Thermodynamic model of Ni(II) solubility, hydrolysis and complex formation with ISA

2.1 Solubility and hydrolysis of Ni(II) in the absence of ISA

The solution chemistry of Ni(II) is characterized by a moderate hydrolysis and the formation of the sparingly soluble oxo-hydroxides under alkaline to hyperalkaline pH conditions. Theophrastite (β–Ni(OH)₂(cr)) is the solid phase controlling the solubility of Ni(II) at T=25°C, transforming into bunsenite (NiO(cr)) above T=77°C [12]. Several experimental studies have previously investigated the solubility of β–Ni(OH)₂(cr) in aqueous systems. These publications were critically reviewed in the NEA–TDB volume dedicated to Ni [13]. One of the relevant shortcomings identified in many of the reviewed solubility studies was the insufficient knowledge/characterization of the Ni solid phase controlling the solubility, especially in terms of crystallinity (e.g. particle size) and presence of impurities (e.g. Na⁺, Cl⁻). The effect of particle size on the solubility constant of a solid is a well-known effect which is particularly critical for metal oxides [14], [15], [16]. This is also reflected in the large differences of log₁₀*K°_s,0{β–Ni(OH)₂(cr)} reported in the literature (see Table 1). Indeed, the recent review by Brown and Ekberg [18] classified the solubility data available for β–Ni(OH)₂(cr) with respect to their crystallinity and proposed log₁₀*K°_s,0{β–Ni(OH)₂(cr)}=(11.75±0.13) for the microcrystalline phase and (10.96±0.20) for the more crystalline one.

Several hydrolysis species of Ni(II) are selected in the NEA–TDB review, namely NiOH⁺, Ni₂OH³⁺, Ni₄(OH)₄⁴⁺ and Ni(OH)₃⁻ (see Table 1). The consideration in the selected chemical model of Ni(OH)₃⁻ as the only species forming under alkaline to hyperalkaline conditions was based on a single solubility study at 25°C [20]. A very large uncertainty was assigned to the selected hydrolysis constant to reflect the outcome of additional experimental data gathered at higher temperatures [27], [28]. Solubility data reported in Gayer and Garret [20] was also re-interpreted within the ThermoChimie project including the predominance under alkaline to hyperalkaline pH conditions of both Ni(OH)₂(aq) and Ni(OH)₃⁻ [17]. Conversely, more recent solubility studies with NiO(cr) and β–Ni(OH)₂(cr) did not observe the formation of Ni(OH)₃⁻ up to pH≈13 [12], [26], [29], [30]. Instead, these authors proposed the only formation of Ni²⁺ and Ni(OH)₂(aq) in the aqueous phase. Felipe–Sotelo et al. [31] found also a very low solubility of Ni(II) in 0.02 M NaOH (≈5·10⁻⁸ M). This observation is again not consistent with the formation of a very stable Ni(OH)₃⁻ species. The very discrepant results available in the literature are possibly related with the very strong Ni(II)–carbonate complexation (log₁₀β°₁₁=(4.2±0.4) for Ni²⁺+CO₃²⁻⇔NiCO₃(aq), as selected in [13]), which requires that solubility experiments in the alkaline pH range are performed in inert-gas atmosphere under strict exclusion of CO₂. The uncertainties affecting the thermodynamically calculated solubility and hydrolysis of Ni(II) under alkaline to hyperalkaline conditions represent an important limitation when assessing the chemical behaviour of this radionuclide in cementitious systems, and deserves further experimental studies.

2.2 Complexation of Ni(II) with ISA

Only a very limited number of experimental studies are available in the literature dedicated to the complexation of Ni(II) with ISA [25, 31–34].¹ From these studies, only Warwick et al. [32] and Almond et al. [33] provide thermodynamic data for Ni(II)–ISA aqueous complexes forming under the alkaline to hyperalkaline pH conditions relevant in cementitious systems (see Table 2). Both studies combined analogous experimental techniques (spectrophotometry and potentiometric titrations) and used very high Ni(II) concentrations (up to 0.01 M) for the determination of the stoichiometry of the complexes forming. Note that under hyperalkaline pH conditions, these concentrations of Ni(II) are clearly above the solubility limit of β–Ni(OH)₂(cr) (both crystalline and micro-crystalline phases, see Section 2.1). Warwick et al. [32] and Almond et al. [33] conducted additional sorption experiments at lower [Ni(II)] to determine the stability constants of the Ni(II)–ISA complexes according with the stoichiometry derived from spectroscopic/potentiometric measurements. Both Warwick et al. [32] and Almond et al. [33] proposed the formation the aqueous species NiISA⁺ and Ni₂(OH)₄ISA⁻ prevailing at pH≈7 and pH≈13, respectively. Although insufficiently characterized in the original publications, these studies reported also the formation of the solid Ni₂(OH)₃ISA(s) at 7.2< pH <9.6. Felipe-Sotelo et al. [31] investigated the solubility of Ni(II) in the absence and presence of cellulose degradation products (CDP), a complex mixture of polyhydroxycarboxylic compounds. The authors observed a clear increase in the solubility of Ni(II) at pH≈12 – 13 in the presence of CDP, although no quantitative interpretation was provided due to the intrinsic chemical complexity of their system.

Experimental data reported in Warwick et al. [32] were re-interpreted by Grivé et al. [6]. The latter authors argued that although polynuclear species may explain the data obtained at high [Ni(II)] (in spectrophotometric and potentiometric titrations), the formation of these species is very unlikely at the low [Ni(II)] used in the sorption experiments (≈10⁻⁹ M). Instead, Grivé et al. [6] were able to properly explain sorption data by only defining the monomeric species NiISA⁺ and Ni(OH)₃ISA²⁻. Note however that sorption experiments were only performed at pH=13, and thus a conclusive experimental evidence of the stoichiometry of the Ni(II)–OH–ISA complex/es prevailing in this pH-region at low [Ni(II)] cannot be attained from these data only. These uncertainties represent a relevant limitation in the assessment of the chemical behaviour of Ni(II) in cementitious systems in the presence of cellulose degradation products.

3.1 Chemicals

All solutions were prepared with purified water (Milli-Q academic, Millipore) and purged for 2 h with Ar before use to remove traces of O₂ and CO₂. All samples were prepared, stored and handled inside an inert gas (Ar) glovebox (O₂<5 ppm) at T=(22±2)°C. A commercial Ni(OH)₂(s) (Acros Organics) was used as solubility-controlling phase in all experiments. NaCl, NaNO₃ and Ca(OH)₂(s) (all of them p.a.) were obtained from Merck. HCl and NaOH Titrisol^® (Merck) were used to adjust the pH in the sample preparation. Carbonate impurities in 1.0 M NaOH (Titrisol) were quantified as (3.1±0.2)·10⁻⁵ M.

NaISA(s) was synthesized in the present study from the alkaline degradation of α-lactose hydrate (Sigma Aldrich) following the approach summarized in Section 3.2. A Chelex^® 100 ion exchange resin (Na-form, analytical grade, Sigma-Aldrich) was used for the conversion of Ca(ISA)₂(s) into NaISA. Diethyl ether (C₄H₁₀O, ACS reagent grade, VWR BDH Prolabo^®) was used to remove water from the final product.

3.2 Synthesis and characterization of NaISA(s)

The calcium salt of isosaccharinic acid was synthetized following the procedure reported by Whistler and BeMiller [36] with some modifications from Vercammen [37] and Evans [35]. In a first step, α-lactose hydrate was contacted with an aqueous solution saturated with Ca(OH)₂(s), and the mixture stirred during 3 days at room temperature in an inert gas (Ar) glovebox. The resulting suspension was heated for 10 h and filtered whilst hot. A final volume reduction was performed in a rotary evaporator, and the mixture was left overnight at T=9°C. The resulting white crystals (Ca(ISA)₂(s)) were removed by filtration and washed with cold water, ethanol and acetone.

Ca(ISA)₂(s) was converted into NaISA(s) using a cation exchange resin in the Na-form. An accurate description of the method is reported by Greenfield et al. [38], Glaus et al. [39], Pointeau et al. [40], Colàs [41], among others. Briefly, 2 g of Ca(ISA)₂(s) were suspended in 500 mL of Milli-Q water in the presence of 25 g of resin. The mixture was agitated with a magnetic stirrer for approximately 1 h, and then filtered with filter paper (Whatman blue ribbon, <2 μm). The filtrate was evaporated on a heating plate at T=60°C until a brown viscous liquid was obtained. The remaining water content was removed using water-free diethyl-ether. The combination of repeated addition/evaporation of diethyl ether with a cooling step (T=9°C, laboratory fridge) resulted in a pale yellow solid phase, NaISA(s).

Both Ca(ISA)₂(s) and NaISA(s) were characterized using XRD (X-ray diffraction), (solution) ¹H and ¹³C NMR (nuclear magnetic resonance), quantitative chemical analysis and TOC (total organic content). XRD measurements were performed using a D8 Advance diffractometer (Bruker AXS) equipped with a Cu radiation tube. The resulting diffractograms were compared with data reported in the literature for Ca(ISA)₂(cr), and confirmed the only presence of the Ca-salt of ISA [42]. Appropriate amounts of Ca(ISA)₂(s) and NaISA(s) were dissolved in weakly alkaline solutions (pH≈9) and the resulting solutions characterized using ¹H and ¹³C NMR. NMR spectra of these samples were recorded at T=300 K on a Bruker Avance III 400 spectrometer. The results confirm that ISA is the main organic component in both Ca(ISA)₂(s) and NaISA(s) (>95%).

Ratios of Ca:ISA and Na:ISA in Ca(ISA)₂(s) and NaISA(s) synthesized in the present work were quantified by a combination of quantitative chemical analysis and TOC measurements. Appropriate amounts of both solid phases were dissolved in water, and [Na] and [Ca] were quantified by ICP–OES (Optima 8300 DV, Perkin Elmer) and ICP–MS (X-Series II, Thermo Scientific), respectively. Aliquots of the same samples were also investigated by TOC using a Shimadzu TOC5000 equipment. The combination of these data resulted in Ca:ISA and Na:ISA ratios of 1:2 and 1:1, respectively, confirming the successful synthesis of the targeted Ca(ISA)₂(s) and NaISA(s) compounds.

3.3 pH Measurements

A combination glass pH electrode (type ROSS, Orion), freshly calibrated against dilute standard pH buffers (pH 7–13, Merck), was used to determine the molal H⁺ concentration, [H⁺] (with pH_m=–log₁₀[H⁺]). The experimentally measured pH values (pH_exp) are related to [H⁺] by pH_m=pH_exp+A_m, where A_m is given as a function of background electrolyte concentration. A_m-factors used in this work for NaCl and NaNO₃ were taken from Altmaier et al. [43] and Herm et al. [44], respectively. In NaCl–NaOH solutions with [OH⁻] >0.03 M, the H⁺ concentration was calculated from the given [OH⁻] and the conditional ion product of water.

3.4 Solubility measurements with Ni(OH)₂(s) in the absence and presence of NaISA

Batch solubility experiments in the absence of ISA were performed from undersaturation conditions with a commercially obtained Ni(OH)₂(s). A total of 32 independent batch samples were prepared using 20 mg of Ni(OH)₂(s) in 20 mL per experiment. Experiments were performed at constant ionic strength in 0.5 and 3.0 M NaCl–NaOH solutions with 7.5≤ pH_m ≤13. One additional solubility sample was prepared in 0.5 M NaNO₃ with pH_m≈9.3 to assess the possible role of Ni(II)–Cl aqueous complexes in 0.5 M NaCl systems. [Ni] and pH_m were monitored at regular time intervals for up to 310 days. Dissolved [Ni] was measured after 10 kD ultrafiltration by ICP–MS (Thermo X-Serie II). The detection limit of ICP–MS for Ni in 0.5 and 3.0 M NaCl–NaOH solutions was determined as log₁₀[Ni]≈−7.9 and −7.0, respectively (3σ of repeated blank measurements). Experimental molar concentrations of Ni (M, mol·L⁻¹) determined by ICP–MS were transformed to molal units (m, mol·kg⁻¹ H₂O) using the conversion factors reported in Guillaumont et al. [45].

Ni(II) solubility experiments in the presence of NaISA were conducted using the same solid phase and experimental approach as in the absence of NaISA. A total of 28 independent batch samples were prepared in 0.5 M NaCl–NaOH–NaISA solutions with 0.01 M≤[ISA⁻]≤0.2 M and 9≤ pH_m ≤13. [Ni] and pH_m were monitored at regular time intervals for up to 290 days.

The original Ni(OH)₂(s) solid phase material was characterized before the start of the solubility experiments by XRD using a Bruker D8 Advance diffractometer (Cu Kα radiation) equipped with a Sol-X detector. For this purpose, a small amount (1–2 mg) of the original solid phase pre-equilibrated in a 0.1 M NaCl solution with pH_m≈11 was washed 3 times with ethanol (2 mL) under Ar-atmosphere to remove the matrix solution. After the last cleaning step, the solid was suspended in approximately 20 μL ethanol, transferred to a capped silicon single crystal sample holder (Dome, Bruker), dried in the Ar-box under protective atmosphere for a few minutes before sealing of the sample holder, and transferred outside the glovebox for the collection the XRD diffractogram. XRD data were collected within 8°≤2Θ≤80°, with a step size of 0.04° and 6 s accumulation time per step. Solid phase from selected solubility experiments in the absence and presence of NaISA were characterized after attaining equilibrium conditions (constant [Ni] and pH_m) following the same approach, and the collected diffractograms were compared with the XRD of the original Ni(OH)₂(s) material with the aim of evaluating the possible alteration of the solid phase in the course of the solubility experiments.

3.5 Development of chemical, thermodynamic and activity models

The development of a correct chemical model (set of equilibrium reactions defining the solution chemistry of a given system) for the behaviour of Ni(II) in alkaline to hyperalkaline pH conditions is based upon solid phase characterization and slope analysis of the solubility curves (log₁₀[Ni] vs. log₁₀[H⁺] and log₁₀[Ni] vs. log₁₀[ISA]), taking also into account previously reported chemical models for Ni(II) both in the absence and presence of ISA. This step sets the basis for the subsequent evaluation of thermodynamic and activity model parameters. The specific ion interaction theory (SIT) has been adopted in the present work to account for ion interaction processes and ionic strength effects [46], in agreement with the approach adopted within the NEA–TDB reviews [13], [45]. Within the SIT formalism, activity coefficients γ_j are calculated according with:

where D is the Debye–Hückel term, z_j the charge of an ion j, I_m the molal ionic strength, m_k the molality of all ions k present in solution and ε(j, k, I_m) the specific ion interaction parameter. Experimental solubility data and thermodynamic models derived in the present work in the absence and presence of ISA are systematically compared with thermodynamic calculations using NEA–TDB [13] and ThermoChimie [17] databases, as well as with the recent review by Brown and Ekberg [18]. These are clearly the most comprehensive and up-to-date thermodynamic data selections for the systems investigated in the present work.

One of the main uncertainties still affecting the complexation of (hard) metal cations with ISA (or other polyhydroxycarboxylates in general) is the possible role of the alcohol groups in the chelation of the M^z+ cation. Consequently, in experimental studies conducted under alkaline to hyperalkaline pH conditions, the release of protons eventually involved in the complexation reaction can be attributed to both hydrolysis of the M^z+ cation or deprotonation of the α-hydroxyl group of ISA:

where x=1+y, and ISA_−H²⁻ corresponds to an ISA ligand with deprotonated carboxylic and α-hydroxyl groups. The type of complex forming has no impact on the mass-action law (except for the number of water molecules involved in the reaction), and thus does not affect the accordingly derived equilibrium constant/s for systems at low or intermediate ionic strength where the influence of the water activity is negligible. For the sake of simplicity, the quotation M(OH)_xISA^z−1−x has been formally preferred in the present work. This must not be taken as a definitive indication of the type of complex forming. A detailed and conclusive proof-of-concept is thus still missing, but this aspect was not targeted within the work presented in this study.

Like other polyhydroxycarboxylic acids such as gluconic acid (GLU), ISA undergoes dehydration in acidic conditions to form a lactone L (HISA⇔L+H₂O(l)) [47]. Because the formation of a lactone involves the reorganization of the ISA molecule, lactonization is a much slower process compared to the deprotonation reaction. Lactone formation has no relevance in the alkaline conditions investigated in this study, and thus has been disregarded in the thermodynamic interpretation of the Ni(II)–ISA system.

4.1 Solubility of Ni(II) in NaCl and NaNO₃ systems

Ni(II) experimental solubility data determined in the present work in NaCl–NaOH and NaNO₃ solutions in the absence of ISA are shown in Figure 2. Only values of log₁₀[Ni] quantified above the detection limit of ICP–MS for the given salt concentration are provided in the Figure. Note that in 3.0 M NaCl systems with pH_m≥10.5, all values of log₁₀[Ni] fell below the calculated detection limit and thus have been omitted. Solid lines in Figure 2 correspond to the solubility of β–Ni(OH)₂(cr) calculated using thermodynamic data derived in the present work (see Section 4.3), selected in NEA–TDB [13], ThermoChimie [17] and reported in the review by Brown and Ekberg [26] for a microcrystalline phase.

Figure 2:

Ni(II) experimental solubility data determined in the present work in 0.5 M NaCl–NaOH, 0.5 M NaNO₃ and 3.0 M NaCl–NaOH. Solid lines corresponding to the solubility of β–Ni(OH)₂(cr) calculated according with the thermodynamic model derived in the present work (green line: 0.5 M NaCl; blue line: 3.0 M NaCl), selected in NEA–TDB [13] (red line), ThermoChimie [17] (black line) and in Brown and Ekberg [18] (purple line).

Constant pH_m and log₁₀[Ni] readings confirm that 310 days is sufficient contact time to attain thermodynamic equilibrium in all the investigated NaCl–NaOH and NaNO₃ systems. Two main regions can be identified in the experimentally determined solubility data:

• pH_m≤10: A steep decrease of the solubility with a well-defined slope of –2 (log₁₀[Ni] vs. pH_m) is observed in this pH-region for both 0.5 M and 3.0 M NaCl systems, indicating that two H⁺ are taken up in the equilibrium reaction controlling the solubility of Ni(II). Solubility data in 0.5 M NaNO₃ agree very well with solubility data in 0.5 M NaCl, indicating that both chloride and nitrate have a similar impact on the solubility of Ni(II) in this pH_m-region. Note further that the very small stability constants selected in the NEA–TDB for NiCl⁺ (log₁₀K°₁₁=0.08±0.6) and NiNO₃⁺ (log₁₀K°₁₁=0.5±1.0) complexes suggest that their contribution to the overall Ni(II) solubility is very minor for this background electrolyte concentration. Thermodynamic calculations using NEA–TDB, ThermoChimie or the selection in Brown and Ekberg [18] clearly underestimate experimental solubility determined in the present work, very likely due to differences in crystallinity (e.g. particle size) of the solid phase (see also discussion in Section 4.3).

• pH_m≥10: Solubility data in 0.5 M NaCl–NaOH show a pH_m-independent trend up to pH_m≈13, thus confirming that no H⁺ are involved in the equilibrium reaction controlling the solubility of Ni(II) in this pH_m-range. These experimental observations are in disagreement with the increase in solubility calculated for this pH_m-region using thermodynamic data in NEA–TDB [13] and ThermoChimie [17], due to the selection of the anionic hydrolysis species Ni(OH)₃⁻ in both databases. On the contrary, our experimental observations are in line with NiO(cr) and β–Ni(OH)₂(cr) solubility data reported by Palmer and co-workers [12], [29], [30] (see Section 2.1). A good agreement is also obtained with recent Ni(II) solubility data in 0.02 M NaOH solutions, approached from both under- and oversaturation conditions [31]. Note however that, although the trend in our solubility data is in agreement with thermodynamic calculations using the selection in Brown and Ekberg [18], this model predicts a far too low solubility in this pH_m-region compared to our observations. A detailed discussion on this discrepancy is provided in Section 4.3.

4.2 Solid phase characterization

XRD analyses of the solid phase used in the present study confirm the only presence of Ni(OH)₂(s) as a solid phase controlling the solubility of Ni(II) (Figure 3). XRD patterns before and after solubility experiments are identical, and show a good match with the reference spectra of β–Ni(OH)₂(cr) (PDF 73-1520). Reflections of NaCl can be also observed in the solid phases recovered from solubility experiments in 3.0 M NaCl. This results from the insufficient removal of adhering matrix solution in concentrated NaCl solutions. In spite of this, XRD patterns corresponding to β–Ni(OH)₂(cr) can be unequivocally identified for these systems. Note that XRD patterns collected in the present work are virtually the same as those reported in Palmer and Gamsjäger [12] for β–Ni(OH)₂(cr), although notably narrower peak widths were observed by the latter authors. This observation indicates a more crystalline material than the one used in the present work.

Figure 3:

XRD spectra of selected solid phases from Ni(II) solubility experiments in 0.5 and 3.0 M NaCl. Red and brown marks indicate peak positions for β–Ni(OH)₂(cr) and NaCl reference spectra (PDF 73-1520 and PDF 05-0628, respectively).

4.3 Thermodynamic interpretation of Ni(II) solubility in the absence of ISA

Solid phase characterization by XRD in combination with slope analyses of experimental solubility data are used to derive the chemical reactions (4) and (5) as controlling the solubility of Ni(II) at 8≤ pH_m ≤13. One of the critical issues discussed by Gamsjäger et al. [13] on the solubility of Ni(II) is the possible presence of basic salts contaminating β–Ni(OH)₂(cr), and the adverse impact on the determination of accurate thermodynamic functions of the latter solid. The satisfactory match of our solid phase with XRD patterns of β–Ni(OH)₂(cr) and the well-defined slope of –2 determined for the solubility data within 8≤ pH_m ≤9.5 indicates that it is possible to disregard the presence of Na_xNi(OH)_2+x (s) or Ni(OH)_2–x Cl_x(s) in the investigated solubility systems. The chemical model can be thus explained by using the equilibrium reactions:

With

and

Based on the proposed chemical model, conditional solubility constants for the chemical reaction (4) were determined from experimental solubility data in 0.5 M and 3.0 M NaCl with 8≤ pH_m ≤9.5 according with equations (6) and (7). Note however, that in this pH_m-region the formation of NiCl⁺ is also predicted for 0.5 and 3.0 M NaCl solutions. In order to account for the contribution of NiCl⁺ to [Ni]_tot, the stability constant reported for reaction (10) in Gamsjäger et al. [13] was recalculated to I=0.5 and 3.0 M NaCl by SIT, and [NiCl⁺] calculated accordingly. No selection of ε(NiCl⁺, Cl⁻) was provided by Gamsjäger et al. [13], and thus this interaction coefficient was estimated in the present work from ε(NiCl⁺, ClO₄⁻) based on the correlation between Cl⁻ and ClO₄⁻ coefficients described in Guillaumont et al. [45].

log₁₀β°_1,1=(0.08±0.60) [Gamsjäger et al. [13]]

with

ε(Ni²⁺, Cl⁻)=(0.17±0.02) kg·mol⁻¹ [Gamsjäger et al. [13]]

and

ε(NiCl⁺, ClO₄⁻)=(0.47±0.06) kg·mol⁻¹ [Gamsjäger et al. [13]]

ε(NiCl⁺, Cl⁻)=0.028+0.38 ε(NiCl⁺, ClO₄⁻)=(0.21±0.06) kg·mol⁻¹ [estimated in p.w.]

The SIT-plot resulting from the values of log₁₀*K′_s,0(I=0.5 M NaCl) and log₁₀*K′_s,0(I=3.0 M NaCl) is shown in Figure 4. Uncertainties of log₁₀*K°_s,0 (intercept) and –Δε (slope) are calculated following the NEA guidelines for the estimation of errors [48], which accounts also for the uncertainties of the experimental errors in log₁₀*K′_s,0.

Figure 4:

SIT-plot for the solubility reaction β–Ni(OH)₂(cr)+2 H⁺ ⇔Ni²⁺+2 H₂O(l). The size of the symbols is representative of the uncertainty of the experimentally determined log₁₀*K′_s,0 (±0.09, as 2σ).

The slope of the SIT-plot corresponds to –Δε=–(ε(Ni²⁺, Cl⁻) – 2ε(H⁺, Cl⁻))=(0.01±0.05) kg·mol⁻¹. Considering ε(H⁺, Cl⁻)=(0.12±0.01) kg·mol⁻¹ as reported in Gamsjäger et al. [13], the value ε(Ni²⁺, Cl⁻)=(0.25±0.05) kg·mol⁻¹ can be calculated. This result is in moderate agreement with the value currently selected in Gamsjäger et al. [13] (0.17±0.02).

The solubility product determined in the present work for β–Ni(OH)₂(cr) (log₁₀*K°_s,0=12.10±0.11) is clearly larger than the value selected in the NEA–TDB [13] (log₁₀*K°_s,0=(11.03±0.28)). However, our value is not very different from the recent recommendation by Brown and Ekberg [18] for the microcrystalline phase (log₁₀*K°_s,0{β–Ni(OH)₂(cr)}=(11.75±0.13), see also Table 1). Minor discrepancies arising with the solubility product reported by Palmer and Gamsjäger [12] (log₁₀*K°_s,0=(11.67±0.20)) can be clearly attributed to differences in the crystallinity/particle size of the investigated solids. Hence, the greater crystallinity of the solid phase used in Palmer and Gamsjäger [12] is supported by the narrower peak widths in their XRD diffractograms compared to our study, and is full in line with the expected solid obtained under the hydrothermal conditions used by these authors in the synthesis of β–Ni(OH)₂(cr) (up to 140°C).

A conditional equilibrium constant for reaction (5) was calculated as the average of log₁₀[Ni] values determined within 10≤ pH_m ≤13 in 0.5 M NaCl. Considering ε(Ni(OH)₂(aq), Na⁺/Cl⁻)=0 (by definition in SIT), we find:

log10K′s,(1,2)=log10K°s,(1,2)=–(7.6±0.4)

where uncertainty is calculated as 2σ. Combining log₁₀*K°_s,(1,2) with log₁₀*K°_s,0 reported above, we obtain:

log10K°(1,2)=–(19.7±0.4)

This value is significantly greater than log₁₀*K°_(1,2)=–21.15 reported by Palmer and co-workers [30] and recommended in Brown and Ekberg [18]. These authors derived log₁₀*K°_(1,2) from solubility experiments with NiO(cr) in the temperature range 25–350°C [27], [30]. The combination of this value with log₁₀*K°_s,0 selected in [18] for microcrystalline β–Ni(OH)₂(cr) results in log₁₀*K°_s,(1,2)=–(9.40±0.14). The calculated solubility at pH_m>10 obtained using these data is almost two orders of magnitude lower than our experimentally measured log₁₀[Ni] in this pH_m-region (see Figure 2). A close inspection of the original experimental data suggests that the value of log₁₀*K°_(1,2) reported by Palmer et al. [30] and recommended in Brown and Ekberg [18] is possibly underestimated, very likely due to the inherent problems associated with the investigation of the solubility with a metastable phase (e.g. NiO(cr) at T=25°C)². Note that if assuming β–Ni(OH)₂(cr) as the solid phase controlling the solubility of Ni(II) at T=25°C in [30], the combination of log₁₀*K°_s,(1,2)=–(8.5±0.2) reported for this system (experimental value, table 3 in [30]) with log₁₀*K°_s,0{β–Ni(OH)₂(cr)}=(11.67±0.20) reported by the same authors in [12] results in log₁₀*K°_(1,2)=–(20.17±0.30). This value agrees within the uncertainties with log₁₀*K°_(1,2) determined in the present work. In a conference paper [29], the same authors reported experimental solubility data for NiO(cr) and β–Ni(OH)₂(cr) extending up to pH_m=13, and determined at T=25°C log₁₀*K°_s,0{β–Ni(OH)₂(cr)}=(11.6±0.2) (Figure 4 in [29]) and log₁₀*K°_s,(1,2)=–(8.6±0.1) (Figure 5 in [29]). The combination of both solubility constants results in log₁₀*K°_(1,2)=–(20.2±0.2), which again agrees within the uncertainties with log₁₀*K°_(1,2) determined in the present study.

Figure 5:

Experimental solubility data of Ni(II) determined in the present work in 0.5 M NaCl–NaOH solutions, in the absence and presence of NaISA (0.01, 0.1 and 0.2 M). Solid lines corresponding to the solubility of β–Ni(OH)₂(cr) (thick lines) and underlying aqueous speciation (thin lines) in the absence and presence of NaISA as calculated with the thermodynamic model derived in the present work. Dashed lines corresponding to the solubility of β–Ni(OH)₂(cr) as calculated with the current thermodynamic selection in ThermoChimie [17].

Solubility data collected in the present work clearly do not support the formation of the anionic hydrolysis species Ni(OH)₃⁻. Experimental data shown in Figure 2 for 0.5 M NaCl–NaOH solutions with 10.0≤ pH_m ≤13.0 indicate a constant log₁₀[Ni]_tot≈–7.6. The solubility data collected in 3.0 M NaCl–NaOH solutions with 10.0≤ pH_m ≤14.0 are in all the cases below the detection limit of the technique for this salt concentration. These observations support the findings by Palmer and co-workers, and are in disagreement with the predominance of Ni(OH)₃⁻ species under hyperalkaline pH conditions as selected in the NEA–TDB [13] based on a single experimental solubility study [20].

5.1 Solubility of Ni(II) in 0.5 M NaCl– NaOH–NaISA systems

The experimentally measured solubility of Ni(II) in the presence of [ISA]=0.01, 0.1 and 0.2 M is shown in Figure 5. The figure includes thermodynamic calculations for the solubility of β–Ni(OH)₂(cr) in the absence and presence of ISA using thermodynamic data derived in the present work (details of the model in Section 5.3), as well as thermodynamic calculations in the presence of ISA based on the thermodynamic data selection in ThermoChimie [17]. Note that ThermoChimie considers log₁₀*K°_s,0{β–Ni(OH)₂(cr)}=(11.03±0.28) as currently selected in the NEA–TDB [13]. This value is significantly lower than log₁₀*K°_s,0{β–Ni(OH)₂(cr)} determined in the present work (see Section 4.3), and thus the calculated solubility (in the absence of ISA) is lower than [Ni] experimentally measured in the present work.

Experimental data in Figure 5 show a clear and steadily increase of Ni(II) solubility with increasing [ISA]. As the solubility limiting solid Ni(II) phase is the same in all investigated samples, this clearly indicates significant Ni(II)–ISA complexation. The increase in solubility is more evident above pH_m≈10, and becomes almost pH-independent at pH_m≥11. Below pH_m≈10, the impact of ISA on the solubility of Ni(II) becomes less relevant. In the case of [ISA]=0.01 M, the solubility curve in the presence of ISA eventually merges with the solubility of Ni(II) in the absence of ISA at pH_m≈9. This observation reflects a distinct pH_m-dependency of the solubility of Ni(II) in the absence and presence of ISA within this pH_m-region, consequently involving a different number of H⁺ in the corresponding chemical reactions controlling the solubility in both systems.

The increase in the solubility of Ni(II) with slope of +1 predicted by Thermochimie [17] in the presence of ISA at pH_m≥9.5 (due to the formation of Ni(OH)₃ISA²⁻) is not reproduced by experimental evidences obtained in the present work. A slight pH_m dependency can be claimed at pH_m values above 12.5, however, confirmed by the experimental data collected in our work up to pH_m=13.

5.2 Solid phase characterization

The comparison of the XRD data collected for solubility experiments in the absence and presence of ISA shows that no solid phase alteration took place in the course of the experiments with ISA (Figure 6). The collected XRD patterns perfectly match those of β–Ni(OH)₂(cr) (PDF 73-1520), and thus the latter solid phase is considered to control the solubility of Ni(II) in the thermodynamic interpretation summarized in the following section.

Figure 6:

XRD spectra of selected solid phases from Ni(II) solubility experiments in 0.5 M NaCl–NaISA in the absence and presence of NaISA (0.2 M). Red marks indicate peak positions for β–Ni(OH)₂(cr) reference spectrum (PDF 73-1520).

5.3 Thermodynamic interpretation of Ni(II) solubility in the presence of NaISA

On the basis of slope analyses and solid phase characterization, chemical reactions (12)–(14) are proposed to be controlling the solubility of Ni(II) in the presence of ISA.

with

log10*K′s,(1,1,1)=log10[NiOHISA(aq)]–log10[ISA–]–log10[H+]

log10*K′s,(1,2,1)=log10[Ni(OH)2ISA−]–log10[ISA−]

log10*K′s,(1,3,1)=log10[Ni(OH)3ISA2−]+log10[H+]−log10[ISA−]

The fit of Ni(II) solubility data in the presence of [ISA]=0.01, 0.1 and 0.2 M, in combination with the chemical model proposed above, results in a consistent set of conditional solubility constants satisfactorily explaining all experimental data collected in this work. Uncertainties reported for the corresponding log₁₀*K′_s,(1,n,1) values are calculated as 2σ.

log10*K′s,(1,1,1)(I=0.5 M NaCl)=(5.3±0.3)

log10*K′s,(1,2,1)(I=0.5 M NaCl)=−(5.5±0.5)

log10*K′s,(1,3,1)(I=0.5 M NaCl)=−(18.3±0.7)

The experimental solubility data were also analysed deliberately including the species NiISA⁺ in the fit. This attempt was not converging, because Ni(II) solubility within 8≤pH_m≤10 has an obviously different dependency on pH_m in the absence (slope {log₁₀[Ni] vs. pH_m}≈–2, predominance of Ni²⁺ in solution) and presence (slope {log₁₀[Ni] vs. pH_m}≈–1, predominance of NiOHISA(aq) in solution) of ISA. Warwick et al. [32] and Almond et al. [33] proposed 2.1≤ log₁₀*K′ ≤2.6 for the equilibrium reaction Ni²⁺+ISA⁻⇔NiISA⁺, based on polarographic and potentiometric measurements at pH≈7. Although our experimental data do not allow to either confirm or disregard the formation of NiISA⁺ at pH≈7, we can safely claim that the impact of this species on the solubility of β–Ni(OH)₂(cr) is rather minor, and that the stability constants reported by Warwick et al. [32] and Almond et al. [33] are probably overestimated.

The predominance of the species NiOHISA(aq) in the pH_m-range 8–10 provides indirect information on the structure of the Ni(II)–ISA complex forming. For the same pH_m-range but in the absence of ISA, the species Ni²⁺ has been shown to prevail in solution. It appears evident that the complexation of Ni²⁺ with ISA⁻ (thus with a strong electron-donor) cannot enhance the acidity of the Ni²⁺ cation and promote its hydrolysis, otherwise absent (for this pH_m-range) in ISA-free solutions. Instead, as discussed in Section 3.5, the complexation of Ni²⁺ with ISA⁻ is expected to enhance the acidity of the α-OH group of the ligand, which is deprotonated above –log₁₀[H⁺]≈8: the complex forming is very likely NiISA_−H(aq). Note that in the absence of any (hard-Lewis) metal cation, the deprotonation of the α-OH group of ISA has been estimated to take place at –log₁₀[H⁺]≈14.3 [35].

The Ni(II)–ISA species forming at pH_m≥12.5 has been formulated as Ni(OH)₃ISA²⁻. However, this formulation is also unlikely considering the aqueous speciation of Ni(II) in the absence of ISA, where the formation of the anionic species Ni(OH)₃⁻ has not been observed within the investigated pH_m-range. Thus, a structure invoking the deprotonation of the α-OH group of ISA, Ni(OH)₂ISA_−H²⁻, appears again more likely. In the absence of definitive spectroscopic proof for the proposed hypotheses, we have maintained the nomenclature of Ni(II)–ISA complexes involving only the hydrolysis of Ni(II), Ni(OH)_xISA^1−x (with x=1–3).

Experiments in the presence of NaISA have been conducted at I=0.5 M NaCl–NaOH, and thus the extrapolation to I=0 has been done by using the following SIT ion interaction coefficients:

ε(ISA⁻, Na⁺)=–(0.07±0.01) kg·mol⁻¹ (in analogy to Hox⁻, as proposed in [47])

ε(NiOHISA(aq), Na⁺/Cl⁻)=0 [by definition in SIT]

ε(Ni(OH)₂ISA⁻, Na⁺)=–(0.05±0.10) kg·mol⁻¹ [estimated by charge analogy] [49]

ε(Ni(OH)₃ISA²⁻, Na⁺)=–(0.10±0.10) kg·mol⁻¹ [estimated by charge analogy] [49]

and

log10*K°s,(1,1,1)=log10*K′s,(1,1,1)+log10γNiOHISA(aq)  + log10aw–log10γISA−−log10γH+

log10*K°s,(1,2,1)=log10*K′s,(1,2,1)+log10γNi(OH)2ISA−− log10γISA−

log10*K°s,(1,3,1)=log10*K′s,(1,3,1)+log10γNi(OH)3ISA2− +log10γH+–log10γISA−−log10aw

resulting in:

log10*K°s,(1,1,1)=(5.6±0.3)

log10*K°s,(1,2,1)=−(5.5±0.5)

log10*K°s,(1,3,1)=−(18.9±0.7)

The combination of log₁₀*K°_s,(1,n,1) (n=1–3) with log₁₀*K°_s,0{β–Ni(OH)₂(cr)} determined in Section 4.3, allows the calculation of the equilibrium constants for the formation of the complexes NiOHISA(aq), Ni(OH)₂ISA⁻ and Ni(OH)₃ISA²⁻ as summarized in Table 3.

The comparison of thermodynamic calculations using the model derived in the present work with experimental solubility data is provided in Figure 5 (as a function of pH_m), and further in Figure 7 as a function of log₁₀[ISA]. A good agreement is obtained between the experimental and calculated Ni(II)-solubilities for all investigated systems, thus supporting the chemical and thermodynamic models derived for Ni(II) in the presence of ISA.

Figure 7:

Experimental Ni(II) solubility data determined in the present work in 0.5 M NaCl–NaOH at increasing NaISA concentrations (0.01, 0.1 and 0.2 M; red symbols). Solubility data determined for the same pH_m in the absence of ISA are included (green symbols) for comparison. Solid lines corresponding to the overall solubility of β–Ni(OH)₂(cr) calculated with the thermodynamic model derived in the present work (thick lines) and underlying aqueous speciation (thin lines).

5.4 Chemical, thermodynamic and activity models for the system Ni²⁺–Na⁺–H⁺–Cl^––OH^––ISA^––H₂O(l)

Table 3 summarizes the chemical and thermodynamic models derived in the present work or reported in Gamsjäger et al. [13] for Ni(II) in the absence and presence of ISA⁻. These models properly explain experimental solubility data collected at 8≤ pH_m ≤13. Table 4 provides all SIT ion interaction coefficients used in the present work and involving Ni(II), either as reported in Gamsjäger et al. [13] or estimated in the present work.