Assessment of trace metal binding kinetics in the resin phase of diffusive gradients in thin films

The dynamic technique of diffusive gradients in thin films (DGT), that measures metal speciation in situ, has found wide environmental application. Simple interpretation of the metal accumulation in terms of a solution concentration has assumed that trace metals do not penetrate beyond the surface of the binding layer, but penetration, although theoretically discussed has not yet been directly measured. Multiple binding layers were used to enable analysis of different depths of a DGT binding phase (Chelex-100 or iminodiacetate resins). In simple metal solution (no ligand) at pH 7, metal penetration to the back layer was low and similar for all metals. However, at lower pH up to 42% of an individual metal accumulated in the back resin layer. This was most noticeable for Mn at pH 4 and 5, but Cd and Co were also affected at pH 4. These results were consistent with rate limited binding, particularly for Mn. A kinetic model successfully fitted the data and allowed derivation of a binding rate constant and the mean distance that metals penetrate into a resin gel (λ_M). Only for Mn, Co and Cd were experimentally derived λ_M values greater than the diameter of a Chelex-100 resin bead. For most situations, then, the penetration into the binding layer is negligible and binding of trace metal ions can be regarded as instantaneous, validating the simple use and interpretation of DGT. For weakly binding metals at low pH the slower binding allows penetration, which may affect the DGT measurement.     

Performance characteristics of suspended particulate reagent-iminodiacetate as a binding agent for diffusive gradients in thin films

The performance characteristics of an alternative binding agent, suspended particulate reagent-iminodiacetate (SPR-IDA), for use with DGT methodology were investigated. The parameters investigated during this study included gel hydration, blank levels, elution factor (f_e), capacity, the effects of pH on the binding of trace metals by DGT. The novel application of this resin for use as a quantitative standard for laser ablation ICP-MS was also evaluated. To further constrain the results for the SPR-IDA binding agent, parallel experiments were performed using resin gel containing Chelex 100, which has been widely reported in the literature. Hydration results showed that the SPR-IDA resin gel reached a stable dimension and weight within ∼30 min and was dimensionally stable for ≤6 months. The measured DGT blanks for the SPR-IDA resin were 0.0023, 0.15, 0.21, 0.0033 and 0.011 ng disc⁻¹ for Co, Ni, Cu, Cd and Pb, respectively. The elution factor differed for the two resin types with the Chelex 100 recoveries slightly lower than previous reports and the SPR-IDA resin showing on average ∼5-9% better recoveries than DGT containing Chelex 100. The measured capacity of DGT discs containing the SPR-IDA binding agent was 0.26 mg Cd, similar to the calculated value of 0.29 mg Cd, indicating the entire resin layer was available for metal uptake.Both resin types performed equally well when deployed in 1 mM NaNO₃ solutions with DGT measurements of ∼100% of direct solution measurements for Co, Ni and Cd. However, DGT measurements of Cu and Pb systematically decreased with increasing solution pH down to ∼50% of solution values at pH 8.0, due to artifacts resulting from colloid formation during the addition of the metals. This was remedied by adding the metals as dilute salt standards and addition of Mg(NO₃)₂ to eliminate adsorption to the container walls. In the latter experiments, DGT measured concentrations of Co, Ni, Cu, Cd and Pb were in agreement with solution concentrations. Deployment of DGT in solutions with increasing concentrations of trace metals yielded linear results, suggesting that quantitative analysis using simplified laser ablation techniques should be possible using this newly characterized SPR-IDA resin gel.     

Re-assessment of chelating ion-exchange resins for trace metal analysis of sea water

The behaviour of the chelating ion-exchange resin Chelex-100 for collection of trace metals from sea water has been studied by anodic stripping voltammetry after acid digestion of the sea water sample and the resin effluent. All the naturally occurring, electrochemically reducible species of Cu, Pb, Cd and Zn are chelated by the resin; this fraction of these metals is regarded as the dissolved fraction. Centrifugation showed that some of the metal liberated by acid digestion is associated with colloidal species. Neither this nor the metal adsorbed on fine particles is affected or removed by the chelating resin.     

Mercury depth profiles in river and marine sediments measured by the diffusive gradients in thin films technique with two different specific resins

The diffusive gradients in thin films technique (DGT) was used to measure depth profiles of mercury in river and marine sediments in situ to a spatial resolution of 0.5 cm. Agarose gel was used as the diffusive gel in the DGT probes. Two different selective resins—Chelex 100 with iminodiacetic groups and Spheron-Thiol with thiol groups incorporated in the polyacrylamide resin gel—were tested. The different capture efficiencies of the two adsorbents enabled the fractions of mercury bound in different species in sediment pore water to be estimated. Mercury concentrations obtained by DGT with Spheron-Thiol resin were very similar to those obtained after centrifugation. This indicates that DGT with Sheron-Thiol resin reports on total dissolved mercury levels. The concentration of mercury measured by DGT with Chelex-100 resin was much lower (by a factor of 5–20) for the same sediment samples. Chelex-100 does not have such a high affinity to mercury as Spheron-Thiol, and so it only reports on the content of labile mercury species, such as inorganic ions and weak complexes. The content of labile mercury species in the river sediment was approximately 20% of the total dissolved mercury in pore water, whereas in marine sediment only 7% of the mercury was present as labile species.     

Performance of the diffusive gradients in thin films technique for measurement of trace metals in low ionic strength freshwaters

A series of experiments were undertaken to investigate the effect of ionic strength and the concentration of free sodium ions in the resin gel on the performance of the diffusive gradients in thin films (DGT) technique. When the free sodium ion concentration in the resin gel was estimated by the time-dependent release into solution, it agreed with a previous estimate. However, equilibration with different volumes of water gave a higher value, suggesting that inherent averaging in the time-dependent release method underestimates the free concentration. DGT measurements of Cu and Cd were made over a wide range of ionic strengths (from 3 μmol l⁻¹ to 0.8 mol l⁻¹). For all the ionic strengths above 100 μmol l⁻¹ there was no significant difference between measurements made by DGT and measurements made directly on the solution using atomic absorption spectroscopy. Below 100 μmol l⁻¹ results were erratic. They did not comply with a theory that predicts high results for DGT based on enhancement of the diffusion coefficient of trace metal cations by counter diffusion of sodium ions. When Cd in solutions with a range of ionic strengths was measured by DGT there was no difference whether the resin gels were in Na or Ca form. Rather than counter diffusion of Na ions, it is suggested that the spurious behaviour at low ionic strength is due to interactions of the trace metals with the diffusion gel when there are insufficient excess cations present.     

Investigation of DGT as a metal speciation technique for municipal wastes and aqueous mine effluents

This paper reports the results of an investigation on the performance of the Diffusive Gradient in Thin Films (DGT) Technique in speciation of metals in aqueous samples of municipal wastes and mine effluents. The DGT was assessed regarding its suitability for in situ determination of metal speciation in municipal wastes and aqueous mine effluents. As the thickness of the diffusive gel layer of the DGT was increased to 0.40, 0.80, and 1.60 mm, a decrease in the amount of accumulated metal mass was observed for most of the metals studied in all the effluent samples. However, the results were different from one field-study site to another. Effect of kinetics also was observed in the amount of accumulated metal mass by the DGT. The computer speciation code, Windermere Humic Aqueous Model (WHAM VI), was used to predict the metal speciation of Cd, Cu, Ni, Pb, Co, and Zn, and WHAM predictions were compared with those of the experimentally determined metal speciation by the DGT technique (free and labile metal ions). This comparison showed good similarities between the theoretically predicted WHAM VI values and the experimentally measured values by DGT. The DGT technique was found to be simple and useful for investigating chemical speciation of trace metals in aqueous samples of municipal wastes and aqueous mine effluents.     

Diffusion characteristics of agarose hydrogel used in diffusive gradients in thin films for measurements of cations and anions

The agarose hydrogel has been increasingly used as a diffusive layer in diffusive gradients in thin films (DGT) measurements. However its diffusive characteristics have not been examined in detail. In this study, the performance of agarose gel was tested in DGT measurements of eight cations (Fe(II), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Pb(II), and Cd(II)) and eight anions (P(V), As(V), Cr(VI), Mo(VI), Sb(V), Se(VI), V(V), and W(VI)). It was found that the thickness of agarose, a key parameter in the calculation of DGT measured concentration, remained unchanged after hydration followed by storage under the following conditions: pH 2–11, ionic strength 0–1.0 M, temperature 4–40 °C, and with the storage time extending to 300 d. Enrichment of cations and repelling of anions were observed in the gel under the ionic strengths of < 2–3 mM and <1 mM (NaNO₃), respectively, which was attributed to the electrostatic interactions of these ions with the fixed negatively charged groups (mainly pyruvate) in the gel. The diffusion coefficients of cations and anions through the agarose gel (plus a PVDF filter membrane) were on average 1.10 ± 0.04 times of the reported diffusion coefficients through the agarose cross-linked polyacrylamide (APA) hydrogel, typically used in DGT technique. The working pH ranges for the agarose gel-assembled DGTs were 4–10 and 5–9 for anions and cations, respectively. The use of agarose gel, either individually or along with different filter membranes, affected the overall diffusion rates of cations and anions. The measured DGT concentrations of cations and anions in filtered natural freshwater and seawater were mostly in line with those measured directly. The results showed that the agarose gel can be used as one of the standard diffusive layers in DGT measurements for a wide range of inorganic and organic analytes.     

Determination of Metal Ions in Natural Waters by Flame-AAS after Preconcentration on a 5-Amino-1,3,4-Thiadiazole-2-Thiol Modified Silica Gel.

ABSTRACT

5-amino-1,3,4-thiadiazole-2-thiol groups attached on a silica gel surface have been used for adsorption of Cd(II), Co(II), Cu(II), Fe(III), Ni(II), Pb(II) and Zn(II) from aqueous solutions. The adsorption capacities for each metal ion were (in mmol.g^?1): Cd(II)= 0.35, Co(II)= 0.10, Cu(II)= 0.15, Fe(III)= 0.20, Hg(II)= 0.46, Ni(II)= 0.16, Pb(II)= 0.13 and Zn(II)= 0.15. The modified silica gel was applied in the preconcentration and quantification of trace level metal ions present in water samples (river, and bog water).     

Application of diffusive gradient in thin films technique (DGT) to measurement of mercury in aquatic systems

The diffusive gradient in thin films (DGT) technique was investigated and used to measure mercury concentration in river water. Mercury ions are covalently bound to amide nitrogen groups of commonly used polyacrylamide, which makes this gel unsuitable as a diffusive medium. In contrast, agarose gel was found as the diffusive gel for mercury measurements. Basic performance tests of agarose DGT verified the applicability of Fick's first law for DGT measurements. Two selective resins, Chelex-100 with iminodiacetic groups and Spheron-Thiol with thiol groups were used. The measured diffusion coefficient in agarose gel was close to that in water. The concentration of mercury in Svitava river measured by DGT with Speron-Thiol resin gel was higher (0.0116 ± 0.0009 μg l⁻¹) than those obtained by Chelex-100 (0.0042 ± 0.0005 μg l⁻¹). Different capture efficiencies of two adsorbents enable to estimate fractions of mercury bonded in different complexes in the river water. The concentrations of mercury found by DGT both Chelex-100 and Speron-Thiol resin gels are much lower than that measured directly in the river water (0.088 ± 0.012 μg l⁻¹). This difference indicates that DGT concerns inorganic ions and labile species only, and that it is not able to include inert organic species and colloids.     

Chelating resins for the concentration of trace elements from sea water and their analytical use in conjunction with atomic absorption spectrophotometry

An investigation has been made of the uptake of trace elements from both distilled water and sea water by the chelating ion-exchange resins Chelex-100 and Permutit S1005. The resins retained the following elements with an efficiency of ca. 100%: Ag, Bi, Cd, Cu, In, Pb, Mo, Ni, rare earths, Re (90% only), Sc, Th, W, V, Y and Zn. Manganese was retained quantitatively only by the Chelex resin. The following elements are removed with 100% efficiency by means of₂N mineral acids: Bi, Cd, Co, Cu, In, Ni, Pb, rare earths, Sc, Th, Y and Zn. Ammonia (4 N) completely removes molybdenum, tungsten, vanadium and rhenium. The resins have been used in conjunction with atomic absorption spectrophotometry for the simultaneous determination of zinc, cadmium, copper, nickel and cobalt in sea waters.     

Use of the diffusive gradients in thin films technique to evaluate (bio)available trace metal concentrations in river water

Concentrations of Cd, Cu, Cr, Pb, Ni and Zn were monitored in the Svitava River (the Czech Republic) during April and September 2005. Total concentrations and total dissolved concentrations were obtained through regular water sampling, and the diffusive gradients in thin films technique (DGT) were used to gain information on the kinetically labile metal concentrations. Each measured concentration was compared with the corresponding average (bio)available concentration calculated from the mass of metal accumulated by the moss species Fontinalis antipyretica. The concentrations of Cd, Pb, Cr and Zn measured using DGT corresponded well with those obtained after the deployment of Fontinalis antipyretica moss bags in the Svitava River, but the concentrations of Cu and Ni did not. The calculated (bio)available Cu concentration correlated well with the total dissolved concentration of Cu, whereas no correlation was found to exist between the concentrations of Ni. Scheme of the Svitava River monitoring station, including the DGT sampling units and Fontinalis antipyretica moss bags Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Simultaneous multi-element analysis for trace metals in sea water by inductively-coupled plasma/atomic emission spectrometry after batch preconcentration on a chelating resin

Batch treatment with Chelex-100 resin was investigated for preconcentration of trace metals in sea water followed by determination by inductively-coupled plasma atomic emission spectrometry. The preconcentration conditions such as resin weight, stirring time, and amount of ammonium acetate buffer solution were carefully examined for effective multi-element preconcentration from sea water. The resin weight could be decreased to 0.5 g (dry weight) for 1 l of sea water, which was much less than that required in the column method, and a preconcentration factor of 100 was achieved. Al, Ti, V, Mn, Fe, Co, Ni, Cu, Zn, Y, Mo, Cd and Pb in sea water were measured with good precision. The detection limits ranged from 6 to 180 ng l^?1. The time required for one sample by the batch method was only 3 h.     

Measuring bioavailable trace metals from freshwater sediments by diffusive gradients in thin films (DGT) in monitoring procedures for quality assessment

An experimental design using passive samplers was set up in our laboratories with the aim of preparing a procedure for the assessment of trace metals bioavailability in freshwater sediments. Trace metal (Cd, Cu, Pb, Ni, and Zn) bioavailability in sediment samples were measured by diffusive gradients in thin films (DGT) devices and compared to those simultaneously extracted (SEM) in 1N HCl with acid-volatile sulfide (AVS). During experiments DGT devices were exposed at various times (from 4 to 336 h) in sediments with different physical and chemical properties and metal content, after equilibration with ambient water (1:2) for 24 h. Trace metal were progressively accumulated in DGT units and after at least 24-48 h metal fluxes became constant. No relation was found between metal available fractions measured by DGTs and total concentrations in sediments or pore waters. On the contrary good relations were found between available metals measured by DGT and metals simultaneously extracted (SEM) in HCl 1N with acid volatile sulfide (AVS).     

Speciation of lead in seawater and river water by using Saccharomyces cerevisiae immobilized in agarose gel as a binding agent in the diffusive gradients in thin films technique

Saccharomyces cerevisiae immobilized in agarose gel is proposed as a binding agent for the diffusive gradients in thin films (DGT) technique for determination of Pb in river water and seawater. DGT samplers were assembled with the proposed binding agent (25-mm disk containing 20%, m/v, S. cerevisiae and 3.0%, m/v, agarose) and a diffusive layer of cellulose (3MM Chr chromatography paper of 25-mm diameter). The effects of some DGT parameters (e.g., immersion time, ionic strength, and pH) were evaluated. Elution of Pb from the binding agent was effectively done with 1.75 mol L(-1) HNO(3). The deployment curve (between 2 and 24 h) was characterized by a significant uptake of Pb (346 ng Pb h(-1)) and good linear regression (R(2) = 0.9757). The experimental results are in excellent agreement with the predicted theoretical curve for mass uptake. Consistent results were found for solutions with ionic strengths of 0.005 mol L(-1) or greater and within a pH range of 4.5-8.5. Interferences from Cu (20:1), Mn (20:1), Fe (20:1), Zn (20:1), Ca (250:1), and Mg (250:1) in Pb retention were negligible. Determination of Pb in spiked river water samples (from the Corumbataí and Piracicaba rivers) performed using the proposed device was in agreement with total dissolved Pb, whereas measurements in seawater suggest that of the various species of Pb present in the samples, only cationic Pb species are adsorbed by the agarose-yeast gel disks. The in situ concentration of Pb obtained at two different sites of the Rio Claro stream (Corumbataí basin) were 1.13 ± 0.01 and 1.34 ± 0.04 μg L(-1). For 72-h deployments, a detection limit of 0.75 μg L(-1) was calculated. The combination of inductively coupled plasma optical emission spectroscopy and in situ deployments of DGT samplers during the 72-h period makes possible the determination of labile Pb in river water.     

Metal speciation measurement by diffusive gradients in thin films technique with different binding phases

Since its invention in the mid-1990s, the diffusive gradients in thin films (DGT) technique has rapidly become one of the most promising in situ sampling techniques for trace metal measurement in natural waters. We investigated here the possibility of using DGT devices with different binding phases to determine different DGT labile fractions of Cd and Cu in laboratory solutions and in natural waters. Several binding phases were studied, including conventional Chelex 100 resin imbedded polyacrylamide hydrogel (Chelex) and several recently developed binding phases, poly(acrylamide-co-acrylic acid) (PAM-PAA) gel, poly(acrylamidoglycolic acid-co-acrylamide) (PAAG-PAM) gel, Whatman P81 cellulose phosphate ion-exchange membrane (P81), and poly(4-styrenesulfonate) (PSS) aqueous solution. Laboratory testing in metal solutions spiked with EDTA or humic acid suggested that all the DGT devices measured only free metal ions and inorganic metal complexes. Upon field testing at both freshwater and seawater sites it was found that the DGT labile metal concentrations measured by different binding phases can be significantly different, suggesting that the DGT labile metal fractions were dependent on binding strength of the binding phase. By designing binding phases that can compete with different natural water complexing ligands to varying extents, it is possible to use these different DGT devices to measure metal speciation in natural waters.     

Solid phase extraction and diffusive gradients in thin films techniques for determination of total and labile concentrations of Cd(II), Cu(II), Ni(II) and Pb(II) in Black Sea water

Total dissolved and labile concentrations of Cd(II), Cu(II), Ni(II) and Pb(II) were determined at six locations of the Bourgas Gulf of the Bulgarian Black Sea coast. Solid phase extraction procedure based on monodisperse, submicrometer silica spheres modified with 3-aminopropyltrimethoxysilane followed by the electrothermal atomic absorption spectrometry (ETAAS) was developed and applied to quantify the total dissolved metal concentrations in sea water. Quantitative sorption of Cd, Cu, Ni and Pb was achieved in the pH range 7.5–8, for 30?min, adsorbed elements were easily eluted with 2?mL 2?mol?L^?1 HNO₃. Since the optimal pH for quantitative sorption coincides with typical pH of Black Sea water (7.9–8.2), on-site pre-concentration of the analytes without any additional treatment was possible. Detection limits achieved for total dissolved metal quantification were: Cd 0.002?µg?L^?1, Cu 0.005?µg?L^?1, Ni 0.03?µg?L^?1, Pb 0.02?µg?L^?1 and relative standard deviations varied from 5–13% for all studied elements (for typical Cd, Cu, Ni and Pb concentrations in Black Sea water). Open pore diffusive gradients in thin films (DGT) technique was employed for in-situ sampling and pre-concentration of the sea water and in combination with ETAAS was used to determine the proportion of dynamic (mobile and kinetically labile) species of Cd(II), Cu(II), Ni(II) and Pb(II) in the sea water. Obtained results showed strong complexation for Cu and Pb with sea water dissolved organic matter. The ratios between DGT-labile and total dissolved concentrations found for Cu(II) and Pb(II) were in the range 0.2–0.4. For Cd and Ni, these ratios varied from 0.6 to 0.8, suggesting higher degree of free and kinetically labile species of these metals in sea water.     

Trace metal accumulation in tissues of sole (Solea senegalensis) and the relationships with the abiotic environment

The distribution patterns and the organ-specific accumulation trends of 10 trace metals (iron, manganese, zinc, copper, chromium, nickel, cobalt, lead, cadmium and silver) and 4 major elements (sodium, potassium, calcium and magnesium) in 10 different tissues (heart, muscle, kidney, stomach, intestine, liver, gill, gonads, white skin and dark skin) of a benthic fish species (Solea senegalensis) from a densely populated coastal area affected by anthropogenic activities, the Bay of Cadiz (SW Spain), have been investigated. High variability of metal concentrations among tissues were found for Ca, Fe, Zn, Cu, Pb and Ag. Factor analysis was applied to study this variability. Five principal components were found explaining the 92.95% of the total variance and similarities in behavioural patterns of bioaccumulation were described. They associated Mg, Cr, Ni and Mn to intestine and stomach tissues (PC1), Ag, Cu and Cd to liver (PC2), Zn, K and Co to gonads (PC3), Na, Fe and Pb to gill, heart and kidney tissues (PC4) and Ca, Pb and Mn to gill and dark skin (PC5). The metallic concentration in the sediment and water was also studied. The pollution in this area was found moderate with outstanding values of Zn, Cu and Pb (average values of 139, 50.4 and 75.6?mg?kg^?1, respectively) in sediment and dissolved Cu (average value of 2.5?µg?L^?1). Metal bioconcentration trends followed the order Zn?>?Cu?>?Cd?>?Pb for dissolved metals in seawater, Cu?>?Zn?>?Cd?>?Pb?≈?Mn?>?Fe?≈?Ni?≈?Co for metals associated to particulate matter and Zn?≈?Cu?>?Cd?>?Mn?>?Co?≈?Fe?>?Ni?≈?Pb?>?Cr for metals in the sediment. Higher values were found for copper in liver, zinc in gonads and lead in gill, showing the relationship between biotic and abiotic environment. In addition, Cd bioconcentration factors were found high in liver and gill showing the sensitivity of sole to this metal even at low concentrations.     

Trace metals species in sea-water-I: removal of trace metals from sea-water by a chelating resin

A significant fraction of the copper, lead, cadmium and zinc in sea-water exists in a form which is not retained by a chelating resin (Chelex-100) or extracted by ammonium pyrrolidinedithiocarbamate. Anodic stripping voltammetric results suggest that the major part of the unavailable trace metal is adsorbed on, or occluded in, organic or inorganic colloidal particles. An ionic equilibria computer program was used to predict the effect of various complexing agents on trace metal species in sea-water. Citric acid and amino-acids, with the exception of l-cysteine, were shown to be unimportant as complexing agents, and the ability of an EDTA-like ligand to complex Cu, Pb, Cd and Zn is controlled entirely by the concentrations of the ligand and of "labile" Fe(III) and Cr(III) in sea-water, since these two ions together will react quantitatively with EDTA. l-Cysteine, if present in sea-water, would also complex the trace metals.     

Synthesis and analytical properties of a chelating resin functionalised with bis-(N,N'-salicylidene)1,3-propanediamine ligands

A polystyrenedivinylbenzene-based macroreticular resin was functionalised with bis-(N,N'-salicylidene)1,3-propanediamine ligands and its analytical properties have been investigated. The pH dependence of metal resin chelation has been determined for Cu(II), Ni(II), Co(II), Zn(II), Fe(II), Mn(II), Pb(II), Cd(II) and Cr(III). Trace amounts of these metal ions were quantitatively retained on the resin at neutral pH and easily recovered by elution with 1 N hydrochloric acid. The resin exhibits good chemical stability and fast equilibration with the metal ion making it useful for rapid concentration of trace amounts of metal ions on the resin columns.     

Donnan effects in the steady-state diffusion of metal ions through charged thin films

The steady-state diffusion of metals ions through thin films with fixed charged groups was investigated using diffusive gradients in thin films (DGT) measurements. Copolymers of acrylamide and sodium acrylate cross-linked with N,N'-methylenebisacrylamide were used as diffusive gels. The rate of diffusion of cadmium ions through the gels was measured by determining the mass of cadmium bound to a backing chelex resin after a known deployment time. Variation of the ionic strength as well as the fixed charge density and the thickness of the gel layer allowed evaluation of the impact of the Donnan partitioning and the diffusion layer in solution on the observed steady-state flux of ions through the layer. The results underscore that, as the Donnan partitioning increases, the impact of the diffusion layer in solution becomes more significant. At modest Donnan potentials, Donnan partitioning controls the net flux of metal ions, whereas at conditions of increasing Donnan potential, i.e., at decreasing ionic strength, the flux is increasingly limited by diffusion in solution. An analytical expression is developed to describe the influence of Donnan partitioning on the observed steady-state flux of metal ions.