Application of Parallel Factor Analysis for Time-Resolved Laser

Jun 7, 2010 - Analysis for Time-Resolved Laser. Fluorescence Spectroscopy: Implication for Metal Speciation. Study. TAKUMI SAITO,* , †. HIROKAZU SAO...
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Environ. Sci. Technol. 2010, 44, 5055–5060

Application of Parallel Factor Analysis for Time-Resolved Laser Fluorescence Spectroscopy: Implication for Metal Speciation Study T A K U M I S A I T O , * ,† H I R O K A Z U S A O , † KEISUKE ISHIDA,‡ NOBORU AOYAGI,⊥ TAKAUMI KIMURA,⊥ SHINYA NAGASAKI,§ AND SATORU TANAKA† Department of Nuclear Engineering and Management, Department of Quantum Engineering and Systems Science, and Nuclear Professional School, School of Engineering, The University of Tokyo, 7-3-1 Bunkyo-ku, Tokyo 113-8656, Japan and Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan

Received December 7, 2009. Revised manuscript received May 21, 2010. Accepted May 28, 2010.

Time-resolved laser fluorescence spectroscopy (TRLFS) is an analytical technique capable of discriminating different chemical species of a fluorescent metal ion such as UO22+, Cm3+, and lanthanides. Although TRLFS has been widely used to investigate the speciation of the fluorescent metal ions, extracting quantitative and structural information from multiple TRLFS data measured as a function of chemical and physical parameters is not a simple task. The purpose of this study is to apply parallel factor analysis (PARAFAC) for the interpretation of a series of TRLFS data. PARAFAC is a robust technique because it utilizes the entire information contained in a multiway TRLFS data set. The complexation of Eu3+ by acetate was studied as a test case for the PARAFAC decomposition. It is shown that three factors are necessary and sufficient to explain the systematic variations in the original data set. The resulting spectra, decay, and relative concentrations of the factors were all in agreement with the fluorescent properties and the complexation behaviors of Eu3+-acetate complexes. Based on these results, it was concluded that PARAFAC is a promising data analysis tool for TRLFS used for the speciation studies of fluorescent metal ions.

Introduction Reaction and transport of metal ions in aquatic and soil environments are important to the availability or toxicity of metal ions to living organisms (1) as well as for assessing the risks imposed by the release of toxic metals to environments (2, 3) and developing effective remediation techniques for contaminated environments (4). In soil, aquatic, and un* Corresponding author phone: +81-3-5841-8924; fax: +81-3-58418924; e-mail: [email protected]. † Department of Nuclear Engineering and Management, The University of Tokyo. ‡ Department of Quantum Engineering and Systems Science, The University of Tokyo. § Nuclear Professional School, The University of Tokyo. ⊥ Nuclear Science and Engineering Directorate, JAEA. 10.1021/es9036995

 2010 American Chemical Society

Published on Web 06/07/2010

derground environments, metal ions undergo various chemical reactions with geological and biological components such as small ligand molecules (5), organic or inorganic colloids (2, 6), microorganisms (7) and macroscopic mineral surfaces (8), showing a distribution of the different chemical species (i.e., speciation) at a given chemical and physical condition (1). Considering the direct link of this speciation to the environmental behaviors of metal ions, it is no surprise that much research has been devoted to measure, understand, and model it. The speciation of a metal ion can be investigated by tracking the progress of the reactions and/or by examining the physical, chemical, or structural properties of the species. Various spectroscopic techniques with different probe wavelengths are widely used for these purposes (8-18). Timeresolved laser fluorescence spectroscopy (TRLFS) is a particular technique for fluorescent metal ions such as uranyl (UO22+) (5, 10-12, 14), curium (Cm3+) (15, 16, 19), and lanthanides (13, 16, 19). Because TRLFS can offer the spectral and temporal resolution together with its relatively high sensitivity, it has been applied for a variety of systems both with simulated samples in laboratory experiments (11-16, 19) and natural samples (5, 10). The discriminating capability of TRLFS relies on the fact that different chemical species of a fluorescent metal ion have different spectral shapes and decay lifetimes. For instance, emission and excitation spectra of UO22+ and Cm3+ vary upon complexation with ligand molecules (11, 16), adsorption on mineral surfaces (12, 14, 15), and uptake in solid phases (19). The hyper-sensitive 5D0 f 7F2 transition of europium (Eu3+), which is frequently used as a chemical analogue of trivalent actinides, is useful to track the progress of the reactions (13). Fluorescence lifetime reflects the molecular-scale environment of a fluorophore. Especially, for Cm3+ and middle lanthanides, it directly relates to the number of water molecules in the first coordination sphere, from which one can estimate the number of bound ligand molecules or functional groups (13, 15, 16). In spite of these capabilities, it is not easy to estimate the number of different species, their concentrations, and their chemical or structural information from TRLFS data due to overlapped spectra and/ or similar fluorescence lifetimes. One can overcome such difficulties by statistical techniques such as two-way factor analysis (FA), in which a data matrix is decomposed into a product of two matrices containing physically meaningful factors (12, 14, 16, 19). Chang et al. (14) used the evolving factor analysis (EFA) combined with multivariate curve resolution (MCR) to analyze the TRLFS data (wavelength × time) of UO22+ adsorbed on gibbsite at different chemical conditions, and revealed the presence of four surface species and their dependence on the conditions. Gabriel et al. (12) applied EFA followed by iterative rotation of the factor axes to resolve the pure spectra and the decay curves of two surface species of UO22+ on silica. It must be noted that the original experiments were designed to obtain multiway TRLFS data arrays in these examples, that is, wavelength × time × chemical conditions, but only wavelength × time subarrays were individually analyzed by FA. The objective of this study is to demonstrate the effectiveness of parallel factor analysis (PARAFAC) (20, 21) in interpreting a series of TRLFS data so that one can extract as much information as possible for the study of the speciation of a fluorescent metal ion. In PARAFAC a multiway data array is decomposed into loading matrices of factors assuming multilinearity among the factors. The complexation of Eu3+ with acetate was studied by TRLFS. The choice of the VOL. 44, NO. 13, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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system was not made to explore unknown species from environmental issues, but to access the capabilities of PARAFAC in the analysis of TRLFS data. The physical interpretability of the PARAFAC decomposition of TRLFS data requires that the basic structure of a PARAFAC model correspond to the physical model of the fluorescence of dilute samples. Because of this special structure, PARAFAC is free of rotational ambiguity, that is, the obtained factors are unique except for the permutation and scaling indeterminacy (20, 21). This is different from two-way FAs, where one needs to rotate abstract factor axes to find chemically recognizable factors (ex. the MCR in ref 14 and the iterative rotation in ref 12). It will be shown that because of this robustness, the speciation of the Eu3+/aceate system and the structural information of the species can be recovered by applying PARAFAC to the TRLFS data set measured as a function of the total concentration of acetate and that PARAFAC could be an excellent data-mining tool for TRLFS, assisting our understanding of complicated speciation of a fluorescent metal ion as frequently encountered in natural environments. PARAFAC. PARAFAC is a modeling method for multiway data originally developed in psychometrics and has gained popularity also in chemometrics (20, 21). The application of PARAFAC for TRLFS is limited in the literature (22, 23). Russell and Gouterman (22) and Selli et al. (23) employed PARAFAC, which was also denoted as the principal component factor analysis in ref 22, for analyzing the TRLFS data of the mixtures of metal-porphyrin complexes and polycyclic aromatic hydrocarbons, respectively. Here, a brief introduction of PARAFAC is given. More detailed information can be found in refs 20 and 21. Since we are interested in TRLFS data obtained as a function of a chemical condition, the entire data set can be expressed by a three-way array, X, where the underbar is used to signify the multiway (>2-way) nature of the array. In three-way PARAFAC, it is assumed that X follows the trilinear form: M

xijk )

∑a

imbjmckm

+ eijk

(1)

m)1

where xijk is an element of X, aim, bjm, and ckm are elements of the loading matrices of the first (i ) 1... I), A, second (j ) 1... J), B, and third modes (k ) 1... K), C, respectively, m () 1... M) stands for different factors, and eijk is an element of the residual array. In our analysis, the first mode of X corresponds to the total concentration of acetate and the second and third modes correspond to the spectral and temporal profiles, respectively. The PARAFAC model of eq 1 was fitted using an alternating least-squares (ALS) (20, 21). Column-wise orthogonal random matrices were used for the initialization and the same PARAFAC model was fitted to check for local minima. For the stability and the interpretability of the obtained model (20, 21), it is helpful to constrain PARAFAC. Here, non-negativity constraints were applied on the first and second modes and unimodal constraint was employed on the third. The estimation of the number of factors (M) is particularly troublesome for the PARAFAC modeling. The following criteria or analyses are known to be potentially useful for the estimation and validation of M (21, 24): rank analysis of I × JK matrix obtained by unfolding X, split-half analysis, core consistency, and sum of squared residuals (SSR). In this study we used the core consistency, SSR, and split-half analysis for the estimation of M, which was further validated by comparing the original and reconstructed data, and assessing the obtained profiles of factors in the three modes in terms of the chemistry of the Eu3+/acetate system as well as the spectroscopic properties of the Eu3+ complexes. 5056

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Experimental Section Sample Preparation. All samples were prepared using milli-Q water and p.a. grade chemicals purchased from Wako Pure Chemical Industries, unless otherwise noted. Sixteen solutions having different concentrations of acetate and total volumes of 10 mL were prepared. The concentrations of Na+ were kept at a constant value (1.0 M) among the different batches by adding varied amounts of 4 M NaClO4 stock solution prepared from the analytical grade NaClO4 · H2O (Merck). Europium was added as 50 mM Eu(ClO4)3 solution to achieve the constant Eu3+ concentrations of 1.0 mM. The stock Eu3+ solution was made from Eu2O3 by dissolving it in a slightly abundant perchloric acid solution. The concentration of acetate (cAc) was varied from 0 to 200 mM with two stock solutions of sodium acetate (4.0 mM and 1.0 M). The pH of the samples was measured by a pH meter (ORION 5-star, Thermo Fisher Scientific) with a ROSS combined electrode (Thermo Fisher Scientific, 1 M NaCl as the inner filling solution) and adjusted to 5.00 ( 0.01 by adding small amounts of HClO4 and NaOH solutions with different concentrations (0.1 M and 70 wt % for HClO4 and 0.01, 0.1, and 1 M for NaOH). An aliquot of each sample was transferred to a quartz cuvette for the subsequent TRLFS measurement. The absorption spectra of the same samples were measured by a UV/vis spectrometer (V-550, JASCO) to check for possible changes in the molar absorption coefficients upon the complexation by acetate. The observed absorbance at 394 nm did not show any systematic changes, although the spectra were contaminated by noise due to the relatively low molar absorption coefficients of the Eu3+ complexes. TRLFS Measurement. The TRLFS experiments were performed in a room with constant temperature of 293 K. The excitation source was second harmonics of a femto-sec Ti:sapphire laser (Tsunami, Spectra-Physics) coupled with a regenerative amplifier (Spitfire, Spectra-Physics) and a frequency doubler/pulse selector (model 3890, SpectraPhysics) to increase the output energy and to convert the wavelength of the seed light to 394 nm. The laser power at the sample location and the repetition rate were 174 ( 5 µJ/pulse and 1 kHz, respectively. The fluorescence from the sample was collected at 90° with respect to the excitation beam by two plano-convex fused silica lenses (3 cm diameter, f ) 40 mm) into the entrance slit of a Czerney-Turner spectrograph (Shamrock RS 303i, 300 lines/mm, Andor Technology). The width of the entrance slit was 200 µm. The resulting spectra were measured by a time-gated ICCD camera (iStar, Andor Technology). Fifty temporal scans were performed with the gate width and step of both 19 µs and with the initial delay of 20 µs. For each sample 200 spectra were accumulated. After background subtraction, the obtained TRLFS data (wavelength × time) of each sample was normalized by the peak intensity of the 5D0 f 7F1 transition at 591 nm in the first frame of the temporal coordinate (j ) 1) and gathered to a 16 × 716 × 50 data array (acetate concentration × wavelength × time), and processed by PARAFAC, using the N-way Toolbox for Matlab (25).

Results and Discussion Fluorescence Spectra and Decays of the Eu3+/Acetate System. Normalized fluorescence spectra of Eu3+ at t ) 20 µs as a function of the total concentration of acetate are shown in Figure 1a and b. The fluorescence spectra of Eu3+ have five characteristic peaks, resulting from the transitions from the 5D0 to 7FJ states, where J ) 0 to 4 (Figure 1a) (13). The 5D0 f 7F1 transition at 591 nm is a magnetic-dipole (MD) allowed transition and its intensity is largely independent of chemical environments around Eu3+. The 5D0 f 7F2 transition at 616 nm is an electric-dipole (ED) allowed “hyper-sensitive”

FIGURE 1. Normalized fluorescence spectra of the Eu3+acetate solutions at t ) 20 µs as a function of the total concentration of acetate (cAc ) 0-200 mM): (a) the spectra at the entire range of wavelength and (b) magnification of the region between 660 and 715 nm (the 5D0 f 7F4 transition). transition and its intensity increases as lowering the symmetry around a central Eu3+ ion. The intensity ratio of the 5D0 f 7 F2 transition to the 5D0 f 7F1 transition (I∆J)2/I∆J)1) increases from 0.3 at cAc ) 0 mM to 2.7 at cAc ) 200 mM. The 5D0 f 7 F0 transition at 579 nm is also an ED transition in origin and forbidden in high symmetry around Eu3+, thus virtually invisible at the relatively low concentrations of acetate. The 5 D0 f 7F4 transition is also an example of the environmentsensitive ED-allowed transition of Eu3+ (Figure 1b). In the absence of acetate it consists of a main peak at 698 nm and a shoulder around 688 nm. With an increase of the acetate concentration the main peak gradually shifts to shorter wavelength and the intensity around 688 nm increases. The 5 D0 f 7F3 transition is again an ED-allowed transition and its intensity is virtually unchanged with the acetate concentration. Consequently, the variations of the 5D0 f 7F0, 7F2, and 7F4 transitions strongly reflect the progress of the complexation of Eu3+ ions with acetate ligands. The decay of the Eu3+ fluorescence is also affected by the complexation with acetate. In Figure S1a and b in the Supporting Information, the fluorescence decays of Eu3+ at cAc ) 0.01 and 100 mM are presented. It is apparent that the lifetime of the Eu3+ fluorescence becomes longer at the higher concentrations of acetate. The hydrated water molecules serve as effective quenchers for the Eu3+ fluorescence due to vibrational energy transfer to the surrounding water molecules from the Eu3+ excited state. Upon complexation, some of the surrounding water molecules are replaced with ligand molecules and the fluorescence lifetime of Eu3+ tends to increase (13, 26, 27). Although it is possible to qualitatively explain the variation of Eu3+ fluorescence as increasing the acetate concentration, extracting quantitative and structural information on different Eu3+ species from the variation is far more difficult. This is mainly because (i) at room temperature spectral broadening partly conceals the spectral shifts among Eu3+ species, which, together with the relatively poor resolution of the spec-

trograph necessary to cover a wide spectral range, leads to strongly overlapped spectra of different Eu3+-acetate species and (ii) the fluorescence lifetimes of Eu3+-acetate complexes are close to each other as discussed below. Number of Factors in the PARAFAC Decomposition. As in the case for two-way FAs, the first step when using the PARAFAC model is the determination of the number of factors (M in eq 1) that capture systematic variations in a multiway data array. In Figure S2 in the Supporting Information, the SSR and core consistency are plotted as a function of M. The SSR is expected not to decrease further for an appropriate number of factors, because additional factors only explain random noises. In contrast, the core consistency is a measure of the “appropriateness” of a given PARAFAC model. A PARAFAC model is thought to be appropriate if it follows component-wise trilinearity as given in eq 1. In other words, allowing the interactions between the components does not improve the model further (21, 24). From Figure S2, it can be seen that for M > 3 the SSR hardly changes and the core consistency is close to 0, suggesting that the PARAFAC models considerably deviate from trilinearity and, therefore, are inappropriate (24). The split-half analysis for M ) 2, 3, and 4 also shows that only the PARAFAC models with M ) 2 and 3 were stable with respect to the division of the data set. Consequently, the proper number of factors in the present system can be concluded to be 3, although the core consistency of 56.8% at M ) 3 indicates that the chosen PARAFAC model somewhat deviates from the trilinear assumption. The determined number of factors (M ) 3) was further checked by assessing the residuals between the reconstructed and original data. In Figure S3 in the Supporting Information, the residual matrices between the original data and the reconstructed data by the PARAFAC model at 31.6 mM acetate with different M are shown. At M ) 2 (Figure S3a) the residuals heterogeneously distributed, that is, the model both strongly over- and underestimated the fluorescence of Eu3+. At M g 3 (Figures S3b and c), on the other hand, the residuals were more or less homogeneous, because they were dominated by random noise. Another way to judge the quality of the model is to use the fact that the results of appropriate PARAFAC decomposition must be in good agreement with the known chemistry of the system under consideration. This point will be discussed below. PARAFAC Decomposition of the Eu3+-Acetate TRLFS Data. In Figure 2 the results of the PARAFAC decomposition with M ) 3 are shown. Figure 2a, b, and c are the pure fluorescence spectra, fluorescence decays, and the relative concentration profiles as a function of the acetate concentration of the three factors (factors 1, 2, and 3). The same pure component spectra are separately presented in Figure S4 in the Supporting Information. Note that the spectra and the decays were normalized by the peak intensities at 591 nm and the intensities at the first point (i.e., t ) 20 µs), respectively, and that the concentration profiles obtained from the PARAFAC decomposition were divided by the two normalization coefficients above to keep the quantitative information contained in the original data set. The values of I∆J)2/I∆J)1 and the fluorescence lifetimes (τ) obtained by fitting to single exponential function are presented in Table 1. Here, the lifetimes and the associated errors are given as the mean and 2σ values of the lifetimes obtained from the jack-knife technique (28). In the jack-knife method (28), the PARAFAC model with M ) 3 was repeatedly applied for the data array constructed from the original array by removing one of the sample entries so that the error of the PARAFAC modeling could be assessed and outliers could be detected. Factor 1, which predominates at relatively low cAc, has the lowest I∆J)2/ I∆J)1 and the shortest lifetime among the three. No peak corresponding to the 5D0 f 7F0 transition exists around 579 VOL. 44, NO. 13, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Calculated speciation of the Eu3+/acetate system. The stability constants for EuAc2+ and EuAc2+ and the protonation constant for the acetate ligand are given in Table 2.

TABLE 2. Reported and Optimized Stability Constants of EuAc2+ and EuAc2+ log β species

reported values

this work

EuAc2+ EuAc2+ HAc

1.94 ( 0.01a 3.19 ( 0.03a 4.59 ( 0.01b

2.05 ( 0.26 3.31 ( 0.35

a From ref 29 (0.5 M NaClO4). NaClO4).

FIGURE 2. Pure fluorescence spectra (a), fluorescence decays (symbols) (b), and relative concentration profiles (c) of the factors obtained by the PARAFAC decomposition with M ) 3 (factor 1: red; factor 2: green; and factor 3: blue). The spectra are normalized by the intensities at 591 nm, and the decays by those at the first point at t ) 20 µs. The resulting normalization coefficients are used to calculate the relative concentration profiles. The fluorescence decay curves on a logarithmic scale are presented in the inset graph and the results of monoexponential fitting are shown as lines (see Table 1).

TABLE 1. Peak Ratios, Fluorescence Lifetimes, and Hydration Numbers of the Three Factors Obtained by the PARAFAC Decomposition factors

I∆J)2/I∆J)1a

τ (µs)b

NH2Oc

factor 1 factor 2 factor 3

0.30 1.52 2.69

109.6 ( 0.2 129 ( 1 173 ( 4

9.1 ( 0.4 7.7 ( 0.4 5.6 ( 0.4

a I∆J)1 and I∆J)2 stand for the fluorescence intensities of the 5D0 f 7F1 transition at 591 nm and the 5D0 f 7F2 transition at 616 nm, respectively. b Errors are estimated according to the jack-knife technique (28). c Calculated by eq 2. Errors ((0.4) are the values designated by the original authors in ref 26.

nm and the peak of the 5D0 f 7F4 transition consists of a main peak at 698 nm and a shoulder around 688 nm. Factor 5058

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b

From ref 30 (1 M

2 appears with an increase of cAc and becomes dominant at -2 < log cAc < -1. Factor 3 only appears at log cAc > -2 and predominates at log cAc > -1. From Table 1 it can be easily seen that the values of I∆J)2/I∆J)1 and the fluorescence lifetimes of these factors increase in the order of factors 2 and 3. Compared with the spectrum of factor 1, those of factors 2 and 3 have the peaks corresponding to the 5D0 f 7 F0 transition, whose spectral shapes and intensities are similar to each other. The peaks corresponding to the 5D0 f 7 F4 transition are blue-shifted with respect to that of factor 1, and now consist of two resolved peaks at 688 and 695 nm. The intensity of the former peak is larger for factor 3 than factor 2, and the opposite is the case for the latter peak. Implications for the Eu-Acetate Speciation. The relative concentration profiles of the three factors in Figure 2c can be compared with the speciation of the Eu3+/acetate system presented in Figure 3, which was calculated with the reported stability constants of the Eu3+/acetate complexes (29) and the protonation constant of acetate (30) listed in Table 2. The stability constants obtained at 0.5 M NaClO4 (29) were used instead of those for 1.0 M NaClO4 (31), which turned out to deviate from the ionic strength dependency of the stability constants reported by different researchers (see Table S1 and Figure S5 in the Supporting Information). Although the hydrolysis of Eu3+ was included in the calculation (13), its contribution was negligible. By comparing Figure 2c with Figure 3, it is concluded that factors 1, 2, and 3 correspond to Eu3+, EuAc2+, and EuAc2+, respectively. The existing ranges of the three species agree well between the PARAFAC-derived and calculated speciation, although the PARAFAC decomposition overestimates the maximum contributions of EuAc2+ and EuAc2+ possibly due to the weak deviation from the trilinear assumption in PARAFAC, as indicated by the value of the core consistency (Figure S2b), caused by the presence of relatively fast excited-state reactions among the Eu3+ species (32). The above conclusion and the validity of the present PARAFAC decomposition can also be supported by that fact that the observed increases of the I∆J)2/I∆J)1 ratio and the fluorescence lifetime in the order of Eu3+ (factor 1), EuAc2+ (factor 2), and EuAc2+ (factor 3) are in line with a

known change of the fluorescence properties of Eu3+ upon complexation (13, 26, 27). As mentioned above, the fluorescence lifetime of a Eu3+ complex is related to the number of hydration water molecules, NH2O, in the first coordination shell. Although the fluorescence of Eu3+ can be quenched to some extent by water molecules in the second shell as well as specific functional groups in ligand molecules such as methyl groups (27), we used an empirical equation proposed by Kimura and Kato (26) for the estimation of NH2O: NH2O )

1.05 - 0.44 τ

(2)

where τ is the fluorescence lifetime in milliseconds and the possible error in NH2O was estimated as (0.4 by the original authors. Considering both the error associated with NH2O and the total coordination number of 8-9 of Eu3+ aquo ion, the values of NH2O for the three factors in Table 1 agree with the stoichiometries of the corresponding species. The NH2O of factor 3, EuAc2+, lies on the lower margin of the acceptable error and is likely due to the deviation from trilinearity above. Alternatively, this may suggest the bidentate coordination of a carboxylic group to Eu3+ (33) but further experiments would be needed to obtain conclusive evidence. It is noteworthy that PARAFAC successfully discriminates the fluorescence lifetime of EuAc+ complexes from that of Eu3+ aquo ions. According to Table 1, they are different only by 19.4 µs, thus it is difficult to separate them by the conventional multiexponential fitting analysis. This point is clearly illustrated in Figure S6 and Table S1 in the Supporting Information, where the fluorescence decay at 591 nm at cAc ) 17.8 mM, where both Eu3+ and EuAc2+ predominate, are analyzed by fitting to mono- and biexponential functions. The results of both fittings are hardly indistinguishable, although the biexponential fitting is slightly better on a statistical basis. The lifetimes associated with the biexponential fitting, which is a proper model here, suffer from large errors and do not seem to make sense on the basis of the stoichiometries of Eu3+ and EuAc2+ as well. Finally, the relative concentration profiles in Figure 2c were used to determine the stability constants (log β) of the Eu3+-acetate complexes, EuAc2+ and EuAc2+. Before this, it is necessary to confirm that the relative concentrations in Figure 2c can be considered as “real” relative concentrations. As both the absorbance at 394 nm and the fluorescence intensities of the 5D0 f 7F1 transition, which are insensitive to surrounding environments of Eu3+, vary only marginally (data not shown), it can be safely assumed that both the molar absorption coefficients and quantum yields are similar among Eu3+ aquo ion and the Eu3+/acetate species and that the relative concentration profiles from PARAFAC can be used for the determination of the stability constants. In the last column of Table 2 the optimized stability constants for EuAc2+ and EuAc2+ are given, obtained by a standard leastsquares technique. In Figure S7 in the Supporting Information the calculated relative concentration profiles are shown together with those from the PARAFAC decomposition. The obtained stability constants for EuAc2+ and EuAc2+ seem reasonable, compared with those reported by Grenthe (29). However, they suffer from the relatively large errors and the relative concentration profiles from PARAFAC deviate from the calculated speciation at relatively large cAc, where EuAc2+ and EuAc2+ coexist possibly due to the same reason above. The PARAFAC modeling was applied for a series of Eu3+ TRLFS data obtained as varying the acetate concentration to decompose the pure spectra, decay curves, and concentration profiles of the free Eu3+ and Eu3+-acetate complexes. The number of the species, their existing ranges, and the associated structural information such as the I∆J)2/I∆J)1 ratios

and the fluorescence lifetimes all agree with the fluorescent properties and the complexation behaviors of the species. This approach should work for the TRLFS data of UO22+ and Cm3+ as well. Especially, the systems in which potentiometric titration fails due to low concentrations of reactants, the presence of reaction products with low solubilities or proton ambiguity problem, are suitable for TRLFS combined with the PARAFAC modeling. Further improvement in the PARAFAC decomposition would be achieved by adding another variable to TRLFS, for instance, in the case of systems with Eu3+, by scanning excitation energy around the 7F0 f 5 D0 transition (578-581 nm), where both states are nondegenerate and the transition is known to be sensitive to different Eu3+ species (34). For the quantitative use of the relative concentration profiles obtained from a PARAFAC model, possible deviation from trilinear assumption must be evaluated, for instance, by comparing the analysis with a multimode model without such assumption like the MCRALS method (35).

Acknowledgments This research was supported in part by Japan Society for the Promotion of Science through a Grant-in-Aid for Scientific Research (A) (20246137) and a Grant-in-Aid for Young Scientific Research (19686059). We thank Dr. Shimojo for the use of a UV/vis spectrophotometer.

Supporting Information Available (i) Decay of the fluorescence spectra of Eu3+ at two different acetate concentrations; (ii) SSR and core consistency as a function of M; (iii) color maps of the residual matrices between the original TRLFS data and the reconstructed data by PARAFAC at 31.6 mM acetate with different M; (iv) pure spectra of the 3 factors; (v) list and plot of the reported stability constants between Eu3+ and acetate at different salt levels; (vi) lifetime analyses by mono- and biexponential fitting for the fluorescence decay at 591 nm and at cAc ) 17.8 mM; and (vii) comparison among the relative concentration profiles of three Eu-acetate species obtained from the PARAFAC decomposition and the thermodynamic calculation with the optimized stability constants. This material is available free of charge via the Internet at http://pubs.acs.org.

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