# Study of Ca\_nUO\_2(CO\_3)\_3(4--2n)\-- complexes using CE-ICP-MS with polyetheretherketone (PEEK) capillaries

Ruopei Sun, Erwan Dupuis, Jean Aupiais, Pascal E. Reiller

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Ruopei Sun, Erwan Dupuis, Jean Aupiais, Pascal E. Reiller. Study of Ca_nUO_2(CO_3)_3(4--2n)\-- complexes using CE-ICP-MS with polyetheretherketone (PEEK) capillaries. Dalton Transactions, 2025, 54 (2), pp.719-727. 10.1039/d4dt02781g. cea-04867460

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# Study of Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-) complexes using CE-ICP-MS with polyetheretherketone (PEEK) capillaries

Ruopei Sun,<sup>a</sup> Erwan Dupuis,<sup>a</sup> Jean Aupiais,<sup>b</sup> and Pascal E. Reiller<sup>*</sup>

<sup>a</sup> Université Paris-Saclay, CEA, Service de Physico-Chimie (SPC), F-91191 Gif-sur-Yvette CEDEX, France

<sup>b</sup> CEA, DAM, DIF, Arpajon Cedex, F-91297, France

<https://doi.org/10.1039/d4dt02781g>

## Abstract

The formation constants of Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-) complexes have been determined directly using capillary electrophoresis coupled with inductively coupled plasma mass spectrometry (CE-ICP-MS) in 0.1 M NaCl and at room temperature. Instead of conventional fused silica, polyetheretherketone (PEEK), a neutral organic material, was used as the capillary material to avoid interactions between uranyl and silica. Since PEEK is not optically transparent, a macrocyclic neutral complex, Ga-NOTA was used to measure the electroosmotic flux directly with the ICP-MS. The impact of Joule effect was evaluated to control the temperature during electrophoreses. To alter the reversible interaction that arose from continuous use, a two-mode electrophoresis strategy was adopted. The observed mobilities of the samples showed a satisfactory correlation with the theoretical charge calculated previous data (Shang & Reiller, Dalton Trans., 2020, 49, 466). The successive formation constants obtained in this work, log<sub>10</sub>K(CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup>) = 5.28 ± 0.39 and log<sub>10</sub>K(Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)) = 8.46 ± 0.67 at 0.1 M NaCl were extrapolated to infinite dilution using Davies equation, yielding log<sub>10</sub>β°(CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup>) = 27.12 ± 0.39 and log<sub>10</sub>β°(Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)) = 30.30 ± 0.67. These values are in excellent agreement with Shang & Reiller (Dalton Trans., 2020, 49, 466). This is further verifying the thermodynamic data available for these species, and validating PEEK-based capillary electrophoresis for the measurement of thermodynamic constants of inorganic complexes in alkaline media.

## Introduction

The alkaline earth(II)triscarbonatoactinyl(VI) (Ae-An(VI)-CO<sub>3</sub>) complexes have attracted extensive attention since their identification in a seepage water from a German uranium mine in the 1990s.<sup>1</sup> They have been shown to form with alkaline earths from Mg to Ba,<sup>2</sup> and for actinyl ions U(VI)<sup>3,4</sup> and Pu(VI).<sup>5</sup> Accounting for the abundance of carbonate and calcium in the environment, the Ae-U(VI)-CO<sub>3</sub>
complexes are considered as the dominating species in certain natural waters,⁴,⁶ especially in those close
to a nuclear waste disposal site.⁷ The formation of Ca-U(VI)-CO₃ complexes is supposed to enhance
the mobility of uranium in aqueous media,⁸⁻¹⁰ and seems to hinder the adsorption on minerals.¹¹,¹²
Researchers have applied various methods to study and understand the behaviour of the complexes,
ultraviolet-visible (UV-Vis) absorption spectroscopy,¹³,¹⁴ extended X-ray Absorption Fine Structure
(EXAFS),¹⁵⁻¹⁸ anion exchange,²,¹⁹,²⁰ ion selective electrodes (ISE),¹⁴ time-resolved laser-induced
luminescence spectroscopy (TRLFS).¹,²¹⁻²⁶

Besides the techniques used above, capillary electrophoresis coupled with inductively coupled plasma mass spectrometry (CE-ICP-MS) combines the separating power of capillary electrophoresis (CE) and the high sensitivity and selectivity of inductively coupled plasma mass spectrometry (ICP-MS), which enables analysing samples at very low concentrations, i.e. less than 10⁻⁷ M for Pu and Np.²⁷ CE-ICP-MS has been already applied to study the complexation and hydrolysis of actinides²⁸⁻³¹. Fused silica is predominantly used as the capillary material for its high durability, low thermal expansion and UV-transparency. Nevertheless, the surface of silica is highly reactive;³²⁻³⁴ depending on the chemical system studied, undesirable broadening and distortion of peaks can occur.³⁵,³⁶ A great deal of effort has been done to minimize the interaction between the capillary and the analyte, such as dynamic modification and permanent coatings.³⁵,³⁷⁻³⁹ However, these modifications are not always stable against time or the solutions used in CE and may bring interferences to the analytes.³⁹ In addition, the interactions between uranyl and silica are well known in our case in particular.³²⁻³⁴ Organic polymer capillaries could be an attractive alternative as they are chemically more inert than fused silica. Nonetheless, only a few studies have been conducted with these materials, yet.⁴⁰⁻⁴²

Polyetheretherketone (PEEK) capillaries were chosen to investigate the behaviour of Ca-U(VI)-CO₃ complexes in this study. They have been wildly used in chemical analysis, such as liquid chromatography,⁴³,⁴⁴ ion chromatography,⁴⁵ and electrospray,⁴⁶ owing to its high chemical resistance, thermal stability, robustness, and flexibility. As an example, fused silica is not suitable for electrophoresis at pH 11-12, due to increased SiO₂ solubility.³²,⁴⁷

The aim of this study is to validate the use of the PEEK capillaries for the determination of thermodynamic constants for actinide complexation in general, and actinyl(VI) in particular, under alkaline and carbonated conditions. The physico-chemical inertness of PEEK towards actinyl(VI) species will be verified. Due to the opacity of PEEK capillaries in the UV-visible spectroscopic range, the complex between gallium(III) and N,N',N''-triazacyclononanetriacetic acid (NOTA)⁴⁸ will be validated as a neutral marker of the electroosmotic flow for CE-ICP-MS measurements. The Joule effect, which is affecting temperature inside the capillary, will be determined. Finally, a series of Ca-
U(VI)-CO₃ samples in 0.1 M NaCl, following the protocol from Shang & Reiller,²⁵ will be studied at room temperature using a PEEK capillary, to calculate the corresponding formation constants, and ascertain the analytical strategy for Ae-An(VI)-CO₃ complexation constant determinations using CE-ICP-MS.

## Experimental

### Electrolytes

The electrolyte solutions were prepared at an ionic strength of 0.1 mol/kg<sub>w</sub> by dissolving NaCl (Merck, 99.99 Suprapur) in Millipore deionized water (Alpha-Q, 18.2 MΩ.cm); 25 mM of Tris buffer (Sigma-Aldrich, ultrapur) was added to keep the pH constant during electrophoresis; CaCl₂ solution of 0.01 and 0.1 mol/kg<sub>w</sub> were prepared dissolving calcium chloride (Acros Organics, ACS reagent) in deionized water to control the calcium content. Carbonate was introduced by adding NaHCO₃ (Sigma-Aldrich, ACS reagent) solution, with the concentration calculated from the atmospheric equilibrium at the desired pH using thermodynamic data from Table 1. The samples were later left open to air for two hours to reach equilibrium. All the electrolytes were prepared by weighing.

### Sample preparation

The U(VI) stock solution was prepared by dissolving U₃O₈ in 37% hydrochloric acid (SCP Science, PlasmaPurePlus) during one week. Aqueous uranium concentration of this stock solution was determined by inductively coupled plasma mass spectroscopy (ICP-MS). A sub-stock uranium solution of 50 µmol/kg<sub>w</sub> was prepared diluting an appropriate amount of U(VI) stock solution in an 0.1 mol/kg<sub>w</sub> NaCl solution. This sub-stock solution was further diluted in the background electrolytes to obtain a final concentration of 5 µmol/kg<sub>w</sub> of U(VI). In order to control the performance of PEEK capillary, 5 µmol/kg<sub>w</sub> of CsCl was spiked in the solution. Finally, 1% of Ga-NOTA was spiked in the solution as the electroosmotic marker.

### Control of pH values

Following preceding works,²⁵,²⁶,⁴⁹ the pH measurements were performed at room temperature. The pH meter (SevenEasy S20, Mettler Toledo) was calibrated regularly with four pH buffers (1.68, 4.01, 6.87, and 9.18, SI Analytics) to ensure the accuracy. Potential values read on the pH-meter were plotted against the pH values of the buffers to perform the linear regression and to calculate the 95% confidence interval. This strategy allowed controlling the uncertainty of pH measurement below 0.05 pH unit. For each sample and electrolyte, the pH value was determined after the equilibrium with atmospheric CO₂ and regularly checked before the electrophoresis experiments.
## Joule effect

Since PEEK has been seldom used as capillary for electrophoresis, the Joule effect during electrophoresis process had to be evaluated before experiments to control the evolution of temperature during the electrophoresis process. The PEEK capillary was filled with a 0.1 M NaCl solution, and a series of voltage from 1 to 20 kV was applied to measure the corresponding current. The experiments were done at 15, 20, 25, 35, 45, and 55°C, while the temperature was regulated by the CE system (Agilent) itself. For these experiments, the CE was not coupled to the ICP-MS and the entirety of the capillary was located in the instrument's air-cooled cassette.

## Electroosmotic flow measurement using Ga-NOTA

Since the PEEK capillary is not transparent to the ultraviolet detector used in conventional capillary electrophoresis, a complex between $Ga^{3+}$ and 2,2',2''-(1,4,7-triazacyclononane-1,4,7-triyl)triacetic acid (NOTA), a highly stable neutral complex ($log_{10}K = 30.98$ in 0.1 M KCl at 25°C),⁵⁰ was chosen as the marker to calculate the electroosmotic mobility. Considering the complexing ability of NOTA³⁻, a Ga-NOTA solution were prepared by dissolving $Ga(NO_3)_3·9H_2O$ (Fluka, puriss.) in excess in deionized water with NOTA (CheMatech) to ensure NOTA would not form complex with uranium.

## Electrophoresis

Capillary electrophoresis separations were conducted using a commercial 7100 CE system (Agilent). PEEK capillaries—inner diameter (i.d.) 50/75/100 µm, outer diameter (o.d.) 360 µm, IDEX Health & Science—were cut to 105 cm and were conditioned for 10 min with 2% $HNO_3$, 10 min with deionized water, and 10 min with 0.1 M NaOH (Merck, >99%) before use. Before and between each electrophoresis experiment, the capillary was rinsed with 2% $HNO_3$ for 2 min, deionized water for 2 min, and background electrolyte for 2 min. Samples were injected in the capillary at 50 mbar for 7 s, and the electrophoresis were carried out at the desired voltage between -5 and +5 kV, under a pressure of 50 mbar.

The CE was coupled with a single quadrupole ICP-MS (Xseries II, Thermo Scientific) using a MiraMist CE nebulizer (Burgener Research). The argon flowrate of the nebulizer was set to 0.9 mL/min, using a dedicated, high-pressure mass flow controller; the make-up liquid (90% background electrolyte + 10% ethanol, w/w) was introduced using a pressure controller (Fluigent) at ca. 10 µL/min.
## Theoretical

### Calculation of mobility and stability constants

Formation of Ca-U(VI)-CO₃ complexes and their formation constants can be described as follows:

$$n\text{Ca}^{2+} + \text{UO}_2(\text{CO}_3)_3^{4-} \rightleftharpoons \text{Ca}_n\text{UO}_2(\text{CO}_3)_3^{(4-2n)-}$$

$$K_n = \frac{[\text{Ca}_n\text{UO}_2(\text{CO}_3)_3^{(4-2n)-}]}{[\text{Ca}^{2+}]^n [\text{UO}_2(\text{CO}_3)_3^{4-}]} \quad (1)$$

where square brackets represents concentration on the molality scale (mol/kgw).

Considering the kinetics of the complexes during electrophoreses, Sonke and Salters⁵¹ defined a metal-ligand half life t₁/₂ and categorized the electrophoretic behaviour into three cases: (i) stable complexes (t₁/₂ > 10³ s), the equilibrium is significantly slower than the duration of electrophoresis, consequently each complex appears as an individual peak; (ii) labile complexes (t₁/₂ < 10⁻³ s), the equilibrium is sufficiently fast compared to the duration of electrophoresis and all the complexes turn out to be one single peak; (iii) potential disequilibrium (10⁻³ s < t₁/₂ < 10³ s), this case should be avoided because it leads to deformed peaks or double peaks, which are complicated to interpret. Ca-U(VI)-CO₃ complexes seemed to be the labile case experimentally since we only observed one uranium peak in the electropherograms.

The electrophoretic mobility of this peak can be measured with Equation 2,

$$\mu = \frac{L^2}{V} \left( \frac{1}{t} - \frac{1}{t_{\text{eof}}} \right) \quad (2)$$

where μ is the electrophoretic mobility (m² V⁻¹ s⁻¹) of the peak, L is the length of the capillary (m), V is the applied voltage (V), t is the migration time of the uranium peak (s), and t eof is the migration time of the neutral marker.

This peak is a mixture which contains all the species UO₂(CO₃)₃⁻, CaUO₂(CO₃)₃²⁻ and Ca₂UO₂(CO₃)₃(aq). Therefore, the global mobility can also be expressed as a sum of all species according to their molar fraction α.⁵²
$$ \mu = \sum_{i=0}^{n} \alpha_{Ca_nUO_2(CO_3)_3^{(4-2n)-}} \times \mu_{Ca_nUO_2(CO_3)_3^{(4-2n)-}} \quad (3) $$

Applying equation (1), equation (3) can be simplified as:

$$ \mu = \frac{\mu_0 + [Ca^{2+}]\mu_1K_1 + [Ca^{2+}]^2\mu_2K_2}{1 + [Ca^{2+}]K_1 + [Ca^{2+}]^2K_2} \quad (4) $$

where $\mu_n$ and $K_n$ are the electrophoretic mobility and formation constant of $Ca_nUO_2(CO_3)_3^{(4-2n)-}$, respectively. Equation (4) was implemented in Origin 8.0 (OriginLab, USA) to calculate the constants by fitting the $Ca^{2+}$ concentration of each sample and their observed mobility.

## Ionic strength correction

The Davies equation, since its general form depends only on the ionic strength of the solution, is wildly used to extrapolate the thermodynamic constants to infinite dilution for solutions of an ionic strength less than 0.3 mol/L.⁵³ This equation can be written as follows:

$$ \log_{10}\gamma_i = -Az_i^2\left(\frac{\sqrt{I_m}}{1+\sqrt{I_m}}-0.3 I_m\right) \quad (5) $$

where $\gamma_i$ is the activity coefficient, A is a parameter depending on temperature,⁵⁴ $z_i$ is the charge of the particular ion $i$, and $I_m$ is the ionic strength of the solution on the molal scale.

Therefore, for the formation of a complex $ML_j$, the formation constant to infinite dilution can be written as:

$$ \log_{10}K_j^\circ = \Delta\log_{10}\gamma + \log_{10}K_j \quad (6) $$

in which $\Delta\log_{10}\gamma = \log_{10}\gamma(ML_j) - \log_{10}\gamma(M) - j\log_{10}\gamma(L)$.

Using Davies equation (Equation 5), $\Delta\log_{10}\gamma$ can be calculated as:

$$ \Delta\log_{10}\gamma_i = -A\Delta z_i^2 \left( \frac{\sqrt{I_m}}{1+\sqrt{I_m}} - 0.3 I_m \right) \quad (7) $$
where $\Delta z^2 = z(ML_0)^2 - z(M)^2 - j z(L)^2$.

The widely accepted review of thermochemical data on uranium is based on the specific ion interaction theory (SIT).⁵⁴ Equation 8 is then expressed as follows for a species M towards a counter ion X from the background electrolyte.

$$ \Delta \log_{10} \gamma_M = -Az_i^2 \frac{\sqrt{I_m}}{1 + 1.5\sqrt{I_m}} + \left( \sum_i \nu_M \varepsilon(M, X, I_m) m_X \right) \quad (8) $$

where $\nu_M$ is the stoichiometric parameter of the species—positive for production and negative for consumption.

# Results and Discussion

## Control of the Joule effect

The temperature difference between the inner capillary and the outer surface during the electrophoresis was calculated based on the method developed by Evenhuis et al.⁵⁵

$$ \Delta T = \frac{G_T - G_0}{\gamma G_0} \quad (9) $$

where $\Delta T$ is the temperature difference, $\gamma$ is the thermal coefficient of electrical conductivity, $G_T$ and $G_0$ are the conductance at a certain temperature T and free of Joule effect, respectively.

The conductance G can be expressed as:

$$ G_T = \frac{i}{V} = \frac{\pi \kappa_e d_i^2}{4L} \quad (10) $$

where i is the measured current of the capillary, V is the applied voltage, $\kappa_e$ is the electrical conductivity, $d_i$ is the inner diameter and L is the length of the capillary.

Among the parameters, $\kappa_e$ can be calculated by the following equation:

$$ \kappa_e = \frac{L i}{SV} \quad (11) $$
where S is the cross-section area of the capillary.

Fig. 1 illustrates an example of the Joule effect on an i.d. 100 µm, o.d. 360 µm PEEK capillary at 0.1 M NaCl of ionic strength. From the measured current and voltage, the electrical conductivity $\kappa_e$ of each voltage step was calculated and plotted against the dissipated power P/L (Fig. 1a). The conductivity free from Joule effect $\kappa_e^0$ at each temperature was then obtained by the extrapolation when P = 0. By fitting the $\kappa_e^0$ values against their corresponding temperature (Fig. 1b), the thermal coefficient was calculated to be $\gamma = (18.8 \pm 0.3) \text{ m}\Omega^{-1} \text{ m}^{-1}$. The temperature difference for each voltage value was calculated with Equation (9). The maximum voltage for a 105 cm, 100 µm i.d., and 360 µm o.d. PEEK capillary is calculated to be 4 kV to limit the temperature difference to less than 1°C. For the 75 µm i.d. capillary, the maximum is 5 kV.

<figure><img src="image_2.png" /></figure>

Fig. 1. Variation of $\kappa_e$ of 0.1 M NaCl with P/L for PEEK capillary under different temperatures (a), and variation of $\kappa_e$ of 0.1 M NaCl as a function of the temperature free of Joule heating (b). i.d. 100 µm o.d. 360 µm, L = 105 cm. Red blocks: confidence band at a probability of 95%.

## Validation of Ga-NOTA as the electroosmotic marker

For conventional CE, the electroosmotic mobility is generally determined by adding an electrically neutral molecule, which is detectable in the UV range through the optical window on the fused silica capillary. This is not applicable with PEEK capillaries since they are not UV-visible transparent. Ga-NOTA has been used and proved to be a valid electroosmotic marker with fused silica and for an acidic pH.⁴⁸ To verify its applicability for PEEK capillaries and neutral or even basic pH, the sample spiked with Ga-NOTA was injected and flushed by the electrolyte at 50 mbar. It can be seen in Fig. 2a that without voltage, $Cs^+$, the performance marker, Ga-NOTA, the electroosmotic marker, and uranium, the analyte were migrating altogether through the capillary. This is strongly suggesting that no strong interaction occurs in the capillary. When a +5 kV voltage was applied to the system, it can be observed
that the absence (Fig. 2b) or presence (Fig. 2c) of Ga-NOTA as the electroosmotic marker did not change the behaviour of neither $Cs^+$ nor $UO_2(CO_3)_3^{4+}$.

Furthermore, the same experiments were done adding calcium ($c_{Ca} = 4.69 \ 10^{-3} \ mol/kg_w$). It can be seen in Fig. 3a, that without applied voltage, Ca did not change the behaviour of Cs, Ga-NOTA, or uranium. When a +5 kV tension was applied, neither $Cs^+$, as the performance marker (Fig. 3b), nor Ga-NOTA, as the electroosmotic marker (Fig. 3c), were affected compared to Fig. 2b,c. The peak of uranium in presence of Ca exhibited lower mobility, which corresponds to the formation of $Ca_nUO_2(CO_3)_3^{(4-2n)-}$ complexes.

## Strategy to compensate uranium interaction with the capillary

However, after a monitoring of the electropherograms with the time of use, an interaction between the capillary and uranium can be observed (Fig. 4). After checking that all uranium was always retrieved after experiments at varying pH (Figure S1), one can observe that the peak of U appeared slightly later than the one of Cs and Ga. This interaction did not occur with Ga and Cs but only U, and seemed to enhance with the number of experiments with the same capillary. As all uranium can be retrieved by the electrolyte flow, one can assume that this interaction could be cancelled out.

<figure><img src="image_3.png" /></figure>

Fig. 2. Electropherograms of a U(VI) sample without voltage (a), a U(VI) sample without Ga-NOTA under +5 kV (b), a U(VI) sample with Ga-NOTA under +5 kV (c): i.d. 75 µm, o.d. 360 µm, 105 cm PEEK capillary, $c_U = 5 \ \mu mol/kg_w$, pH = 9.0, I = 0.1 M NaCl, $c_{NOTA} = 12.8 \ \mu mol/kg_w$, ratio Ga : NOTA = 1 : 0.75.
<figure><img src="image_4.png" /><figcaption>Fig. 3. Electropherograms of a Ca-U(VI) sample without voltage (a), a Ca-U(VI) sample without Ga-NOTA under +5 kV (b), and a Ca-U(VI) sample with Ga-NOTA under +5 kV (c): i.d. 75 µm o.d. 360 µm, L =105 cm PEEK capillary, c<sub>U</sub> = 5 × 10<sup>-6</sup> mol/kg<sub>w</sub>, c<sub>Ca</sub> = 4.69 × 10<sup>-3</sup> mol/kg<sub>w</sub>, pH = 9.0, I = 0.1 M NaCl, c<sub>NOTA</sub> = 12.8 µmol/kg<sub>w</sub>, ratio Ga : NOTA = 1 : 0.75.</figcaption></figure>

Assuming that the interaction was always against the direction of electrolyte flow, we attempted to
compensate the effect by performing electrophoreses for one sample twice: first with a positive voltage;
and second with a negative voltage. Hereafter, by calculating the half sum value, the interaction could
be cancelled out (Equation 12-14). For instance, we treated the results of a Ca-U(VI) sample as
described above (Fig. 5), the values in single modes varied significantly but ultimately each pair gave
similar half sum values with a tolerable uncertainty.

$$
\mu_{\text{obs+}} = \mu_{\text{app+}} - \mu_{\text{eo}} + \mu_{i} \quad (12)
$$

$$
\mu_{\text{obs-}} = \mu_{\text{app-}} - \mu_{\text{eo}} - \mu_{i} \quad (13)
$$

$$
\mu_{\text{calc}\pm} = \frac{\mu_{\text{app}+} + \mu_{\text{app}-} - 2\mu_{\text{eo}}}{2} \quad (14)
$$

where $\mu_{\text{obs}\pm}$ represent the electrophoretic mobilities in positive and negative modes, $\mu_{\text{calc}\pm}$ is the half sum, $\mu_{\text{app}\pm}$ are the apparent mobilities in the two modes, $\mu_{\text{eo}}$ is the electroosmotic mobility and $\mu_i$ is the factor of interaction.

Keeping all these validations and hypotheses in mind, the formation of the Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(4-2n)- complexes is implying a modification of both charge and mobility starting from UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> to CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup>, and finally to Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq). The change of mobility can be monitored by performing CE-ICP-MS experiments on a series of samples following the protocol proposed by Shang and Reiller<sup>25</sup> at 0.1 M NaCl ionic strength, by simultaneously decreasing pH and increasing Ca
concentration at constant atmospheric CO₂(g) partial pressure, to avoid both the precipitation of both calcite (CaCO₃) and UO₃·2H₂O—see Shang and Reiller²⁵ for details. The calculated speciation of the samples is shown in Fig. S2 of the ESI and experimental data points of log₁₀[Ca]total-pH are shown on Fig. S3 of the SI. One can see that species other than triscabonato species are minor. Furthermore, the theoretical charge of the samples were calculated using the data from Shang and Reiller²⁵ (red dots, Fig. 6b and Table 1). These calculated charges can be compared with the experimentally determined electrophoretic mobilities to see if they are correlated. Fig. 6a presents the observed electrophoretic mobility of each sample in the two modes. In a general manner, the observed anionic mobility values decrease with the complexation of UO₂(CO₃)₃⁻ by Ca²⁺. The mobility of some samples varies due to the interaction. However, once the half sum values were calculated, they showed good agreement with the calculated charges (R² = 0.9604).

<figure><img src="image_5.png" /><figcaption>Fig. 4. Flush test results of Ca-U(VI) samples with the same capillary before electrophoresis (a), after 23 times of electrophoresis (b) and 39 times of electrophoresis (c); i.d. 100 µm, o.d. 360 µm, 105 cm PEEK capillary, c<sub>U</sub> = 5 × 10<sup>-6</sup> mol/kg<sub>w</sub>, c<sub>NOTA</sub> = 12.8 µmol/kg<sub>w</sub>, ratio Ga : NOTA = 1 : 0.95.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 5. Variation of measured mobility in two modes and their half sum values of a Ca-U(VI) sample: Voltage = ± 4 kV, i.d. 100 µm, o.d. 360 µm, L = 105 cm PEEK capillary, c<sub>U</sub> = 5 × 10<sup>-6</sup> mol/kg<sub>w</sub>, c<sub>Ca</sub> = 1.71 × 10<sup>-4</sup> mol/kg<sub>w</sub>, pH = 8.44, I = 0.1 M NaCl, c<sub>NOTA</sub> = 12.8 µmol/kg<sub>w</sub>, ratio Ga : NOTA = 1 : 0.95.</figcaption></figure>

Calculation of the constants

Among the parameters in Equation 4 (μ<sub>n</sub>, [Ca<sup>2+</sup>], K<sub>n</sub>), μ<sub>0</sub> was determined to be -3.71 × 10<sup>-4</sup> cm<sup>2</sup> V<sup>-1</sup> s<sup>-1</sup>
with a uranium sample without calcium at pH 9 since the speciation is 100% of UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4+</sup> under
this condition (Fig. 7). The only comparable study on PuO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4+</sup> at I = 0.202 mol/kg<sub>w</sub> gave a lesser
negative value of -1.52 × 10<sup>-4</sup> cm<sup>2</sup> V<sup>-1</sup> s<sup>-1</sup>.<sup>56</sup> The μ<sub>2</sub> value was assumed to be as Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq) is a
neutral species under our conditions, even if molecular modelling calculations seemed to suggest that
alkaline cation as Na<sup>+</sup> can form Na<sub>m</sub>Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(4-2n-m)- complexes<sup>57,58</sup> particularly under seawater
conditions.<sup>58</sup> Moreover, we adopted the reasonable approximation [Ca<sup>2+</sup>] = [Ca<sub>total</sub>], considering that
C<sub>Ca</sub> is significantly higher than C<sub>U(VI)</sub>, the complexed calcium is negligible in front of the total
concentration. Hence, Equation 4 can be simplified as follows:

$$
\mu = \frac{-3.71 + [\text{Ca}_{\text{total}}] \mu_1 K_1}{1 + [\text{Ca}_{\text{total}}]K_1 + [\text{Ca}_{\text{total}}]^2 K_2} \quad (15)
$$

Fitting the total concentration of calcium vs. the half sum mobility of each sample (Fig. 8), most data
points fell within the 95% confidence band and the free parameters were calculated to be μ₁ = -(2.35
± 0.74) × 10⁻⁴ cm² V⁻¹ s⁻¹, log₁₀ K₁ = 3.57 ± 0.39, and log₁₀ K₂ = 5.89 ± 0.67. These log₁₀ K values are
compared favourably with the one determined by Shang and Reiller²⁵ under the same conditions but
with a different technique. Applying Davies equation, the two formation constants at infinite dilution
are log₁₀ K₁° = 5.28 ± 0.39 and log₁₀ K₂° = 8.46 ± 0.67. The cumulative stability constants of the two
complexes were further calculated to be $log_{10}\beta_1^\circ = 27.12 \pm 0.39$ and $log_{10}\beta_2^\circ = 30.30 \pm 0.67$, respectively, using the selected thermodynamic data for $UO_2(CO_3)_3^{4-}$ from Grenthe, *et al.*⁵⁴ (Table 1).

Fitting the data in Fig. 8 to Equation 4 with $\mu_2$ as a free parameter, leads to similar values albeit with higher uncertainty (see Figure S4 and Table S5 of the SI).

One can also use the SIT parameters $\varepsilon(Ca_nUO_2(CO_3)_3^{(4-2n)-},NaCl)$ values from Shang and Reiller²⁵. Equation 8 allows to obtain $log_{10}K_1^\circ = 5.33 \pm 0.39$, $log_{10}K_2^\circ = 8.55 \pm 0.67$, $log_{10}\beta_1^\circ = 27.17 \pm 0.39$, $log_{10}\beta_2^\circ = 30.39 \pm 0.67$.

<figure><img src="image_7.png" /></figure>

Fig. 6. Observed mobility of the samples in negative and positive mode (a), half sum mobility of the two modes and the calculated charge of each sample. $\pm 4$ kV, (b): i.d. 100 µm, o.d. 360 µm, L = 105 cm PEEK capillary, $c_U = 5 \times 10^{-6}$ mol/kg<sub>w</sub>, 0.1 mol/kg<sub>w</sub> NaCl, $c_{\text{NOTA}} = 12.8$ µmol/kg<sub>w</sub>, ratio Ga : NOTA = 1 : 0.95.

<figure><img src="image_8.png" /></figure>

Fig. 7. Electropherograms of a sample without calcium at pH 9. (a) negative mode with -4 kV; (b) positive mode with +4 kV. i.d. 100 µm o.d. 360 µm, 105 cm PEEK capillary, $c_U = 5 \times 10^{-6}$ mol/kg<sub>w</sub>, 0.1 M mol/kg<sub>w</sub> NaCl, $c_{\text{NOTA}} = 12.8$ µmol/kg<sub>w</sub>, ratio Ga : NOTA = 1 : 0.95.
Whatever the extrapolation methods, these constants are in excellent agreement with the experimental values determined recently by Shang and Reiller²⁵ and other existing stability constants obtained in the last decades (cf. Table 2). This further validates the experimental determinations and compilations proposed otherwise,⁴,⁵⁴ and verifies and validates the feasibility of using PEEK capillary for the determination of thermodynamic data of Ca-An(VI)-CO₃ complexes.

<table><caption>**Table 1 Stability constants at 25°C and I_m = 0 used in this work**</caption><thead><tr><th>Reaction</th><th>Log<sub>10</sub>K°</th><th>Reference</th></tr></thead><tbody><tr><td>CO<sub>2</sub>(g) + H<sub>2</sub>O ⇌ CO<sub>3</sub><sup>2-</sup> + 2H<sup>+</sup></td><td>-18.15 ± 0.06</td><td>Grenthe, et al.<sup>54</sup></td></tr><tr><td>UO<sub>2</sub><sup>2+</sup> + CO<sub>3</sub><sup>2-</sup> ⇌ UO<sub>2</sub>CO<sub>3</sub>(aq)</td><td>9.94 ± 0.03</td><td>Grenthe, et al.<sup>54</sup></td></tr><tr><td>UO<sub>2</sub><sup>2+</sup> + 2CO<sub>3</sub><sup>2-</sup> ⇌ UO<sub>2</sub>(CO<sub>3</sub>)<sub>2</sub><sup>-</sup></td><td>16.61 ± 0.09</td><td>Grenthe, et al.<sup>54</sup></td></tr><tr><td>UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>-</sup></td><td>21.84 ± 0.04</td><td>Grenthe, et al.<sup>54</sup></td></tr><tr><td>Ca<sup>2+</sup> + UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>5.26 ± 0.01</td><td>Shang and Reiller<sup>25</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>8.65 ± 0.02</td><td>Shang and Reiller<sup>25</sup></td></tr><tr><td>Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>27.20 ± 0.04</td><td>Shang and Reiller<sup>25</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>30.49 ± 0.05</td><td>Shang and Reiller<sup>25</sup></td></tr><tr><td>Ca<sup>2+</sup> + UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>5.28 ± 0.39</td><td>This work Davies<sup>53</sup></td></tr><tr><td>Ca<sup>2+</sup> + UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>5.33 ± 0.39</td><td>This work SIT<sup>25</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>8.46 ± 0.67</td><td>This work Davies<sup>53</sup></td></tr><tr><td>Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>8.55 ± 0.67</td><td>This work SIT<sup>25</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>27.12 ± 0.39</td><td>This work Davies<sup>53</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>27.17 ± 0.39</td><td>This work SIT<sup>25</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>30.30 ± 0.67</td><td>This work Davies<sup>53</sup></td></tr><tr><td>2Ca<sup>2+</sup> + UO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>30.39 ± 0.67</td><td>This work SIT<sup>25</sup></td></tr></tbody></table>

<table><caption>**Table 2 Existing stability constants of Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(4-2n)- complexes**</caption><thead><tr><th>Method</th><th>log<sub>10</sub>β<sub>1</sub>°</th><th>log<sub>10</sub>β<sub>2</sub>°</th><th>Ionic strength correction method</th><th>Reference</th></tr></thead><tbody><tr><td>Time-resolved laser-induced fluorescence spectroscopy (TRLFS)</td><td>25.40 ± 0.25</td><td>30.55 ± 0.25</td><td>Davies<sup>53</sup></td><td>Bernhard, et al.<sup>16</sup></td></tr><tr><td>Fluorescence titration</td><td></td><td>29.8 ± 0.7</td><td>SIT<sup>54</sup></td><td>Kalmykov and Choppin<sup>22</sup></td></tr><tr><td>Anion exchange</td><td>27.18 ± 0.06</td><td>30.70 ± 0.05</td><td>Davies<sup>53</sup></td><td>Dong and Brooks<sup>2</sup></td></tr><tr><td>TRLFS and titration</td><td>27.27 ± 0.14</td><td>29.81 ± 0.19</td><td>SIT<sup>54</sup></td><td>Lee and Yun<sup>21</sup></td></tr><tr><td>Ca<sup>2+</sup> selective electrode potentiometry</td><td>27.00 ± 0.04</td><td>30.84 ± 0.04</td><td>SIT<sup>54</sup></td><td>Endrizzi and Rao<sup>14</sup></td></tr><tr><td>TRLFS (in NaCl)</td><td>27.20 ± 0.04</td><td>30.49 ± 0.05</td><td>SIT<sup>54</sup></td><td>Shang and Reiller<sup>25</sup></td></tr><tr><td>TRLFS (in NaClO<sub>4</sub>)</td><td>27.26 ± 0.04</td><td>30.53 ± 0.06</td><td>SIT<sup>54</sup></td><td>Shang, et al.<sup>26</sup></td></tr><tr><td>Anion exchange</td><td>27.27 ± 0.04</td><td>29.8 ± 0.2</td><td>Davies<sup>53</sup></td><td>Maia, et al.<sup>20</sup></td></tr><tr><td>Data selection</td><td>27.00 ± 0.20</td><td>30.80 ± 0.40</td><td>SIT<sup>54</sup></td><td>Grenthe, et al.<sup>54</sup></td></tr><tr><td>Data selection</td><td>27.09 ± 0.09</td><td>30.42 ± 0.15</td><td>SIT<sup>54</sup></td><td>Reiller<sup>4</sup></td></tr><tr><td>CE-ICP-MS</td><td>27.12 ± 0.39</td><td>30.30 ± 0.67</td><td>Davies<sup>53</sup></td><td>This work</td></tr><tr><td>CE-ICP-MS</td><td>27.17 ± 0.39</td><td>30.39 ± 0.67</td><td>SIT<sup>54</sup></td><td>This work</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Fig. 8. Fitting of total calcium concentration against half sum mobility of each sample. Red blocks: confidence band at a probability of 95%.</figcaption></figure>

## Conclusions

The thermodynamic formation constants of Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>) complexes have been successfully obtained in PEEK capillary based CE-ICP-MS. These values are showing excellent agreement with those determined otherwise. This further verifies the available thermodynamic constants and validates the use of PEEK for their determination in alkaline and carbonated media. To apply this material for CE-ICP-MS measurements, which was seldom used in the field, we evaluated the impact of Joule effect, applied a valuable electroosmotic marker Ga-NOTA, and adopted a two-mode strategy to cancel out the interaction that arose from continuous use. Compared to fused silica capillary, PEEK capillaries do not need any modification to minimize the interaction between the analyte and the capillary, i.e. uranium-silica interactions in particular, suggesting that it could be a promising choice for other actinide complexes.

## Author contributions

Ruopei Sun: investigation, data curation, formal analysis, visualization, writing – original draft. Erwan Dupuis: conceptualization, supervision, methodology, formal analysis, validation, writing – review & editing. Jean Aupiais: methodology, writing – review & editing. Pascal E. Reiller: supervision, conceptualization, methodology, validation, funding acquisition, writing – review & editing.

## Data availability

The data supporting this article have been included as part of the Supplementary information. The database used in PhreeqC to calculate the theoretical charge of the samples was Thermochimie 12a, by
implementing the thermodynamic data of Ca-U(VI)-CO₃ complexes determined by Shang and Reiller²⁵,
which are listed in Table 1.

## Acknowledgements

This work was financed by ONDRAF-NIRAS (contract CCHO 2021-0440/00/00). Dr Hélène Isnard is acknowledged for her help during the dissolution of U₃O₈. Dr. Chengming Shang and Dr. Laurent Vio are acknowledged for preliminary experiments in fused silica capillary.

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