We present the analysis of diffusion-controlled annihilation of excited U(VI) complexes in aqueous media that leads to appearance of rapid non-exponential fluorescence decay. We show that under typical experimental conditions the impact of annihilation processes can’t be neglected when determining U(VI) complexes fluorescence lifetimes: at excitation intensities between 106 W/cm2 and 108 W/cm2, the rate of excited states deactivation increases, and then an opposite trend is observed. The latter can be interpreted as the consequence of optical breakdown in water.
© 2013 Optical Society of America
The aqueous speciation of uranium is the key parameter that determines its migration in geosphere under oxic conditions [1, 2]. It has been studied extensively due to the role of uranium as the element of concern in nuclear waste and spent nuclear fuel disposal , remediation of legacy sites and abandoned uranium mines [4, 5]. Besides, uranium speciation is important to develop effective in situ uranium leach procedures for its mining [6–8]. Various methods exist to study uranium speciation [9–12]: microcalorimetry, potentiometry, spectrophotometry, ion chromatography, EXAFS, Raman spectroscopy etc. Another wide-spread technique is time-resolved laser induced fluorescence spectroscopy (TRLFS), a method that utilizes the sensitivity of photophysical parameters of U(VI) compounds (positions of fluorescence peaks in emission spectra and lifetimes of excited states) to its coordination environment and may provide speciation information at rather low uranium concentrations [10, 13–15].
Under oxic environmental conditions uranium is present in hexavalent state, whose chemistry is related to the uranyl moiety, . Uranyl has been extensively studied in literature by means of optical spectroscopy (see  and references therein), therefore, a huge amount of experimental data about its photophysical properties has been accumulated. However, the values of excited state lifetimes of U(VI) complexes obtained by different groups and the number of components used for fluorescence decay curves fitting differ significantly – e.g., for uranyl fluoride [17–20] and sulfate [21, 22] complexes. Moreover, the processes of ligand exchange in U(VI) complexes complicates the analysis of their fluorescence decay .
The problems associated with TRLFS use for U(VI) speciation are best illustrated in , where the “round-robin” test when 13 independent laboratories measured fluorescence decay curves for the same set of samples was performed. One of the results of this experiment was the discrepancy in fluorescence lifetimes obtained by different researchers, while the positions of peaks in fluorescence emission spectra are similar. These facts impose restrictions on TRLFS usage for quantitative analysis of U(VI) species in aqueous solution.
In the present study we found a rapid component which makes a significant contribution to fluorescence decay of U(VI) complexes. This contribution shows nonlinear dependence on the intensity of laser radiation. The model was proposed that explains this fact and takes into account diffusion-controlled process of fluorescence quenching caused by energy transfer between excited complexes. If the excited state is of triplet nature, such a process is called triplet-triplet annihilation . However, the nature of uranyl excited state is still a debatable issue [25, 26], so here we’ll use the general term “excited states annihilation”. The proposed model is in good agreement with experimental dependencies, and corresponding approximation gives parameters which are consistent with the theoretical conception. Considerable deviations in excited state lifetime values may take place if this process is neglected when fluorescence decay curves are obtained at high excitation intensities. This effect can be one of the number of reasons (e.g., speciation changes due to sorption on the surface of the cuvette )that lead to misinterpretation of excited state decay rates and the number of components in the system when determining U(VI) speciation with TRLFS.
Fluorescent response of uranium fluoride complexes to laser nanosecond excitation with varied intensity is being investigated in this study. At excitation intensities between 106 W/cm2 and 108 W/cm2, the rate of excited states deactivation increases, and then an opposite trend is observed. The latter can be interpreted as the consequence of optical breakdown in water.
2. Theoretical background
Upon excitation with nanosecond UV laser pulses, uranyl is excited into the upper excited states, then undergoing fast (∼ 10 ps) relaxation to the lowest one . Moreover, at high excitation intensities, two- or multiphoton absorption is possible , which can lead to uranyl photoionization (according to Ref. , the ionization potential for uranyl is −9.4 ± 0.5 eV). Both photoionization and non-unity quantum yield of relaxation from the upper energy levels can result in the decrease of population of the lowest excited state, which is responsible for luminescence , and is completely formed after the end of laser pulse.
Fluorescence decay of mixture of M U(VI) complexes is usually described by a multiexponential signal decay after the end of pulsed excitation :(1) is derived under assumption of constant decay probability: 16] and reversible electron transfer [30–32], while the second group involves collisional quenching due to water exchange in the first hydration sphere .
At the same time an additional channel of excited state deactivation is possible to appear at high excitation intensity I. This channel is connected with interaction of excited states via intermolecular energy transfer as the fluorescence emission band of U(VI) complexes overlaps with the excited state absorption band [34, 35]. Since the electronic transition in U(VI) complexes responsible for fluorescence emission is forbidden [25, 26], the Förster energy transfer mechanism , operating with dipole-dipole interactions, seems unreliable. We consider Dexter (exchange) energy transfer  in the system of U(VI) complexes. This process has typical values of interaction range of about the collisional radius and is responsible, e.g., for triplet-triplet annihilation in solutions of organic fluorophores . The electron transfer mechanism has been proposed to be responsible for uranyl quenching by metal ions [39, 40] and halide ions [30,31], and interaction distance of about 4–5 Å was obtained in  from the slope of the dependence of quenching constants on the quencher’s ionization potential using the formula for electron tunneling through a rectangular barrier.
As U(VI) complexes possess fluorescence lifetime in microsecond range (about 1.5 μs for hydrated aqueous uranyl-cation  and over 100 μs for U(VI) fluoride complex (UO2F2)aq[17, 18] at ambient temperature), two excited fluorophores can approach each other as close as the interaction distance: for excited (UO2F2)aq complex, assuming the self-diffusion coefficient D = 7.6 × 10−6 cm2s−1[41, 42], the diffusion length can be estimated as Eq. (4) are concentration of excited uranyl complexes, uranyl doubled self-diffusion coefficient and uranyl doubled radius, correspondingly. We also take into account the fact the rate of self-quenching should be divided by a factor of 2 because each interaction of an excited pair results in deactivation of only one excited complex. Effective deactivation rate of an excited uranyl complex in the presence of annihilation is determined by 16] and bimolecular quenching caused by the interaction between excited complexes (annihilation) can be regarded as independent. This results in the form of kinetic equations proposed for the description of the annihilation process, where the rates of radiative and non-radiative [16,30,31] decay of the excited state and excited complexes annihilation are the summands in the overall rate of excited state deactivation (see Eq. (6)).Eq. (9) is the ratio of an excited state deactivation rate caused by annihilation to an excited state deactivation rate in absence of annihilation.
Fluorescence intensity is given by the following expression:Eq. (9). The absolute value of the slope of fluorescence decay curve in semilogarithmic scale is equal to effective deactivation rate of excited U(VI) complexes:
Thus, the slope of fluorescence decay curve in semilogarithmic scale depends on the concentration of excited complexes ξ, which, in turn, depends on the intensity of excitation pulse. The major difference between the curves obtained at low (γξ0τ ≪ 1) and high (γξ0τ ≪ 1) excitation intensities will be manifested on the initial stage t < τ. In the latter case the second summand in Eq. (6) exceeds the first one.
The population of the excited state after the end of the laser pulse can be estimated by integration of Eq. (7) over duration of the laser pulse. Since laser pulse duration (several nanoseconds) is much less than typical fluorescence lifetimes of uranyl complexes (over microsecond), the second and the third terms on the right-hand side of Eq. (7) can be neglected. Thus one can obtain the following expression for ξ0:
The following parameters of laser radiation are used in most studies that are dedicated to investigation of uranium(VI) aqueous solutions fluorescence decay curves: wavelength 266 nm, pulse duration 10 ns, pulse energy 1–4 mJ (e.g., Ref. ). For an average absorption cross-section σ = 0.76 × 10−18 cm2 taken from [46, 47], the exponent factor in Eq. (12) is equal to unity in the case of laser beam diameter of about 1 mm. Here, we didn’t take into account the processes of photoionization and spontaneous relaxation from the upper excited states to the lowest one with less than 100% efficiency that can result in a decrease of ξ0. Further assuming that r equals 4 Å (typical doubled radius of uranyl mononuclear complex ) and uranyl concentration is M in Eq. (8), we obtain γ ∼ 105 s−1. These estimations show that the contribution of the second summand on the right-hand side of Eq. (6) can’t be neglected for typical values of experimental parameters, and diffusion-controlled annihilation of excited states has a significant influence on the shape of fluorescence decay curves in their initial stage.
3. Experimental setup
A custom-built laser fluorometer was used for TRLFS measurements of U(VI) aqueous solutions (Fig. 1). A frequency-quadrupled Nd:YAG laser with following parameters was used for fluorescence excitation: wavelength 266 nm (4-th harmonic of Nd:YAG laser radiation), pulse duration 10 ns, pulse energy 2 mJ, repetition rate 10 Hz. The laser beam (1) was focused with a 10 cm focusing lens (2) and a 45° mirror (3) into 1 × 1 × 4 cm quartz cell (4) through its bottom. The fluorescence signal emitted at angle of 90 degrees was transmitted to the poly-chromator (Azov optomechanical plant, Russia) through a fiber-optic cable consisting of seven horizontally aligned fibers each with a 600 μm diameter (5) and detected with an intensified CCD camera (Deltatek, Russia). The registration system allowed us to measure fluorescence spectra with temporal resolution and has been described in detail elsewhere . The energy of laser pulses transmitted through the cell was measured with a thermoelectrical sensor (Ophir, Israel) (6).
When measuring fluorescence decay curves, the duration of the gating pulse was set to 2.5 μs, while its position with respect to the exciting laser pulse was controlled with 50 ns precision. Gating pulse duration of 100 ns was used to measure Raman scattering of water which was used as a reference signal proportional to the laser pulse energy, and the registration beginning coincided with the laser pulse. Fluorescence decay curves of U(VI) complexes were measured for different positions of laser beam waist center Δ relative to optical fiber position (see Fig. 1), thus allowing us to vary the intensity of the exciting radiation in registration volume in the 105 − 109 W/cm2 range while keeping pulse energy fixed.
Beam focusing leads to the changes of its cross section along the propagation axis in the acceptance area. As the measured fluorescence signal was integrated over the whole detection volume, this could lead to errors in determination of annihilation rate due to variation in excitation intensity with height. Taking into account the fact that the acceptance angle of the fiber used was 10°, its diameter was 0.6 mm, and the distance between fiber and the beam axis was 4 mm, the height of the acceptance area for the geometry of the setup can be estimated as 2 mm. As the focusing angle was 0.05 radian, the change of the beam diameter in the signal acceptance area didn’t exceed 0.2 mm. Hence a 30% deviation of intensity in acceptance volume took place for an average beam diameter of 0.6 mm. The magnitude of error in excitation intensity estimation is inversely proportional to the average beam diameter in the acceptance area and was taken into account when determining annihilation rate.
The precision of waist positioning was better than 0.2 mm. Beam width at the optical fiber position was measured by imaging a fluorescent uranium sample with CMOS camera (Deltatek, Russia) with precision not worse than 10%.
Approximation of measured fluorescence decay curves was performed with Python script using curve_fit function of SciPy library  which implements Levenberg-Marquardt algorithm.
All of the samples were prepared in deionized Millipore water using U(VI) stock solution in 1 M HClO4 with total concentration of uranium 0.1 M. An aliquot of uranium stock solution was added to 15 ml of solution with ionic strength 0.1 M and known concentration of NaF. NaClO4 was used as a non-complexing background electrolyte . The sample with concentrations of [NaF] = 2 × 10−3 M, M and pH 3.0 was used to illustrate the effect of excited states annihilation on fluorescence decay curves. Distribution of uranium fluoride complexes in the sample calculated with HYDRA-MEDUSA software  using the stability constants from  shows the domination (∼ 75%) of a single component (UO2F2)aq in solution at pH values 3 – 6. This fact was then verified experimentally by time-resolved fluorescence spectroscopy. All measurements were performed at ambient temperature (25 ± 1)°C.
5. Results and discussion
Fluorescence decay curves measured for different vertical displacements between waist center and receiving fiber Δ (see Fig. 1) and, consequently, for different excitation intensities in detection volume are shown in Fig. 2. Each point of the represented curves was acquired by integration of corresponding fluorescence spectra over wavelength in the 480 to 580 nm region. The shift of fluorescence emission spectra maxima acquired for time delay 0.5 μs and 200 μs relative to excitation pulse for single intensity value did not exceed 0.5 nm and spectral band shapes obtained for 0.5 μs delay at different intensities did not differ, while the fluorescence emission spectrum of (UO2F2)aq. is 3 nm red shifted as compared to UO2F+. This fact implies the dominance of the same U(VI) complex impact into every measured fluorescence spectrum.
As it can be seen in Fig. 2, the initial stage of fluorescence decay curves (up to 50 μs) excited states deactivation rates differ significantly for various displacements Δ, corresponding to different values of laser intensity in the detection volume. For Δ ≥ 19.5 mm fluorescence decay curves normalized to the intensity of the first point are identical and can be fitted using Eq. (1) with the number of components M = 1 and the excited state lifetime τ = 112.3 ± 1.3 μs, while for Δ = 4.5 mm, the dependence is not monoexponential and its biexponential (M = 2) approximation with Eq. (1) gives the following values: τ1 = 13.4 ± 0.6 μs, τ2 = 97.0 ± 1.5 μs. The appearance of a fluorescent component with a greater relaxation rate in the initial region of the kinetic curves obtained for high excitation intensities I can be explained using a hypothesis of excited states annihilation. For small excitation intensities, the fraction ξ0 of excited complexes after the end of laser pulse is low; hence, the second summand in Eq. (6) is small and fluorescence decay curves obtained at Δ ≥ 19.5 mm coincide. The ξ0 value increases as the intensity I grows, the average distance between excited complexes decreases and, as a result, the probability of their diffusion-controlled convergence with subsequent quenching, caused by energy transfer, increases. The fluorescence decay curve, obtained at Δ = 0 is absent in Fig. 2: the observed peculiarity for this waist position will be discussed below.
Fluorescence decay curves were processed as follows. The tail (t > 50 μs) of the curve measured for maximum displacement Δ = 39.5 mm, i.e. for the minimum excitation intensity I = 2 × 105 W/cm2 in the detection volume, was approximated by monoexponential decay with a lifetime of τ0 = 122.9 ± 1.0 μs. The shape of the fluorescence decay curve was constant in the range of displacement values Δ = 39.5 − 19.5 mm (Fig. 2); thus, we interpret its 15% deviation from the straight line in semilogarithmic scale as the consequence of the presence of a second U(VI) complex in solution. After that each curve was approximated by Eq. (10) with a fixed excited state lifetime in absence of annihilation effect τ = τ0, and γξ0 was determined. At the same time, the fraction of excited complexes ξ0 was estimated using Eq. (12). The values of γξ0 and A0 = Πkrnξ0 obtained from approximation with Eq. (10) and the values of ξ0 evaluated from Eq. (12) are shown in the Table 1 for three different displacements Δ. Parameter γ was obtained by division of determined γξ0 values by corresponding ξ0 values calculated with Eq. (12).
The averaging of γ values shown in Table 1 gives γ = (11.6 ± 2.5) × 104 s−1 and the corresponding value of the collisional (exchange) interaction radius r = (3.9 ± 0.8) Å was obtained using Eq. (8). The obtained value is comparable to the doubled radius of uranyl complex .
Figure 3 demonstrates dependencies of the parameter γξ0τ0 and the fluorescence intensity at the initial point of kinetic curves A0 on the vertical displacement Δ between a beam waist center and an optical fiber. Note, that the fluorescence intensity shown in Fig. 3 is normalized to a reference signal – Raman scattering (RS) of water molecules. This procedure was performed for the purpose of eliminating the factors which affect signal intensity and are difficult to control. The intensity of RS IRS must be constant for constant laser pulse energy in a detection volume for any position of the beam waist. However this assumption is being violated in some cases, e.g., for Δ < 9.5, a decrease of IRS was observed. This fact will be discussed later.
Figure 3 is symmetrical relative to the waist position Δ = 0 due to the symmetry of the light collection scheme. Figure 3 demonstrates the following pattern: at first, as the beam waist center approaches the optical fiber acceptance area (values of Δ from 40 down to 5.5 mm), the excited state deactivation rate increases and the value A0/IRS decreases. This fact is consistent with the annihilation process and the decrease of the amplitude can be partly explained by Eq. (12). In case of small values of ξ0, the amplitude of the registered signal should not depend on Δ: the decrease of the light collection volume is compensated by the increase of ξ0. In case of absorption saturation connected with ground state depletion (ξ0 ∼ 1), the amplitude should decrease as the beam waist center approaches the optical fiber acceptance area because the width of the fluorescing area in front of the fiber decreases. Note that the decrease of the amplitude can’t be explained by annihilation processes since it can not reveal itself on a time scale of 1 μs: for the U(VI) complex under investigation, the excited state lifetime and the rate of excited state annihilation are τ ∼ 100 μs and γ−1 ∼ 10 μs, so in this case the second and the third summands on the right-hand side of Eq. (7) can be neglected. The non-zero values of the γξ0τ parameter at low excitation intensities (Δ > 20 mm) are due to the effect of the 15% impact of the second uranyl species (UO2F+), that occures with a shorter lifetime, on the overall fluorescence decay on the initial stage.
In the area where the beam waist center is close to the optical fiber acceptance area (|Δ| < 2 mm) and the excitation intensity is at maximum (I ∼ 109 W/cm2), an abrupt decrease of the deactivation rate is observed and fluorescence decay curves become similar to the curves measured for large Δ, and, consequently, small ξ0 values. We explain this fact by the appearance of an additional process of two-photon ionization of water, which leads to optical breakdown and accompanying effects [52, 53]. Figure 4 demonstrates the dependence of laser radiation energy transmitted through a cuvette with a sample on a beam waist position Δ.
As shown in Fig. 4 a drop of transmitted energy is observed when the beam waist is inside the sample volume. If the beam waist is above water surface, the transmitted energy is doubled. This dependence can be explained by energy consumption for water breakdown and laser radiation scattering by the generated plasma. A transitional region for values of Δ ∼ 10 mm in Fig. 4 corresponds to a passage of an area where values of intensity are sufficient for water ionization, through the water surface. A similar dependence was observed in a paper , where laser-induced water breakdown was investigated.
It has been observed that as the deactivation rate decreases for |Δ| < 2 mm (Fig. 3), the intensity of elastic scattering at 266 nm increases almost two orders of magnitude (data not shown). On the basis of these facts we assumed that the decrease of both γξ0 and the amplitude normalized to RS signal A0/IRS are connected with water ionization and the corresponding processes, such as photochemical processes involving uranium(VI) complexes like . As it is known  that uranyl is effectively quenched by reversible electron transfer mechanism (in case of quenching by halides  and metals with variable valency ), it is likely that the increase in free (solvated) electrons concentration in solution would favor this deactivation pathway. This hypothesis is also supported by the observed decrease in average intensity of enhanced elastic scattering pulses near the beam waist (Δ ∼ 0 mm) in aqueous uranyl solution compared to distilled water that can be due to involvement of generated electrons in uranyl quenching. It is important to mention that the significant increase in the rate of excited state deactivation upon the increase of excitation intensity in the acceptance area is already observed at constant value of fluorescence decay curve amplitude (Fig. 3, Δ = 7 – 20 mm). Hence, we consider that in this range of intensities, additional uranyl deactivation processes (uranyl photoionization and water optical breakdown followed by photochemical quenching) are negligible, while the excited states annihilation can be observed. In contrast, in the |Δ| < 2 mm range, additional deactivation processes lead to decrease of ξ0, and excited state annihilation is masked.
In the present paper the dependence of characteristics of fluorescence decay curves of uranium(VI) complexes on excitation intensity has been observed, investigated and characterized. The interpretation of experimental data was given within a model assuming the presence of excited states annihilation in the system. Our experiments show that this process should be taken into account when determining excited states lifetimes of uranium(VI) complexes in case of laser intensities I ∼ 107 W/cm2. Extrapolation of fluorescence decay characteristics measured at high excitation intensity to the case of low excitation intensity may produce misrepresentation of excited state decay rates and even of the number of components in the system. The parameters of the setup used in the present study are analogous to typical values of parameters for most experimental studies dealing with TRLFS measurement of U(VI) complexes. Approximation of experimental curves with the proposed model considering excited stated annihilation (see Eq. (9)) and absorption saturation (see Eq. (12)) gives values of an annihilation rate γ = (11.6 ± 2.5) × 104 s−1 and a collisional (exchange) interaction radius r = (3.9 ± 0.8) Å, which have the expected order of magnitude. Abnormal (in context of the proposed model) dependence of excited state deactivation rate at intensities I ∼ 109 W/cm2 has been observed. A hypothesis is proposed, which describes this effect using the extensively studied processes of two-photon ionization of water and related phenomena: plasma formation and light scattering by free (solvated) electrons. It is also proposed that photochemical reaction involving uranyl quenching by generated electrons is responsible for the decrease of both excited state deactivation rate and amplitude at these excitation intensity values. We reckon that photochemical processes involving uranium(VI) complexes in aqueous solutions in regime of water optical breakdown require further investigation.
The reported study was partially supported by RFBR, research project No 12-05-01132-a, and by the Ministry of Education and Science of the Russian Federation (contract No 14.515.11.0080). We are also grateful to the anonymous reviewers for the valuable comments on the manuscript.
References and links
1. A. Meinrath, P. Schneider, and G. Meinrath, “Uranium ores and depleted uranium in the environment, with a reference to uranium in the biosphere from the Erzgebirge/Sachsen, Germany,” J. Env. Radioact. 64, 175–193 (2003). [CrossRef]
2. J. Fuger, “Thermodynamic properties of actinides aqueous species relevant to geochemical problems,” Radiochim. Acta 58/59, 81–91 (1992).
4. L. Johnson, C. Ferry, Ch. Poinssot, and P. Lovera, “Spent fuel radionuclide source-term model for assessing spent fuel performance in geological disposal,” J. Nucl. Mater. 346, 56–65 (2005). [CrossRef]
5. D. W. Shoesmith, “Fuel corrosion processes under waste disposal conditions,” J. Nucl. Mater. 282, 1–31 (2000). [CrossRef]
6. I. Grenthe, Chemical Thermodynamics of Uranium, (Universal, 1992).
7. R. Guillaumont, T. Fanghänel, J. Fuger, J. Grenthe, V. Neck, D. Palmer, and M. Rand, Update on the Chemical Thermodynamics of Uranium, Neptunium, Plutonium, Americium and Technetium, (Elsevier Science Publishers B.V., 2003).
8. H. Zanker, W. Richter, V. Brendler, and H. Nitsche, “Colloid-borne uranium anf other heavy metals in the water of mine drainage gallery,” Radiochim. Acta 88, 619–624 (2000). [CrossRef]
9. C. May, P. Worsfold, and M. Keith-Roach, “Analytical techniques for speciation analysis of aqueous long-lived radionuclides in environmental matrices,” Trends Anal. Chem. 27, 160–168 (2008). [CrossRef]
10. Z. Szabo, T. Toraishi, V. Vallet, and I. Grenthe, “Solution coordination chemistry of actinides: Thermodynamics, structure and reaction mechanisms,” Coord. Chem. Rev. 250, 784–815 (2006). [CrossRef]
11. S. Tsushima, S. Nagasaki, S. Tanaka, and A. Suzuki, “A raman spectroscopic study of uranyl species adsorbed onto colloidal particles,” J. Phys. Chem. B 102, 9029–9032 (1998). [CrossRef]
12. S. Nguyen, R. Silva, H. Weed, and J. Andrews, “Standard gibbs free-energies of formation at the temperature 303.15-k of 4 uranyl silicates - soddyite, uranophane, sodium boltwoodite, and sodium weeksite,” J. Chem. Therm. 24, 359–376 (1992). [CrossRef]
13. G. Geipel, “Some aspects of actinide speciation by laser-induced spectroscopy,” Coord. Chem. Rev. 250, 844–854 (2006). [CrossRef]
14. T. Arnold, N. Baumann, E. Krawczyk-Bärsch, S. Brockmann, U. Zimmermann, U. Jenk, and S. Weiss, “Identification of the uranium speciation in an underground acid mine drainage environment,” Geochim. Cosmochim. Acta 75, 2200–2212 (2011). [CrossRef]
15. R. N. Collins, T. Saito, N. Aoyagi, T. E. Payne, T. Kimura, and T. D. Waite, “Applications of Time-Resolved Laser Fluorescence Spectroscopy to the Environmental Biogeochemistry of Actinides,” J. Env. Qual. 40, 731–741 (2011). [CrossRef]
16. S. Formosinho, H. Burrows, M. Miguel, M. Azenha, I. Saraiva, A. Ribeiro, I. Khudyakov, R. Gasanov, M. Bolte, and M. Sarakha, “Deactivation processes of the lowest excited state of [UO2(H2O)(5)](2+) in aqueous solution,” Photochem. Photobiol. Sciences 2, 569–575 (2003). [CrossRef]
17. M. Moriyasu, Y. Yokoyama, and S. Ikeda, “Anion coordination to uranyl ion and the luminescence lifetime of the uranyl complex,” J. Inorg. Nucl. Chem. 39, 2199–2203 (1977). [CrossRef]
18. Z. Fazekas, T. Yamamura, and H. Tomiyasu, “Deactivation and luminescence lifetimes of excited uranyl ion and its fluoro complexes,” J. All. Comp. 271, 756–759 (1998). [CrossRef]
19. J. Beitz and C. Williams, “Uranyl fluoride luminescence in acidic aqueous solutions,” J. All. Comp. 250, 375–379 (1997). [CrossRef]
20. I. Billard, E. Ansoborlo, K. Apperson, S. Arpigny, M. Azenha, D. Birch, P. Bros, H. Burrows, G. Choppin, L. Couston, V. Dubois, T. Fanghanel, G. Geipel, S. Hubert, J. Kim, T. Kimura, R. Klenze, A. Kronenberg, M. Kumke, G. Lagarde, G. Lamarque, S. Lis, C. Madic, G. Meinrath, C. Moulin, R. Nagaishi, D. Parker, G. Plancque, F. Scherbaum, E. Simoni, S. Sinkov, and C. Viallesoubranne, “Aqueous solutions of uranium(VI) as studied by time-resolved emission spectroscopy: A round-robin test,” Appl. Spectrosc. 57, 1027–1038 (2003). [CrossRef] [PubMed]
21. G. Geipel, A. Brachmann, V. Brendler, G. Bernhard, and H. Nitsche, “Uranium(VI) sulfate complexation studied by time-resolved laser-induced fluorescence spectroscopy (TRLFS),” Radiochim. Acta 75, 199–204 (1996).
23. I. Billard and K. Lutzenkirchen, “Equilibrium constants in aqueous lanthanide and actinide chemistry from time-resolved fluorescence spectroscopy: The role of ground and excited state reactions,” Radiochim. Acta 91, 285–294 (2003). [CrossRef]
24. H. Sternlicht, G. Robinson, and G. Nieman, “Triplet-triplet annihilation and delayed fluorescence in molecular aggregates,” J. Chem. Phys. 38, 1326–1335 (1963). [CrossRef]
27. M. E. D. G. Azenha, H. D. Burrows, S. J. Formosinho, M. G. M. Miguel, A. P. Daramanyan, and I. V. Khudyakov, “On the uranyl ion luminescence in aqueous solutions,” J. Lumin. 48–49, 522–526 (1991). [CrossRef]
28. T. J. Barker, R. G. Denning, and J. R. G. Thorne, “Applications of Two-Photon Spectroscopy to Inorganic Compounds. 1. Spectrum and Electronic Structure of Cs2UO2Cl4,” Inorg. Chem. 26, 1721–1732 (1987) [CrossRef]
29. G. H. Dieke and A. B. F. Duncan, Spectroscopic properties of uranium compounds (McGraw-Hill Book Co, 1949).
30. Y. Yokoyama, M. Moriyasu, and S. Ikeda, “Electron transfer mechanism in quenching of uranyl luminescence by halide ions,” J. Inorg. Nucl. Chem. , 38, 1329–1333 (1979). [CrossRef]
31. Y. Park, Y. Sakai, R. Abe, T. Ishii, M. Harada, T. Kojima, and H. Tomiyasuk, “Deactivation Mechanism of Excited Uranium(VI) Complexes in Aqueous Solutions,” J. Chem. Soc. Faraday Trans. 86, 55–60 (1990). [CrossRef]
32. S. V. Lotnik, L. A. Khamidullina, and V. P. Kazakov, “Influence of temperature on the lifetime of electronically excited uranyl ion: I. Liquid and supercooled H2SO4 solutions” Radiochem. 45, 550–554 (2003) [CrossRef]
34. R. Hill, T. Kemp, D. Allen, and A. Cox, “Absorption-spectrum, lifetime and photoreactivity towards alcohols of excited-state of aqueous uranyl-ion (UO2+/2),” J. Chem. Soc. Faraday Trans. I 70, 847–857 (1974). [CrossRef]
35. A. Bakac and H. Burrows, “Uranyl ion: A convenient standard for transient molar absorption coefficient measurements,” Appl. Spectrosc. 51, 1916–1917 (1997). [CrossRef]
36. T. Förster, “Zwischenmolekulare Energiewanderung und Fluoreszenz,” Ann. Phys. 2, 55–75 (1948). [CrossRef]
37. D. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21, 836–850 (1953). [CrossRef]
38. A. Monguzzi, R. Tubino, and F. Meinardi, “Upconversion-induced delayed fluorescence in multicomponent organic systems: Role of Dexter energy transfer,” Phys. Rev. B 77, 196112 (2008).
39. M. Marcantonatos, “Mechanism of quenching of uranyl-ion luminescence by metal-ions,” Inorg. Chim. Acta 24, 53–55 (1977). [CrossRef]
40. H. Burrows, A. Cardoso, S. Formosinho, and M. Miguel, “Photophysics of the excited uranyl-ion in aqueous-solutions .4. Quenching by metal-ions,” J. Chem. Soc. Faraday Trans. I 81, 49–60 (1985). [CrossRef]
41. G. Marx and H. Bischoff, “Transport processes of actinides in electrolyte-solutions. 1. Determination of ionic mobilities of uranium in aqueous-solutions at 25° by radioisotope method,” J. Radioan. Chem. 30, 567–581 (1976). [CrossRef]
42. S. Kerisit and C. Liu, “Molecular simulation of the diffusion of uranyl carbonate species in aqueous solution,” Geochim. Cosmochim. Acta 74, 4937–4952 (2010). [CrossRef]
43. A. Einstein, “The motion of elements suspended in static liquids as claimed in the molecular kinetic theory of heat,” Ann. Phys. 17, 549–560 (1905). [CrossRef]
44. M. von Smoluchowski, “Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen,” Zeitschr. Phys. Chem. 92, 129–168 (1917).
45. S. I. Wawilow, “The lifetime of the excited molecules in the fluorescent aqueous solutions,” Zeitschr. Phys. 53, 665–674 (1929). [CrossRef]
46. S. McGlynn and J. Smith, “Electronic structure, spectra, and magnetic properties of actinyl ions. 1. Uranyl ion,” J. Mol. Sp. 6, 164–187 (1961). [CrossRef]
47. J. Bell and R. Biggers, “Absorption spectrum of uranyl ion in perchlorate media. I. Mathematical resolution of overlapping band structure and studies of environmental effects,” J. Mol. Spectrosc. 18, 247–275 (1965). [CrossRef]
48. A. A. Banishev, D. V. Maslov, and V. V. Fadeev, “A Nanosecond Laser Fluorimeter,” Phys. Instrum. Ecolog. Med. Biolog. 49, 430–434 (2006).
49. E. Jones, Tr. Oliphant, and P. Peterson, and others, “SciPy: Open source scientific tools for Python” (2001), http://www.scipy.org/.
50. I. Puigdomenech, “Chemical Equilibrium Diagrams”, https://sites.google.com/site/chemdiagr/
51. A. Kirishima, T. Kimura, O. Tochiyama, and Z. Yoshida, “Speciation study on complex formation of uranium(VI) with phosphate and uoride at high temperatures and pressures by time-resolved laser-induced uorescence spectroscopy,” Radiochim. Acta 92, 889–896 (2004). [CrossRef]
52. D. Nikogosyan, A. Oraevsky, and V. Rupasov, “2-photon ionization and dissociation of liquid water by powerful laser uv-radiation,” Chem. Phys. 77, 131–143 (1983). [CrossRef]
53. A. Vogel, K. Nahen, D. Theisen, and J. Noack, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses. 1. Optical breakdown at threshold and superthreshold irradiance,” IEEE J. Sel. Top. Quantum Electron. 2, 847–860 (1996). [CrossRef]
54. S. Kudryashov and V. Zvorykin, “Microscale nanosecond laser-induced optical breakdown in water,” Phys. Rev. E 78, 036404 (2008). [CrossRef]
55. A. B. Yusov and V. P. Shilov, “Photochemistry of f-elements ions,” Russ. Chem. Bull. 49, 1925–1953 (2000). [CrossRef]