Complexation of Cm(III) with Fluoride in Aqueous Solution in the

Nov 5, 2010 - However, one paper deals with the temperature dependency (5−45 °C) of the fluoride ... which is well below the solubility limit of tr...
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J. Phys. Chem. B 2010, 114, 15626–15634

Complexation of Cm(III) with Fluoride in Aqueous Solution in the Temperature Range from 20 to 90 °C. A Joint TRLFS and Quantum Chemical Study Andrej Skerencak,*,†,‡ Petra J. Panak,†,‡ Volker Neck,† Michael Trumm,†,‡ Bernd Schimmelpfennig,† Patric Lindqvist-Reis,† Reinhardt Klenze,† and Thomas Fangha¨nel‡,§ KIT - Campus Nord, Institut fu¨r Nukleare Entsorgung, D-76344 Eggenstein-Leopoldshafen, Germany, Ruprecht-Karls UniVersita¨t Heidelberg, D-69120 Heidelberg, Germany, and European Commission, JRC, Institute for Transuranium Elements, D-76125 Karlsruhe, Germany ReceiVed: August 17, 2010; ReVised Manuscript ReceiVed: September 29, 2010

The formation of hydrated CmF2+ and CmF2+ species in aqueous solutions are studied in the temperature range of 20-90 °C at different fluoride concentrations and at constant ionic strength as well as at constant fluoride concentration and different ionic strengths by means of time-resolved laser fluorescence spectroscopy (TRLFS). The molar fractions of the Cm3+ aqua ion, CmF2+, and CmF2+ species are determined by peak deconvolution of the emission spectra. An increase of the mono- and difluoro complexes is observed with increasing fluoride concentration and/or increasing temperature. Using the specific ion interaction theory (SIT), the thermodynamic stability constants log K01 (CmF2+) and log K02 (CmF2+) as well as the values of ∆ε1 and ∆ε2 are determined as a function of temperature. The log K01 values increase from 3.56 ( 0.07 to 3.98 ( 0.06 and the log K02 values increase from 2.20 ( 0.84 to 3.34 ( 0.21 with increasing temperature from 20 to 90 °C. The value of ∆ε1 determined at 25 °C is in good agreement with literature data and shows a negligible temperature dependency in the studied temperature range. The value of ∆ε2 also shows only a moderate variation in the studied temperature range. The thermodynamic standard state data (∆rH0m, ∆rS0m, ∆rG0m) are determined from the temperature dependence of the equilibrium constants at Im ) 0 using the integrated Van’t Hoff equation. The fluorescence lifetime of the 6D′7/2(Cm3+) state is found to be constant at 63 ( 5 µs with increasing fluoride concentration. A model based on density functional theory (DFT) calculations is introduced to account for the additional quenching occurring through the near second sphere waters in the [Cm(H2O)8F]2+(H2O)18 complex. 1. Introduction In some countries, deep salt formations are in discussion as long-term repositories for highly active nuclear waste. This approach requires well-founded knowledge of the aquatic chemistry and thermodynamics of radioactive elements in diluted and concentrated electrolyte solutions. Although a multitude of studies have been performed previously on the complexation of trivalent lanthanides and actinides with different inorganic ligands,1-4 most of these studies are limited to ambient temperature. Due to radioactive decay, temperatures in the close vicinity of a repository may reach up to 200 °C. Hence, for a detailed understanding of the aquatic chemistry of trivalent actinides under near-field conditions, studies on the complexation with different ligands at elevated temperatures are necessary. Fluoride ions are an inherent part of native salt deposits, and natural brines show fluoride concentrations on the order of up to 10-2 m H2O. As F- is a ligand with intermediate complexation strength toward trivalent actinides in aqueous solution, fluoride complexes of actinides are relevant for a nuclear waste repository in deep salt formations. Different techniques such as solvent extraction,5 ion exchange,6 potentiometric methods,7-9 titration calorimetry,10,11 and spectroscopy12,13 have been applied to study * Corresponding author. Phone: +49-7247-826024. Fax: +49-7247823927. E-mail: [email protected]. † Institut fu¨r Nukleare Entsorgung. ‡ Ruprecht-Karls Universita¨t Heidelberg. § Institute for Transuranium Elements.

the complexation of trivalent lanthanides and actinides with fluoride. These studies are mostly limited to ambient temperatures. However, one paper deals with the temperature dependency (5-45 °C) of the fluoride complexation of the trivalent rare earth ions in aqueous solution.6 In that study, the formation of the hydrated mono- and difluoro complexes, LnF2+ and LnF2+, was found to increase with increasing temperature from 5 to 45 °C; for example, log K′1 (EuF2+) increases from 3.63 ( 0.02 to 3.81 ( 0.01, and log K′2 (EuF2+) increases from 2.26 ( 0.10 to 2.49 ( 0.03 (Ic ) 0.025 M). In the same study, the enthalpy of the complex formation was determined for both complexation reactions; thus, ∆rH1 and ∆rH2 of 8.19 ( 0.42 and 18.58 ( 1.15 kJ · mol-1 were obtained, respectively. In another paper, the complexation of U(VI) with fluoride in aqueous solution was studied in the temperature range from 25 to 70 °C by means of spectrophotometry.13 The results of that study showed that the stability constants log β0n of the UO2Fn2-n complexes (n ) 1, 2, 3, 4) increased in the studied temperature range by about 2, 3, 8, and 11-fold, respectively. In the present study the complexation of Cm3+aq with fluoride is studied in the temperature range from 20 to 90 °C by timeresolved laser fluorescence spectroscopy (TRLFS). Due to its favorable spectroscopic properties (i.e., high sensitivity, high quantum yield, and fluorescence lifetime in the submillisecond range), Cm(III) is well-suited for complexation studies in aqueous systems in nature-like conditions and is here chosen as a representative for trivalent actinides. Thus luminescence studies of Cm(III) at submicromolar concentration levels are

10.1021/jp107794u  2010 American Chemical Society Published on Web 11/05/2010

CmF2+ and CmF2+ Species in Aqueous Solutions

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feasible, which is well below the solubility limit of trivalent actinides in natural waters.14 The fluorescence lifetime (τ) is sensitive to changes in the local environment and can be used to calculate the number of water molecules (n) in the first coordination sphere of Cm3+. This is possible since a water molecule provides efficient nonradiative decay pathways through coupling with highfrequency vibrational overtones, which results in a decrease of the fluorescence lifetime. The decay rate constant (kobs ) τ-1) is related to n according to

kobs ) krad + knonrad + n · kH2O

(1)

where krad is the rate constant for the radiative deexcitation processes, knonrad is the rate constant for the nonradiative processes, and kH2O is an additional rate constant accounting for quenching processes via coordinated water molecules. However, since krad and knonrad are not easily obtained, it is common to use empirical equations introduced by Horrocks and Kimura:15,16

for Eu3+: n(H2O) ) 1.07 · kobs - 0.62

(2)

for Cm3+: n(H2O) ) 0.65 · kobs - 0.88

(3)

Thus, the fluorescence lifetime typically increases for complexation reactions when water molecules are expelled from the first hydration shell of Cm3+ and Eu3+. 2. Experimental Section 2.1. Sample Preparation. To avoid changes in the concentrations due to temperature-dependent change of solution densities, all concentrations are expressed on the molal concentration scale (mol/kg H2O, m). The Cm(III) concentration (89.7% Cm-248, 9.4% Cm-246, 0.3% Cm-244, and 0.6% of Cm-243, Cm-245, and Cm-247) in the TRLFS samples is fixed at 10-7 m by adding a defined quantity of a 2.12 × 10-5 m Cm(III) stock solution in 0.101 m HClO4 to the sample solutions. Two independent sets of samples are prepared. The first set of samples has different total fluoride concentration ranging from [F-]total ) 0.3 × 10-3 m to 3.4 × 10-3 m (obtained by adding small aliquots of a 4.15 × 10-2 m NaF stock solution) and constant ionic strength (Im ) 0.1 m (NaClO4)). The total proton concentrations of the solutions are set to [H+]total ) 7.04 × 10-4 m with HClO4. Hereby the amount of H+ generated by the protolysis of H2O can be neglected since its contribution to the total proton concentration at every studied temperature is about 5 to 3 orders of magnitude lower than the amount of H+ introduced by the addition of HClO4. The second set of samples is prepared at different ionic strengths and constant fluoride concentration, obtained by adding small quantities of solid NaClO4 · H2O to a sample with [F-]total ) 2 × 10-3 m, Im ) 0.25 (NaClO4) and [H+]total ) 7.04 × 10-4 m until Im ) 3.93 is reached (the amount of added NaClO4 · H2O is controlled by weighing the cuvette before and after the addition). All chemicals are purchased from Merck and are of suprapure grade. 2.2. TRLFS. An excimer pumped dye laser system (Lamba Physics EMG 201 and FL 3002) with a pulse energy of 2 to 4 mJ at a repetition rate of 10 Hz is used for excitation. The spectra are recorded by an optical multichannel analyzer, consisting of a polychromator (Jobin Yvon HR320) with a 1200 line mm-1 grating and a time-gateable intensified photodiode array with

1024 Si photodiodes (Spectroscopy Instruments ST 180, IRY700 9). Details on the setup of the TRLFS system are given elsewhere.17 Experiments are performed in a quartz cuvette embedded in a water-circulated, temperature-controlled (by a Lauda RE 104/E100 thermostat) copper block. The excitation wavelengths are 396.6 and 394 nm for the Cm3+ and Eu3+ experiments, respectively. To determine the fluorescence lifetime of the 6D′7/2 multiplet, the emission intensity of the 6D′7/2 f 8S′7/2 transition of Cm3+ is measured at different delay times (∆t ) 10 µs) between t ) 0 and t ) 300 µs. The corresponding 5D0 lifetime of Eu3+ is measured by recording the 5D0 f 7F1-2 transitions. The lifetime (τ) is obtained by fitting the integrated intensity (I) at time t after the laser pulse according to

( τt )

I(τ) ) I0 · exp -

(4)

with I0 being the initial intensity at t ) 0. 2.3. Density Functional Theory (DFT) Calculations. For both the complexes [MX(H2O)8]2+(H2O)18 (M ) Cm, Eu; X ) F, Cl), the central metal ion is coordinated by one F- or Clion, respectively, eight H2O molecules in the first and 18 H2O molecules in the second hydration shell leading to a total of 26 coordinated water molecules. All calculations are carried out in gas-phase. Since our interest is focused on relative differences in bond lengths and vibrational frequencies, no further model is used to describe the interaction with the solvent. DFT is used, employing the B3-LYP functional18-23 as implemented in the TURBOMOLE program package.24-29 The structures are optimized using basis sets of TZVP quality on the water molecules and fluoride/chloride ions, as well as an f-in-core effective core potential (ECP) and associated basis set on Cm(III)/Eu(III).30-32 To ensure numerical precision, the optimized structures and vibrational frequencies are obtained by employing the m5 grid in all DFT calculations. 3. Results and Discussion 3.1. Emission Spectra. The emission spectra of the 6D′7/2 f 8S′7/2 transition of Cm3+ are displayed in Figure 1a at four selected fluoride concentrations ((0.3, 1.1, 2.5 and 3.4) × 10-3 m; Im ) 0.1) at 20, 60, and 90 °C. Due to a successive decrease of the emission intensity with increasing temperature, the displayed spectra are normalized to equal peak area. The decrease of the emission intensity becomes more pronounced at higher temperatures, suggesting a general increase of the sorption of Cm(III) to the cuvette walls with increasing temperature.33 Also the population of the short-lived 6P′5/2 electronic level at ∼3400 cm-1 above the emitting 6D′7/2 level may contribute to a minor extent to the decrease of the intensity at elevated temperatures.34 At ambient temperature the spectra consist of two emission bands, which can be assigned to the Cm3+ aqua ion (λmax ) 593.8 nm) and a CmF2+aq complex (λmax ) 601.3 nm).12 With increasing fluoride concentration and/or increasing temperature, the relative intensity of the monofluoro complex increases while that of the aqua ion decreases. At the highest fluoride concentrations and temperatures studied, an even further red-shift of the spectra is observed. This red-shift is attributed to the formation of a third emission band, which can be assigned to a hydrated difluoro complex CmF2+aq with a peak maximum at about 604.5 nm.12 To derive the molar fractions of the Cm3+aq, CmF2+aq, and CmF2+aq species, peak deconvolution of the experimental spectra

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Figure 1. (a) TRLFS emission spectra of Cm(III) at [F-]total ) (0.3; 1.1; 2.5; 3.4) × 10-3 m (Im ) 0.1 m) and at T ) 20, 60, and 90 °C. (b) Exemplary peak deconvolution of a spectrum at T ) 50 °C and [F-]total ) 2.5 × 10-3 m.

is performed. An example of a peak-deconvoluted spectrum is shown in Figure 1b (for additional peak-deconvoluted spectra, see the Supporting Information). The speciation as a function of the total fluoride concentration at 20, 40, 70, and 90 °C and at constant Im ) 0.1 (NaClO4) is shown in Figure 2. At 20 °C the species distribution is governed by a mixture of the Cm3+ aqua ion and the CmF2+aq complex. Even at the highest fluoride concentrations, the CmF2+aq complex is only a minor species with a molar fraction of less than 10%. With increasing temperature, the speciation shifts toward higher complexation; e.g., at 90 °C and [F-]total > 2.3 × 10-3 m, the CmF2+aq complex becomes the dominating species of the system (for detailed speciation of all studied samples, see Tables S1 and S2 and Figures S1 and S2 in the Supporting Information). 3.2. Fluorescence Lifetime. The time dependent decrease of the emission intensity is monoexponential for all studied samples. The 6D′7/2 fluorescence lifetime is 63 ( 5 µs at 20 °C, independent of the fluoride concentration. This value is the same as that of the Cm3+ aqua ion and is in agreement with previous findings.12 However, the fact that the lifetime is not affected by the fluoride complexation is peculiar since the number of water molecules in the first coordination shell of the CmF2+ and

Skerencak et al. CmF2+ complexes is most likely lower than the hydration number of the Cm3+ aqua ion. Therefore, the fluorescence lifetimes of the complexed species are expected to be longer than that of the Cm3+ aqua ion. Assuming that the overall coordination number is unchanged upon complexation, the hydrated mono- and difluoro complexes can be ascribed as [Cm(H2O)8F]2+ and [Cm(H2O)7F2]+. Their expected lifetimes according to eq 3 should be about 73 and 83 µs, respectively, both of which are significantly longer than that of the aqua ion (65 ( 5 µs). This peculiarity may be due to the fact that the water molecules in the second hydration shell are strongly hydrogen bonded to the fluoride ion(s) in the first hydration shell and therefore may significantly contribute to the quenching of the 6D′7/2 state. However, for a 10-5 molal solution of Eu3+ in 10-4 m F- the mean lifetime of the 5D0 state is 127 ( 5 µs. This value is in good agreement with the calculated lifetime using eq 2. A more detailed discussion on this topic is given in the section describing the results of the DFT calculations. Increasing the temperature from 20 to 90 °C results in a slight decrease of the fluorescence lifetimes from 63 to 55 ( 5 µs. Also, the lifetimes at increased temperatures are independent of the fluoride concentration. As discussed above, since the fluoride complexation increases with increasing fluoride concentration and temperature, the decrease in the fluorescence lifetime at elevated temperatures is in contrast to the predicted increase by eq 3. Such a temperature dependency was recently reported for Cm3+ in diluted HClO4 and NaNO3 up to 200 °C.34,35 The reason for the decrease in the 6D′7/2 lifetime for Cm3+ in aqueous solution at elevated temperatures is not well understood at present. It is possible that this effect is caused by an increase of the thermal population of the short-lived 6P′5/2 electronic level located about 3255 cm-1 above the 6D′7/2 level.34 3.3. DFT Calculations. In the previous section, the fact that the Cm3+ (6D′7/2) lifetime remains unchanged upon fluoride complexation is attributed to an additional quenching contribution caused by strongly hydrogen bonded water molecules in the second hydration shell. To validate this assumption, DFT calculations are performed on 9-fold coordinated monofluoro and monochloro complexes, [MX(H2O)8]2+(H2O)18 (M ) Cm, Eu; X ) F, Cl). The chloro complexes are introduced because of their analogous structures to those of the fluoro complexes but with the difference that their fluorescence lifetimes have proven to be longer than that of the Cm3+ aqua ion.36,37 The frequencies of the symmetric and asymmetric vibrational stretching modes involving the second shell hydrogen atoms and the fluoride/chloride ions in the first shell, as well as the corresponding modes of the OH bonds of the first shell water molecules are calculated. Also, the distances of the protons to the halide, to the according oxygen atom, and to the Cm(III)/ Eu(III) center ion are obtained. The results are summarized in Table 1 and Figure 3. Thereby, the equilibrium position of the hydrogen atom is taken as the center of gravity of the longitudinal vibrational mode and represents an average distance of the vibrational mode to the Eu(III)/Cm(III) center. First the [MF(H2O)8]2+(H2O)18 (M ) Cm, Eu) complexes are discussed. The Cm-F distance is 234 pm (Figure 3, index 1). This is by 23 pm shorter than the average distance of a coordinated first shell water molecule (Figure 3, index 2). The length of the proton-fluoride hydrogen bond is 162 pm (Figure 3, index 3). This distance is elongated by 64 pm compared to the average OH bond length of a first shell water molecule (Figure 3, index 4). This is expected for a hydrogen bond in comparison to a chemical bond. Although fluoride forms strong hydrogen bonds with protons from second-shell water molecules,

CmF2+ and CmF2+ Species in Aqueous Solutions

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Figure 2. Experimentally determined molar fractions of Cm3+ aqua ion (circles), CmF2+aq (triangles), and CmF2+aq (squares) as a function of total fluoride concentration at T ) 20, 40, 70, and 90 °C.

TABLE 1: Distances and Vibrational Frequencies between Atom Pairs of DFT-Optimized [MX(H2O)8]2+(H2O)18 (M ) Cm, Eu; X ) F, Cl) Complexesa [CmF(H2O)8]2+(H2O)18 index M-X M-OH2 H· · ·X H-O H-O M· · ·H M-H

1 2 3 4/9 5/8 6 7

b

-1

d/pm

ν/cm

234 257 162 98 99 333 320

374 178c/181d 3564c/3558d 3409c/3337d

[EuF(H2O)8]2+ (H2O)18 -1

d/pm

ν/cm

230 254 163 98 99 330 317

379 181c/188d 3564c/3558d 3420c/3355d

[CmCl(H2O)8]2+(H2O)18 -1

d/pm

ν/cm

293 254 215 98 99 392 317

168 155c/147d 3475c/3467d 3435c/3359d

[EuCl(H2O)8]2+ (H2O)18 d/pm

ν/cm-1

291 251 215 98 99 391 313

193 174c/182d 3567c/3561d 3548c/3462d

a Atom-pair contacts (bonds) are represented with -, while the symbol · · · represents atom pairs spaced by two bonds, alternatively one hydrogen bond. b Index according to Figure 3. c Symmetric stretch. d Asymmetric stretch.

the bond length of the corresponding OH-bond (99 pm; Figure 3, index 5) matches almost exactly the bond length of an OHbond of a first-shell water molecule (98 pm; Figure 3, index 4). This shows that the substitution of a first shell water molecule with a fluoride ion induces little changes in the overall bond lengths of the complex. Because of the short M-F distance, second-shell protons, which form a hydrogen bridge to the fluoride ion, show a short distance to the central metal cation of 333 pm (Figure 3, index 6). This matches the distance of the protons of a first-shell water molecule to Cm(III) (320 pm) fairly well (Figure 3, index 7). Furthermore, comparing the OH vibrational modes of the Cm3+ aqua ion and the OH · · · F · · · HO vibrational modes of the complexed species, only little change is observed. Hereby, the vibrational modes are essentially decoupled. The frequencies of the symmetric and asymmetric vibrational stretching modes of the second-shell OH-bonds to the fluoride are 3408.67 and 3336.81 cm-1, respectively (Figure 3, indices 5 and 8). The frequencies are similar to the analogous H · · · O · · · H vibrational modes of a first-shell water molecule

(3564.36/3558.42 cm-1; Figure 3, indices 4 and 9). This supports the hypothesis derived from the experiment, that the energy of the excited Cm(III) can be transferred to vibrational modes of two OH-bonds from second-shell waters, which are connected via hydrogen bonds to the fluoride ion. These modes are then capable of efficiently quenching the excited state of Cm(III), similar to OH vibrational modes of first-shell water. Therefore, the fluorescence lifetime of the first excited state of Cm(III) remains unchanged upon complexation with fluoride ions. Experimental studies show that such energy transfer mechanism is not observed for the hydrated CmCl2+ complex, and the lifetime increases according to eq 3.36,37 For both complexes ([MCl(H2O)8]2+(H2O)18 (M ) Cm, Eu), the frequencies of the symmetric and asymmetric vibrational stretching modes of the second-shell protons to the chloride ion (3435/3359 cm-1 for Cm(III) and 3548/3462 cm-1 for Eu(III); Figure 3, indices 5 and 8) are comparable to the analogous OH vibrational modes of a first-shell water (3475/3467 cm-1 for Cm(III) and 3567/ 3561 cm-1 for Eu(III); Figure 3, indices 4 and 9). Of more

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Skerencak et al. The free fluoride concentration is governed by the temperaturedependent equilibrium

[HF]eq h [H+]eq + [F-]eq with the temperature-dependent thermodynamic stability con0 stant KHF (T) defined as

0 KHF (T) )

[H+]eq · [F-] γH+(T) · γF-(T) aH+(T) · aF-(T) · ) aHF(T) [HF]eq γHF(T) (5)

Hereby, [F-]eq, [H+]eq and [HF]eq are the molal concentrations of the respective species at equilibrium conditions, ai(T) is the temperature-dependent activity, and γi(T) is the temperature 0 (T) values dependent activity coefficient of species i. The KHF are available in the temperature range from 25 to 200 °C in the literature.38 The calculation of the free fluoride concentration of a solution at a given ionic strength requires the conditional ′ (T). The conditional stability constant at stability constant KHF a given ionic strength can be calculated according to eq 6.

γHF(T) [H+]eq · [F-]eq 0 ′ (T) ) KHF ) KHF (T) · [HF]eq γH + (T) · γF-(T)

(6)

Figure 3. Structures of (a) [CmF(H2O)8]2+(H2O)18 and (b) [CmCl(H2O)8]2+(H2O)18, calculated by DFT. The corresponding Eu(III) complexes (not shown) have similar structures.

importance are the differences between the fluoride and chloride complexes. First, due to the larger ionic radius of Cl-, the distance of the chloride ion to the Cm(III) is 293 pm. This is by 59 pm longer than the length of the Cm(III) fluoride bond (Figure 3, index 1). Second, for the Cm(III) complex, the length of the hydrogen bond to the chloride ion is by about 53 pm longer compared to the fluoride complex (Figure 3, index 3). Additionally, the distance of the protons forming the hydrogen bridge to the chloride to the central Cm(III) cation is 59 pm longer compared to the fluoride complex (Figure 3, index 6). The Eu(III) chloride complex shows similar distances (see Table 1). These results show that due to the elongated bond lengths of the Cm(III)/Eu(III)-chloride complexes, an effective energy transfer to second-shell waters is not possible, which is in good agreement with experimental data.37 The results of the quantum chemical calculations show that the structure of the [EuF(H2O)8]2+(H2O)18 complex is comparable to that of the corresponding Cm(III) complex (see Table 1). However, the energy transfer to second-shell waters is less effective than for the Cm(III), resulting in an increase of the Eu(III) fluoride lifetime with increasing F- complexation. The reason for the difference in the quantity of intramolecular energy transfer processes for Cm(III) and Eu(III) will be the subject of future investigations. 3.4. Thermodynamic Data. In order to calculate the stability constants for the formation of the CmF2+aq and CmF2+aq complexes, the free fluoride concentration at equilibrium conditions [F-]eq must be determined as a function of temperature.

The therefore required activity coefficients are available only at 25 °C in the literature. However, the temperature-dependent activity coefficients γi(T) can be calculated using the specific ion interaction theory (SIT) in form of the BrønstedGuggenheim-Scatchard approach, recommended in the Nuclear Energy Agency Thermochemical Database (NEATDB) reviews.1,3 According to the SIT, the logarithm of the temperature-dependent activity coefficient γi(T) of an aqueous species i is given by eq 7.

log γi(T) ) zi2D(T) +

∑ εik(T) · mk

(7)

where zi is the charge of ion i, εik(T) is the temperaturedependent ion interaction parameter for a pair of oppositely charged ions i and k, mk (mol/kg H2O) is the molal concentration of the ion k, and D(T) is the temperaturedependent Debye-Hu¨ckel term: D(T) ) A(T) · (Im)0.5/(1 + Baj(T) · (Im)0.5). The temperature-dependent Debye-Hu¨ckel parameters A(T) and Baj(T) are taken from NEA-TDB3 for each temperature. Im is the molal ionic strength. According to the SIT, the activity coefficients of neutral species are assumed to be one (γHF ) 1) and do not have to be considered. An import issue when using the SIT at T > 25 °C is the temperature dependency of the ion interaction coefficients εik(T). A variety of ion interaction coefficients for various ion pairs is given in the NEA-TDB,3 but these data are restricted to T ) 25 °C. In a recent paper, the εik(T) values for a set of mono-, di-, and trivalent cations with Cl-, OH-, and acetate were determined up to 200 °C.39 Since the background electrolyte used in the present work is ClO4-, the εik(T) for a Cl- medium given in39 cannot be used directly. However, the available data can be used for an error estimation when using εik(25 °C) for calculations at elevated temperatures. For this purpose, the

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Figure 4. Activity coefficients of H+, F-, and Cl- as a function of temperature in 0.1 m NaCl solution calculated with the SIT approach using (a) constant εik(25 °C) and (b) temperature-dependent εik(T).38

temperature-dependent activity coefficients of H+ and F- in a 0.1 m Cl- solution are calculated in the temperature range from 20 to 90 °C using two different approaches: The first approach applies temperature-independent εik values given in the NEATDB3 for 25 °C (ε(H+, Cl-)25 °C ) 0.12 ( 0.01, ε(F-, Na+)25 °C ) 0.02 ( 0.02). The second approach applies temperaturedependent εik(T) values given in ref 39. Unfortunately, no ε(F-, Na+)(T) values are available in ref 39. Therefore, an estimation of ε(Cl-, Na+)(T) is used for comparison. The results of the two approaches are shown in Figure 4. A comparison of the γH+ values calculated by the two described approaches shows only minor differences with increasing temperature. The calculated γCl- values are systematically about 0.02 larger than the corresponding γF values. However, the temperature dependency of the two activity coefficients is almost equal in the studied temperature range. This shows, that the error introduced by using εik(25 °C) values for ionic strength corrections according to the SIT in the temperature range of 20 to 90 °C is small and can be neglected. Hence, the temperature-dependent conditional stability con′ (T) were calculated with the SIT approach, using the stants KHF 0 (T) values given in ref 38 and εik(25 °C) values given in the KHF ′ (T) values for a 1.0 m NEA-TDB.3 The so calculated log KHF NaClO4 solution are in good agreement with literature values ′ (T) given for the same solution in the temperature of log KHF range from 25 to 55 °C,40 thus verifying the approach applied in the present work. In order to calculate free fluoride concentration at a given total fluoride concentration, ionic strength, and temperature, the following assumptions are made: First, NaF and NaClO4 are at every temperature completely dissociated in aqueous solution. Second, the total concentrations of F- and H+ in solution can be expressed by eq 8

[F-]total ) [F-]eq + [HF]eq

(8)

Figure 5. Free fluoride concentration at equilibrium conditions as a function of temperature (T ) 20-90 °C). (a) [F-]total ) 0.3 × 10-3 m; (b) [F-]total ) 3.4 × 10-3 m.

of H+ introduced by the addition of HClO4.41 Combining eq 6, 8, and 9, the free fluoride concentration at equilibrium conditions can be calculated as a function of temperature according to eq 10.

[F-]eq ) ′ (T)) + -([H+]total - [F-]total + KHF ′ (T))2 + 4KHF ′ (T) · [F-]total √([H+]total - [F-]total + KHF 2

(10) Hereby, KHF ′ (T) is the temperature-dependent dissociation constant according to eq 6. The free fluoride concentration as a function of temperature at two total fluoride concentrations and Im ) 0.1 (NaClO4) is shown in Figure 5. The temperature-dependent stepwise conditional stability constants for the formation of Cm(III) fluoride complexes at a given ionic strength are calculated according to eq 11

and eq 9.

K1′(T) ) +

+

[H ]total ) [H ]eq + [HF]eq

(9)

Hereby, [F-]total is the total molal fluoride concentration in solution, and [H+]total is the total molal proton concentration. The concentration of H+ generated by the protolysis of H2O can be neglected, since its amount at each studied temperature is by 5 to 3 orders of magnitude lower than the concentration

[CmF2+](T) · ([F-](T))-1 3+ [Cm ](T)

(11)

and eq 12

K2′(T) )

[CmF+ 2 ](T) 2+

[CmF ](T)

· ([F-](T))-1

(12)

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TABLE 2: ∆εn Values for the Stepwise Formation of Cm(F)n3-n Complexes (n ) 1, 2) in Perchlorate Solution as Function of Temperature T (°C)

∆ε1 [kg · mol-1]

∆ε2 [kg · mol-1]

20 30 40 50 60 70 80 90

-0.13 ( 0.01 -0.12 ( 0.01 -0.13 ( 0.01 -0.14 ( 0.01 -0.13 ( 0.01 -0.14 ( 0.01 -0.14 ( 0.01 -0.14 ( 0.01

-0.11 ( 0.20 -0.17 ( 0.08 -0.18 ( 0.05 -0.18 ( 0.04 -0.16 ( 0.03 -0.14 ( 0.02 -0.13 ( 0.02 -0.13 ( 0.01

summarized in Table 3. The error bars are estimated by determining an upper and lower limit for log Kn0, considering a maximum error of ∼10% in the peak deconvolution. For further evaluation, average values for log Kn0 (n ) 1, 2) are calculated at each temperature (see Table 3). In order to compare the log Kn0 values with literature data, the stability constants are interpolated to 25 °C. The equilibrium constant log K01 (CmF2+, 25 °C) ) 3.61 ( 0.07 is slightly larger than that for the analogous complex of Am(III) with fluoride log K10 (AmF2+, 25 °C) ) 3.4 ( 0.3 recommended in the NEATDB,3 although still within the error range. The temperature dependency of the log K10 values obtained in this work can be compared to literature data given in ref 6. Since the observed values in ref 6 are reported for an ionic strength of Im ) 0.025 M, the log Kn0 values determined in this work are extrapolated to the same ionic strength prior to comparison, using the approach described above. The so calculated value for log K1′(CmF2+, 25 °C) is by ∼0.5 logarithmic units lower than the corresponding value for Eu(III) in ref 6. This small discrepancy may result from the fact that Eu(III) is used as a metal ion. Nevertheless, the temperature-dependent increase of the log K1′ values determined in the present work is in excellent agreement with the literature data given in ref 6 in the corresponding temperature range. A comparison of the stability constant for the second complexation reaction shows that the present value of log K20 (CmF2+, 25 °C) ) 2.28 ( 0.7 is slightly lower than the literature value of log K20 (AmF2+, 25 °C) ) 2.4 ( 0.5 recommended in the NEA-TDB review for the analogous complex of Am(III) with fluoride, but also within the error range. The literature data reported in ref 6 shows an increase of log K2′ (EuF2+, 25 °C) from 2.26 ( 0.1 to 2.49 ( 0.03 in the temperature range from 5 to 45 °C. Their value at 25 °C is by 0.37 logarithmic units higher than the corresponding value for log K2′ (CmF2+, 25 °C) obtained in this work. Furthermore, the increase of the log K2′ values from 25 to 45 °C reported in ref 6 is by 0.36 logarithmic units smaller than the increase determined in the present work in the same temperature range. The stepwise stability constants show a linear correlation with the reciprocal temperature. Therefore, their temperature dependency is described by the integrated Van’t Hoff equation (eq 14),3,42 assuming that the change in the heat capacity of reaction, 0 , is zero and the change in the standard molar enthalpy ∆rCp,m of reaction, ∆rH0, is constant within the studied temperature range.

The molar fractions of the Cm(III) fluoride species are derived by peak deconvolution (see Section 3.1). The stability constants log Kn0(T) at zero ionic strength are related to the conditional stability constants log Kn′(T) by eq 13.

log K0n(T) ) log Kn′(T) - ∆(z2) · D(T) + ∆εn(T) · Im

(13) Hereby, Im is the ionic strength, and ∆(z2) ) -6 for n ) 1 and ∆(z2) ) -4 for n ) 2. For a data set of log Kn′ at different ionic strengths, log Kn0 can be derived by plotting log Kn′ ∆(z2)D versus Im and linear fitting of the data (linear SIT regression). Thereby, the y axis intercept at x ) 0 corresponds to log Kn0 and the slope to -∆εn. The ∆εn values of the stepwise formation of the Cm(F)n3-n (n ) 1, 2) species are determined at each temperature using the linear SIT regression. The results are summarized in Table 2. The values for ∆ε1 at T ) 20 °C are in good agreement with the values calculated from the data given in the NEA-TDB for the formation of analogous AmFn3-n complexes in perchlorate solution (∆ε1 (25 °C)calc ) (-0.12 ( 0.01) kg · mol-1). As shown in Table 2, almost no variation of ∆ε1 with increasing temperature is observed. The determined ∆ε2 value at 20 °C is by 0.13 kg · mol-1 larger than the value calculated from the data given in the NEA-TDB review. Due to the small fraction of CmF2+ species present at this temperature and the consequential uncertainty in the peak deconvolution, the value of ∆ε2 (20 °C) has a fairly large error of (0.20. Hence, the value of ∆ε2 ) -0.24 ( 0.02 kg · mol-1 recommended by the NEA-TDB is within the error range of the value determined in this work. An increase in temperature results in a slight increase up to a constant mean value of ∆ε2 ) -0.14 ( 0.07 kg · mol-1. Two sets of temperature-dependent stepwise stability constants log Kn0 (n ) 1, 2) at zero ionic strength are derived from the two series of measurements at variable [F-]total (Im ) const) and variable Im ([F-]total ) const), respectively. The results are

log K0n(T) ) log K0n(T0) +

(

∆rH0(T0) 1 1 R ln 10 T0 T

)

(14)

TABLE 3: Stepwise Thermodynamic Stability Constants log Kn0 (n ) 1, 2) of the Complexes CmF2+aq and CmF2+aq Derived from Measurements at (a) [F-]total ) variable, Im ) 0.1 and (b) Im ) variable, [F-]total ) 2.0 × 10-3m; (c) Mean Values of log Kn0 T [°C] 20 30 40 50 60 70 80 90

(a) log K01 Im ) const 3.62 3.67 3.73 3.79 3.85 3.92 3.99 4.05

( ( ( ( ( ( ( (

0.02 0.04 0.06 0.08 0.06 0.04 0.04 0.01

(b) log K01 Im ) var. 3.50 3.62 3.64 3.69 3.79 3.82 3.89 3.91

( ( ( ( ( ( ( (

0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01

(c) log K01 mean value 3.56 3.65 3.69 3.74 3.82 3.87 3.94 3.98

( ( ( ( ( ( ( (

0.07 0.07 0.10 0.16 0.09 0.07 0.07 0.06

(a) log K02 Im ) const 2.21 2.39 2.60 2.76 2.89 3.03 3.15 3.25

( ( ( ( ( ( ( (

0.77 0.64 0.48 0.40 0.29 0.17 0.14 0.08

(b) log K02 Im ) var. 2.19 2.30 2.60 2.79 3.01 3.14 3.32 3.43

( ( ( ( ( ( ( (

0.83 0.31 0.20 0.15 0.11 0.08 0.06 0.05

(c) log K02 mean value 2.20 2.35 2.60 2.78 2.95 3.09 3.23 3.34

( ( ( ( ( ( ( (

0.84 0.69 0.55 0.47 0.41 0.26 0.25 0.21

CmF2+ and CmF2+ Species in Aqueous Solutions

J. Phys. Chem. B, Vol. 114, No. 47, 2010 15633 is about 15 J/(mol · K)-1 lower than the value in the present work. 0 (EuF2+) ) 18.58 ( 1.15 kJ/mol-1 reported The value of ∆rHm in ref 6 is about 14 kJ/mol-1 lower than the value for ∆rH0m(CmF2+aq) obtained in this work. These discrepancies may result partially from the fact that no ionic strength correction was done for the reported literature data. Additionally, the use of different metal ions, Eu3+ and Cm3+, may also affect the thermodynamic data of the fluoride complexation. Using the 0 0 , ∆rSm data given in the NEA-TDB3 and the values for ∆rHm 0 and ∆rGm, the standard molar enthalpies and entropies of 0 0 , Sm ) as well as the free molar enthalpies of formation (∆fHm 0 ) of the respective Cm(III) fluoride species are formation (∆fGm derived. The results are displayed in Table 5. The values for ∆fG0m,25 °C determined in the present work for CmF2+aq and CmF2+aq are in excellent agreement with the values for the analogous Am(III) complexes given in the NEA-TDB (∆fG0m,25 °C0 + (AmF2+) ) (-899.6 ( 5.3) kJ · mol-1; ∆fGm,25 °C(AmF2 ) ) -1 3 (-1194.9 ( 5.1) kJ · mol ). 4. Summary

Figure 6. Equilibrium constants log K0n (n ) 1, 2) at zero ionic strength for the formation of Cm(F)n3-naq as a function of the reciprocal temperature (squares) and model calculation according to the integrated Van’t Hoff equation. (a) n ) 1; (b) n ) 2.

TABLE 4: Thermodynamic Data Evaluated in the Present Work for the Formation of Cm(III) Fluoride Complexes

log K0n (20 °C) log K0n (90 °C) 0 ∆ rG m (kJ · mol-1)20 °C 0 ∆ rH m (kJ · mol-1) 0 ∆ rS m (J · mol-1 · K-1)

Cm3+ + F- S CmF2+

CmF2+ + F- S Cm(F)+ 2

3.56 ( 0.07 3.98 ( 0.06 -20.54 ( 0.39 12.09 ( 2.15 109.48 ( 6.55

2.20 ( 0.84 3.34 ( 0.21 -13.22 ( 4.71 33.01 ( 14.33 155.14 ( 41.59

Hereby, T and the reference temperature T0 ) 298.15 K (25 °C) are absolute temperatures, given in Kelvin and R · ln(10) ) 19.145 J · mol-1 · K-1. The fits according to eq 14 are displayed in Figure 6. The increase of the stability constants with the reciprocal temperature of both reactions is described adequately by this model in the range from 3.4 × 10-3 to 2.8 × 10-3 K-1. The standard molar reaction enthalpies and entropies for the stepwise formation of the Cm(III) fluoride complexes are summarized in Table 4. A comparison with literature data shows 0 (CmF2+aq) ) 12.09 ( 2.15 kJ/ that the present value of ∆rHm -1 -1 mol is about 4 kJ/mol higher than the value of ∆rH0m(EuF2+) for the formation of the analogous Eu(III) complex.6,11 The value 0 (EuF2+) ) 94.8 ( 0.3 J/(mol · K)-1 reported in ref 11 for ∆rSm

In the present work, the temperature dependency of the complexation of aqueous Cm(III) with fluoride ions is investigated. TRLFS measurements are performed in the temperature range from 20 to 90 °C, showing a successive shift of the emission spectra to higher wavelengths with increasing temperature due to an increasing complexation at elevated temperatures. Using the SIT, the stability constants log Kn0 (n ) 1, 2) for zero ionic strength are calculated for the CmF2+aq and CmF2+aq complexes. In the narrow temperature range studied, the assumption of a constant change of enthalpy and zero change of heat capacity of the complexation reactions is valid, and the temperature dependency of the stability constants is described properly by the integrated Van’t Hoff equation. Hereby, the 0 0 0 0 , ∆rSm , ∆rGm , ∆ f Hm , thermodynamic standard state data (∆rHm 0 0 Sm , ∆fGm ) is determined for the formation of the mono- and difluoride complexes. At increased temperatures, the fluorescence lifetime drops by about 10 µs, being independent of the fluoride concentration. This small decrease can be attributed to progressive population of the short-lived 6P′5/2 level located above to the main fluorescent 6D′7/2 level. The fluorescence lifetimes of the Cm(F)n3-n (n ) 1, 2) complexes are not affected by the fluoride concentration at each temperature. DFT calculations on [MX(H2O)8]2+(H2O)18 (M ) Cm, Eu; X ) F, Cl) confirmed that the two second-shell water molecules building hydrogen bridges to the first-shell fluoride ion show vibrational frequencies and distances similar to those of the Cm(III) ion compared to first-shell water. This indicates that an energy transfer from the excited Cm(III) to longitudinal vibrational modes of these second-shell water molecules occurs. This additional quenching mechanism gives a possible explanation for the invariant fluorescence lifetime of the Cm(III) fluoride complexes. Supporting Information Available: Speciation of the studied samples as a function of temperature; peak deconvo-

TABLE 5: Thermodynamic Data Evaluated in the Present Work for the Species CmF2+aq and CmF2+aq Together with the Literature Data for F- and Am3+ 3 0 ∆ fG m (kJ · mol-1) 25 °C 0 ∆ fH m (kJ · mol-1) 0 Sm (J · mol-1 · K-1) a

F-

Am3+

CmF2+aq

CmF2+aq

-281.5 ( 0.7a -335.4 ( 0.7a -13.8 ( 0.8a

-598.7 ( 4.8a -616.7 ( 1.5a -201.0 ( 0.2a

-900.7 ( 5.9b -939.2 ( 5.1b -105.3 ( 7.6b

-1195.4 ( 11.3b -1241.6 ( 20.1b 36.0 ( 22.0b

Data taken from the NEA-TDB.3 b Present work.

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J. Phys. Chem. B, Vol. 114, No. 47, 2010

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