Release of indium from In2O3 nanoparticles in model solutions and synthetic seawater.

Indium oxide (In2O3) nanoparticles (NPs) are used in electronic devices, from which indium (as its nanoparticulate form or as other generated chemical species) can be released to natural waters. To assess for the impacts of such releases (e.g. toxic effects), information on the kinetics and thermodynamics of the In2O3 dissolution processes is key. In this work, the evolution with time of the dissolution process was followed with the technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) by measuring the free indium concentration ([In3+]). AGNES can determine the free ion concentration in the presence of nanoparticles without a prior separation step, as shown in the case of ZnO nanoparticles, a procedure that is more accurate than the typical sequence of centrifugation+filtration+elemental analysis. Excess of indium oxide NPs were dispersed in 0.1 mol L-1 KNO3 at various pH values ranging from 2 to 8. Additional dispersions with bulk In2O3 at pH 3 or NPs in synthetic seawater at pH 8 were also prepared. The temperature was carefully fixed at 25 °C. The dispersions were continuously stirred and samples were taken from time to time to measure free indium concentration with AGNES. 180-day contact of In2O3 to solutions at pH 2 and 3 was not enough to reach equilibrium. The dissolution of the NPs at pH 3 was faster than that of the bulk (i.e. non nanoparticulate) material. Equilibrium of the NPs with the solution was reached at pH 4 and 5 in KNO3 and at pH 8 in seawater, in shorter times for higher pH values, with free indium concentrations decreasing by a factor of 1000 for each increase in one pH unit. The solubility products of In(OH)3 and In2O3 were compared. Equilibration of NPs with synthetic seawater took <18 days, with an average free [In3+] (up to 196 days) of 1.03 amol L-1.

Back Accumulation of Diffusive Gradients in Thin-Films Devices with a Stack of Resin Discs To Assess Availability of Metal Cations to Biota in Natural Waters.

Determining species, concentrations, and physicochemical parameters in natural waters is key to improve our understanding of the functioning of these ecosystems. Diffusive Gradients in Thin-films (DGT) devices with different thicknesses of the resin or of the diffusive disc can be used to collect independent information on relevant parameters. In particular, DGT devices with a stack of two resin discs offer a simple way to determine dissociation rate constants of metal complexes from the accumulation of the target metal in the back resin disc. In this work, simple approximate expressions for the determination of the dissociation rate constant are reported and applied to a model Ni nitrilotriacetic complex as well as to Zn complexes in the Mediterranean Osor stream. Once the physicochemical parameters are known, one can plot the labile fraction of the metal complexes in terms of the thickness of the diffusion domain. These plots reveal a strong dependence on the nature of complexes as well as on the characteristics of the diffusion domain, and they are of high interest as predictors of availability to biota whose uptake is limited by diffusion.

A new tool for the determination of humic substances in natural waters: Pulsed voltammetry approach.

Humic substances (HS) in natural waters can be determined with a new, simple and sensitive method based on their influence on the background current in a differential pulse - adsorptive cathodic stripping voltammetry. The proposed method, termed PB-HS (pulsed background - humic substances) is discussed in detail, including its application in natural samples from the Krka River estuary. The method was additionally compared with absorbance measurements as well as with the typical electrochemical HS quantification in natural waters based on HS complexation with molybdenum (Mo). A good correlation between methods was observed, with PB-HS showing slightly better sensitivity to humic compounds than classical spectrophotometry. Higher HS concentrations measured with the Mo-method may be due to the enhanced hydrophobicity reached at pH 2 that is required by the method. Advantages of the proposed PB-HS method, compared to existing voltammetric methods for HS quantification, are that it does not require any reagent addition (except buffer) and that it can be used at the natural pH of water as well as in a wide salinity range, which is crucial for its application in estuarine waters.

Direct determination of free Zn concentration in samples of biological interest.

The speciation of essential metal ions in biological fluids, such as blood plasma and serum, is of fundamental importance to understand the homeostasis of these elements. The activity of metal ions such as Zn2+ in extracellular media is thought to affect their interaction with membrane-bound transporters, and thus is critical for their cellular uptake. Previous approaches to determine "free" Zn2+ (i.e. the hexa-aquo ion) are based on separation by either chromatography or ultrafiltration, or on metallochromic dyes. However, both types of approach are prone to affect the relevant equilibria. These drawbacks can be circumvented with the electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping), since it can measure free zinc concentration without perturbing the sample speciation. Here, a Bovine Serum Albumin (BSA) + Zn synthetic mixture and Fetal Bovine Serum (FBS) are analyzed as proof of concept. Adsorption of BSA on the surface of the Hanging Mercury Drop Electrode (HMDE), despite the advantage of its renewal, is so intense that it blocks appropriate attainment of the required equilibrium, and only estimations of [Zn2+] can be derived. In contrast, a rotating disc electrode with a thin mercury film deposited on it (TMF-RDE) is advantageous because of its small volume and enhanced mass transfer. Protein adsorption can be prevented by covering the TMF-RDE with Nafion. A free Zn concentration [Zn2+] = 2.7 nmol L-1 was found at pH 7.0, total Zn 20 µµmol L-1 and BSA 600 µµmol L-1. A sample of FBS with fixed pH 7.2 (MOPS 0.08 mol L-1) yielded [Zn2+] = 0.25 nmol L-1. This methodology opens the way to free metal concentration determinations in biological fluids.

Effective concentration signature of Zn in a natural water derived from various speciation techniques.

The uptake of nutrients or toxicants by different organisms in aquatic systems is known to correlate with different fractions of the nutrient's or toxicant's total concentration. These fractions can be provided by different analytical techniques, from which the better correlation is expected to be found for those with a characteristic length comparable to that in the considered organism uptake. An effective concentration signature can be built up with the concentration values associated to the availability (i.e. fluxes in dynamic techniques) of the nutrient or toxicant measured by various analytical techniques with different characteristic lengths. Here, this new representation was obtained for the pool of Zn complexes in the Mediterranean stream Riera d'Osor (Girona, Catalonia, Spain) with a suite of four analytical techniques. Absence of Gradients and Nernstian Equilibrium Stripping (AGNES) and Polymer Inclusion Membrane (PIM) devices provided the free Zn concentration. Linear Anodic Stripping Voltammetry provided a labile fraction (defined here as cLASV, higher than the free concentration), related to the diffusion layer scale. Diffusion Gradients in Thin-films provided higher labile fractions (known as DGT concentrations, cDGT) connected to the different characteristic lengths of different configurations (e.g. one or two resin discs) longer, in any case, than that corresponding to LASV. The combination of the information retrieved by the techniques allowed to quantify lability degrees of the pool of Zn complexes and to build up the effective concentration signature for this water.

A new approach to improve the accuracy of DGT (Diffusive Gradients in Thin-films) measurements in monitoring wells.

The Diffusive Gradients in Thin-films (DGT) technique represents an ideal tool for monitoring water quality of inorganic species in systems with a high flow such as rivers, streams, lakes and seas. However, in low-flow systems (non-turbulent waters), the influence of a diffusive boundary layer (DBL) formed on the surface of the DGT device has been observed, which can lead to erroneous measurements by DGT. Therefore, the use of DGT in wells for groundwater monitoring is still very limited until now. In this sense, the present study evaluates the applicability of the DGT technique in non-turbulent and low-flow water systems. We propose a new way to calculate the DBL with the objective to carry out a robust DGT analysis in environmental monitoring wells. For this purpose, DGT devices with different diffusive gel thicknesses were deployed in an experimental set-up simulating a groundwater monitoring well. A DBL thickness (for each element) was calculated from the slopes of the linear regressions between the DGT accumulated mass of metal and the deployment time (4, 8, 12, 24 and 48 h) for each of the two diffusive gel thicknesses. The mean DBL thickness (averaging the individual DBL thicknesses calculated from the slopes) was 0.06 cm. The concentrations of the analysed elements were corrected with this DBL with the result that the metal concentrations measured by DGT improved and were highly approximated to their actual total values in this non-complexing medium.

Dissolved iodide in marine waters determined with Diffusive Gradients in Thin-films technique.

For the first time, Diffusive Gradient in Thin-films (DGT) focuses on the inorganic iodine species iodate (IO3-) and iodide (I-). A silver-doped Cl resin (AgdCl), which is known to selectively accumulate I-, was used to make a binding gel. Laboratory investigations were designed to verify the suitability of the AgdCl-DGT method to measure the total I- concentration in environmental waters. Total recovery of I- was obtained using an elution solution containing 100 mmol L-1 KCN. DGT validation experiments in 10 mmol L-1 NaCl showed linear accumulation of I- over time, contrary to IO3-, thus confirming the selectivity of AgdCl-binding gel. The AgdCl-DGT measurement of total I- concentration was independent of pH (4.5-8.8) and was not impacted by the presence of bicarbonate (1-5 mmol L-1). Finally, the performance of AgdCl-DGT samplers were tested in two continental waters and a synthetic seawater. The AgdCl-DGT samplers measured 27-33% of the total I- concentration in the two continental waters up to 24 h of deployment time, whereas the AgdCl-DGT response retrieved the total I- concentration in seawater up to 72 h (106 ± 7%). The difference in DGT response was attributed to the low ionic strength of the two continental waters, limiting the application of AgdCl-DGT method to media with higher ionic strength.

Speciation of Inorganic Compounds in Aquatic Systems Using Diffusive Gradients in Thin-Films: A Review.

The speciation of trace metals in an aquatic system involves the determination of free ions, complexes (labile and non-labile), colloids, and the total dissolved concentration. In this paper, we review the integrated assessment of free ions and labile metal complexes using Diffusive Gradients in Thin-films (DGT), a dynamic speciation technique. The device consists of a diffusive hydrogel layer made of polyacrylamide, backed by a layer of resin (usually Chelex-100) for all trace metals except for Hg. The best results for Hg speciation are obtained with agarose as hydrogel and a thiol-based resin. The diffusive domain controls the diffusion flux of the metal ions and complexes to the resin, which strongly binds all free ions. By using DGT devices with different thicknesses of the diffusive or resin gels and exploiting expressions derived from kinetic models, one can determine the labile concentrations, mobilities, and labilities of different species of an element in an aquatic system. This procedure has been applied to the determination of the organic pool of trace metals in freshwaters or to the characterization of organic and inorganic complexes in sea waters. The concentrations that are obtained represent time-weighted averages (TWA) over the deployment period.

Availability of metals to DGT devices with different configurations. The case of sequential Ni complexation.

The analytical technique DGT (Diffusive Gradients in Thin-films) is able to gain access to a wealth of information by carefully interpreting accumulation data from passive samplers with different configurations (i.e. different thicknesses of its constituent layers). A set of DGT devices were simultaneously deployed in solutions of Ni and nitrilotriacetic acid (NTA) of different concentrations to measure the availability of Ni in these solutions. Accumulations indicate that the availability of Ni depends on both the thickness of the resin and the thickness of the diffusive gel. In both cases, the lability degree increases as the thickness increases. As the formation of successive complexes (such as Ni(NTA)2) proceeds, the availability of the metal decreases, which is quantitatively explained by reducing the formulation to a case with only one complex, but with an effective dissociation rate constant that decreases as the concentration of NTA increases. Simple analytical expressions are reported to quantify the lability degree in the different DGT configurations. These results indicate that a set of different DGT devices can characterize the availability of a cation in a natural sample with uptake processes at different spatial or time scales. Alternatively, and from a more fundamental point of view, information on speciation, mobilities and labilities of the species present in natural samples can be obtained with a set of DGT configurations.

Risk factors for non-diabetic renal disease in diabetic patients.

BACKGROUND: Diabetic patients with kidney disease have a high prevalence of non-diabetic renal disease (NDRD). Renal and patient survival regarding the diagnosis of diabetic nephropathy (DN) or NDRD have not been widely studied. The aim of our study is to evaluate the prevalence of NDRD in patients with diabetes and to determine the capacity of clinical and analytical data in the prediction of NDRD. In addition, we will study renal and patient prognosis according to the renal biopsy findings in patients with diabetes. METHODS: Retrospective multicentre observational study of renal biopsies performed in patients with diabetes from 2002 to 2014. RESULTS: In total, 832 patients were included: 621 men (74.6%), mean age of 61.7 ± 12.8 years, creatinine was 2.8 ± 2.2 mg/dL and proteinuria 2.7 (interquartile range: 1.2-5.4) g/24 h. About 39.5% (n = 329) of patients had DN, 49.6% (n = 413) NDRD and 10.8% (n = 90) mixed forms. The most frequent NDRD was nephroangiosclerosis (NAS) (n = 87, 9.3%). In the multivariate logistic regression analysis, older age [odds ratio (OR) = 1.03, 95% CI: 1.02-1.05, P < 0.001], microhaematuria (OR = 1.51, 95% CI: 1.03-2.21, P = 0.033) and absence of diabetic retinopathy (DR) (OR = 0.28, 95% CI: 0.19-0.42, P < 0.001) were independently associated with NDRD. Kaplan-Meier analysis showed that patients with DN or mixed forms presented worse renal prognosis than NDRD (P < 0.001) and higher mortality (P = 0.029). In multivariate Cox analyses, older age (P < 0.001), higher serum creatinine (P < 0.001), higher proteinuria (P < 0.001), DR (P = 0.007) and DN (P < 0.001) were independent risk factors for renal replacement therapy. In addition, older age (P < 0.001), peripheral vascular disease (P = 0.002), higher creatinine (P = 0.01) and DN (P = 0.015) were independent risk factors for mortality. CONCLUSIONS: The most frequent cause of NDRD is NAS. Elderly patients with microhaematuria and the absence of DR are the ones at risk for NDRD. Patients with DN presented worse renal prognosis and higher mortality than those with NDRD. These results suggest that in some patients with diabetes, kidney biopsy may be useful for an accurate renal diagnosis and subsequently treatment and prognosis.

Time weighted average concentrations measured with Diffusive Gradients in Thin films (DGT).

Time weighted average (TWA) concentrations can improve the assessment of water quality. DGT (Diffusive Gradients in Thin films) devices have been suggested as simple tools to measure TWA metal concentrations, but the connection of TWA with cDGT has not been rigorously discussed. It is shown here that cDGT is the average DGT-labile concentration along the deployment, which suggests that it is well suited to correlate with toxicity effects. In terms of real species, cDGT is a good estimator of the TWA concentration for simple metal solutions (no ligands are present) when the accumulation takes place under perfect sink conditions. Differences between cDGT and the TWA concentration for short pulses (<40 min), when the transient regime becomes relevant, are reported. In the presence of complexes, cDGT contains the TWA of the product of the labile fraction times the diffusivity of the complex (relative to that of the free metal). This means that cDGT can underestimate the TWA of the total metal concentration due to the presence of complexes less mobile than the free metal or not fully labile. These findings are illustrated with Cd, Ni, Mg or Ni + nitrilotriacetic acid (NTA) solutions. When only one complex is relevant, as in the Ni + NTA system, a simple correction factor can yield the TWA concentration from cDGT.

Dissolution and Phosphate-Induced Transformation of ZnO Nanoparticles in Synthetic Saliva Probed by AGNES without Previous Solid-Liquid Separation. Comparison with UF-ICP-MS.

The variation over time of free Zn2+ ion concentration in stirred dispersions of ZnO nanoparticles (ZnO NPs) prepared in synthetic saliva at pH 6.80 and 37 °C was followed in situ (without solid-liquid separation step) with the electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping). Under these conditions, ZnO NPs are chemically unstable due to their reaction with phosphates. The initial stage of transformation (around 5-10 h) involves the formation of a metastable solid (presumably ZnHPO4), which later evolves into the more stable hopeite phase. The overall decay rate of ZnO NPs is significantly reduced in comparison with phosphate-free background solutions of the same ionic strength and pH. The effective equilibrium solubilities of ZnO (0.29-0.47 mg·L-1), as well as conditional excess-ligand stability constants and fractional distributions of soluble Zn species, were determined in the absence and presence of organic components. The results were compared with the conventional ultrafiltration and inductively coupled plasma-mass spectrometry (UF-ICP-MS) methodology. AGNES proves to be advantageous in terms of speed, reproducibility, and access to speciation information.

Towards improving the electroanalytical speciation analysis of indium.

The geochemical fate of indium in natural waters is still poorly understood, while recent studies have pointed out a growing input of this trivalent element in the environment as a result of its utilisation in the manufacturing of high-technology products. Reliable and easy-handling analytical tools for indium speciation analysis are, then, required. In this work, we report the possibility of measuring the total and free indium concentrations in solution using two complementary electroanalytical techniques, SCP (Stripping chronopotentiometry) and AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) implemented with the TMF/RDE (Thin Mercury Film/Rotating Disk Electrode). Nanomolar limits of detection, i.e. 0.5 nM for SCP and 0.1 nM for AGNES, were obtained for both techniques in the experimental conditions used in this work and can be further improved enduring longer experiment times. We also verified that AGNES was able (i) to provide robust speciation data with the known In-oxalate systems and (ii) to elaborate indium binding isotherms in presence of humic acids extending over 4 decades of free indium concentrations. The development of electroanalytical techniques for indium speciation opens up new routes for using indium as a potential tracer for biogeochemical processes of trivalent elements in aquifers, e.g. metal binding to colloidal phases, adsorption onto (bio)surfaces, etc.

In situ measurements of micronutrient dynamics in open seawater show that complex dissociation rates may limit diatom growth.

In this first in situ study of the dynamic availability of phytoplankton micronutrients, a SeaExplorer glider was combined with Diffusive Gradients in Thin Films and deployed in the Mediterranean Sea. On the basis of their labile metal complex pools, we discovered that Fe and Co can be potentially limiting and Cu co-limiting to diatom growth, contrary to the generally accepted view that phosphorus (phosphate) is the growth limiting element in the Mediterranean Sea. For flagellates and picoplankton, phosphorus remains the main element limiting growth. Our in situ measurements showed that organic complexes of Fe and Cu (>98% of total dissolved concentration), dissociate slower than inorganic complexes of Co, Cd and Ni (>99% of total dissolved concentration being free ions and inorganic complexes). This strengthens the potential growth limiting effect of Fe and Cu versus phosphate, which is present as a free ion and, thus, directly available for plankton.

Comparison of different speciation techniques to measure Zn availability in hydroponic media.

Four analytical techniques are compared: AGNES (Absence of Gradients and Nernstian Equilibrium Stripping), LASV (Anodic Stripping Voltammetry with Linear stripping), DGT (Diffusive Gradients in Thin films) and PIM (Polymer Inclusion Membranes). These techniques have been designed to provide the free ion concentration or a labile fraction, complementarily contributing to an integrated description of speciation and availability. Their simultaneous application to the determination of free Zn concentrations or labile fluxes in seven solutions of a hydroponic medium reveals characteristics of each technique and correlations between their results. All dynamic results can be interpreted in terms of a general theoretical framework on fluxes. Indeed, in techniques under diffusion-limited conditions in the sample, the flux can be split into the free contribution (linearly proportional to the free fraction), plus the contribution of the complexes (where mobility, lability and abundance of complexation are intertwined). A methodology to compute lability degrees is developed. Measurements with PIM devices confirm that diffusion in the sample solution is not rate limiting, so its flux is proportional to the free metal in the donor solution. A proportionality between the responses of any given two techniques is observed, which suggests that, for the low ligand-to-metal concentration ratios used in the present work, any of these techniques would correlate similarly with uptake, toxic or nutritional measurements.

Metal (Pb, Cd, and Zn) Binding to Diverse Organic Matter Samples and Implications for Speciation Modeling.

This study evaluated the influence of dissolved organic matter (DOM) properties on the speciation of Pb, Zn, and Cd. A total of six DOM samples were categorized into autochthonous and allochthonous sources based on their absorbance and fluorescence properties. The concentration of free metal ions ( CM2+) measured by titration using the absence of gradients and Nernstian equilibrium stripping (AGNES) method was compared with that predicted by the Windermere humic aqueous model (WHAM). At the same binding condition (pH, dissolved organic carbon, ionic strength, and total metal concentration) the allochthonous DOM showed a higher level of Pb binding than the autochthonous DOM (84- to 504-fold CPb2+ variation). This dependency, however, was less pronounced for Zn (12- to 74-fold CZn2+ variation) and least for Cd (2- to 14-fold CCd2+ variation). The WHAM performance was affected by source variation through the active DOM fraction ( F). The commonly used F = 1.3 provided reliable CPb2+ for allochthonous DOMs and acceptable CCd2+ for all DOM, but it significantly under-predicted CPb2+ and CZn2+ for autochthonous DOM. Adjusting F improved CM2+ predictions, but the optimum F values were metal-specific (e.g., 0.03-1.9 for Pb), as shown by linear correlations with specific optical indexes. The results indicate a potential to improve WHAM by incorporating rapid measurement of DOM optical properties for site-specific F.

Polymer inclusion membrane to access Zn speciation: Comparison with root uptake.

Metal speciation studies can be performed with a new technique based on a functionalized membrane. The estimation of not only the total amount of metal, but also the metal available to living organisms is very important. In this context, we have investigated the use of a polymer inclusion membrane (PIM) in a new tool for the determination of free metal ion concentration. In order to check the usefulness of PIM devices in metal speciation studies and metal availability to potato plants (Solanum tuberosum), Zn has been chosen as a case study. The PIM designed for Zn transport uses polyvinyl chloride (PVC) as polymer and di-(2-ethylhexyl) phosphoric acid (D2EHPA) as carrier, with 0.01M nitric acid in the receiving solution. The stability of the PIM has been demonstrated and good linearity of PIM-device fluxes (JPIM) with free metal concentration was observed for total metal concentrations ranging from 3µM up to 70µM. The presence of different ligands, such as ethylenediaminetetraacetic acid (EDTA), humic acid (HA) and citrate, greatly influences the measured JPIM because the formation of metal complexes in the donor phase decreases the free Zn concentration in the sample. Good correlation has been found when comparing PIM fluxes and metal accumulation in potato plants roots in the presence of EDTA. But, the root uptake did not change when adding citrate and HA to the hydroponic medium, so the uptake does not always follows the Free Ion Activity Model (FIAM). These ligands might induce physiological changes in the roots and enhance metal uptake.

Free indium concentration determined with AGNES.

Indium is increasingly used in electronic devices, from which it can be mobilized towards environmental compartments. Speciation of In in waters is important for its direct ecotoxicological effects, as well as for the fate of this element in the environment (e.g. fluxes from or towards sediments). Free indium concentrations in the environment can be extremely low due to hydrolysis, especially important in trivalent cations, to precipitation and to complexation with different ligands. In this work, the free indium concentration (which is a toxicologically and geochemically relevant fraction) in aqueous solutions at pH3 has been measured with an adapted version of the electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping). Speciation measurements in mixtures of indium with the ligands NTA (nitrilotriacetic acid) and oxalate indicate that the values of their stability constants in the NIST46.6 database are less adequate than those published in some more recent literature. The extraordinary lability and mobility of In-oxalate complexes allow the measuring of free indium concentrations below nmol/L in just 25s of deposition time.

Speciation of Zn, Fe, Ca and Mg in wine with the Donnan Membrane Technique.

Free concentrations of Zn2+, Fe3+, Ca2+ and Mg2+ in a red wine (Raimat, Catalonia, Spain) have been determined, with the Donnan Membrane Technique (DMT) for the first time. The required equilibration time benefits from the acceptor solution including major cations. K+ and Na+, mainly unbound to any ligand in the sample, have been identified as suitable reference ions. A free Zn concentration of 1.76µmolL-1 determined with DMT was in excellent agreement with the free Zn concentration independently provided by the electroanalytical technique Absence of Gradients and Nernstian Equilibrium Stripping (AGNES), 1.7µmolL-1, amounting to 14.4% of the total Zn. The free concentrations found in this wine were 1.79µmolL-1 Fe3+, 1.11mmolL-1 Ca2+ and 3.4mmolL-1Mg2+ (8.82%, 40% and 57% of their total concentrations). Prior to the application of the techniques to the red wine, they had been cross-validated in Zn-tartrate solutions.

Extending the Use of Diffusive Gradients in Thin Films (DGT) to Solutions Where Competition, Saturation, and Kinetic Effects Are Not Negligible.

DGT (Diffusion Gradients in Thin films) was designed to sample trace metals in situ at their natural concentrations. The setup and the experimental deployment conditions were established to allow interpretation of a linear accumulation of metal with time, using a simple expression based on a steady-state flux under perfect sink conditions. However, the extension of DGT to a wide range of analytes and its use under varied conditions has shown that, in some situations, these conditions are not fulfilled, so that accumulations with time are nonlinear. Previously, when such curvature was observed, concentrations in solution could not be reliably calculated. Here, we present fundamentally derived equations that reproduce the time accumulation for three situations: (i) kinetic limitations in the binding to the resin, (ii) saturation or equilibrium effects, or (iii) non-negligible competitive effects. We show how the accumulations can be quantified, in terms of the required kinetic and thermodynamic constants, and provide practical guidance for their use to obtain reliable estimates of solution concentrations. Solutions containing Mg or Mn, where all three situations can prevail, are used as examples. Calculated concentrations show reasonable agreement with the experimentally known values and with the results of a numerical model of the system, significantly improving the estimations based on perfect sink conditions. Such an approach opens up the possibility of using DGT more widely in challenging systems and allows DGT data to be interpreted more fully.