ISIDORE, a Probe for In Situ Trace Metal Speciation Based on the Donnan Membrane Technique and Electrochemical Detection Part 2: Cd and Pb Measurements during the Accumulation Time of the Donnan Membrane Technique

The Donnan membrane technique (DMT), in which a synthetic or natural solution (the “donor”) is separated from a ligand-free solution (the “acceptor”) by a cation-exchange membrane, is a recognized technique for measuring the concentration of a free metal ion in situ, with coupling to electrochemical detection allowing for the quantification of the free metal ion directly on site. However, the use of the DMT requires waiting for the free metal ion equilibrium between the donor and the acceptor solution. In this paper, we investigated the possibility of using the kinetic information and showed that non-equilibrium experimental calibrations of Cd and Pb with the ISIDORE probe could be used to measure free metal concentrations under conditions of membrane-controlled diffusion transport. The application of this dynamic approach made it possible to successfully determine the concentration of free Cd in synthetic and natural river samples. Furthermore, it was found that the determination of free Cd from the slope was not affected by the Ca concentration ratio between the acceptor and donor solution, as opposed to the traditional approach based on Donnan equilibrium. This ISIDORE probe appears to be a promising tool for determining free metal ions in natural samples.


Introduction
The chemical forms of dissolved metals are mainly dependent on organic ligands that may strongly modify their bioavailability [1]. Therefore, different approaches have been proposed to determine metal speciation in natural samples. Some approaches involve the deployment of in situ exposure devices, such as a diffusive gradient in thin film (DGT) [2], permeation liquid membrane (PLM) [3], or the Donnan membrane technique (DMT) [4]. These devices, which accumulate metals after appropriate exposure in the field, are generally collected for measurement in the laboratory by inductively coupled plasma either with mass spectrometry (ICP-MS) or optical emission spectrometry (ICP-OES) detection. Other approaches involve the use of in situ measurements built on the hyphenation of a separation technique such as a gel-integrated microelectrode (GIME) [5,6] or a permeation liquid membrane (PLM) [7] hyphenated with an electrochemical detection system. Electrochemical techniques have also demonstrated their suitability for the in situ analysis of metal speciation with minimal sample preparation, reducing the risk of sample contamination and, consequently, the risk of speciation change [8]. Thus, direct in situ measurements such as the Absence of Gradient and Nernstian Equilibrium Stripping The average plateau value was calculated from the average of all plateau points, while the slope value was calculated by keeping the points recording from 0 h 31 min to 2 h 34 min for Cd and from 1 h 16 min to 4 h 22 min for Pb, corresponding to the linear accumulation of free metals in the DMT (Figure 1). For both metals, good linearity with correlation factors larger than 0.99 was obtained during the accumulation phase, indicating that the flux of metal ions across the membrane is constant and opening up the possibility of using the slope as dynamic information (Figure 1).
This experiment was repeated for the four concentrations of Cd and Pb. For each concentration, the slope and plateau values were determined and plotted against the free ion concentration in the donor estimated by Visual Minteq (Figure 2). As expected, the metal ion flux depends on the concentration of free metal in the donor, with higher The average plateau value was calculated from the average of all plateau points, while the slope value was calculated by keeping the points recording from 0 h 31 min to 2 h 34 min for Cd and from 1 h 16 min to 4 h 22 min for Pb, corresponding to the linear accumulation of free metals in the DMT (Figure 1). For both metals, good linearity with correlation factors larger than 0.99 was obtained during the accumulation phase, indicating that the flux of metal ions across the membrane is constant and opening up the possibility of using the slope as dynamic information (Figure 1).
This experiment was repeated for the four concentrations of Cd and Pb. For each concentration, the slope and plateau values were determined and plotted against the free ion concentration in the donor estimated by Visual Minteq (Figure 2). As expected, the metal ion flux depends on the concentration of free metal in the donor, with higher concentrations resulting in higher fluxes. Thus, for both metals, the slope value of accumulation increases linearly with the free ion concentration in the donor, suggesting that this value can be used for calibration.

Behaviour of Cd and Pb in the Membrane
The behaviour of the two metal ions is quite different since the plateau is reached after approximately 5 h for Cd but requires more than 10 h for Pb ( Figure 1). In order to understand the difference in behaviour between Cd and Pb, we sought to determine whether the diffusion of the free metals across the membrane was controlled by solution diffusion or diffusion in the membrane. The charged membrane constitutes a Donnan phase where the metal ion concentrations will be higher than in the two adjacent solutions (donor and acceptor). Furthermore, as these solutions are kept well mixed by continuous circulation, the thicknesses of the inner and outer diffusion layers are fixed after a short initial transient time. Finally, as the electrolyte concentration is assumed to be equal in the acceptor and donor, there is no electrostatic potential gradient in the membrane, and ion transport between the solution and the membrane will be controlled by the diffusion layer at the membrane interface.
The problem can be formulated as two diffusion layers (one on the acceptor side and one on the donor side) separated by a negatively charged membrane that can be crossed by cationic species. From a mathematical point of view, this is a complex problem described by a set of differential equations varying in time and space. The two transport equations in the solution are similar, simplifying the problem somewhat, and can be further simplified if one type of transport is clearly dominant over the other. The two types of transport are called membrane-controlled or solution-controlled diffusion.
and membrane diffusion-controlled fluxes (Equation (3)): where Ci,tot,acc and Ci,tot,don are the total concentrations of ion i in the acceptor and donor solutions, respectively, while Ci,ac and Ci,don are the concentration of the free ion i in the

Behaviour of Cd and Pb in the Membrane
The behaviour of the two metal ions is quite different since the plateau is reached after approximately 5 h for Cd but requires more than 10 h for Pb ( Figure 1). In order to understand the difference in behaviour between Cd and Pb, we sought to determine whether the diffusion of the free metals across the membrane was controlled by solution diffusion or diffusion in the membrane. The charged membrane constitutes a Donnan phase where the metal ion concentrations will be higher than in the two adjacent solutions (donor and acceptor). Furthermore, as these solutions are kept well mixed by continuous circulation, the thicknesses of the inner and outer diffusion layers are fixed after a short initial transient time. Finally, as the electrolyte concentration is assumed to be equal in the acceptor and donor, there is no electrostatic potential gradient in the membrane, and ion transport between the solution and the membrane will be controlled by the diffusion layer at the membrane interface.
The problem can be formulated as two diffusion layers (one on the acceptor side and one on the donor side) separated by a negatively charged membrane that can be crossed by cationic species. From a mathematical point of view, this is a complex problem described by a set of differential equations varying in time and space. The two transport equations in the solution are similar, simplifying the problem somewhat, and can be further simplified if one type of transport is clearly dominant over the other. The two types of transport are called membrane-controlled or solution-controlled diffusion.
Weng et al. presented a detailed mathematical formulation of the problem and a detailed numerical solution as well as an approximated analytical solution to solution diffusion control (valid if the complexation in the donor and acceptor are equal) (Equation (2)) [30]: and membrane diffusion-controlled fluxes (Equation (3)): where C i,tot,acc and C i,tot,don are the total concentrations of ion i in the acceptor and donor solutions, respectively, while C i,ac and C i,don are the concentration of the free ion i in the acceptor and donor solutions, t is the time (s), A e is the effective surface area of the membrane, D i is the diffusion coefficient of ion i in water, D i,m is the apparent diffusion coefficient of ion i in the membrane (D i,m = D i /λ i m 2 ·s −1 with λ i the tortuosity factor for ion i in the membrane), B is the Boltzmann factor, δ is the thickness of diffusion layer in solution, δ m is the thickness of the membrane, V acc is the volume of the acceptor solution, and P i,ac and P i,don are the complexation factors in the acceptor and donor solutions. In order to understand whether there is solution diffusion control or membrane diffusion control for our systems, we performed calibration curves for Cd and Pb. When the transport is controlled by solution diffusion (Equation (2)), all parameters are previously estimated, respectively, D Cd (7.3 × 10 −10 m 2 ·s −1 ) and D Pb = 8.1 × 10 −10 m 2 ·s −1 ) [32], V acc (7 × 10 −6 m 2 ), and δ = 1 × 10 −4 m in our previous work [27], and finally A e = 2.74 × 10 −4 m 2 which corresponds to 20% of the membrane surface, as suggested by Weng 2005 [30]. Using these values, we obtained a prediction for the time to reach 95% of equilibrium concentration (t95%) of 2 h 55 min for Cd and 2 h 33 min for Pb, which is much shorter than the experimental results. Indeed, using these parameter values, Equation (2) does not provide a good fit to the experimental curves (Cd Figure 3A and Pb Figure 3C), suggesting that Cd and Pb transport are not controlled by solution diffusion.
Molecules 2023, 28, x FOR PEER REVIEW 5 of 12 acceptor and donor solutions, t is the time (s), Ae is the effective surface area of the membrane, Di is the diffusion coefficient of ion i in water, Di,m is the apparent diffusion coefficient of ion i in the membrane (Di,m = Di/λi m 2 ·s −1 with λi the tortuosity factor for ion i in the membrane), B is the Boltzmann factor, δ is the thickness of diffusion layer in solution, δm is the thickness of the membrane, Vacc is the volume of the acceptor solution, and Pi,ac and Pi,don are the complexation factors in the acceptor and donor solutions. In order to understand whether there is solution diffusion control or membrane diffusion control for our systems, we performed calibration curves for Cd and Pb. When the transport is controlled by solution diffusion (Equation (2)), all parameters are previously estimated, respectively, DCd (7.3 × 10 −10 m 2 ·s −1 ) and DPb = 8.1 × 10 −10 m 2 ·s −1 ) [32], Vacc (7 × 10 −6 m 2 ), and δ = 1 × 10 −4 m in our previous work [27], and finally Ae = 2.74 × 10 −4 m 2 which corresponds to 20% of the membrane surface, as suggested by Weng 2005 [30]. Using these values, we obtained a prediction for the time to reach 95% of equilibrium concentration (t95%) of 2 h 55 min for Cd and 2 h 33 min for Pb, which is much shorter than the experimental results. Indeed, using these parameter values, Equation (2) [33]. In our case, the best estimate for B is a value of 13.7; however, this is a rough estimate as our electrolyte is a mixture of 3 mM Ca(NO 3 ) 2 and 5 mM acetate buffer for which the calculation of a Donnan factor is quite involved. The best description of the Cd and Pb transport data for the four concentrations was obtained for a P i,ac of 2.75 and 8 (Cd Figure 3B, Pb Figure 3D), leading to prediction times to reach equilibrium (t95%) at 4 h 22 min and 11 h 27 min, which are in good agreement with the experimentally determined times. According to Weng et al., there is no significant effect of the ligands on the equilibrium time when P i is relatively small (<50) [30]. Thus, it is clear that both Cd and Pb transport is controlled by diffusion in the membrane.
Membrane diffusion control provides a simple dynamic equation describing the accumulation of metal ions in the acceptor over time since only free metal ions contribute to transport and accumulation. For trace metal speciation, membrane diffusion control is preferable to solution diffusion control because of its simplicity since, for all practical purposes, the DMT functions as an ion-selective electrode, where only the free metal concentration is relevant during both calibration and sample measurements. On the other hand, if solution diffusion control is the control mechanism, Equation (2) must be modified to take into account the contribution of labile complexes to transport and the impact of the different diffusion coefficients of metal complexes in the transport and in the thickness of the diffusion layer as described by Domingos et al. for the Permeation Liquid Membranes (PLM) [18].
Although metal transport by diffusion in solution or in the membrane can be approximated by models, the fit is not perfect, especially for higher metal concentrations. This is probably due to an incomplete physico-chemical description of the membrane, namely the Donnan effect and its impact on transport across the membrane and the fact that in our device, the outer and inner geometries are quite different, which can impact the solution transport. A better theoretical description of this transport is therefore required, for example, to explain the differences between Cd and Pb ions.

Analysis of Synthetic and Natural Samples
Finally, the Isidore probe was applied to synthetic and natural Cd-doped samples. Figure 4 shows the free Cd concentrations determined from the plateau (Donnan equilibrium) and the slope (dynamic accumulation) for different samples. As expected, the calibration curve is close to the y = x line, which confirms the idea that it is possible to cut the measurement time in half using the slope instead of the plateau. However, the results of the river samples show differences in free Cd concentrations depending on the determination method, slope or plateau (Table 1). This behaviour is particularly marked for the synthetic river samples, which show an overestimation between 34 and 64% ( Figure 5 red triangles). Table 1 shows that this overestimation of the calculated equilibrium concentration is not linked to the presence of fulvic acids. Therefore, this overestimation may involve the behaviour of Ca during the experiment. Indeed, during the calibration of the ISIDORE probe, the composition of the donor and acceptor solutions are identical (3 mM), and therefore the Ca concentration in the donor and acceptor solutions is in equilibrium. In the case of synthetic and natural waters, we noticed an imbalance in the Ca composition, with ratios [Ca 2+ ] don /[Ca 2+ ] acc between 0.4 and 0.7. Similar ratios are observed for natural samples, but the effects are probably attenuated due to the lower concentrations of free Cd.      In the DMT system, the presence of a multivalent cation in the background solution (usually, Ca 2+ ) is necessary to compete with the target metal for binding to the membrane and to ensure sufficient transport of the target cation through the membrane [25]. However, according to Equation (1), the concentration of Cd measured in the acceptor solution at Donnan equilibrium is equal to that measured in the donor solution only when the concentration of Ca is the same on both sides [4]. The Cd concentration determined from the plateau was therefore corrected by the ratio [Ca 2+ ] don /[Ca 2+ ] acc . Figure 5 shows the Cd concentrations determined from the slope versus the Cd concentrations determined from the plateau after correction according to Equation (1). A good correlation is obtained between the two methods (r 2 = 0.92) regardless of the type of samples. These results show that the Ca concentration is an important parameter to consider when determining the free metal concentration at equilibrium, but it does not seem to affect the accumulation rate of Cd in the acceptor solution. Determining the free ion metal during the accumulation time appears to be an interesting alternative to the Donnan equilibration method because this approach is both faster and not affected by the Ca concentrations in the donor and acceptor solutions. ]plateau for the different samples: calibration, Cd-doped synthetic river with fulvic acids at 5 mg/L (4 replicates) or without fulvic acids (3 replicates), and natural samples doped in Cd (Uzein river-4 replicates) or naturally contaminated in Cd (Riu Mort river-1 replicate). Samples were spiked with 89 nM Cd except for the Riu Mort sample, which was naturally contaminated with Cd (36 nM). The analytical conditions are the same as in Figure 1. (1) for the different samples: calibration, Cd-doped synthetic river with fulvic acids at 5 mg/L or without fulvic acids, and natural samples doped in Cd (Uzein river) or naturally contaminated in Cd (Riu Mort river). Samples were spiked with 89 nM Cd except for the Riu Mort sample, which was naturally contaminated with Cd (36 nM). The analytical conditions are the same as in Figure 1.

Synthetic River Natural Samples Cd
Cd + FA Uzein + Cd Riu Mort
Ultra-pure milli-Q water (resistivity 18.2 MΩ cm) was employed in all the experiments. A stock solution of acetate buffer (0.1 M, pH 4.6) was prepared by mixing appropriate amounts of CH 3 COOH and CH 3 COONa. A stock solution of synthetic river water was prepared as follows: 10 mM NaHCO 3 , 1 mM MgSO 4 , 2 mM CaCl 2 , and 0.5 mM KNO 3 , which corresponds to an ionic strength of 19 mM and a pH of 7.5 ± 0.2.
The cation exchange membrane (VWR International, Radnor, PA, USA) used in this work has a matrix of polystyrene/divinylbenzene with sulphonic acid groups that are fully deprotonated above pH 2. The ion-exchange capacity is 0.8 meq g −1 , the thickness of the membrane δ m is 1.6 × 10 −4 m, and its surface area is 5.3 cm 2 [4].

Equipment
Stripping Chronopotentiometry (SCP) measurements were performed with an Eco Chemie µ-Autolab III potentiostat controlled by the GPES 4.9 (Eco Chemie) software package. Temperature and pH were checked with a multi-parameter analyser (WTW 340i). The flow-cell (DropSens) was modified to fit the homemade screen-printed sensor (SPE). The SPE was prepared in the laboratory by means of a carbon commercial ink (Electrodag ® PF 407A) for the working and counter electrodes and an Ag/AgCl 3:2 ink (Electrodag ® 6037 SS) for the pseudo-reference electrode [27]. Prior to any electrochemical measurements, a thin layer of mercury was deposited onto the surface of the screen-printed electrode. The Hg deposition on the working surface area was carried out using an acetate buffer solution (0.1 M, pH = 4.6) doped in Hg at 0.83 mM. ICP-MS measurements were performed with an Agilent ICP-MS (7500 series, Agilent Technology, Santa Clara, CA, USA) and Ca concentration was measured by an iCAP 6000 series (Thermo Scientific™, Waltham, MA, USA).

ISIDORE Probe
The design of the ISIDORE probe measurement is explained in detail by Parat and Pinheiro [27]. Briefly, a DMT cell containing the acceptor solution is immersed in a donor solution, i.e., river water. The acceptor solution, in which the free metal ions present in the donor solution will accumulate, is connected to a flow-cell in which an SPE is placed. The circulation of the solution from the DMT to the measuring cell is achieved by means of a peristaltic pump (Labcraft Hydris 05) ( Figure 6).
Before analysis, the DMT membranes were prepared by shaking them several times in succession with EDTA (0.1 M) to remove trace metal impurities, then 1 M Ca(NO 3 ) 2 and 3 mM Ca(NO 3 ) 2 , which is the concentration of the background electrolyte solution used in the experiment. In the last step, the pH is controlled to ensure no more protons are released.

ISIDORE Probe
The design of the ISIDORE probe measurement is explained in detail by Parat and Pinheiro [27]. Briefly, a DMT cell containing the acceptor solution is immersed in a donor solution, i.e., river water. The acceptor solution, in which the free metal ions present in the donor solution will accumulate, is connected to a flow-cell in which an SPE is placed. The circulation of the solution from the DMT to the measuring cell is achieved by means of a peristaltic pump (Labcraft Hydris 05) ( Figure 6).  [27].
Before analysis, the DMT membranes were prepared by shaking them several times in succession with EDTA (0.1 M) to remove trace metal impurities, then 1 M Ca(NO3)2 and 3 mM Ca(NO3)2, which is the concentration of the background electrolyte solution used in the experiment. In the last step, the pH is controlled to ensure no more protons are released.
For all the experiments described below, the acceptor solution is composed of a mixture of 3 mM of Ca(NO3)2 solution and 5 mM acetate buffer in order to maintain a constant pH (4.6 in this study) during the electrodeposition of the metal on the surface of the electrode [34] and also to avoid overlap of Cd and Pb peaks [27]. For all the experiments described below, the acceptor solution is composed of a mixture of 3 mM of Ca(NO 3 ) 2 solution and 5 mM acetate buffer in order to maintain a constant pH (4.6 in this study) during the electrodeposition of the metal on the surface of the electrode [34] and also to avoid overlap of Cd and Pb peaks [27].
The ISIDORE probe was calibrated for four different concentrations of Cd and Pb, corresponding to free Cd concentrations of 39, 78, 117, and 157 nM and free Pb concentrations of 14, 28, 43, and 56 nM. The assembly of a clean DMT and a new SPE was performed for each concentration. The background solution in both donor and acceptor solutions was 3 mM Ca(NO 3 ) 2 buffered at pH 4.6 with 5 mM of acetate buffer. The acetate buffer was used to keep the pH constant on both sides throughout the experiment. As there were no ligands in the acceptor solution, the concentration of free ions in the donor solution corresponds to that measured in the acceptor solution. The donor solution was kept under stirring throughout the experiment.
Electrochemical detection was carried out in two steps, a deposition step followed by a stripping step. In the first step, the deposition potential of −1.6 V was maintained for 120 s under a solution flow of 2 mL·min −1 , after which the flow was stopped for 10 s and the potential maintained at −1.6 V. Then, in the stripping step, the potential signal was measured as a function of time under an applied stripping current of I s = 10 µA.

Natural Samples
Two freshwater rivers were used. The first river is the "Luy de Béarn", a 76.6 km long French river that starts at Andoins (Pyrénées-Altantiques, southwestern France) and ends at Gaujacq, where the "Luy de Béarn" merges with the Adour. For this river, named here the "Uzein River", two points were sampled, one upstream and one downstream of the Uzein wastewater treatment plant north of Pau (France). The second river selected was the "Riou Mort", a small river (21.1 km) tributary of the "Lot" (the second longest river in France) in the Massif Central. Due to the presence of the Decazeville coalfield, the "Riou-Mort" river is naturally contaminated with Cd and Zn [35]. Sample analyses are presented in Table 2.

Conclusions
In this study, the possibility of determining free ion concentrations with the Donnan membrane technique was investigated in order to reduce the measurement time. Comparisons of the concentration determined at Donnan equilibrium (traditional method, 6 h) with that calculated during accumulation showed that the free ion concentration could be estimated with the ISIDORE probe after only 3 h of accumulation for the two metals, Cd and Pb. Comparison between the theoretical and experimental curves showed that Cd and Pb transport was both controlled by diffusion in the membrane. The application of the ISIDORE probe on synthetic and natural river samples showed a good correlation between the two approaches, dynamic and equilibrium, and revealed that special attention should be paid to the Ca concentration when determining the free Cd concentration from the plateau.