Article pubs.acs.org/est
Limits of the Linear Accumulation Regime of DGT Sensors Sandrine Mongin,†,* Ramiro Uribe,†,§ Carlos Rey-Castro,† Joan Cecília,‡ Josep Galceran,† and Jaume Puy†,* †
Departament de Química and AGROTECNIO, ‡Departament de Matemàtica, ETSEA, Universitat de Lleida, Rovira Roure 191, 25198, Lleida, Spain § Departamento de Física, Universidad del Tolima, Ibagué, Colombia S Supporting Information *
ABSTRACT: A key question for the practical application of DGT (Diffusive Gradients in Thin films) as dynamic sensors in the environmental monitoring of trace metals is the influence of pH and dissolved ligands over the linear accumulation regime. Protons compete with metal ions for the binding to the DGT resin sites at relatively low pH, whereas high affinity dissolved ligands compete with resin sites for the binding of metals. Any of the two phenomena can lead to a departure from the linear accumulation regime and an underestimation of the actual species concentration in solution. These effects are studied here through numerical simulation of the diffusion-reaction processes in both gel and resin domains using a detailed chemical model of metal ions and protons interacting with resin sites. Results were tested successfully against experimental data of the Cd-NTA representative system. Charts to delimitate the range of experimental conditions (pH, ligand concentration and strength) where the linear accumulation regime prevails, can be helpful for designing sampling strategies in field conditions. For example, it is foreseen that perturbations of linear regime within 10 h of deployment are negligible above pH 5 and weak complexation (log K′ < 0) or above pH 7 and strong complexation (log K′ < 3), where K′ is the effective stability constant. These plots can also be approximately used for partially labile systems whenever the time is replaced with the product lability degree times t.
1. INTRODUCTION In a broad sense, dynamic analytical techniques for the determination of metal fluxes in environmental waters are mostly based on a metal binding material that disturbs the distribution of metal species in a solution layer adjacent to the sensor. The amount of metal measured is related to the metal flux coming from the free metal and from the dissociation of the complexes.1,2 Voltammetry is widely applied as a dynamic technique, but techniques using a chelating resin for the binding of metals have increased their use because of their simplicity and capacity for multielemental determination.3−5 Among these techniques, diffusive gradients in thin films (DGT) is one of the most widespread.6 The principle of this technique is that metals diffuse through a diffusion domain of a well-defined thickness, composed by a hydrogel and a membrane filter, to finally accumulate in an adjacent binding layer, which consists of a chelating resin (usually Chelex) suspended in a hydrogel. DGT is a powerful technique for in situ measurement,1,6 and it has been successfully applied to the measurement of trace metals,7 radionuclides,8 and phosphate,9 in fresh10 and marine water,11 as well as a range of determinands in sediments12 and soils.13 The typical equation describing the accumulated mass measured by the DGT as a linear function of the metal © 2013 American Chemical Society
concentration in the medium and the time of deployment relies on several assumptions.6 A crucial one is that the surface of the resin layer acts as a perfect planar sink, implying that the binding to the resin is strong, irreversible, almost instantaneous and that the accumulated metal amount is well below the capacity of the resin. However, experimental studies have shown that the proportion of metal accumulated can be influenced by the strength of the binding phase under certain conditions.14,15 Lehto et al.16 used numerical models of the DGT system to explore how the resin strength may have an impact on the metal accumulation. Moreover, experimental observations showed that metal accumulation in the DGT can critically decrease at low pH values.6,17,18 In fact, at low pH, the major binding functional groups of the resin phase are predominantly in acidic forms.14 Therefore, the proton competition can reduce the effective strength of the resin. Likewise, the presence of ligands in solution may compete with the resin sites for the uptake of metal ions,19 which, again, lowers the effective strength of the resin.16 Received: Revised: Accepted: Published: 10438
February 6, 2013 June 26, 2013 August 14, 2013 August 14, 2013 dx.doi.org/10.1021/es400609y | Environ. Sci. Technol. 2013, 47, 10438−10445
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and MR2 were identified.21,22 Thus, instead of the simple M + R ⇌ MR binding model, the Cd binding to the resin sites is described by the following reactions:
In all these situations, where the perfect sink assumption for the sensor does not hold, the linear relationship of the metal accumulation with deployment time and bulk concentration fails, limitating the range of applicability of the DGT technique. This limitation, as it will be shown, can be avoided with the help of physicochemical models of the reaction-diffusion processes taking place in the sensor devices. In this work, a simulation tool that takes into account the detailed binding stoichiometry between metal and resin groups is developed in order to study the effect of two competitors, proton and ligand, on the amount of metal accumulated in the sensors. The simulated results are checked against cadmium ion experiments at several pH values, given that the behavior of cadmium in the DGT6,20 and its complexation with Chelex resin4,21,22 are wellknown. The competition effect of a strong ligand is investigated with different concentrations of NTA (nitrilotriacetic acid) at a convenient pH. No parameters of the Cd binding to Chelex and NTA are fitted in this work. Instead, values previously reported in the literature are used. The resulting numerical reaction-diffusion model predicts sensor performance within and beyond the standard linear regime. This new tool can be useful in the design of experimental strategies (e.g., the choice of deployment time), and in the assessment of the accuracy of results in actual environmental samples. It can also provide guidance for future developments of novel sensor configurations and resin compositions.
(1)
The equilibrium condition reads:
K=
ka c* = Cd L * c L* kd cCd
Cd + 2H 2R ⇌ Cd(HR)2 + 2H
(4)
3. MATERIALS AND METHODS 3.1. Experimental Details. DGT holders (piston type, 2 cm diameter window), diffusive gels (0.8 mm thick) and Chelex resin (0.4 mm thick) discs from DGT Research Ltd. were used. A 5 L polyethylene exposure chamber was thermostatted at 25 ± 0.1 °C and stirred at 240 rpm. The DGTs were deployed in solutions of 10−3 mol·L−1 and 10−5 mol·L−1 Cd (prepared from Cd(NO3)2) with or without NTA (Fluka, analytical grade) at different concentrations (2 × 10−5 mol·L−1, 1.8 × 10−3 mol·L−1 and 8 × 10−3 mol·L−1). The ionic strength was kept at 0.05 mol·L−1 NaNO3 (Merck, Suprapur). Solutions were analyzed by ICP-OES. Additional experimental details are given in the SI. 3.2. Numerical Simulations. The parameters used for the simulations are presented in SI Tables SI.1 and SI.2. All these values of the model parameters were taken from bibliography or obtained from independent experimental measurements. This is the case of the maximum resin binding capacity which yields a concentration of sites in the resin layer of 0.147 mol· L−1. Therefore, no ad hoc fitting of the simulation model was necessary to describe the experimental Cd accumulation data shown in the Results Section.
ka
kd
(3)
The overbar (here and everywhere in the text) represents species in solid phase. These reactions are assumed to be so fast that local equilibrium conditions can be applied. Experimental fulfillment of this condition is discussed in Levy et al.25 The Cd and proton ion binding equilibrium constants of the chelating sorbent22 are detailed in the SI (Table SI.1). Initial conditions are defined by the bulk concentrations in the solution and null concentrations of Cd, L and CdL everywhere in the sensor. The numerical solution is achieved by using a finite difference method (see details in SI, Section 2).
2. MODEL FOR DGT ACCUMULATION Let us consider the complexation of cadmium with a generic ligand L (which corresponds to NTA3‑ in the particular case of the experimental results reported here) according to the following scheme: Cd + L ⇌ CdL
Cd + 2H 2R ⇌ CdR 2 + 4H
(2)
where K, ka, and kd are, respectively, the equilibrium, association, and dissociation rate constants of the complexation process, whereas ci* labels the concentration of species i in the bulk solution. The charges of the different species are omitted for simplicity. As detailed in the Supporting Information (SI), both CdNTA and Cd(NTA)2 species could be formed. However, for the conditions used in this work, eq 1 can reproduce the detailed CdNTA binding results provided effective values for the kinetic and stability constants are used (see SI, Section 1). Following our previous model,23 we assume diffusion of the species through the membrane filter and diffusive gel, as well as penetration into the resin layer, where the free metal is bound to the resin sites. Additionally, in the model version presented here, the detailed metal binding reactions to the resin and the metal-proton competition are considered by the suitable exchange equilibria 3−4.21,22 In fact, previous studies showed different patterns for the binding of the metal ions to the Chelex resin groups (R). For copper and nickel, the mechanism involves only the formation of a MR complex.22 Formation of MR and MR2 complexes have been reported for iron, whereas for lead, the complexes PbR and PbHR are formed.21,24 In the case of cadmium and zinc metal ions, both complexes, M(HR)2
4. RESULTS AND DISCUSSION 4.1. Impact of pH on the DGT Accumulation from a Solution without Ligand. During the deployment of the sensors, four different regimes corresponding to different elapsed times can be distinguished: (i) transient; (ii) linear; (iii) decaying flux, and (iv) bulk-resin equilibrium. At the beginning of the deployment, a short transient takes place along which the mass accumulated per unit of time (i.e., the flux) increases as time increases. During this period, the accumulation is not linear with time, but usually it is so short that it is not noticed and can be practically neglected. Afterward, a quasi steady-state regime is achieved, in which the flux of metal reaches its maximum value. In this regime the resin acts as a perfect sink (we assume a strong and fast metal binding) for the metal and the accumulation is linear with time: nSS =
* At DCd cCd g
(5)
where nSS is the number of accumulated moles predicted when the model only considers this steady-state regime, DCd is the diffusion coefficient of cadmium in the gel, cCd * is the bulk 10439
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concentration of cadmium in the deployment solution, A is the exposed gel area, t is the time of deployment and g is the thickness of the sensor including the diffusive gel, the filter and any possible diffusive boundary layer.23,26 Equation 5 and the consequences below can be extended to the case of fully labile complexes with the same mobility as the free metal. For sufficiently long times, the flux starts to decrease, the slope of the accumulation curve bends due to less resin sites being available until, eventually, the net flux vanishes when equilibrium is reached (there is no gradient of concentration and the complexed sites in the resin are in equilibrium with the bulk metal concentration). Experimental accumulation data in DGT devices deployed in a 10−5 mol·L−1 solution of Cd at pH 4 are reported in Figure 1, which also depicts (see the straight blue line in the figure) the expected Cd accumulations based on the perfect sink model.
(using the parameters listed in SI Table SI.1). This line agrees reasonably well with the experimental values, taking into account that no parameter was fitted. The curve shows a typical saturation-type behavior: for short deployment times, a quasilinear accumulation is observed; at intermediate times there is a decrease of the slope and for long enough times a constant accumulation is finally achieved. Agreement between calculations and experimental data of Figure 1 is almost perfect when a small increase (ca. 0.2 log units) in the resin protonation constants (with respect to literature values) is introduced in the chemical model. However, the influence of this small uncertainty becomes negligible at higher pH values. The departure from perfect sink behavior can be understood from the inset of Figure 1, which depicts the metal concentration profile inside the DGT sensor (calculated by the numerical simulation model) as a function of the deployment time. As can be seen, the metal concentration inside the resin layer increases relatively fast with time due to the progressive occupation of the finite number of resin sites over time as the deployment proceeds. Alternatively, the effect can be described as a reduction of the effective binding affinity to the resin sites at low pH. In any case, the metal concentration at the resin−gel interface starts to increase, so that the concentration gradient decreases and, thus, the profiles flatten with time as equilibrium between the chelating resin and the bulk metal concentration is approached. A maximum amount of cadmium accumulated in the DGT is reached when the chemical equilibrium with the bulk metal concentration is achieved in the resin layer and there are no gradients of concentration for all species (see SI Section 3 for an explanation of the equilibrium calculations). For simplicity, we label this regime as “bulk-resin equilibrium”. This maximum number of moles, depicted with the red dashed line in Figure 1, decreases as both pH or the metal concentration decrease (for instance, compare the red dashed lines in Figure 1 and SI Figure SI.4). For solutions containing metal only, deviations of the DGT from the perfect sink model will depend on the deployment time, pH and metal concentration. Figure 2 illustrates these effects by plotting the ratio n/nSS vs. pH, total metal concentration and deployment time. The ratio n/nSS is calculated as the Cd moles actually accumulated in the DGT divided by the moles calculated with eq 5 for the steady-state model. In these figures, the concentrations of cadmium are 2.8 × 10−8 mol·L−1 (Figure 2a), 10−5 mol·L−1 (Figure 2b), and 10−3 mol·L−1 (Figure 2c). Simulation results are represented by continuous lines, whereas experimental measurements (from this work and from literature 6) are depicted as markers. The good agreement between simulation and experimental data for the different concentrations and deployment times depicted in Figure 2 supports, once again, the accuracy of the present simulation model. This fact is particularly remarkable, taking into account that no model parameters were fitted in the simulations. At low pH, the observed accumulation lies below the value expected from the perfect sink behavior (n/nSS < 1). In these conditions, the proton concentration is high, causing a strong competition with the metal for the binding sites of the resin. As pH increases, the ratio n/nSS for the curves of Figure 2a and b increases up to 1 indicating that in this case, the metal arrives and gets bound to the resin under diffusion-limited conditions along the entire deployment time. This increase (with respect to lower pH values) also indicates that saturation of the total
Figure 1. Moles of Cd accumulated by DGT at pH 4 from a solution with 10−5 mol·L−1 Cd. The inset represents the metal concentration profiles (numerical simulation) for different deployment times: 5, 50, and 150 h. Black line: theoretical accumulation predicted by numerical simulation. Blue line: predicted accumulation if the DGT is considered as a perfect sink (eq 5). Red dashed line: moles of Cd accumulated by DGT in bulk-resin equilibrium conditions (calculated from the chemical binding model of the resin sites, as detailed in Section 3 of the SI). Markers: experimental measurements (at least 2 replicates) with standard deviation indicated by the error bars. See SI Table SI.1 for the parameters.
Equation 5 predicts an indefinite linear accumulation with time. In contrast, experimental values at pH 4 show an asymptotic behavior in clear divergence from the blue line corresponding to eq 5 indicating that these DGT sensors do not work as a perfect sink after a few hours due to the proton competition effects at pH 4 (4% difference between the experimental accumulations and the linear expectations at 24 h deployment increasing up to 18% at 48 h; 20% difference between linear and numerical simulation at 20 h). If eq 5 was used to deduce the metal concentration in solution, the result would underestimate this concentration with an error that will increase as time increases. The departure from linear accumulation in DGT at low pH has previously been reported in the bibliography (see e.g., Gimpel et al.20 and Zhang and Davison6). These authors consider that a pH above 5 is required for an accurate DGT Cd measurement. The black continuous line depicted in Figure 1 stands for the expected Cd accumulation calculated with the numerical simulation of the model described in the previous section 10440
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arriving gets bound to the resin, as time increases, the free metal concentration in the resin domain rises due to the decrease in the amount of available resin sites resulting from occupation by protons and metal ions and, therefore, the flux departs from the constant steady-state value. Curves in Figure 2a almost superimpose to those of Figure 2b indicating a strikingly small dependence of n/nSS on the bulk metal concentration at a given pH. Actually, the bulk metal concentration increases from Figure 2a to Figure 2b leading to an increase of the metal accumulation, n, in Figure 2b, but also to an increase of nSS, so that n/nSS remains almost constant. A different situation arises in presence of a very high metal concentration (Figure 2c) (industrial wastewaters and mine tailings17,18). The experimental accumulation at long times (5 and 8 days in Figure 2c) could not approach the value n/nSS =1 at high pH indicating that now, complete saturation of the resin with metal ions takes place. Some generalizations can be deduced from Figure 2: for example, for 2 h of deployment, a ratio n/nSS = 1 is reached above pH 5. This is observed independently of the metal concentration (compare the red lines in Figure 2a−c). At higher deployment times, the adequate pH range for the measurements is shifted to higher values. For instance, at a deployment time of 5 days (or 8 days), the DGT measurements approach the perfect sink value above pH 6, (Figure 2ab). The effect of proton competition on cadmium accumulation described here can be quantitatively extended to other cations, provided that the corresponding thermodynamic and diffusive parameters are available. Binding constants and stoichiometries for the metal-proton-Chelex system can be found, for example, in the works of Pesavento and co-workers21,22,24 for a number of metals such as Zn(II), Pb(II), Fe(III), Cu(II), Ni(II), and Mn(II). Note that Zn2+ and Cd2+ ions show almost the same diffusion coefficient, stoichiometric ratios and binding constants with Chelex21 so that the model simulation results shown here would, in principle, also hold for Zn(II) quite accurately. Cu(II) binds more strongly to the resin sites, and, therefore, the influence of pH should be weaker. On the other hand, Mn(II) shows a weaker binding to the resin sites and, therefore, departures from linear accumulation should appear at higher pH. Competition effects with major cations might also hinder the accumulation of trace metals by the chelating resin. Monovalent major cations such as Na+ and K+ show low binding affinity for Chelex, so that their competition effects are expected to be weak. Divalent cations (Ca2+, Mg2+) show higher binding affinities than monovalent ones, but still weaker than those of heavy metal cations. Several examples of the influence of major ions have been reported in the literature.18,27,28 4.2. Impact of the Concentration of a High Affinity Ligand on the DGT Accumulation. Parallel to Figure 1, Figure 3 gathers the Cd accumulations in DGT devices deployed in Cd-NTA systems at three NTA concentrations: 2 × 10−5 mol·L−1 (Figure 3a), 1.8 × 10−3 mol·L−1 (Figure 3b) and 8 × 10−3 mol·L−1 (Figure 3c), all of them at pH 6 and a total cadmium concentration of 10−5 mol·L−1. Assuming labile behavior of the system, in agreement with previous results,23,29 the accumulation corresponding to the steady state regime at any time is given by
Figure 2. Effect of pH and deployment time on DGT measurements, assessed by the ratio n/nSS, for different Cd concentrations: 2.7 × 10−8 mol·L−1 (Figure 2a)), 10−5 mol·L−1 (Figure 2b)) and 10−3 mol·L−1 (Figure 2c)). Lines: theoretical accumulations predicted by numerical simulation for different times, 2 h (red line), 1 day (black line), 5 days (green line), and 8 days (blue line). Markers: experimental measurements at 2 h from Zhang and Davison6 (red symbols), and experimental data (at least two replicates) from this work (blue and green symbols for 5 and 8 days, respectively), with standard deviation smaller than the size of the marker. See SI Table SI.1 for values of other parameters.
number of resin sites with M was not responsible for the low accumulations at low pH. Instead, in the rising part of the curves of Figure 2a and b, a non-null metal concentration at the resin/gel interface is responsible for the lower accumulation in comparison to diffusion-limited conditions. Notice in Figure 2a and b that, for a fixed pH, n/nSS decreases as the deployment time increases. Even though at short times most of the metal
nSS = 10441
* + DCdNTA cCdNTA * * + DCdNTA 2cCdNTA DCdcCd 2 g
At
(6)
dx.doi.org/10.1021/es400609y | Environ. Sci. Technol. 2013, 47, 10438−10445
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bending of the curve) after a short deployment time (8 h for the highest NTA concentration), whereas at the lowest NTA concentration (Figure 3a), the accumulation is linear up to 7 h. The accumulation value for the bulk-resin equilibrium regime (red dashed line) decreases as the concentration of NTA increases, indicating that the ligand competes with the resin for the binding of metal. It can be observed that, for a given total Cd concentration, an increase in the ligand concentration leads to an increase in the curvature of the accumulation (i.e., sooner departure from perfect sink behavior). To illustrate the simultaneous influence of the ligand concentration and the pH in the DGT accumulation, the ratio n/nSS is plotted in Figure 4 for a total cadmium concentration of 10−5 mol·L−1.
Figure 3. Moles of cadmium accumulated by DGT sensors at pH 6 in presence of a total Cd concentration of 10−5 mol·L−1 and three NTA concentrations: (a) 2 × 10−5 mol·L−1; (b) 1.8 × 10−3 mol·L−1; (c) 8 × 10−3 mol·L−1. Black line: theoretical accumulation predicted by numerical simulation. Blue line: predicted accumulation if the DGT is considered as a perfect sink (eq 6). Red dashed line: moles of Cd that the DGT sensors accumulate in bulk-resin equilibrium conditions (see Section 3 of the SI for details). Markers: experimental measurements. See SI Table SI.2 for the model parameters.
Figure 4. . Effect of pH and ligand properties on DGT measurements, assessed by the ratio n/nSS, in immersion solutions of 10−5 mol·L−1 total cadmium concentration after 10 h of deployment. Pattern (see legend) shows the theoretical ratio predicted by numerical simulation. Orange circles: experimental measurements. Parameters in SI Table SI.2. (a) effect of NTA concentration and (b) in terms of the effective stability constant of the complex (K′).
where DCdNTA = 0.7 × DCd30 and DCdNTA2 =0.7 × DCdNTA. Equation 6 should now be used instead of eq 5 for the steady state regime. Figure 3 also shows the simulation results of Cd accumulation (black line), the maximum accumulation corresponding to equilibrium with bulk Cd concentration (calculated as detailed in SI, red dashed line) and the number of moles accumulated assuming perfect sink behavior (blue line). As can be observed, the simulation model again reproduces with good accuracy the experimental data in the three conditions. For the two highest NTA concentrations (Figure 3b and c), the results show a saturation-type behavior (i.e.,
Each pattern of the contour plot corresponds to a fixed range of n/nSS values. The filling pattern of the orange circles depicts the experimental values of n/nSS. The agreement between experimental data and modeling results is acceptable, which validates the chemical model used in this work also in presence of ligand. It is arbitrarily defined that perfect sink behavior is fulfilled for n/nSS ratios larger than 0.95, which is represented by the 10442
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these sites in this water with 0.5 mg of fulvic acid per liter leads to K′ values lower than 0, so for 10 h of deployment, this model predicts (without explicit consideration of the heterogeneity of the mixture of ligands34) a linear accumulation regime. 4.3. Linear or Nonlinear Regime? In order to verify whether the DGT sensor is working in the linear regime in real sample conditions, we propose a simultaneous deployment of two different sensors: one with twice the resin mass of the other. Three different cases can occur (see Figure 5):
black area in Figure 4. Linear accumulation-time plots are obtained at pH > 5 for NTA concentrations lower than 10−5 mol·L−1, after 10 h deployment. If the ligand concentration is lower than 10−6 mol·L−1 (i.e., much lower than the total Cd concentration), the ligand has no effect on the DGT accumulation, and the results revert to those in absence of ligand, that is, only the pH affects the accumulation. Accumulation at pH > 8 deviates from perfect sink behavior at ligand concentrations higher than 10−3 mol·L−1. Model calculations (see SI Figure SI.5) indicate that these conclusions can be safely extrapolated to lower Cd concentrations (closer to those relevant in most actual aquatic systems). In fact, as discussed above regarding the results shown in Figure 2a and b, the ratios n/nSS at a given ligand concentration are rather insensitive to the total amount of metal (in conditions far below the complete resin saturation). The linear operation regime of DGT is shifted toward higher pH and lower ligand concentrations ranges for longer deployment times, which might result relevant even in waters with very low metal concentrations. For instance, at a deployment time of 8 days (SI Figure SI.6), the DGT measurements approach the perfect sink value only above pH 6, depending also on the NTA concentration. E.g.: pH ≥ 6 for NTA concentrations lower than 10−6 mol·L−1, pH ≥ 7 for NTA concentrations lower than 10−5 mol·L−1, pH above 8 for NTA concentrations lower than 10−4 mol·L−1, etc. Figure 4a can be used to locate the linear operation regime of the DGT technique for other Cd complexes whenever the diffusion coefficient of these complexes is similar to the CdNTA species (DML = 0.7 DM, a typical ratio for small ligands). In this case, extension of Figure 4a can be simply achieved by replacing the ordinate axis with the effective stability constant of the complex K′ (ratio between the concentrations of complexed and free metal). The resulting figure is depicted as Figure 4b, which indicates that the perturbation of the perfect sink behavior in 10 h of deployment time is negligible above pH 5 or pH 7 for low (log K′
