Lucija Knežević

Emanuele Zanda

Elvira Bura-Nakić

Montserrat Filella

Vladimir Sladkov
email: vladimir.sladkov@ijclab.in2p3.fr

Vanadium(IV) and vanadium(V) complexation by succinic acid studied by affinity capillary electrophoresis. Simultaneous injection of two analytes in equilibrium studies

Keywords: Affinity capillary electrophoresis / Complexation / Stability constants/ Vanadium / Succinic acid pot.potentiometry, ESEEM sp.electron spin echo envelope modulation spectrosccopy, sp. -spectrophotometry

The interaction of V(IV) and V(V) with succinic acid was investigated by affinity capillary electrophoresis (ACE) in aqueous acid solutions at pH values 1.5, 2.0 and 2.4, and different ligand concentrations. V(IV) and V(V) form protonated complexes with succinic acid ligand at this pH range. The logarithms of the stability constants, measured at 0.1 mol L -1 (NaClO4/HClO4) ionic strength and 25°C, are logβ111=7.4±0.2 and logβ122=14.1±0.5 for V(IV), and logβ111=7.3±0.1 for V(V), respectively. The stability constant values, extrapolated to zero ionic strength with the Davies equation, are logβ°111=8.3±0.2 and logβ°122=15.6±0.5 for V(IV) and logβ°111=7.9±0.1 for V(V). The application of ACE to the simultaneous equilibria of V(IV) and V(V) (injection of two analytes) was also attempted. When the results were compared with those obtained when introducing only one analyte in the capillary, using the traditional version of the method, similar stability constants and precision are obtained. The possibility of studying two analytes simultaneously decreases the time needed for the determination of the constants; this feature is especially valuable when working with hazardous materials or when only small quantities of ligand are available.

Introduction

Thermodynamic data on complex equilibria of metal ions are very important, not only for fundamental knowledge reasons, but also in many diverse fields, such as toxicology, clinical and biological chemistry, geochemistry and environmental chemistry, and analytical and industrial processes [START_REF] Hummel | Where to find equilibrium constants?[END_REF]. Affinity capillary electrophoresis (ACE) is gaining an increasingly prominent place in metal ion equilibrium studies [START_REF] Timerbaev | Recent progress of capillary electrophoresis in studying the speciation of actinides[END_REF][START_REF] Varenne | Capillary electrophoresisinductively coupled plasma-mass spectrometry hyphenation for the determination at the nanogram scale of metal affinities and binding constants of phosphorylated ligands[END_REF][START_REF] Sursyakova | Composition and stability constants of copper(II) complexes with succinic acid determined by capillary electrophoresis[END_REF][START_REF] Huclier-Markai | A comparative thermodynamic study of the formation of scandium complexes with DTPA and DOTA[END_REF][START_REF] Konášová | Study of solvent effects on the stability constant and ionic mobility of the dibenzo-18-crown-6 complex with potassium ion by affinity capillary electrophoresis[END_REF][START_REF] Sladkov | Affinity capillary electrophoresis in studying the complex formation equilibria of radionuclides in aqueous solutions[END_REF][START_REF] Sornosa-Ten | Effects of preorganization in the chelation of UO22+ by hydroxamate ligands: cyclic PIPO-vs. linear NMA[END_REF][START_REF] Sladkov | Assignment of complex species by affinity capillary electrophoresis: The case of Th(IV)-desferrioxamine B[END_REF]. This technique has been successfully used, not only for the determination of complex stability constant with a 1 to 1 metal/ligand ratio, but also in the study of more complicated systems [START_REF] Sladkov | Interaction of uranyl with Se(IV) and Se(VI) in aqueous acid solutions by means of capillary electrophoresis[END_REF][START_REF] Sladkov | Uranyl complexation with acetate studied by means of affinity capillary electrophoresis[END_REF]. ACE is useful for establishing the stoichiometries of the complexes formed because the changes in the mobility of the complexes enables deduction of their degree of protonation [START_REF] Sladkov | Assignment of complex species by affinity capillary electrophoresis: The case of Th(IV)-desferrioxamine B[END_REF][START_REF] Sladkov | Interaction of uranyl with Se(IV) and Se(VI) in aqueous acid solutions by means of capillary electrophoresis[END_REF]. In this respect, ACE offers undeniable advantages over other classical methods.

A further interesting advantage of ACE is that it requires only a small quantity of analyte for thermodynamic equilibrium studies [START_REF] Sladkov | Assignment of complex species by affinity capillary electrophoresis: The case of Th(IV)-desferrioxamine B[END_REF]. This is especially important when working either with highly toxic or radiotoxic substances or with precious ligands.

The separation efficiency of the ACE also allows the study of simultaneous complexation equilibria including two or more metal ions with the same ligand. Although the possibility of using ACE for simultaneous determination of binding constants of several proteins with a ligand was pointed out in a pioneer work [START_REF] Chu | Use of affinity capillary electrophoresis to measure binding constants of ligands to proteins[END_REF], to our knowledge, this feature has not been explored in equilibrium studies of complexation of metal ions yet.

The differences between aqueous V(IV) and V(V) species offer the possibility of investigating whether the simultaneous equilibria of these metal ions. Since V(IV) and V(V) are present as VO(H2O)5 2+ [START_REF] Makinen | The structural basis of action of vanadyl (VO2+) chelates in cells[END_REF][START_REF] Rubinson | Concerning the form of biochemically active vanadium[END_REF][START_REF] Krakowiak | A Coordination Chemistry Study of Hydrated and Solvated Cationic Vanadium Ions in Oxidation States +III, +IV, and +V in Solution and Solid State[END_REF] and VO2(H2O)4 + [START_REF] Rubinson | Concerning the form of biochemically active vanadium[END_REF][START_REF] Krakowiak | A Coordination Chemistry Study of Hydrated and Solvated Cationic Vanadium Ions in Oxidation States +III, +IV, and +V in Solution and Solid State[END_REF][START_REF] Mehio | Theoretical study of the coordination behavior of formate and formamidoximate with dioxovanadium(v) cation: implications for selectivity towards uranyl[END_REF] ions, respectively, in aqueous solution, their different charges allow their easy separation by capillary electrophoresis.

There is a growing interest in the study of vanadium because of the potential environmental hazards linked to its increasing use [START_REF] Watt | Vanadium: A Re-Emerging Environmental Hazard[END_REF]. Vanadium is becoming important in energy storage because of its use as a valuable microalloying component. Such applications provide important opportunities in carbon dioxide reduction initiatives [START_REF] White | Vanadium: environmental hazard or environmental opportunity? A perspective on some key research needs[END_REF][START_REF] Santos | Assessing the role of vanadium technologies in decarbonizing hard-to-abate sectors and enabling the energy transition[END_REF]. Although large vanadium concentrations can cause harmful effects on ecosystems [START_REF] Teng | Environmental geochemistry and ecological risk of vanadium pollution in Panzhihua mining and smelting area, Sichuan, China[END_REF][START_REF] Nnama | Vanadium pentoxide induces hematological, oxidative stress and histological changes in Oryctolagus cuniculus[END_REF], the element seems to play a dual role in environmental systems since it is also considered, at micro concentration levels, as an element of beneficial character with a range of application for human welfare [START_REF] Hanus-Fajerska | A Dual Role of Vanadium in Environmental Systems-Beneficial and Detrimental Effects on Terrestrial Plants and Humans[END_REF].

Disentangling these apparently contradictory facts requires that vanadium is studied "to understand properly and contextually apply the chemistry of vanadium to its toxicological properties, environmental chemical forms and the development of new regulations and standards in order to maximize the benefits and mitigate any potential risks of utilizing vanadium" [START_REF] White | Vanadium: environmental hazard or environmental opportunity? A perspective on some key research needs[END_REF].

Vanadium is present in oxidation degrees IV and V in most natural waters and soils.

V(IV) is stable in moderately reducing conditions, especially under acidic pH values [START_REF] Gustafsson | Vanadium geochemistry in the biogeosphere -speciation, solidsolution interactions, and ecotoxicity[END_REF].

Among a variety of possible geochemical processes, complex formation with natural organic matter (NOM) present in the aqueous phase may play an important role in the eventual dispersion of vanadium [START_REF] Gustafsson | Vanadium geochemistry in the biogeosphere -speciation, solidsolution interactions, and ecotoxicity[END_REF]. The formation of such complexes typically causes significant changes in migration properties of chemical elements in the environment. Succinic acid is chosen here for complexation studies of V(IV) and V(V) as a simple model of the structurally more complicated NOM [START_REF] Lucks | Aqueous Uranium(VI) Complexes with Acetic and Succinic Acid: Speciation and Structure Revisited[END_REF][START_REF] Sladkov | Complexation of An(VI) with succinic acid in aqueous acid solutions: uranyl vs. plutonyl[END_REF]. Alongside, the complex equilibria of V(IV) and V(V) with succinic acid are poorly investigated. To our knowledge, only a few papers have been published containing stability constants for complexes of V(IV) with succinic acid [START_REF] Shelke | Ternary complexes: Equilibrium studies of mixed ligand complexes of vanadyl ion with some carboxylic and phenolic acids[END_REF][START_REF] Narasimhulu | Formation Constants of Oxovanadium(IV) & Cu(II) Chelates of Dicarboxylic Acids[END_REF][START_REF] Sakurai | A biomimetic model for vanadium-containing bromoperoxidase[END_REF][START_REF] Costa Pessoa | Oxovanadium(IV) complexes of the dipeptides glycyl-L-aspartic acid, L-aspartylglycine and related ligands; a spectroscopic and potentiometric study[END_REF][START_REF] Kornev | Homo-and heteroligand Vanadium(IV) complexes with β-Hydroxyethyliminodiacetic and dicarboxylic acids[END_REF] Existing data are gathered in table 1. Poor agreement is noted amongst the authors. Potentiometric studies [START_REF] Shelke | Ternary complexes: Equilibrium studies of mixed ligand complexes of vanadyl ion with some carboxylic and phenolic acids[END_REF][START_REF] Narasimhulu | Formation Constants of Oxovanadium(IV) & Cu(II) Chelates of Dicarboxylic Acids[END_REF][START_REF] Costa Pessoa | Oxovanadium(IV) complexes of the dipeptides glycyl-L-aspartic acid, L-aspartylglycine and related ligands; a spectroscopic and potentiometric study[END_REF] led to different sets of constants and values being proposed. Even when a larger pH range (2.0-6.7) was used, Costa Pessoa et al. [START_REF] Costa Pessoa | Oxovanadium(IV) complexes of the dipeptides glycyl-L-aspartic acid, L-aspartylglycine and related ligands; a spectroscopic and potentiometric study[END_REF] could not differentiate 111 and 121 complexes. Only one paper [START_REF] Tracey | Interactions of vanadate with mono-and dicarboxylic acids[END_REF] has been found where the interaction of V(V) with succinic acid had been studied by 51 V NMR spectroscopy, but no thermodynamic constants were provided.

The capabilities of ACE provide a suitable tool for the study of the complexation of V(IV) and V(V) with succinic acid. In this study, the possibility of studying V(IV) and V(V) simultaneously is explored. In this approach, two analytes are simultaneously injected and results compared with those obtained with the traditionally ACE methodology using single analyte injection. Finally, the obtained stability constant values are discussed in the light of available data from the literature for complexation of metal cations with succinic acid.

Materials and methods

Chemicals and solutions

All chemicals and reagents used were of analytical grade. 1 M perchloric acid solution was obtained from Fisher Scientific. Sodium perchlorate monohydrate (≥ 99 %) was supplied by Merck. Ammonium vanadate solution (≥ 99 %), vanadyl sulfate hydrate (≥ 99 %), succinic acid (≥ 99 %) and dimethyl sulfoxide (99.9%) were supplied by Sigma Aldrich. All solutions were prepared with fresh, high-purity deionized water (R = 18.2 M cm) produced by a Millipore direct Q cartridge system.

Apparatus, procedure and data treatment

Capillary Electrophoresis measurements. A P/ACE system MDQ capillary electrophoresis instrument (Beckman Coulter, France) was used. The system included a 0-30 kV high-voltage built in power supply equipped with a UV-vis spectrophotometric diode array detector. UV direct detection at 200 nm was used in this work. A capillary (50 µm I.D., 363 µm O.D.) made from fused silica was obtained from Beckman Instruments. It had a total length (Lt) of 31.2 cm and an effective separation length (Ld) of 21 cm. The capillary was housed in an interchangeable cartridge with circulating liquid coolant (temperature 25°C). Every measurement was repeated at least three times. Data acquisition and processing were carried out with Karat 32 software (Beckman Coulter, France).

The capillary was conditioned prior to use by successive washes with 0.1 M sodium hydroxide, deionised water and with the buffer solution used in the study. It was rinsed for 2 minutes (at a pressure of 103.4 kPa) with the buffer between two runs, and kept filled with deionised water overnight.

The procedure used in this study was similar to that previously described in [START_REF] Sladkov | Complexation of An(VI) with succinic acid in aqueous acid solutions: uranyl vs. plutonyl[END_REF]. Series of solutions containing different concentrations of succinic acid were prepared at the desired pH at an ionic strength of 0.1 M, from stock solutions of HClO4 (0.1M), NaClO4 (1 M) and succinic acid. The dissociation of succinic acid was taken into account in the solution preparation. These solutions were used as the background electrolytes (BGE). V(IV) and/or V(V) solutions at fixed concentrations of 5×10 -4 and 1×10 -3 M, respectively were injected in the capillary. In order to avoid hydrolysis and/or polymerisation of the V(IV) and V(V) ions, which could potentially lead to the formation of additional species and/or to the modification of the vanadium species mobility values, the pH value of solutions containing the BGE was < 2.5. At such pH values and V(IV) and V(V) concentrations, the contribution of hydrolysed and polymeric species is not noticeable (Fig. S1).

The normal polarity mode was applied (the injection was performed at the positive capillary end). The sample, containing the analyte (or analytes) and the neutral marker, was injected into the capillary. Dimethyl sulfoxide (0.05% DMSO) was used as a neutral marker for electroosmotic flow mobility determination. The capillary contained BGE with fixed concentrations of succinic acid. Sets of runs were then made for different concentrations of succinic acid (from 0 to 0.4 M) in BGE. The separation voltage applied was 5 kV and the injection time (by a pressure of 3.45 kPa) was 4 s. The value of the applied voltage was chosen to respect the Ohm's law linearity. The current was about 45 µA and the input power was about 0.2 W. In these conditions we can estimate that the effect of Joule heating is insignificant in the thermostated part of the capillary and the deviation from the desired temperature 25°C is at most 1°C [START_REF] Topin | Trace Metal Speciation by Capillary Electrophoresis Hyphenated to Inductively Coupled Plasma Mass Spectrometry: Sulfate and Chloride Complexes of Np(V) and Pu(V)[END_REF][START_REF] Evenhuis | Universal Method for Determining Electrolyte Temperatures in Capillary Electrophoresis[END_REF]. The non-thermostated capillary inlet has no influence on stability constant values obtained under such conditions [START_REF] Sladkov | Effect of non-thermostated capillary inlet in affinity capillary electrophoresis: Uranyl-selenate system at variable temperatures[END_REF][START_REF] Sladkov | Uranyl complexation with selenate at variable temperatures studied by affinity capillary electrophoresis[END_REF][START_REF] Sladkov | Interaction of uranyl with acetate in aqueous solutions at variable temperatures[END_REF]. The separation was performed at constant forward pressure of 1.4 kPa.

The electrophoretic mobility µ (m 2 s -1 V -1 ) was calculated by using the following expression:

µ = LtLd(1/t-1/teof)/U (1)
where Lt (m) was the total capillary length, Ld (m) the length between the capillary inlet and the detection window, U the applied voltage in V, t (s) the migration time of the studied species, and teof (s) the migration time of a neutral marker.

All concentration and constant calculations were performed with the EXCEL and ORIGIN software programs. The experimental points were fitted by a least squares curve method.

pH measurements. The pH was controlled with a pH-meter. pH-meter GLP-21 (Crison, France) and a combination electrode was used for pH measurements after calibration against NIST standards (4.01 and 7.00). The pH values of the solutions were in an interval of 0.05

units from desired values.

Perchlorate measurements. Combined ion specific electrode (ISE) "Fisher brand" for perchlorate from Fisher Scientific was used to check perchlorate concentrations of stock solutions and to control ionic strength. The RSD was less than 2%.

Ionic strength corrections

The Davies equation [37] was used to calculate activity coefficients of ions at low ionic strengths. The equation works fairly well up to ionic strengths (Im) of 0.1 mol kg -1 .

The Davies equation for the activity coefficient (γ) of an ion i of charge zi is at 25°C: log10γi = -0.5102 zi 2 (Im 1/2 /(1 + Im 1/2 ) -0.3Im)

3 Results and discussion

3.1 Monitoring of V(IV) and V(V) electrophoretic mobility: two analytes vs one.

The electropherograms obtained with an injection from the sample, containing the mixture of V(IV) and V(V) species, in the presence of different concentrations of succinic acid in BGE at pH=2 and an ionic strength 0.1 mol L -1 (HClO4-NaClO4) are presented in Figure 1A.

For comparison, the electropherograms obtained in the case of separate injections of V(IV) and V(V) are also shown in Figure 1B and 1C, respectively. As expected, the number of analytes injected does not have any influence on their mobilities. Only one peak is observed for each vanadium species, whose mobility is decreased with the increase of succinic acid concentration in BGE. This indicates that we deal with kinetically labile complexes [START_REF] Sladkov | Affinity capillary electrophoresis in studying the complex formation equilibria of radionuclides in aqueous solutions[END_REF][START_REF] Krylov | Kinetic CE: Foundation for homogeneous kinetic affinity methods[END_REF]. The equilibrium is sufficiently fast and the time required for equilibrium negligible compared with the separation time. The kinetic behaviour of the aqua complexes of metal ions can serve as a reference point for complex formation reactions. The loss of the first water molecule from the first coordination sphere is an important step in complex formation of metal cations [START_REF] Helm | Water exchange on metal ions: experiments and simulations[END_REF], and is often the rate determining step. For V(IV) aqua-complex (VO(H2O)5 2+ ), the half life for four equatorial water ligand exchange is ~1 ms. The half time for a water ligand located opposite to the doublebonded oxygen is about 10 -11 s [START_REF] Rubinson | Concerning the form of biochemically active vanadium[END_REF][START_REF] Reuben | Magnetic resonance studies of ion solvation. The hydration of the vanadyl(IV) ion[END_REF]. For V(V) (VO2(H2O)4 + ), the water rate exchange constant is estimated at 10 8.2 s -1 [START_REF] Yamada | Kinetics and mechanism of the complexation reactions of pervanadyl ion with some aminopolycarboxylates[END_REF]. These values confirm our ACE observation of fast ligand exchange (only one peak is observed). V(V) peaks are narrower than V(IV) examples (Figure 1). This may indicate, that the exchange kinetic is faster for V(IV) than for V(V). This observation also agrees with the kinetic data given above. V(IV) (VO 2+ ) has a double charge in comparison with V(V) (VO2 + ). Thus, as expected, V(IV) mobility is greater (migration time is lower) than for V(V). The mobility observed corresponds to the sum of mobilities of coexisting charged species formed with the ligand under study (eq.3)

𝜇 obs = ∑ 𝛼 𝑖 𝑖 𝜇 𝑖 (3)
In Eq.3, μi stands for the intrinsic electrophoretic mobility and i for the molar fraction of individual species (i) present in the migration band.

The decrease in the global charge of the species when increasing the concentration of succinic acid (migration time increases) (fig. 1) suggests the formation of a less charged complex species with increasing succinic acid concentration.

Chemical equilibria and stability constants

The equilibria of the vanadium species with the succinate ligand (denoted as L 2-further) can be expressed as:

V(IV)

VO 2+ + 𝑛L 2-+ 𝑚H +  VOL 𝑛 H 𝑚 2-2𝑛+𝑚 (4)
with the corresponding stability constant β1nm

𝛽 1𝑛𝑚 = [ VOL 𝑛 H 𝑚 2-2𝑛+𝑚 ] [VO 2+ ][L 2-] 𝑛 [H + ] 𝑚 (5)
V(V)

VO 2 + + 𝑛L 2-+ 𝑚H +  VO 2 L 𝑛 H 𝑚 1-2𝑛+𝑚 (6)
with β1nm

𝛽 1𝑛𝑚 = [VO 2 L 𝑛 H 𝑚 1-2𝑛+𝑚 ] [VO 2 + ][L 2-] 𝑛 [H + ] 𝑚 (7)
Equilibrium constant values can be obtained by fitting experimental mobilities (Tables S2-S6) using the general equation ( 3). A non-linear fitting (NNLS) method is preferred over a linear regression method [START_REF] Bowser | Monte Carlo Simulation of Error Propagation in the Determination of Binding Constants from Rectangular Hyperbolae. 1. Ligand Concentration Range and Binding ConstantJ[END_REF][START_REF] Bowser | Monte Carlo Simulation of Error Propagation in the Determination of Binding Constants from Rectangular Hyperbolae. 2. Effect of the Maximum-Response Range[END_REF][START_REF] Šolínová | Estimation of apparent binding constant of complexes of selected acyclic nucleoside phosphonates with β-cyclodextrin by affinity capillary electrophoresis[END_REF].

In this case, the molar fraction of species to be introduced in equation ( 3) can be written as V(IV)

 1𝑛𝑚 = [VOH 𝑛 L 𝑚 2+𝑛+2𝑚 ] C(V(IV)) = 𝛽 1𝑛𝑚 10 -𝑛pH 𝛼 𝑑𝑖𝑠 [L -] 𝑚 1 + 𝛴𝑚𝛽 1𝑛𝑚 10 -𝑛pH 𝛼 𝑑𝑖𝑠 [L -] 𝑚 (8)
V(V)

 1𝑛𝑚 = [VO 2 H 𝑛 L 𝑚 1+𝑛+2𝑚 ] C(V(V)) = 𝛽 1𝑛𝑚 10 -𝑛pH 𝛼 𝑑𝑖𝑠 [L -] 𝑚 1 + 𝛴𝑚𝛽 1𝑛𝑚 10 -𝑛pH 𝛼 𝑑𝑖𝑠 [L -] 𝑚 (9),
where 𝛼 𝑑𝑖𝑠 is a molar fraction of succinate.

Succinic acid protonation equilibria in aqueous solution are [START_REF] Reuben | Magnetic resonance studies of ion solvation. The hydration of the vanadyl(IV) ion[END_REF]:

H2L ⇆ HL -+ H + , pK1=4.00 (25°C, I=0.1 M) (10)
HL -⇆ L 2-+ H + , pK2=5.24 (25°C, I=0.1 M) (11)
Thus, the total succinic acid concentration is:

C(L)= [H2L] + [HL -] + [L 2-] (12),
We note that the system suffers from a mathematical indetermination, meaning that the product 111111 (eq. 3) is well defined but each individual term, 111 and 111, cannot be precisely determined. A similar case has been already described in [START_REF] Sladkov | A solution-and gas-phase study of uranyl hydroxamato complexes[END_REF]. In this case, to reach convergence it was necessary to make a reasonable guess of the 111 value and to keep this value constant.

The same approach is used in this study.

In the case of V(IV), the best fits were found for the model with two complexes (1:1:1)

and (1:2:2). The constants obtained at different pH values are given in table 2 for the two cases:

that of only one analyte injected and also of two analytes simultaneously injected. The values obtained are practically the same. It is worthwhile to note that our value for logβ111 is very close to that proposed by [START_REF] Costa Pessoa | Oxovanadium(IV) complexes of the dipeptides glycyl-L-aspartic acid, L-aspartylglycine and related ligands; a spectroscopic and potentiometric study[END_REF]. For the second constant (1:2:2) the error is much larger, because the concentration of this species is low in our conditions.

In the case of V(V), only one complex (1:1:1) was found. Again, no significant difference was observed between the values obtained with only one analyte injection or the simultaneous injection of two analytes.

The average values for V(IV) and V(V) complexes are also shown in Table 2. The stability of protonated complexes (1:1:1) for V(IV) and V(V) is practically the same. We extrapolated the stability constant values to zero ionic strength with the use of the Davies equation [START_REF] Timerbaev | Recent progress of capillary electrophoresis in studying the speciation of actinides[END_REF]. Thermodynamic stability constants are also presented in table 2.

Comparison with literature data

A Linear Free Energy Relationship (LFER) is applied to compare our values with literature data for complexes formed by different metal ions with succinate. This approach is commonly used in the literature to compare the affinity of a given ligand for a series of metal cations (M z+ ). The effect of the negatively charged oxygen-donor group of the ligand on complex stability appears to depend on the acidity of the metal ion considered, i.e., the affinity of the metal ion for the archetypal negative O-donor ligand, the OH -ion [START_REF] Hancock | Ligand design for selective complexation of metal ions in aqueous solution[END_REF]. Thus, the stability constant of metal ion complexes with a ligand, containing an oxygen-donor group, correlates with the formation constant KMOH on a log-log scale, indicating that the stability depends primarily on the Lewis acidity of the metal ion, similar to that expected for an electrostatic interaction. Moreover, a similar binding mode can also be inferred from such linear plots.

Figure 3 shows a LFER where logβ111 is plotted as a function of log KMOH for different metal ions, including the logβ111 values for V(IV) and V(V) measured by ACE in this study.

Other stability constant values at 0.1 M ionic strength and 25 °C were taken from the literature (Table S7). A good linear trend is observed for all cations, except for V(V). The logβ111 for V(V) is lower than predicted from the LFER correlation. This suggests that V(V) complexation is not only governed by electrostatic interactions, but that there might be a significant contribution of a steric factor. Indeed, the VO2(H2O)4 + displays a very distorted octahedral configuration with a O=V=O bond angle of ca. 105° [START_REF] Krakowiak | A Coordination Chemistry Study of Hydrated and Solvated Cationic Vanadium Ions in Oxidation States +III, +IV, and +V in Solution and Solid State[END_REF]. This can hamper the electrostatic interaction with the ligand and weaken complex stability. Most probably, for the same reason, the oxalate complexes of V(IV) are more stable than those of V(V) [START_REF] Bruyère | Reduction of vanadium(v) by oxalic acid in aqueous acid solutions[END_REF].

Conclusions

We demonstrate in this study the possibility of using the simultaneous injection in a capillary of two metal cations in equilibria studies by ACE. Certainly, this is a very attractive feature of this method since it can drastically decrease the time needed for equilibria studies and, moreover, allow the fast screening of interactions. This is especially important when manipulating hazardous and/or precious materials. It is expected that three or more analytes can be used simultaneously in equilibria studies provided they have different enough mobilities.

This study also describes a significant contribution to the knowledge of V(IV) and V(V) chemistry. For the first time, to our knowledge, the existence of a protonated V(V) complex

Figure 1 .

 1 Figure 1. Electropherograms of 5x10 -4 M V(IV) and 1x10 -3 M V(V), in the presence of different amounts of succinic acid in BGE. Ligand concentrations in BGE from bottom to the top: 0, 1x10 -3 , 6x10 -3 , 8x10 -3 , 0.04, 0.08, 0.1, 0.2, 0.3 and 0.4 M. Asimultaneous injection of two analytes. Binjection only V(IV). Cinjection only V(V). pH=2, I=0.1 M (NaClO4 -HClO4). Detection wavelength: 200 nm, T=25°C.

Figure 2 .

 2 Figure 2. Mobilities of V(IV) (triangles) and V(V) (circles) at pH=1.5 (empty markers) pH=2 (half-full markers) pH=2.4 (full markers) as a function of total ligand concentration, [H2L], [HL -] -and [L 2-]. Simultaneous injection of two analytes. All other conditions as in figure 1.

Figure

  Figure 3. Plot of the stability constant (log 𝛽111) of different metal ions with succinic acid as a function of the first metal hydrolysis (log KMOH).

Table 1 .

 1 3.Plot of the stability constant (log 𝛽111) of different metal ions with succinic acid as a function of the first metal hydrolysis (log KMOH). Published stability constants for the V(IV)-succinic acid system. The constants are given for the equilibrium: VO 2+ + 𝑛L 2-+ 𝑚H +  VOL 𝑛 H 𝑚 2-2𝑛+𝑚 . If not mentioned otherwise, the values are presented in the form given in the original sources.

	Al 3+

Table 2 .

 2 Stability constant values obtained for V(IV)-succinic acid and V(V)-succinic acid equilibria. Values at I=0.1 M (NaClO4-HClO4), except the last row where I=0 M. T=25°C. only for the same number of analytes injected and different pH values

	** for all measurements

N-analyte injection index *

where C(L) is the total succinic acid concentration, and [H2L], [HL -] and [L 2-] the concentrations of the different forms of succinic acid at equilibrium. At pH ≤ 2.5 succinic acid is mainly present in its completely protonated form, as H2L (Fig. S2).

Protonated complexes with succinic acid for the transition metal ions are known [START_REF] Sladkov | Complexation of An(VI) with succinic acid in aqueous acid solutions: uranyl vs. plutonyl[END_REF][START_REF] Morphy | Towards tumour targeting with copper-radiolabelled macrocycle-antibody conjugates: synthesis, antibody linkage, and complexation behaviour[END_REF], but mostly deprotonated complexes of V(IV) with succinic acid have been described in the literature (Table 1). Only Costa-Pessoa et al. [START_REF] Costa Pessoa | Oxovanadium(IV) complexes of the dipeptides glycyl-L-aspartic acid, L-aspartylglycine and related ligands; a spectroscopic and potentiometric study[END_REF] suggest the formation of a protonated species with V(IV). Owing to the complex charge change linked to protonation or deprotonation, it is possible to distinguish protonated from deprotonated complexes by ACE [START_REF] Sladkov | Affinity capillary electrophoresis in studying the complex formation equilibria of radionuclides in aqueous solutions[END_REF][START_REF] Sladkov | Assignment of complex species by affinity capillary electrophoresis: The case of Th(IV)-desferrioxamine B[END_REF][START_REF] Sladkov | Complexation of An(VI) with succinic acid in aqueous acid solutions: uranyl vs. plutonyl[END_REF]. The identification of the interacting species requires the variation of the concentration of each succinic acid species in order to know which influences the vanadium species mobility [START_REF] Sladkov | Interaction of uranyl with Se(IV) and Se(VI) in aqueous acid solutions by means of capillary electrophoresis[END_REF][START_REF] Sladkov | Uranyl-Se(IV) interaction in aqueous acid solutions studied by time-resolved laser-induced fluorescence spectroscopy (TRLFS) and UV-Vis spectrophotometry[END_REF]. As all succinic species are present in the dynamic equilibria, it is not possible to vary the concentration of only one species without modifying the concentrations of the rest. Thus, it is necessary to plot the V(IV) and V(V) mobilities, measured at different acidic pH values (Figure 2), as a function of the total succinic acid (A), [H2L] (B), [HL -] (C) and [L 2- ] (D) concentrations. We can state unambiguously the similarity of the curves in the case of HL - for V(IV) and V(V). However, in the case of V(V), a slightly lower mobility is observed at pH 2.4, because of about 15% hydrolysis of V(V) and the corresponding formation of a less charged species (Fig. S1A). It can be concluded that only HL -affects the vanadium species mobility. Thus, most probably, we have a formation of mainly protonated complex species of V(IV) and V(V) with succinic ligand in these conditions. The graphs presented in fig. 2 were obtained in the case of simultaneous injection of V(IV) and V(V). As expected, similar graphs are obtained when analytes are introduced separately (Fig. S3).

Considering only the equilibria with HL -as the ligand, different models were explored: formation of one 1:1:1 complex, simultaneous formation of two complexes (1:1:1 and 1:2:2), formation of one 1:2:2 complex, simultaneous formation of two complexes (1:1:1 and 1:2:1). with succinic acid is illustrated and the corresponding stability constant measured. A significant insight is also provided on V(IV)-succinic acid complexation.

Acknowledgements

The authors would like to thank COST NECTAR action (CA18202), Ruđer Bošković Institute, the Centre National de la Recherche Scientifique (CNRS/IN2P3) and Croatian Science Foundation (IP-2018-01-7813, project "REDOX") for their financial support.

CRediT author statement:

Lucija Knežević: Investigation, Formal analysis, Methodology, Data curation, Visualization.

Emanuele Zanda: Formal analysis, Methodology.