Assessment of labilities of metal complexes with the dynamic ion exchange technique

The dynamic ion exchange technique (DIET) is proposed to provide speciation information, which can be used to establish linkswithmetal bioavailability in natural waters. The experimental setup consists of a fewmilligrams of a sulfonic acid type ion exchange resin packed in a plastic microcolumn that is coupled to a peristaltic pump for a sample to interact with the resin which is subsequently eluted. The evolution of both the accumulated number of moles in the resin and the concentration of the effluent can provide information on the dissociation of differentmetal-ligand complexeswhen comparedwith the transport properties. This information can be converted into the lability degree of a given complex or the DIET concentration cDIET, which accounts for the labile fraction contributing to the metal accumulation by the resin column at the operation conditions. cDIET can be extended to columns containing chelating resins (such as those with Chelex) or to chromatography. A comprehensive modelling of the involved phenomena (such as diffusion, advection, reaction kinetics and electrostatic partitioning) leads to the quantitative interpretation of the accumulation time series (accumulation curves) or effluent evolution (breakthrough curves). Particularly simple analytical expressions can be used for short exposure times, when a (quasi) steady-state is attained. These models have been checked against the results from complexes of Cu and Ni with ligands, such as ethylenediamine, and ethylenediaminetetraacetic, iminodiacetic, glutamic, salicylic, malonic and malic acids, which yield complexes with contrasting charges. Caution is advised when estimating the free metal fraction from DIET measurements, as cDIET and the free metal concentration can be considered to be equal only in the case of extremely inert complexes. Additional keywords: availability, ion exchange columns, trace metal speciation. Received 2 October 2018, accepted 21 January 2019, published online 18 February 2019


Introduction
Metal speciation provides crucial information for current paradigms of ecotoxicity (such as the Free Ion Activity (Anderson et al. 1978) and Biotic Ligand (Paquin et al. 2002) Models), and thus several techniques have been developed along the years for this purpose. Among the most recent ones, we can quote voltammetric techniques such as Absence of Gradients and Nernstian Equilibrium Stripping (Companys et al. 2017), membrane-based techniques such those using Polymer Inclusion Membranes (Companys et al. 2018;Vera et al. 2018), Donnan Membranes (Temminghoff et al. 2000) and dialysis membranes (Berggren 1989;Franklin et al. 2007), as well as techniques based on functionalised resins (Alberti et al. 2007;Pesavento et al. 2009;Sunda 1984;Tantra et al. 2016). Among the latter, special mention must be made of the Ion Exchange Technique (IET), developed by Cantwell (Cantwell et al. 1982) and later applied by many others, including Campbell and Fortin (Crémazy et al. 2015;Fortin and Campbell 1998). IET is a column equilibration technique that consists of an accumulation step, where the sample solution is flushed through a column packed with a sulphonic acid type resin until equilibrium is attained. An elution step follows, then the accumulated metal is measured with a suitable elemental analysis technique. This amount can, then, be related to the corresponding free metal concentration in solution via a conditional exchange constant determined by calibrating the system in the conditions of interest.
The knowledge acquired with all the aforementioned techniques is related only to the thermodynamic aspects of the systems studied and, though valuable, in several cases is too limited (Zhao et al. 2016). Dynamic speciation aims at providing information beyond thermodynamics, such as rates of association/dissociation and mobility. In the case of the DGT (Diffusive Gradients in Thin films) passive sampler (Davison 2016), as in many others, a flux is measured and interpreted as a surrogate of the supply from the medium published in Environmental Chemistry 16 (2019) [151][152][153][154][155][156][157][158][159][160][161][162][163][164] 4/43 to the organism, which leads to the determination of cDGT, a kind of effective metal concentration or "labile fraction".
Recent work (Leguay et al. 2016;Nduwayezu et al. 2016;Rowell et al. 2018) has considered the possibility of extracting meaningful information from the time-resolved accumulations in IET columns (that we label as "accumulation curves"). In this new approach, called Dynamic Ion Exchange Technique (DIET), the moles of metal accumulated by the resin (nacc) is recorded as a function of contact time, before equilibrium is reached (see Fig 1a). One could consider DIET as a way of exploiting an early regime (Peijnenburg et al. 2014) in the accumulation curve (see Fig 1b). The initial slope of the accumulation curve (labelled as "accumulation rate", Racc) has been assumed to be related to the free metal concentration in the sample via an empirical relationship (Nduwayezu et al. 2016). In those cases where the effluent concentration is above the quantification limit of the analytical technique, the breakthrough curves (see Fig 1c) can also be recorded, to obtain additional information. The main advantage of DIET over IET is that it is much more economical both in terms of time and sample volume, as it does not require waiting for the full attainment of equilibrium. This can become critical when equilibration is particularly slow, as in the case of highly charged ions (Leguay et al. 2016) or at low ionic strengths. Although the first results seemed promising, it is still unclear whether the accumulation rate actually reflects only the binding of free metal ion or if the labile species contribute as well (Nduwayezu et al. 2016).
Dynamic speciation (van Leeuwen et al. 2005) has been rarely tackled with columns (Alvarez et al. 2004;Bowles et al. 2006;Figura and Mcduffie 1980;Procopio et al. 1997;Wen et al. 2006), perhaps due to a limited interpretative framework. Most work has just relied on semi-empirical fractionation schemes. In general, the recovered fractions of metal reported in literature have been defined operationally, without the support of a published in Environmental Chemistry 16 (2019) 151-164 5/43 theoretical relationship with the thermodynamic, kinetic and transport properties of the different metal species present in the sample. In addition, in most of these cases, the sorbent materials are weakly acidic, chelating resins like Chelex 100 (iminodiacetic functional groups) (Herrin et al. 2001), while little information is found about strongly acidic, ion-exchange resin like Dowex (sulphonate functional groups).
For this reason, the purpose of this work is to interpret DIET via a comprehensive modelling approach, so that information on the kinetic properties of the complexes can be retrieved. Four models are presented (and derived in detail in the Supporting Information, SI) to describe accumulation either by an individual bead or by the column as a whole, either in steady state (SS) or under transient conditions (see Table 1). From the entire modelling exercise, it emerges that Model IV is the most useful for practical purposes, because it describes the early stage experimental data with very simple analytical expressions (see section 3.5.2). The DIET-labile concentration (cDIET) is defined in section 3.6 and practical formulas to compute it are proposed in section 3.8.

Equipment and Reagents
The medium for all of the experiments has the major ion composition of a typical algal growth medium (Ca(II): 6.8×10 -5 mol L -1 ; Mg(II): 8.12×10 -5 mol L -1 ; K(I): 4.22×10 -3 mol L -1 ; all the cations were introduced as nitrate salts), as given in (Fortin and Campbell 2001). In all of the experiments the pH was fixed at 6.0 with 1×10 -3 mol L -1 2-(Nmorpholino)ethanesulfonic acid (MES). The total ionic strength of the medium was I=4.4×10 -3 mol L -1 . The concentrations of the competing ligands were chosen so as to have clearly different values of the free metal fraction of Cu or Ni, as computed with the speciation software Visual MINTEQ (Gustafsson 2016). Details on the reagents and equipment are provided in the SI. The ligands chosen were ethylenediamine (en), 6/43 ethylenediaminetetraacetic (EDTA), iminodiacetic (IDA), glutamic, salicylic, citric, malonic and malic acids.
The experimental setup was similar to a standard IET experiment (Fortin and Campbell 1998) and is schematized in Fig 1a. A known amount of resin was packed in a plastic microcolumn. The resin was then cleaned (with 1.5 mol L -1 HNO3 acid, 0.1 mol L -1 KOH and ultrapure water) and conditioned by flushing a solution identical to the sample background (with no trace metals or ligands), until the pH and ionic strength of the eluate were the same as those at the inlet. In our conditions, stabilisation of the pH required about 20 min. The sample itself was, then, passed through the column for different periods of time (e.g. 5-10-30 min.). After each period, the resin was eluted with 1.5 mol L -1 HNO3 at 0.5 mL min -1 for 20 min and the eluate was collected; the column was renewed and reconditioned, and a new run was started. Unless otherwise specified, the samples were flushed at 4.5 mL min -1 ; the flow rate was checked periodically since the tubing tended to deteriorate over time. The metal uptake can also be followed by measuring the metal concentration in the effluent during the initial pumping of the test solution through the column, instead of eluting the metal accumulated in the beads.

Concentration measurements
All the sample aliquots were acidified to 1% HNO3. Those from the highly acidic eluates had to be diluted accordingly before analysis. All the samples were analysed with ICP-OES (Horiba Jobin Yvon) or ICP-MS (Agilent 7700x).

Accumulation curves
The purpose of this section is the description of the experimental data obtained with DIET in synthetic solutions. First, the plots of metal accumulations in the column vs. time (i.e. accumulation curves) such as those presented in Fig 2 (for a fixed amount of total metal and variable amounts of ligands) were analysed.
In general, four different kinds of accumulation curves were distinguished. First (Fig 2a), systems for which the metal accumulates in the column following a linear trend over time, with a slope (Racc) equal to that of the ligand-free metal solutions. The behaviour of this type of systems indicates (i) a high rate of dissociation within the column and (ii) conditions far away from equilibrium of the solution with the resin (i.e., far from the maximum capacity of the resin). Second (Fig 2b), there are other systems that display accumulation curves where Racc approaches the value observed in the absence of ligands at short exposure times, but it soon decays while the accumulation tends to a constant value, indicative of resin-sample equilibrium. Depending on the lability of the metal complexes and the extent of the buffering of the free metal ion, the rate of metal binding may vary, as can be seen in the case of the Cu-malate complexes: with an increase of the ligand concentration from 1.5×10 -4 mol L -1 to 5×10 -3 mol L -1 , the time to attain equilibrium may decrease from several hours to a few minutes. Third (Fig 2c), there are systems that show linear accumulation curves with a slope (Racc) smaller than that obtained with the ligand-free metal solutions (at the same total metal concentration). This indicates that Racc is not strictly proportional to the total concentration in all cases. In fact, the analysis of data obtained at varying ligand-to-metal ratios in these systems shows a monotonic trend of Racc with the concentration of free metal ion (see also the Ni-EDTA data in Fig 3). Therefore, a question arises as to whether Racc depends exclusively on the value of the free metal ion concentration in the bulk sample (Nduwayezu et al. 2016) or, rather, it reflects the effective rate of dissociation of the metal complexes inside the resin column. In the latter case, DIET results would allow us to obtain information on the labile or inert character of the complexes (i.e., the dynamic speciation).
Finally, a fourth kind of system, typically under ligand excess conditions and very low free metal concentration (e.g., Cu-malate at the highest ligand concentration, shown in  (Pesavento et al. 2010) or Figs 1b and S2 in (Leguay et al. 2016)) and it will be interpreted here in terms of a "steady state plateau", for reasons discussed in section 3.7.
3.3 Modelling of DIET. General assumptions.
To start with the essential component, model I considers just the accumulation by one bead in contact with the sample and its evolution from the initial stages until equilibrium.
It will be shown in section 3.4 that the transient stage before SS is short, so that SS can be safely assumed (model II). A "diffusional" SS regime towards a particular bead is applied later on to the column models III and IV. The next modelling step is to consider all the beads in the whole column: either following the time evolution (model III) or just concentrating in the global steady state (model IV). The advantage of SS models is that simple analytical expressions can be derived (see Table 1). Model IV can be proposed as the de facto model for DIET. In all models, the metal (M) reacts with a ligand (L) to 10/43 produce a complex with stoichiometry 1:1 (ML). Their charges are zM (+2 for the metal ions studied here), zL and zML, where: These charges are usually omitted in the notation of the species for the sake of simplicity (the SI contains a complete list of nomenclature).
As confirmed by the similitude of the accumulation curves of Ni and Cu, the binding of the metal ions to a strong acid cation exchange resin like Dowex can be assumed to be essentially electrostatic (for a description of the binding mechanism in chelating resins such as Chelex see e.g. (Quattrini et al. 2017)). As a first approximation, we neglect the steric interactions that are known to affect metal binding (Fortin et al. 2010). Other common assumptions shared by the four models are: 1.-The supply to an individual resin bead results from diffusion in spherical geometry.
The beads are spheres of fixed radius r0. Diffusion in the solution surrounding the bead extends just to a finite distance r1, defining a diffusion layer of effective thickness δ.

12/43
2.-Given that none of the complexes studied here are macromolecular, all metal species have a similar diffusion coefficient DM (the same value in solution as inside the bead).
3.-Penetration of the different metal species inside the beads is allowed. In timedependent models, all species penetrate according to their charge. In steady-state models (II and IV), the penetration of some species is neglected.
4.-There is instantaneous equilibrium at the bead surface, so that the partitioning Eqn.
(3) applies. It was observed that, after a short transient period (less than half a second), the simulated uptake practically reaches SS (data not shown).

Neutral complexes
Neutral complexes (with partitioning factor χ 0 =1) can penetrate inside the beads. Given that at relatively short times (but once SS has been attained) the existing amounts of M and ML inside the beads are far from equilibrium with each other, we assume that there is no back-association of M and L inside the resin, but just dissociation of ML. Under excess ligand conditions, the metal contribution from complex dissociation inside the bead will be very relevant. This is similar to the treatment of penetration in several DGT  (Mongin et al.2011;Puy et al. 2014;Uribe et al. 2011) where the accumulation is essentially due to this dissociation inside the resin.
As shown in the SI, the lability degree can be computed as: and: ka and kd might differ from the values inside the bead due to electrostatic effects (Altier et al. 2016;Puy et al. 2014), but here they are assumed to be equal.

3.4.2.2
Positively charged complexes In this case, the bead acts as a perfect sink not only for M, but also for ML: As a consequence, due to the direct accumulation of ML, a flux equivalent to the fully labile case ( 1 ξ = ) is expected, even if the actual dissociation kinetics was slow. This inability to discriminate between free metal cations and positively charged complexes was already noted in previous works with the equilibrium IET (Fortin and Campbell 1998).

3.4.2.3
Negatively charged complexes For the extreme case of negative charge and high Boltzmann factor χ, the overall flux of metal to the bead would essentially result from the free metal ions plus some contribution from the dissociation of the complex in the diffusion layer. Dedicated expressions, similar 15/43 to those developed in voltammetry (Salvador et al. 2006), could be derived. However, Eqn. (8) still applies rigorously.

Column models
The modelling of the column considers that the spherical beads receive a flux that may be computed either with Model I or Model II. As the transient period to reach SS for an individual bead has been shown (with Model I) to be much shorter than the typical timescale of the column experiments, we assume in models III and IV that diffusion towards the bead (in the region between r0 and r1) is always under SS. This has been called a "diffusional steady state" (dSS) approximation (Galceran and van Leeuwen 2004). Another assumption of the column models is that there is a flat concentration profile of M and ML inside the bead (this is also supported by simulations with Model I, see Fig SI-1). This, again, is consistent with numerical simulation results of a combined particle and film diffusion control of metal uptake in Chelex resins (Quattrini et al. 2017), which indicates that film diffusion is typically the most relevant resistance to mass transfer at short exposure times.
The total concentration of M in the interstices of the column, outside the diffusion boundary layer, at a given height of the column (z) and a given time (t) since the beginning of the experiment, is denoted as where Q is the flow rate. ρ was set as the experimental ratio of resin volume over the bed length of the column, while α was computed from the height of the SS plateau as per the equation in Table 2. We applied an effective volume fraction ε of 0.18, the theoretical expectation for close-packing of equal spheres with a slight discounting for the volume fraction represented by the overlapping DBLs around the resin particles. corresponding to the attainment of what we identify as the (quasi) steady state. As in DGT, the regime cannot be rigorously termed "steady state" because of the increasing accumulation in the resin, but, for the sake of simplicity in the notation, we will use here the acronym "SS" to indicate this regime. This SS is also consistent with the linearity property is that ξ is independent from z, as in equation (8). On the other hand, Model IV relaxes the condition of ligand-excess, so that it is also consistent with theoretical lability degrees derived from bead models other than Model II.
As detailed in the next subsections, the differences in mathematical treatment between complexes of different charge are minimal (they only concern the interpretation of ξ, which may be analyzed in a second step).

3.5.2.1
Neutral complexes As shown in the SI, the ratio between effluent and feed concentrations can be expressed zchar can be interpreted as the resin bed length that reduces the feed concentration by a factor e=2.718, so that the shorter zchar, the lower will be the effluent total concentration (for a constant zmax).
from which the ξ value could be retrieved (see below).
A conclusion of experimental interest is that the use of very small resin sizes and long columns would improve method sensitivity (when using Eqn. (15)), but, on the other hand, small particle sizes can lead to very low ratios of where Ξ could be called the "system retention degree" (or "apparent column lability degree") which, for fixed total metal and ligand concentrations, increases when the lability degree of the complex increases. This Ξ bears some analogy to the fraction X used by some authors (Bowles et al. 2006;Figura and Mcduffie 1979;Procopio et al. 1997).
One difference is that Ξ is computed only from the SS plateau concentrations, while X is sometimes taken after a fixed volume of sample has gone through the column. Notice that Ξ and X can be used even for a case without ligands. For instance, for the case in absence of ligand shown in Fig SI-6 as red square markers, Ξ=0.1. The Ξ values reported in Table   3, computed using  is that the denominator of equation (20) may not be estimated with enough accuracy.

3.5.2.2
Positively charged complexes Expressions of the SS Model IV for zML>0 can be derived from the case of neutral complexes with the additional change of ξ=1, whenever the lability degree is involved.
So, zchar could be computed with Eqn. (13), leading to identical values with or without ligand. No information on the complex kinetics could be extracted from the effluent concentration (Eqn. (15)) or from Racc (Eqn. (16)). Racc will be directly proportional to the total metal concentration, as already observed for Sm-malate and Sm-citrate (Nduwayezu et al. 2016).

3.5.2.3
Negatively charged complexes As there is practically no penetration of the negative complexes into the beads at the relatively low ionic strength of the experiments, the accumulation will proceed from the flux of free metal, partially supported by the dissociation of the complex within the diffusion layer. This means a very low ξ. However, all the derivations of analytical SS expressions for neutral species (see previous subsection and SI, Model IV) apply rigorously with no other variation.

The DIET-labile fraction (c DIET )
The most recent literature about DGT recognizes that the "concentration" measured with the sampler is not, strictly speaking, the labile fraction, but rather an effective free metal concentration defined as "DGT concentration" (Galceran and Puy 2015;Puy et al. 2016).
In analogy, for a set of complexes denoted with index i we can introduce a "DIET concentration" defined as: Neither calculation is free from disadvantages, as the same considerations drawn for Eqn.

The SS plateau in the breakthrough curve
The presence of the experimental SS plateau was perfectly clear for Cu-IDA at both concentrations of ligand assayed. For instance, in Fig 5, after the sudden initial rise, the effluent concentration stays fixed to approximately 57% of the total sample concentration for at least 1500 s. Given that, all other parameters being equal, the height of the plateau for the experiment in absence of ligand is not higher than 1.7% (see blue squares in Fig   SI-6), it can be safely concluded that the IDA complexes have a reduced lability. for the rest of the systems, both values were reasonably close to each other and to the theoretical ξ value. This is also partially due to r1 having been fitted to 61.6 µm to obtain cDIET concentrations for Cu systems with malate or malonate from the SS plateau could not be computed, as the plateau was not observed. As the accuracy of our measurements did not allow us to distinguish the Racc of such systems from the system in absence of ligand, we suggest full lability (as theoretically expected by ξtheo) and estimate cDIET=cT,M.
For the rest of complexes in Table 3, cDIET values are reasonably in between the fully labile case, when cDIET=cT,M (practically reached for Cu-salicylate), and the completely inert case, when cDIET=cM (approached by the Cu-IDA system).

Positive complexes
Theoretical lability degrees for the Cu-en system computed with Eqn. (8) yielded a value of 1 (see Table 4). Racc is proportional to the total metal concentration (see Fig SI- higher than that for neutral complexes (assuming a common bulk free metal concentration).

Negative complexes
In Table 4, the theoretical lability degree is computed with Eqn. (8), even if only the citrate systems are clearly under conditions of excess ligand. For these systems no determinations of ξ are possible due to the fast attainment of equilibrium (see Fig 4).
Theoretical ξ values for negative complexes with EDTA are practically 0, as expected from the repulsion of the complex from the resin and the strong ML affinity constant.
Consequently, Racc are clearly different from the solutions where the metal is present  Fig SI-9). The values of ξ retrieved from Racc using Eqn. (20) are slightly negative, which we attribute to experimental uncertainties, but in agreement with a practically totally inert behaviour. The values of cDIET are, accordingly, usually slightly lower than (or almost equal to) the theoretical free fraction.
So, in the Cu/Ni-EDTA systems, the use of DIET can effectively determine the free metal ion concentration in the sample.

Conclusions
The (practically) constant effluent concentration, described as "SS plateau", seen at short enough times in the breakthrough curves, is associated to a steady-state regime where the beads act as perfect sink for free metal (i.e., they are far away from equilibrium). This (quasi) steady-state regime also explains the initial linear accumulations having a lower slope (i.e. slower Racc) than for metal solutions in absence of ligand, or solutions of completely labile complexes (that in the probed systems showed an almost complete retention of the metal, so that Racc approximates Q cT,M).
One cannot directly relate Racc to the free metal concentration. While this approximation is reasonable in the case of extremely inert complexes (such as Cu/Ni-EDTA), for the majority of the systems assayed here, the rate of metal accumulation includes a contribution from the dissociation of the metal complex. The DIET-labile concentration cDIET, as defined in equation (21), quantifies the labile concentration of a system in DIET measurements using ion exchange resins. Model IV leads to the practical Eqns. (22) and (23)  Most of the complexes considered were found to be completely labile, in some cases contrasting with previous voltammetric studies ( Agraz et al. 1993). This tendency for DIET to "labilize" the complexes, not dissimilar to the one of DGT (Figura and Mcduffie 1979;Mongin et al. 2011;Puy et al. 2012;van Leeuwen et al. 2005), is a consequence of the complexes penetrating beads with radii being relatively large, in comparison with typical voltammetric reaction layer thicknesses.
The resin bed length has a key role in the retrieved global lability parameter Ξ (see Eqn. (18)). The longer the column, the higher the global lability seen by DIET. This means that each column has an analytical window of labilities, so that future work with columns  Tables   Table 1. Models developed in this work to describe the analyte accumulation by the resin. The models are categorised according to the regimes they assume (only steady-state or all regimes) and the geometry of the system (single spherical resin bead or whole packed column). The    Cu-Malate Cu-Salicylate 5×10 -3 2.34×10 -7 1.00 d ≈1 b 0.95 1.6×10 -3 ≈1 2.23×10 -7 ≈cTM b 1.60×10 -8

Ni-Malonate
a The positively charged species Cu-HGlutamate + , which accumulates in the resin along with the free metal, is present at a bulk concentration equal to 2.36×10 -9 mol L -1 b The initial slope of the accumulation curve (Racc) practically coincides with the one of metal in absence of ligand     Table 3 for composition details. The dotted lines in panels b and c are a guide to the eye.