rate), it is reasonable to assume that the thickness of the DBL obtained in the control experiments can be used universally.
Results and Discussion Diffusion Coefficient Measurements. Measurements of diffusion coefficients were performed on a simple solution of Cu in NaNO3 and on Cu complexed >99.9% by NTA (solution compositions shown in Table 1). Plots of measured mass versus time are shown in Figure 3. A non-zero intercept associated with the initial experimental set up is of no consequence as the slopes of the plots were used to calculate the diffusion coefficients, D (eq 12) (13).
D ) (slope × ∆g)/A × C × 60
(12)
A is the area of the window between the two compartments covered by a gel disk, C is the concentration of Cu or CuNTA introduced in the compartment, and 60 converts the time in minutes from the graph into seconds. This equation gives the value of the diffusion coefficient for the temperature, T, at which the experiment was performed. Equation 13 (12) allows calculation of the value at 25 °C, D25, from its value at any given temperature DT. VOL. 37, NO. 7, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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log DT ) [(1.37023(T - 25) + 8.36 ×
10-4(T - 25)2)/(109 + T)] + log(D25(273 +T)/298) (13)
To test the accuracy of the procedure with an established diffusion coefficient, a control diffusion experiment was performed on a simple solution containing Cu in 0.01 M NaNO3 without NTA. The value of D for Cu without NTA at 17.7 °C was 4.95 ((0.1) × 10-6cm2s-1, which was within 2.4% of the accepted value (13) at 17.7 °C of 5.08 × 10-6 cm2 s-1. The measured value of D for Cu-NTA at 17 °C was 4.29 ((0.016) × 10-6, giving a calculated value at 25 °C of 5.37 ((0.02) × 10-6cm2s-1, only 86% of the value for free Cu of 6.23 × 10-6 cm2s-1 (13). The results show that the Cu-NTA complex diffuses through the gel about 14% more slowly than Cu. As Cu and Ni NTA complexes are expected to have a similar size and structure, it was assumed that a ratio, DM-NTA/DM, of 0.86 could also be applied to Ni. DBL Measurements. The reciprocal of the measured mass in the control solutions was plotted against ∆g for each metal. The thickness of the DBL, δ, was obtained using eq 14, taken from Zhang et al. (16).
1/M ) ∆g/(DCtA) + δ/(DCtA)
(14)
The average value of δ of 0.024 ( 0.002 cm was taken into account in all calculations. DGT Kinetic Experiments. For each experiment with either metal complexes or control solutions, plots of mass of metal measured by DGT versus diffusion layer thickness were obtained (Figures 4 and 5). Measured masses for control solutions and for CuNTA declined with increasing ∆g, consistent with diffusion control. The measured masses indicated that all metal, whether as M in the control solutions or as CuNTA in the presence of NTA, was available to accumulate on the resin, according to eqs 10 and 9, respectively. CuNTA was fully labile within the DGT detection window, with the mass measured by DGT being controlled solely by diffusion. The minimum value of k-1 for CuNTA was obtained by model fits (eq 8). Had a lower value of k-1 been chosen, there would have been appreciable deviation from the data. The resulting estimates of the minimum values of k-1 are shown in Table 2, along with a maximum value for the half-life of the reaction. These estimates of kinetic limits are consistent with reported values for CuNTA (17, 18) obtained by competition with Chelex resin. For Ni in a simple solution the mass declined with ∆g, according to simple diffusion control (Figure 5), and the DGT measurement agreed with the amount of Ni added to the solution, according to eq 3. In the presence of NTA the accumulated mass was much lower and it increased with ∆g, indicating kinetic control. MINEQL+ (version 4.5) was used to calculate the percentage of Ni in solution not bound as NiNTA- (inorganic metal), as 0.26%. It uses the same values of logK for NiNTA as given in the IUPAC Stability Constants Database (14). Equation 8 was then used to model the measured mass of Ni as a function of diffusion layer thickness, using the dissociation rate constant, k-1, as an adjustable parameter (Figure 5). The fitted value of k-1 of 3.6 × 10-5s-1, had a precision of ( 0.5 × 10-5s-1, estimated from model fits that embraced the total scatter in the data (Figure 5). Measurements were also made at a different solution composition (see Tables 1 and 2). These data were fitted equally well using k-1 ) 3.6 × 10-5s-1. Lam et al. (8) have used competitive ligand exchange/ adsorptive cathodic stripping voltammetry for the kinetic speciation of nickel. Dissociation rate coefficients were obtained for NiNTA in a model solution buffered with NH4Cl/NH3, with dimethylglyoxime (DMG) as the competing ligand. Values for k-1 at two different concentrations of Ni 1382
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FIGURE 4. Plots of measured mass of Cu (ng) vs ∆g. The calculated curve for the diffusion-only case (eq 3) is shown by a solid line. The model fit (eq 8) with the lowest possible value of k-1 that fits the data is shown as a dashed line.
FIGURE 5. Plots showing the DGT measured mass of Ni vs ∆g in a simple inorganic solution (control) and in the presence of NTA. The calculated curve for the diffusion-only case (eq 3) is shown by a solid line for the control solution. The solid line for the best model fit to the NiNTA data (eq 8 and k-1 ) 3.6 × 10-5 s-1) is shown with dashed lines corresponding to ( 0.5 × 10-5 s-1. were 0.45 ( 0.09 × 10-5s-1 and 4.0 ( 0.5 × 10-5s-1 (Table 2). The difference between these results was not explained, but it appears to indicate that, unlike our work, their values were
TABLE 2. Dissociation Rate Constants, k-1, Values Obtained for Metal Complexes metal complex
a
k-1 (s-1) this work
CuNTA-
>1.2 × 10-2
NiNTA-
3.6 ( 0.5 × 10-5 (Ni ) 7.1µM) 3.6 ( 0.8 × 10-5 (Ni ) 25.1 µM)
t1/2 (s) this work
