1 Introduction

The chemical thermodynamics of plutonium have been critically discussed in recent OECD/NEA-TDB reviews [1,2] which provide a well ascertained set of thermodynamic data and ion interaction coefficients for the system Pu/e⁻/H⁺/OH⁻/NaClO₄ or NaCl/H₂O. However, there is still a lack of knowledge and it is difficult to ascertain reliable predictions of the total concentration of dissolved plutonium under the geochemical conditions of nuclear waste repositories. The interpretation of experimental results is complicated by redox reactions of aqueous plutonium species, Pu(IV) colloids and solid plutonium phases. In particular the redox reactions of Pu(IV) colloids have not yet been understood. The present paper gives an overview on the solubility of plutonium at 20–25 °C in solutions without complexing ligands (carbonate, phosphate, silicate, etc.) where oxides, oxyhydroxides or hydroxides are the solubility controlling solids. The discussion covers solubility studies in the presence of reducing chemicals [3–7], in the absence of reducing or oxidising agents under Ar atmosphere [8–10] and in the presence of O₂(g)/air [11–15].

Under reducing conditions Pu(III) is the dominant oxidation state in solution. However, there is only one study (Felmy et al. [3]) that provides experimental solubility data for Pu(III) hydroxide, Pu(OH)₃(s), as equilibrium solid phase. Thermodynamic calculations show that Pu(OH)₃(s) is a metastable solid phase, even under reducing conditions. The border line for the conversion into PuO₂(am,hyd) is close to the line for the decomposition of water.

Crystalline PuO₂(cr) is the stable Pu(IV) solid phase. However, recent papers on the solubility of tetravalent actinides [16–20] pointed out that the available solubility data for AnO₂(cr) strongly indicate that the solubility is controlled by small amorphous particles included in the bulk crystalline solids or by amorphous hydrated surface layers. The measured An(IV) concentrations are similar to those determined with oxyhydroxide precipitates AnO_2−n(OH)_2n·xH₂O(am) which may be designated as amorphous hydroxide, An(OH)₄(am), or hydrous oxide, AnO₂·xH₂O(am) or AnO₂(am,hyd). It has to be emphasized that amorphous or slightly crystalline hydrous oxides or oxyhydroxides like aged PuO₂(s,hyd) that may show a weak XRD pattern [10,21] are not well defined compounds. They are inhomogeneous with regard to the degree of hydration and crystallite size. These properties can vary with time of ageing and with the solution conditions affecting the recrystallization kinetics [2]. The selected values for the solubility constant and standard molar Gibbs energy of formation must therefore be considered as average values for this kind of solids formed in aqueous solutions. On the other hand, these are the compounds relevant for aqueous systems and the storage of nuclear waste. Particularly in the case of highly active Pu wastes α-radiation damage leads to the amorphization of PuO₂(cr) [21]. Despite these problems there is good agreement between the values derived for the solubility constant of Pu(IV) hydrous oxide by different authors and approaches [2]: (a) the solubility products calculated in Ref. [16,22] from the available Pu(IV) equilibrium concentrations with the hydrolysis constants for Pu(OH)_n⁴⁻ⁿ reported in Ref. [23], (b) those derived from the solubility of PuO₂(am,hyd) under reducing conditions in equilibrium with Pu³⁺ [4–6], and (c) the value obtained for colloidal PuO₂(am,hyd) particles in equilibrium with Pu³⁺, PuO₂⁺ and PuO₂²⁺ at pH_c = 1.0 [24]. The equilibrium concentration of aqueous Pu(IV) species is usually low compared to those of Pu(III), Pu(V) and Pu(VI) which result from the known redox equilibria and depend on the redox potential and pH.

The solubility of amorphous Pu(V) hydroxide, PuO₂OH(am), is relatively high and does not represent a retention barrier. Oxyhydroxides of Pu(VI) (thermodynamic data are only known for PuO₂(OH)₂·H₂O(cr) [1,2]) might control the solubility under strongly oxidising conditions (e.g., in case of radiolysis in concentrated chloride brines where Pu(VI) is the dominant oxidation state in solution [8,15]), but these conditions are not further discussed here.

A few years ago Haschke et al. [25–28] reported the formation of PuO_2+x(s) which has been discussed very controversially. Recent EXAFS and XPS studies [29,30] report that the formation of PuO_2+x(s,hyd) is a partially oxidised mixed valent hydrated oxyhydroxide (Pu^V)_2x(Pu^IV)_1−2xO_2+x−n(OH)_2n(s,hyd). Our recent analysis of total Pu concentrations, oxidation state distributions and simultaneously measured redox potentials in solubility studies under air and under Ar (with only traces of O₂(g) present) also indicates that oxygen is scavenged by solid PuO₂(s,hyd) yielding mixed valent PuO_2+x(s,hyd) that controls the solubility, i.e., the equilibrium concentrations of both Pu(IV) and Pu(V) [10]. However, the extreme stability of PuO_2+x(s) and the thermodynamic data reported by Haschke et al. [27,28] cannot be correct [31,32]. These important findings are summarized in the present paper; thermodynamic data for PuO_2+x(s,hyd) will be discussed as well.

2 Solubility of plutonium under reducing conditions

If the solubility of plutonium under reducing conditions is controlled by Pu(OH)₃(s) (analogous to other trivalent actinides or lanthanides in the absence of carbonate, phosphate, etc.), the concentration of Pu³⁺ and its hydroxide complexes Pu(OH)_n³⁻ⁿ is given by the solubility product (K_sp = [Pu³⁺][OH⁻]³) and the formation constants (β_n = [Pu(OH)_n³⁻ⁿ]/[Pu³⁺][OH⁻]ⁿ) for the reactions:

Depending on the given redox conditions, the equilibrium between dissolved Pu(III) and Pu(IV) can lead to Pu(IV) concentrations exceeding the solubility of Pu(IV) hydrous oxide; consequently this will lead to the precipitation of PuO₂(am,hyd) and the complete dissolution of Pu(OH)₃(s). Combining reactions (13)–(15) with the equilibrium constants log^∗K°_s,0 = 15.8 ± 0.8 for Pu(OH)₃(s) and −2.33 ± 0.52 for PuO₂(am,hyd) and log K°_III–IV = −17.69 ± 0.04 for the redox couple Pu³⁺/Pu⁴⁺ [2]:

In the case of solubility control by PuO₂(am,hyd), the equilibrium Pu(IV) concentration is given by the solubility product of PuO₂(am,hyd) (K_sp = [Pu⁴⁺][OH⁻]⁴) and the formation constants of the Pu(IV) hydroxide complexes (β_n = [Pu(OH)_n⁴⁻ⁿ]/[Pu⁴⁺][OH⁻ ]⁴). In addition PuO₂(am,hyd) is in equilibrium with aqueous Pu(III) species. The dissolution equilibrium of PuO₂(am,hyd) and the redox equilibrium between Pu⁴⁺ and Pu³⁺:

With this background the results of Felmy et al. [3], the only available study providing solubility data for Pu(OH)₃(s), are discussed here. The experiments were performed at 23 °C under inert-gas atmosphere in the presence of iron powder. The solid was precipitated from a Pu(III) stock solution but not further characterised and suspended either in deoxygenated water or in concentrated chloride solutions (synthetic WIPP brines). The plutonium concentrations (after 1.8 nm filtration) were measured after relatively short equilibration times of 1–24 days. Fig. 1 shows the solubility data in the dilute solutions (I < 0.01 M) and the measured E_h values (those in the chloride brines are similar). The redox potentials are in the range (pe + pH) = 2 ± 1, typical for values in suspensions of corroding iron and clearly above the stability line of Pu(OH)₃(s) at (pe + pH) = −0.4 ± 1.0 (fat dashed line in Fig. 1b). Under these conditions the initial Pu(OH)₃(s) precipitate is metastable and should convert slowly into PuO₂(am,hyd). Fig. 1a shows the equilibrium Pu(III) concentration calculated for Pu(OH)₃(s) as solid phase (dashed line) and also the equilibrium Pu(IV) and Pu(III) concentrations calculated for (pe + pH) = 2 with PuO₂(am,hyd) as solid phase (solid lines). The experimental Pu(III) concentrations of Felmy et al. [3] are between the dashed and solid line. The short equilibration times of 1–24 days are not sufficient for a complete solid phase transformation and the solubility constant derived from the data at pH 6–7, log^∗K°_s,0(Pu(OH)₃(s)) = 15.8 ± 0.8 [3], is most probably correct. However, as indicated by the arrow in Fig. 1a, a number of data points show a tendency to the lower curve expected after transformation into PuO₂(am,hyd).

Contrary to the solubility constant of Pu(OH)₃(s), the equilibrium constant for the reductive dissolution of PuO₂(am,hyd) (Eqs. (19) and (20)) is well ascertained. A few years ago, Fujiwara et al. [4,5] and Rai et al. [6] investigated this reaction directly by measuring the Pu³⁺ concentration in solubility studies with PuO₂(am,hyd) under various reducing conditions: (a) in 0.5, 1.0 and 2.0 M NaClO₄ + 0.001 M Na₂S₂O₄ (pH 3–9) with (pe + pH) = 10 ± 1 [4,5], (b) in 0.005 M CaCl₂ or 0.01 M NaClO₄ + 5.2×10⁻⁴ M hydroquinone (pH 3–9) with (pe + pH) = 4.0 ± 0.5 [6], and (c) in 0.01 M NaCl + 0.001 M FeCl₂ with pe = 11 at pH 2 decreasing to pe = −7 at pH 11 [6]. All results can be consistently described with log^∗K°_IVs/III = 15.5 ± 0.6, close to the value of log^∗K°_IVs/III = 15.4 ± 0.5 based on the NEA-TDB selections [2]. The experimental solubilities and redox potentials in the Na₂S₂O₄ and hydroquinone solutions and the corresponding calculations for (pe + pH) = 10 and 4, respectively, are compared in Fig. 2. As predicted according to Eq. (20), the increase of (pe + pH) from 4 and 10 leads to a decrease of the Pu(III) concentration by about six orders of magnitude.

In a recent study, Nilsson [7] tried to determine the solubility of Pu(OH)₃(s) at ambient temperature in 0.1 M NaCl under a pressure of 50 bar H₂(g) in an autoclave containing a piece of Pt wire. Under these extremely reducing conditions, corresponding to (pe + pH) = −0.85, the X-ray amorphous Pu(OH)₃(am) precipitated from a Pu(III) stock solution was expected to remain stable. However, the Pu concentrations measured after centrifugation (analyzed for [Pu]_tot = [Pu(III)] + [Pu(IV)] after 150, 320 and 480 days and for [Pu(IV)] after 480 days) were much lower than expected for Pu(OH)₃(s) (Fig. 3a) and the redox potentials measured after 480 days were much higher than expected for P(H₂(g)) = 50 bar (Fig. 3b). Obviously, pe was not controlled by the reaction 0.5H₂(g) ⇌ H⁺ + e⁻. From pH changes in their samples in the near neutral pH range and the changed colour of the solid Nilsson [7] concluded that the initially blue Pu(OH)₃(am) transformed into green PuO_2±x(am,hyd), but gave no quantitative data interpretation. Fig. 3 shows that the results can be well explained by Eq. (20) for the reductive dissolution of PuO₂(am,hyd). The measured solubility data are reasonably consistent with the Pu(III) concentrations calculated for the experimental values of (pe + pH) = 8.5 ± 2 and an additional contribution from Pu(IV) colloids. It is difficult to find an explanation for the measured redox potentials, but accepting the measured pe values it is possible to calculate the solubility and aqueous speciation of plutonium.

The concentration line for polymeric Pu(IV) oxyhydroxide species (1.5–2 nm colloids) included in Figs. 2a and 3a (log[Pu(IV)]_coll = −8.3 ± 1.0) was determined in our recent solubility study with Pu(IV) hydrous oxide [10] from the difference of the Pu concentrations measured after 10 kDa ultrafiltration and in unfiltered aliquots taken carefully from the clear supernatant. Similar as in a previous study where we determined the pH-independent concentration of colloidal or polymeric Th(IV) at pH 6.5–13.5 (log[Th(IV)]_coll = −6.3 ± 0.5) [38] the concentration [Pu(IV)]_coll at pH 8–13 was reasonably reproducible and at a constant level. For both Th(IV) and Pu(IV) the level of [An(IV)]_coll is about two orders of magnitude higher than the An(IV) concentration after 1.5 nm ultrafiltration or ultracentrifugation. This is consistent with a model on Pu(IV) polymer formation proposed by Fujiwara et al. [4] who supposed that the concentration of log[Pu(IV)] = −9 measured in 1 M NaClO₄ (pH 7–9) after 2 nm filtration is primarily caused by small Pu(IV) polymers; [Pu(IV)]_tot is expected to include further contributions from eigencolloids larger than 2 nm. The equilibrium concentration of mononuclear Pu(IV) species was calculated to be log[Pu(OH)₄(aq)] = −10.3 ± 0.2 [4] which is close to the value of −10.4 ± 0.5 determined by Rai et al. [9] and used in the present calculations.

3 Solubility of plutonium in redox-inert solutions under argon atmosphere

In a recent study at our laboratory [10], Pu(IV) hydrous oxide was precipitated from an electrochemically prepared Pu(IV) stock solution containing a contamination of 0.5% Pu(VI) and the solubility was determined at I = 0.1 M (NaCl) and 22 ± 2 °C. The work was carried out in an Ar glove box (<10 ppm O₂) using long-lived Pu-242 (t_1/2 = 3.8×10⁵ a) to minimize radiolysis effects. The batch samples at pH 2.5–13 (ca. 20 mg Pu-242 in 50 mL solution) were analyzed after equilibration periods between 6 and 104 days: E_h and pH were measured directly in the samples, the Pu concentrations (total Pu and the different Pu oxidation states) were measured after 10 kDa ultrafiltration (pore size ca. 1.5 nm). The constant values obtained after 34 days indicated that equilibrium was attained. The results are shown in Fig. 4.

The samples at pH 2.5 and 3.0 contained about equimolar concentrations of Pu(III) and Pu(V), whereas the samples at pH > 3 showed only the absorption bands of the PuO₂⁺ ion. Aqueous Pu(IV) species could not be detected by absorption spectroscopy and redox speciation by solvent extraction showed that the Pu(IV) concentrations are very low compared to the total dissolved Pu, almost exclusively non-extractable Pu(V). The Pu(IV) concentrations at pH < 4 are in the expected range (c.f., Fig. 4a). The total Pu concentrations at pH 8–13 were in the range of 10⁻⁹ to 10⁻¹⁰ M, close to values determined by Rai et al. [9] in dilute KOH solutions. The redox potentials measured in samples containing solid and colloidal Pu(IV) have a relatively large experimental uncertainty of ±50 mV [10], but the pe values at pH 4–13 clearly show a linear decrease with pH (slope −1, Fig. 4b). The values of (pe + pH) decreased from 14.9 ± 0.8 after 6 days to 13.5 ± 0.8 after 34 days and to constant values of 11.7 ± 0.8 after 54–104 days.

The Pu(III) concentrations at pH 2.5–3.3 and pe = 10–12 can be described by the reductive dissolution of PuO₂(am,hyd). The experimental Pu³⁺ concentrations and the steep decrease of log[Pu³⁺] at pH > 3 are consistent with Eq. (20) and the calculations for (pe + pH) = 14 ± 1 (c.f., Fig. 4a). However, the experimental Pu(V) concentrations, up to pH 5 at a constant level of log[Pu(V)] = −5 and at pH 5–10 decreasing with a slope of −1, are not consistent with the oxidative dissolution of Pu(IV) hydrous oxide:

The values calculated for the equilibrium constant log K°_IVs/V from the experimental PuO₂⁺ concentrations and pe values deviate up to seven log-units from the value of log K°_IVs/V = −19.8 ± 0.9 based on the data selected in the NEA-TDB [2] for PuO₂(am,hyd) and PuO₂⁺. Similar discrepancies observed in solubility studies under air [13–15] will be discussed below.

Another solubility study under Ar atmosphere was reported by Lierse and Kim [8] who titrated PuO₂(s,hyd) suspensions in 1 M NaClO₄ from pH 12 to pH 1. They obtained a similar solubility curve with log[Pu]_tot decreasing with a slope of −1 from pH 3 to 10, but they did not report oxidation state analysis and redox potential measurements.

4 Solubility of plutonium in the presence of oxygen

4.1 The effect of oxygen on the total Pu concentration in solution

Fig. 5 shows the total Pu and Pu(IV) concentrations measured by Rai et al. [13–15] at pH 1–8 after up to 106 days and a few data from other authors at pH < 2 [11,12] in solubility studies with PuO₂(s,hyd) at I = 0.01–1 M and 20–25 °C. In these studies the solutions were exposed to air and then kept in closed vials. The total Pu concentration at pH < 1.5 (log[Pu]_tot, open points in Fig. 5) is slightly increased compared to log[Pu(IV)]_aq (crosses). It passes through a plateau at pH 1–3 and decreases with a slope of −1 at pH > 3. Aqueous speciation by spectroscopy and solvent extraction showed that the dissolved Pu at pH 1–3 consists mainly of PuO₂²⁺ and PuO₂⁺ while PuO₂⁺ predominates at pH 3–9 [13–15]. The concentration of oxidised Pu ([PuO₂²⁺] + [PuO₂⁺]) at pH < 3 corresponds to the available oxygen in these closed systems, given by the sum of [O₂]_aq = 2.5 × 10⁻⁴ M at P(O₂(g)) = 0.2 bar and O₂(g) in the gas phase above the solution [31].

The Pu concentrations measured by Lierse and Kim [8], Rai et al. [9] and in our previous study [10] under Ar atmosphere containing only traces of O₂(g) are shown for comparison as filled points in Fig. 5. The Pu(V) concentrations at pH > 4 are, within the uncertainties, the same as those determined by Rai et al. [13–15] in samples kept under air. However, the constant level of [Pu(V)] = 10⁻⁵ M at pH < 5 in our study under Ar is considerably lower than the corresponding values under air. It corresponds to the 0.5% Pu(VI) in the initial Pu(IV) stock solution, if this fraction of oxidised Pu is co-precipitated with the Pu(IV) hydrous oxide and re-dissolved in the solubility experiments. The data of Lierse and Kim [8] who titrated PuO₂(am,hyd) suspensions in 1 M NaClO₄ under a continuous Ar stream from pH 12 to pH 1 may be explained if we assume that the Ar stream included a contamination of a few ppm O₂ and that the total amount of oxidised Pu species accumulated during the titration experiment (2–3 months) [31].

4.2 Equilibrium Pu(V) concentrations and redox potentials: evidence for the formation of PuO_2+x(s,hyd)

The Pu concentrations measured in the solubility studies under air or under Ar atmosphere cannot be explained without the knowledge of the redox potentials. It is helpful to divide the experimental data into different pH regions (Figs. 6a and b). Rai [14] has shown that the solubility of PuO₂(am,hyd) under air at pH 1–3 (region A) is dominated by the oxidative dissolution reaction (23) and the redox equilibrium (24) between PuO₂⁺ and PuO₂²⁺:

PuO2(s,hyd) ⇌ PuO2+ + e−

(23)

PuO2+ ⇌ PuO22+ + e−

(24)

The redox potentials in region A, pe = 16.0 ± 0.3 [14], are consistent with the spectroscopically determined PuO₂⁺ and PuO₂²⁺ concentrations and log K°_V/VI = −15.82 ± 0.09 [1,2]. The equilibrium constant derived by Rai [14] for the oxidative dissolution of PuO₂(am,hyd) from the experimental pe values and Pu(V) concentrations, log K°_IVs/V = −19.45 ± 0.23 [14], is also in agreement with the value of log K°_IVs/V = −19.8 ± 0.9 calculated with the standard molar Gibbs energies selected in the NEA-TDB [2] for PuO₂(am,hyd), Pu⁴⁺ and PuO₂⁺ from different, independent data. In our study under Ar [10] the redox potentials at pH 2.5–3.3 are much lower. Hence Pu(VI) is not observed, but only Pu(V) (and Pu(III) as expected according to Eq. (20)). However, the values of pe = 10–12 and log[PuO₂⁺] = −5 are strongly inconsistent with log K°_IVs/V = −19.8 ± 0.9.

At pH 3–4 the pe values in the studies under air [13–15] drop drastically to about 7 log-units lower values (Fig. 6b) while the solubility (log[Pu]_tot ≈ log[PuO₂⁺]) decreases continuously with a slope of −1 (Fig. 6a). Accordingly, the solubility constant log K°_IVs/V derived from the experimental values of pe and [PuO₂⁺] in region C would differ by seven orders of magnitude from the value derived in regions A and B [13,14]. As there was no evident explanation for this discrepancy, it was ascribed to possible experimental problems in the E_h measurements [14,15]. However, our results under Ar (P(O₂(g)) < 10⁻⁵ bar) show that the redox potentials in region C are reproducible within a certain range. Moreover they coincide with those measured by Rai et al. [13–15] under air (P(O₂(g)) = 0.2 bar). The redox potentials in region C and also the slopes of −1 in regions B and C (pe + pH = constant) can neither be explained by equilibria between aqueous Pu species nor by the oxygen partial pressures [10,15]. The experimental results in regions B and C are not consistent with the equilibria:

PuO2(s,hyd) ⇌ PuO2+ + e−

(25)

or

PuO2(s,hyd) + 1/4 O2(g) + H+ ⇌ PuO2+ + 1/2 H2O

(26)

The Pu(V) concentrations and pe values at pH > 3, which are more or less the same in the studies under air [13–15] and under Ar [10] can be explained with PuO_2+x(s,hyd), mixed valent hydrous oxide (Pu^V)_2x(Pu^IV)_1−2xO_2+x(s,hyd) or (PuO_2.5)_2x(PuO₂)_1−2x(s,hyd), as solubility controlling solid phase in equilibrium with both Pu(V) and Pu(IV) in solution. It can be formed by the oxidation of PuO₂(s,hyd) with the oxygen present in the system:

PuO2(s,hyd) + x/2 O2 → PuO2+x(s,hyd)

(27)

or by co-precipitation of Pu(V) during the preparation of Pu(IV) hydrous oxide [10]. At pH < 3 (region A), the Pu(V) fractions in the PuO_2+x(s,hyd) solids are below the Pu(V) saturation line (slope −1) and hence completely soluble. This allows to estimate the Pu(V) fraction in the solids used in the solubility studies from the amount of oxidised Pu dissolved at the plateau at low pH ([Pu(V + VI)]_max) and the total Pu inventory [Pu]_inv in the samples (initially present as solid precipitates). This is 10–12% in the samples of Rai et al. [14,15] under air (x = 0.5 [Pu(V + VI)]_max/[Pu]_inv = 0.05–0.06) and about 0.5% (x = 0.003) in our study under Ar [10]. Haschke et al. [25–28] observed a maximum value of x = 0.27 but they supposed that PuO_2+x(s) should be stable up to x = 0.5 (PuO_2.5(s) = 1/2 Pu₂O₅(s)) [27,28].

The mixed valent hydrous oxide PuO_2+x(s,hyd) = (Pu^V)_2x(Pu^IV)_1−2xO_2+x(s,hyd) may be written formally as (PuO_2.5)_2x(PuO₂)_1−2x(s,hyd) in equilibrium with both Pu(V) and Pu(IV) in solution:

PuO2+x(s,hyd) + (2−3x)H2O(l) ⇌ 2xPuO2+ + (1−2x)Pu4+ + (4 − 6x)OH−

(28)

with:

logKsp(PuO2+x(s,hyd))=2xlog[PuO2+]+(1−2x)log[Pu4+]+(4−6x)log[OH−]=2xlogKsp(PuO2.5inPuO2+x(s,hyd))+(1−2x)logKsp(PuO2inPuO2+x(s,hyd))

(29)

The solubility products for the formal fractions of PuO_2.5(s,hyd) and PuO₂(s,hyd) in PuO_2+x(s,hyd) can be calculated separately, because the dissolved PuO₂⁺ and Pu⁴⁺ ions and their hydroxide complexes do not undergo reversible redox reactions:

Ksp(PuO2.5 in PuO2+x(s,hyd)) = [PuO2+][OH−]

(30)

Ksp(PuO2 in PuO2+x(s,hyd)) = [Pu4+][OH− ]4

(31)

The experimental Pu(IV) concentrations were previously used to calculate the solubility product of PuO₂(am,hyd) [2,16,22] and the evaluation of the PuO₂⁺ concentrations at pH 3–9 is given in detail in our recent paper [10]. The solubility product of PuO_2.5(s,hyd) as a fraction of PuO_2+x(s,hyd) was calculated from the different sets of data determined by Rai et al. [13–15] under air in dilute solutions of low ionic strength and in 0.4 and 4.0 M NaClO₄ and NaCl and from the data determined under Ar atmosphere by Lierse and Kim [8] in 1.0 M NaClO₄ and in our recent work in 0.1 M NaCl. All data sets yield consistent equilibrium constants at I = 0 with a mean value (±2σ) of log K°_sp(PuO_2.5 in PuO_2+x(s,hyd)) = −14.0 ± 0.8 or log^∗K°_s,0(PuO_2.5 in PuO_2+x(s,hyd)) = 0.0 ± 0.8 [10] for the reactions:

PuO2.5(s,hyd) + 1/2 H2O ⇌ PuO2+ + OH−

(32)

or

PuO2.5(s,hyd) + H+ ⇌ PuO2+ + 1/2 H2O

(33)

The solubility product of PuO_2.5(s,hyd) as a formal fraction of PuO_2+x(s,hyd) is five orders of magnitude lower than that of Pu(V) hydroxide (log K°_sp(PuO₂OH(am,hyd)) = −9.0 ± 0.5 [1,2]). It compares well with the values for Np(V) pentoxide: log K°_sp(NpO_2.5(cr)) = −12.2 ± 0.8 (calculated from thermochemical data in Refs. [1,2]) and log K°_sp(NpO_2.5(s,hyd)) = −11.4 ± 0.4 (solubility study of Efurd et al. [40]) and appears to be in a reasonable order of magnitude, in particular as the solubility product of PuO₂(am,hyd) is also about 2 log-units lower than that of NpO₂(am,hyd) (log K_sp = log ([An⁴⁺][OH⁻]⁴); log K°_sp = −58.3 ± 0.5 for Pu(IV) and −56.7 ± 0.5 for Np(IV) [2]).

Solubility control by PuO_2+x(s,hyd) explains the redox potentials at pH > 3 under air, in particular the slope of −1 at pH 3–5 (region B in Fig. 6b) that could not be explained by Rai [14]. At low pH (region A) the Pu(V) fractions in the PuO_2+x(s,hyd) solids are below the Pu(V) saturation concentration and completely soluble, but at pH > 3 they exceed the solubility of PuO_2+x(s,hyd). Combining Eqs. (34) and (35) and the corresponding equilibrium constants (log K°_IVs/V = −19.8 ± 0.9 [2], log^∗K°_s,0(PuO_2.5 in PuO_2+x(s,hyd)) = 0.0 ± 0.8 [10]):

PuO2(s,hyd) ⇌ PuO2+ + e−

(34)

PuO2+ + 1/2 H2O ⇌ PuO2.5(s,hyd) + H+

(35)

yields

PuO2(s,hyd) + 1/2 H2O ⇌ PuO2.5(s,hyd) + e− + H+

(36)

with log K°(36) = − (pe + pH) − 0.5 log a_w = (−19.8 ± 0.9) − (0.0 ± 0.8) = −19.8 ± 1.2. This means that the Pu(V) concentration is controlled by PuO_2+x(s) and the value of (pe + pH) is buffered by the PuO₂(s,hyd) and PuO_2.5(s,hyd) fractions in PuO_2+x(s,hyd), similar as in the case of Fe(II–III) and U(IV–VI) oxide/oxyhydroxide redox buffers (c.f., Section 1.1). This explains the slope of −1 in region B (Fig. 6b) and is, within the range of uncertainty, consistent with the experimental values of (pe + pH) = 18.7 ± 0.6 [14,15], in particular if one takes into account that other redox couples (e.g., PuO₂⁺/PuO₂²⁺) may also contribute to pe.

At pH > 4, the pe values drop to drastically lower values and decrease up to pH 13 with a slope of −1 (c.f., region C in Fig. 6b where the line of (pe + pH) = 12.5 ± 1.2 covers the experimental data). These redox potentials can only be explained if the small colloidal or polymeric Pu(IV) oxyhydroxide species prevailing in neutral to alkaline solution (c.f., Fig. 6a and discussion in Section 2), are taken into consideration. On the one hand they have properties of small solid particles designated here as PuO₂(coll,hyd), on the other hand they must be considered as large polynuclear aqueous species, in equilibrium with both small aqueous species and solid PuO₂(s,hyd):

PuO2(s,hyd) ⇌ PuO2(coll,hyd,aq)

(37)

with log K°_IVcoll = log[Pu(IV)]_coll = −8.3 ± 1.0 [10]. Using Δ_fG°_m(PuO₂(am,hyd)) = −965.5 ± 4.0 kJ/mol [2] an average value of Δ_fG°_m(PuO₂(coll,hyd)) = −918.1 ± 7.0 kJ/mol is calculated for these Pu(IV) colloids or polymers. Their size (1.5–2 nm) is estimated in Ref. [10] by applying Schindler's relation between the standard molar Gibbs energy of formation and particle size [39]. Similar as solid PuO₂(s,hyd), the Pu(IV) colloids or polymers can also be oxidised by oxygen. However, because of their significantly greater standard molar Gibbs energy of formation the Pu(V) fraction is highly soluble:

PuO2(coll,hyd) + x/2 O2 + 2xH+ → (PuO2.5)2x(PuO2)1−2x(coll,hyd) + 2xH+ → 2xPuO2+ + xH2O + (1–2x)PuO2(coll,hyd)

(38)

so that the remaining colloids consist exclusively of Pu(IV). The equilibrium PuO₂⁺ concentration is limited to the solubility of PuO_2.5(s,hyd) in PuO_2+x(s,hyd):

PuO2(coll,hyd) ⇌ PuO2+ + e−

(39)

PuO2+ + 1/2 H2O ⇌ PuO2.5(s,hyd) + H+

(40)

The equilibrium constant for reaction (39), log K°_IVcoll/V = −11.5 ± 1.3, can be calculated from Δ_fG°_m(PuO₂(coll,hyd)) = −918.1 ± 7.0 kJ/mol and Δ_fG°_m(PuO₂⁺) = −852.65 ± 2.87 kJ/mol [1]. Combining Eqs. (39) and (40) yields:

PuO2(coll,hyd) + 1/2 H2O ⇌ PuO2.5(s,hyd) + e− + H+

(41)

with log K°(41) = − (pe + pH) − 0.5 log a_w = (−11.5 ± 1.3) − (0.0 ± 0.8) = −11.5 ± 1.5. This is consistent with the slope of −1 (Fig. 6b) in region C. The calculated value of (pe + pH) = 11.5 ± 1.5 agrees, within the uncertainties, with the experimental values measured under Ar after 54–104 days: (pe + pH) = 11.7 ± 0.8 [10] and under air after 90 and 106 days: (pe + pH) = 12.8 ± 1.1 [13,15]. The redox potentials in region C can be described by equilibria between PuO_2+x(s,hyd), PuO₂⁺ and Pu(IV) colloids which are in Eqs. (39)–(41) considered as small solid particles. This means that the large difference between the pe values in regions B and C (Fig. 6b) can be explained as a particle size effect, i.e., by the formation of small Pu(IV) colloids (1.5–2 nm) with an increased molar surface and standard Gibbs energy compared to PuO₂(am,hyd) precipitates which consist of agglomerates of 3–5 nm crystallites [10,17]. Colloidal Pu(IV) oxyhydroxide particles formed at low pH are larger than 5 nm. They can be detected by laser-induced breakdown detection LIBD [22,42] and have thermodynamic properties of PuO₂(am,hyd), as indicated by the solubility products determined for these particles [22,24,42].

5 The role of Pu(IV) colloids/polymers in the Pu(IV)–Pu(V) redox chemistry

Since tetravalent actinides have a high tendency towards polynucleation and colloid formation the solubility is usually measured after ultrafiltration or ultracentrifugation to remove these species, whereas redox potentials are usually measured directly in the samples [3–7,10,13–15]. As discussed above, the colloidal or polymeric Pu(IV) oxyhydroxide species present in neutral and alkaline solutions have a significant impact on the redox potentials in systems without oxidising or reducing chemicals. They are not “notorious troublemakers” in plutonium chemistry as recently stated by Nilsson [7] but part of the thermodynamic system as illustrated in Fig. 7.

Further experiments reported in Ref. [10] support the conclusion that the redox potentials in near neutral Pu(IV)–Pu(V) solutions correspond to a reversible equilibrium between PuO₂(coll,hyd) particles and PuO₂⁺ ions:

Another recent study indicates that colloidal or polymeric Pu(IV) species play also an important role for the redox behaviour of Pu(IV) in acidic solutions [43]. Electrochemically prepared Pu(IV) solutions at pH_c = 0.3–2.5 were investigated spectroscopically to study the formation of Pu(III), Pu(V) and/or Pu(VI), which is usually ascribed to the disproportionation of Pu(IV) into Pu(III) and Pu(V), followed by the reaction of Pu(V) with Pu(IV) into Pu(VI) and Pu(III) or by the disproportionation of Pu(V) into Pu(III) and Pu(VI). The steady state oxidation state distributions and pe values observed after 10–20 days were consistent with the known redox equilibria [1,2,24,44]. However, particularly the oxidation state distributions observed after short reaction times provide evidence that the underlying mechanism is not consistent with disproportionation reactions but with the formation of PuO₂⁺ from colloidal or smaller polynuclear Pu(IV) species followed by the simultaneous equilibration of the reversible redox couples Pu(V)/Pu(VI) and Pu(III)/Pu(IV) which are related by pe (and pH because of Pu(IV) hydrolysis equilibria) [43]. Contrary to the reversible redox couples Pu³⁺/Pu⁴⁺ and PuO₂⁺/PuO₂²⁺ the PuO₂⁺ and Pu⁴⁺ ions and their mononuclear hydroxide complexes are not directly in equilibrium with each other but only indirectly via their reactions with solid, colloidal or polymeric Pu(IV).

6 Thermodynamic data for PuO_2+x(cr) and PuO_2+x(s,hyd)

In the following sections, thermodynamic data for hydrous PuO_2+x(s,hyd) and for possible anhydrous crystalline compounds like PuO_2.25(cr) = 1/4 Pu₄O₉(cr), PuO_2.5(cr) = 1/2 Pu₂O₅(cr), and PuO₃(cr) are discussed by comparing known standard molar Gibbs energies of formation Δ_fG°_m(298.15 K) of pure and mixed valent anhydrous oxides and hydrous oxyhydroxides of uranium, neptunium and plutonium in the oxidation states An(IV), An(V) and An(VI). The values for hydrous An(IV) and An(V) oxyhydroxides correspond to the formula AnO_2+x(s,hyd), i.e., the contribution of H₂O molecules is not included in the values for Δ_fG°_m(AnO_2+x(s,hyd)). For better comparison, the Δ_fG°_m values for crystalline An(VI) oxyhydroxides with the formula AnO₂O_1−n/2(OH)_n·yH₂O(cr) are also normalized to values referring to the formula AnO₃(cr,hyd) by subtracting (n/2 + y)Δ_fG°_m(H₂O(l)), e.g., the value of Δ_fG°_m(PuO₂(OH)₂·H₂O(cr)) = −1442.4 kJ/mol [1,2] ((n/2 + y) = 2) is transformed into Δ_fG°_m(PuO₃(cr,hyd)) = −968.1 kJ/mol.

6.1 Standard molar Gibbs energies of formation of crystalline An(IV–V–VI) oxides and actinyl(VI) oxyhydroxides Δ_fG°_m(AnO_2+x(cr), 298.15 K)

The standard molar Gibbs energies of formation Δ_fG°_m(AnO_2+x(cr), 298.15 K) selected in the NEA-TDB [1,2] from experimental (thermochemical) data for anhydrous crystalline U(IV–V–VI) oxides, NpO₂(cr), NpO_2.5(cr) = 1/2 Np₂O₅(cr) and PuO₂(cr) are shown in Fig. 8 (filled squares). The normalized values for the actinyl(VI) oxyhydroxides AnO₃(s,hyd) of U(VI), Np(VI) and Pu(VI) (filled circles) were derived from the selected solubility constants [1,2]. Fig. 8 also includes estimated Δ_fG°_m values for NpO₃(cr), PuO₃(cr), and PuO_2.5(cr) (open squares). These estimates for the unknown Np and Pu oxides are based on the two following assumptions.

• (1) The difference between the standard molar Gibbs energies of formation of the known neptunyl(VI) and plutonyl(VI) oxyhydroxides and the (unknown) anhydrous trioxides, NpO₃(cr) and PuO₃(cr), is assumed to be similar as for the analogous U(VI) compounds: Δ_fG°_m(UO₃(cr,hyd), schoepite) − Δ_fG°_m(γ-UO₃(cr)) = −16.5 ± 2.1 kJ/mol [2].
• (2) Mixed valent An(IV–V) and An(IV–VI) oxides are more stable than corresponding mixtures of the pure An(IV) and An(V) or An(VI) oxides (e.g., (1/3)Δ_fG°_m(U₃O₈(cr)) − {(2/3)Δ_fG°_m(UO₃(cr)) + (1/3)Δ_fG°_m(UO₂(cr))} = −15.4 kJ/mol). In Fig. 8, this stabilization effect is illustrated by the deviation of Δ_fG°_m for a mixed valent oxide from the dotted straight line between the Δ_fG°_m values of the pure An(IV) and An(VI) oxides. We may assume that the stabilization energy for mixed valent An(IV–VI) and An(IV–V) oxides is approximately the same for analogous compounds of U, Np and Pu as illustrated by analogous deviations between the solid and dotted lines in Fig. 8.

The data in Fig. 8 clearly show that the standard molar Gibbs energy Δ_rG°_m for the oxidation of dry crystalline An(IV) dioxide AnO₂(cr) with oxygen (Δ_fG°_m(O₂(g)) = 0):

AnO2(cr) + (x/2) O2(g) → AnO2+x(cr)

(43)

is negative for U and positive for Np and Pu. These simple thermodynamic considerations are consistent with the experimental observations that dry NpO₂(cr) and PuO₂(cr) are not oxidised by O₂(g) (c.f., [1], p. 121), and Haschke et al. [25–27]). The close analogy between the known data for Np and Pu compounds (Fig. 8) and the standard molar Gibbs energies of formation that can be estimated for PuO_2.25(cr), PuO_2.5(cr) and PuO₃(cr) (Δ_fG°_m = −995 ± 3, −987 ± 10 and −952 ± 10 kJ/mol, respectively) show that the values reported by Haschke and Allen [28] for PuO_2+x(s) with x = 0.05 to 0.5, e.g., Δ_fG°_m(PuO_2.25(s)) = −1080 kJ/mol and Δ_fG°_m(PuO_2.5(s)) = −1146 kJ/mol [28] are considerably too negative. They are calculated assuming that PuO₂(s) is oxidised by water according to

PuO2(s) + xH2O → PuO2+x(s) + xH2(g)

(44)

The observed formation of H₂(g) [25–28] cannot be explained by the thermodynamics of reaction (44) (Δ_rG°_m(44) > x200 kJ/mol), it must be caused by other mechanisms (e.g., induced by radiolysis effects). Another recent attempt to oxidise PuO₂(cr) with water vapour (under strict exclusion of oxygen) at 315 °C failed [45]. However, it will be shown below that the formation of PuO_2+x(s,hyd) in the presence of both water and oxygen is consistent with thermodynamic balances.

6.2 Standard molar Gibbs energies of formation of hydrous Np(IV–V) and Pu(IV–V) oxides Δ_fG°_m(AnO_2+x(s,hyd), 298.15 K)

Mixed valent hydrous oxide PuO_2+x(s,hyd) = (Pu^V)_2x(Pu^IV)_1−2xO_2+x(s,hyd) is formally written as (PuO_2.5)_2x(PuO₂)_1−2x(s,hyd) which might suggest that it is considered as a solid solution. The chemical nature and structure of PuO_2+x(s,hyd) is not yet clear. However, solubility studies with solids containing considerably different amounts of Pu(V) (x = 0.003 in a study under Ar [10] and x = 0.05–0.06 in studies under air [13–15]) led to very similar Pu(V) concentrations [10] (c.f., Section 4.2). This indicates that the Pu(V) concentration depends much less on the value of x than expected for a solid solution of PuO_2.5(s,hyd) and PuO₂(s,hyd). Accordingly PuO_2+x(s,hyd) is treated as mixed valent compound and the following calculations refer to the definitions given by Eqs. (28)–(31). The standard molar Gibbs energy of formation of mixed valent PuO_2+x(s,hyd) can be calculated from the formal solubility products of the Pu(V) and Pu(IV) fractions (log K°_sp(PuO_2.5 in PuO_2+x(s,hyd)) = −14.0 ± 0.8, log K°_sp(PuO₂ in PuO_2+x(s,hyd)) ≈ log K°_sp(PuO₂(s,hyd)) = −58.33 ± 0.52 [2]) and Δ_fG°_m(PuO₂⁺) = −852.65 ± 2.87 kJ/mol, Δ_fG°_m(Pu⁴⁺) = −477.99 ± 2.70 kJ/mol, Δ_fG°_m(OH⁻) = −157.22 ± 0.07 kJ/mol, and Δ_fG°_m(H₂O(l)) = −237.14 ± 0.04 kJ/mol [1,2]. With the Δ_fG°_m values for the two formal fractions:

• Δ_fG°_m(PuO_2.5 in PuO_2+x(s,hyd)) = −971.2 ± 5.4 kJ/mol
• Δ_fG°_m(PuO₂ in PuO_2+x(s,hyd)) = −965.5 ± 4.0 kJ/mol

the standard molar Gibbs energy of formation of mixed valent PuO_2+x(s,hyd) is given by Eq. (45):

ΔfGm°(PuO2+x(s,hyd))=2xΔfGm°(PuO2.5(s,hyd))+(1−2x)ΔfGm°(PuO2(s,hyd))={2x(−971.2±5.4)+(1−2x)(−965.5±4.0)}kJ/mol

(45)

for the small values of x = 0.003 and x = 0.05–0.06 in the solubility studies under Ar [10] and air [14,15]. Accordingly Δ_fG°_m(PuO_2+x(s,hyd)) is slightly lower than Δ_fG°_m(PuO₂(s,hyd)) = −965.5 ± 4.0 kJ/mol. The values of Δ_fG°_m(NpO₂(s,hyd)) and Δ_fG°_m(NpO_2.5(s,hyd)) can be calculated from the experimental solubility constants for NpO₂(am,hyd) (log K°_sp = −56.7 ± 0.5 [11,19]), and NpO_2.5(s,hyd) (log K°_sp = −11.4 ± 0.4 [40] and −10.1 ± 0.2 [41]) with Δ_fG°_m(Np⁴⁺) = −491.8 ± 5.6 and Δ_fG°_m(NpO₂⁺) = −907.8 ± 5.6 kJ/mol [1,2].

As illustrated in Fig. 9 for Np and Pu the standard molar Gibbs energies of formation of An(IV) hydrous oxides are considerably less negative than those of the corresponding anhydrous crystalline An(IV) dioxides [2,16,17]. The difference of about 40 ± 10 kJ/mol, corresponding to seven log-units in the solubility constants, is due to effects from hydration and crystallinity (particle or crystallite size) as shown for ThO₂(s) [17]. For the pentavalent actinides, e.g. Np(V), the difference between the standard molar Gibbs energies of hydrous oxides used in solubility studies and anhydrous crystalline oxides is much smaller. As a consequence and contrary to the slightly positive standard molar Gibbs energy for the oxidation of dry NpO₂(cr), Δ_rG°_m for the oxidation hydrous NpO₂(am,hyd) is negative, up to x = 0.5 (c.f., Fig. 9a). For hydrous plutonium oxide (Fig. 9b), Δ_rG°_m is slightly negative for x < 0.1 (and possibly up to x = 0.25), whereas Δ_rG°_m is expected to be equal to zero or slightly positive for x > 0.25, if we take into account that the value of Δ_fG°_m = −971.2 ± 5.4 kJ/mol calculated for PuO_2.5(s,hyd) as a small fraction of PuO_2+x(s,hyd), includes a stabilization energy of about 5–10 kJ/mol compared to pure PuO_2.5(s,hyd). Therefore PuO_2+x(s,hyd) is probably not stable beyond values of x > 0.25.

Anhydrous PuO₂(cr) is considerably more stable than Pu(IV) hydrous oxide and cannot be oxidised by O₂(g) unless the H₂O(l) or H₂O(g) creates a surface layer of hydrous oxide. The standard molar Gibbs energy for the hydration of the bulk PuO₂(cr) is of course positive, but Δ_rG°_m for surface hydration is negative [46]. Hence in the presence of both water and oxygen, PuO₂(s) is partially oxidised to PuO_2+x(s) as reported by Haschke et al. [26,27]. However, contrary to the proposed water catalyzed mechanism [26,27], the role of water can be explained in terms of thermodynamics. The oxidation of PuO₂(s) by water and the extremely high stability of PuO_2+x(s) also claimed by Haschke et al. [25–28] can be ruled out.

7 Conclusions

• (1) The solubility and speciation of plutonium in the system Pu/e⁻/H⁺/OH⁻/H₂O (25 °C) can be described in terms of equilibrium thermodynamics, provided pH and redox potentials (pe) are known. A summary of equilibrium constants for solids and aqueous species of plutonium is given in Table 1 (Appendix). They include the values selected in the OECD/NEA-TDB [1,2], oxidation state analogs for unknown data and additional data for mixed valent PuO_2+x(s,hyd) and small Pu(IV) colloids/polymers in neutral to alkaline solutions. It has to be emphasized that irreversible redox reactions can lead to erroneous model predictions and must be excluded from the calculations (e.g., pe is usually not controlled by Eq. (2) and P(O₂(g)). For the reasons discussed previously [16,17] data for anhydrous PuO₂(cr) must be excluded as well.
• (2) Thermodynamic calculations show that the border line for the conversion of Pu(OH)₃(s) into PuO₂(am,hyd) is close to the lower stability line of water. Under most reducing conditions PuO₂(am,hyd) is the solubility controlling solid phase, in equilibrium with aqueous Pu(IV) and Pu(III) species. In the absence of reducing agents, traces of O₂(g) are sufficient to produce mixed valent PuO_2+x(s,hyd). The equilibrium Pu(V) concentrations considerably exceed those of aqueous Pu(IV) species, but they are about 5 log-units lower than Pu(V) concentrations in equilibrium with PuO₂OH(am). The latter is not the solubility limiting solid phase. The solubility of PuO_2+x(s,hyd) can further be raised by Pu(VI) species, particularly at higher redox potentials caused by radiolysis in chloride brines [8,15] or in the presence of carbonate. Plutonyl(VI) oxyhydroxide is only stable under strongly oxidising conditions. The stability line of PuO_2+x(s,hyd) with regard to the transformation into PuO₂(OH)₂·H₂O(cr) is at (pe + pH) = 21.0 ± 1.3, in the range of the upper stability line of water at (pe + pH) = 20.77).
• (3) Aqueous Pu(IV) hydroxide complexes Pu(OH)_n⁴⁻ⁿ are generally of minor importance. Their concentration is low compared to Pu(III) species at (pe + pH) < 14 (under reducing conditions), compared to Pu(V) species at (pe + pH) = 11–16 (in redox-inert solutions and in the presence of oxygen) or compared to Pu(VI) species at (pe + pH) > 16 (in the presence of oxidising agents). The low Pu concentrations in neutral and alkaline solutions are dominated by small Pu(IV) colloids/polymers. They are part of the thermodynamic system and play an important role for the redox reactions between Pu(IV) and Pu(V). As these neutral oxyhydroxide polymers/colloids have a high tendency towards sorption on oxidic and hydroxidic mineral surfaces they are also important species in sorption studies. Accepting that their formation from PuO₂⁺ is a (slow) reversible equilibrium reaction, the sorption of PuO₂(coll,hyd) from Pu(V) solutions has to be expected in any case, regardless whether the sorbing material is reducing or redox-inert, in particular if the Pu(V) concentration exceeds the solubility of PuO_2+x(s,hyd) at given pH. The same holds for Pu(III) solutions exceeding the Pu(III) concentration in equilibrium with PuO₂(am,hyd) at given pH and redox conditions (pe + pH). In this case the sorption of PuO₂(coll,hyd) should dominate as well, regardless whether the sorbing material is oxidising or not. Corresponding observations were made in plutonium sorption studies supported by EXAFS measurements and reported by different authors at international conferences during the last years. The present paper may help to explain these observations.

Appendix