Introduction

Biological and chemical processes facilitate the decay of lignin, which is a major constituent of wood, into stable and water-soluble hydroxybenzoic acids and phenols [1, 2, 3, 4, 5]. Protocatechuic acid (PCA, 3,4-dihydroxybenzoic acid), one of these lignin decay products, forms stable aqueous complexes with uranium(VI) [6]. Therefore, PCA and other lignin decay products may influence the migration behavior of uranium in the near-field of defunct and flooded uranium mines where wood provided mechanical stability to the pits. For example, several millions of cubic meters of wood containing hundreds of thousands of tons of lignin were used during 1946–1990 by the WISMUT enterprise to reinforce the uranium mines in Saxony and Thuringia, Germany [7]. The knowledge of the uranium speciation in mine waters and in the presence of dissolved PCA and other wood decay products is mandatory for predicting the migration properties of the uranium that is still left in the mines and for estimating the corresponding risk for the environment.

Fig. 1.
figure 1

Schematic drawing of the coordination of uranium(VI) with PCA. Bidentate coordination of the carboxyl group (top) and o-diphenolic coordination (bottom). The interatomic distances are taken from Table 4

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Previous Extended X-ray Absorption Fine Structure (EXAFS) studies of aqueous uranium(VI) complexes with PCA showed that at pH 4.3 the carboxyl group of PCA coordinates uranium(VI) in a bidentate mode in the equatorial plane [8]. However, at pH 10.0 the coordination of uranium(VI) occurs via the neighboring phenolic OH groups under formation of a five-membered ring (see Fig. 1). Baraniak et al. [6] determined the complex stability constants for the reaction of uranium(VI) with PCA by potentiometric titration. This method does not give any direct information on the structure of the complexes. On the contrary, several assumptions regarding the composition and structure of the complexes are needed for the interpretation of the potentiometric data. Therefore, we aimed at a direct speciation of the uranium(VI) complexes as a function of pH using the structure-dependent EXAFS signal. Since all uranium species present in a solution contribute to the measured EXAFS signal, it is necessary that the samples contain the desired species nearly to 100%. However, the speciation calculations for the system uranium(VI)/PCA showed that several uranium species coexist over a wide pH range. Therefore, we developed a new approach to the EXAFS analysis aiming at a quantitative decomposition of the EXAFS spectra of mixtures into the different spectral components/constituents. Our approach is based on iterative transformation factor analysis (FA). As a result, we determined the structure and the speciation of uranium(VI) complexes with PCA in the pH range 4.0–6.8.

Experimental

Seven samples were prepared in the pH range 4.0–6.8 at an ionic strength of 0.1 M NaClO4. The total uranium(VI) concentration was 1.0 mM. The PCA concentration was 50.0 mM in all samples. The 0.1 M uranium(VI) stock solution used for sample preparation was prepared from UO2(NO3)2·nH2O (Lachema). The solid was heated at 300 °C for 2 days. The UO3 formed was dissolved in 0.5 M HClO4. UO2(NO3)2·nH2O and PCA (Sigma) were of analytical grade and used without further purification. The pH was measured with a glass electrode (Ingold) and pH meter (Wiss. Technische Werkstätten) with a precision of ±0.05 pH units. All samples were prepared from carbonate-free substances under high-purity nitrogen. The EXAFS measurements were carried out at room temperature at the Rossendorf Beam Line (ROBL) at the European Synchrotron Radiation Facility (ESRF) using a Si(111) double-crystal monochromator [9].

The uranium LIII-edge X-ray absorption spectra of the aqueous uranium(VI)/PCA mixtures were measured in fluorescence mode with a 4-pixel germanium solid-state detector [10]. The maximum electron beam current was 200 mA. For the application of the FA, it is important that the spectra of the samples have a similar statistical error [11]. Therefore, typically eight scans of each spectrum were collected until all averaged spectra reached a similar statistical error. The energy scale was calibrated using the maximum of the first derivative of the uranium LIII-edge X-ray absorption spectrum of the samples. The ionization potential of the uranium LIII-edge was defined as 17185 eV. The EXAFS spectra were analyzed according to standard procedures including statistical weighting of the four fluorescence channels and dead-time correction using the suite of programs EXAFSPAK [12]. The theoretical scattering phases and amplitudes were calculated with the scattering code FEFF6 [13].

Factor analysis

The speciation in solution can change with physicochemical parameters like pH, concentration, temperature etc. Depending on the spectroscopic properties of each individual chemical species or chemical component, the spectra of a series of samples can show a variation depending on the physicochemical parameter varied. In terms of FA, the spectral components are called factors. If the amplitudes of the spectra of the factors are linearly dependent on the concentration of the corresponding chemical species, the measured spectra d k are the sum of the product terms of the n linear independent factors r j and their concentration distributions c jk [14].

$$ {{\bf{d}}_{k} = {\sum\limits_{j = 1}^n {{\bf{r}}_{j} c_{{jk}} \;{\rm{with}}\;k = 1, \ldots ,c\;{\left( {{\rm{number}}\;{\rm{of}}\;{\rm{samples}}} \right)}} }} $$
(1)

The value of c should be larger than n.

Following the notation used by Malinowski [14], one can write Eq. 1 also in matrix notation:

$$ {{\bf{D}} = {\bf{RC}}} $$
(2)

In Eq. 1 and in the following, small bold letters, e.g., d k , denote vectors. Large bold letters, e.g., D, symbolize matrices. The measured spectra d k are collected in the r×c data matrix D with c spectra in the columns at r measuring points. The r×n matrix R contains the spectra of the factors in the columns. The n×c matrix C contains the corresponding relative concentrations of the factors. If only the experimental spectra, which are collected in the data matrix D, are known, the first step of the analysis is the determination of the rank of D. It equals the number of linearly independent spectral components in the measured system. The rank of D is calculated by solving the eigenvalue problem given by:

$$ {{\bf{ZC}}^{{\rm{t}}}_{{{\rm{abs}}{\rm{.}}}} = {\bf{\Lambda C}}^{{\rm{t}}}_{{{\rm{abs}}{\rm{.}}}} } $$
(3)

where Z is the covariance matrix with Z = D t D. The superscript t stands for transpose and the subscript abs. for abstract or non-physical values, respectively. The diagonal elements in the diagonal matrix Λ are the eigenvalues λ. The corresponding eigenvectors are the row vectors of the matrix C abs..

The eigenvectors describe an orthogonal basis of the multidimensional factor space. The decomposition of Z into eigenvalues and eigenvectors can be done by standard procedures [15, 16, 17, 18, 19, 20]. The maximum possible number of eigenvectors and eigenvalues λ equals c, the number of measured spectra. Usually, only n primary eigenvectors (n <c) are responsible for the variation in the data. Some eigenvectors, which are caused by experimental errors in the data, can be neglected (factor compression). To determine the number of the linear independent factors in the data, we use the eigenvalues and the semi-empirical indicator function IND [11]

$$ {IND_{n} = {{RE_{n} } \over {{\left( {c - n} \right)}^{2} }},\;{\rm{where}}\;RE_{n} = {\left( {{{{\sum\limits_{j = n + 1}^c {\lambda _{j} } }} \over {r{\left( {c - n} \right)}}}} \right)}^{{1/2}} \;{\rm{with}}\;n = 1, \ldots ,c - 1} $$

The number of primary factors n is obtained when the IND function reaches its minimum value. When the correct number for n is determined, the experimental error in the data can be calculated with the real error function RE n [11]. A matrix R abs. can be calculated with Eq. 4 using only the primary eigenvectors.

$$ {{\bf{R}}_{{{\rm{abs}}{\rm{.}}}} = {\bf{DC}}^{{\rm{t}}}_{{{\rm{abs}}{\rm{.}}}} } $$
(4)

Since the eigenvectors are orthogonal, the rearranging of Eq. 4 yields the abstract solution for D with:

$$ {{\bf{D}} = {\bf{R}}_{{{\rm{abs}}{\rm{.}}}} {\bf{C}}_{{{\rm{abs}}{\rm{.}}}} } $$
(5)

The matrixes C abs. (n×c) and R abs. (r×n) contain abstract concentrations and abstract spectra of the n primary factors. Through the reduction of the dimensionality of the factor space, i.e., factor compression, the reproduced spectra D in Eq. 5 contain less experimental error than the experimental spectra D in Eq. 2. The extracted error can be determined using the extracted error function XE [11].

To obtain physically interpretable results, the orthogonal basis of the n-dimensional factor space, which is now represented through the n eigenvectors, must be rotated. We used Iterative Target Testing (ITT) with the concentration test vectors c j,test for the non-orthogonal rotation of the basis [14, 21, 22]. Each c j,test contains an incomplete concentration profile for the j'th factor in the measured spectra. All unknown values are set to zero. Known values are held constant during the iteration. A new concentration vector ĉ j,test is generated for the factor j in each cycle between Eqs. 6 and 7

$$ {{\bf{t}}_{j} = {\bf{c}}_{{j,{\rm{test}}}} {\bf{C}}^{{\rm{t}}}_{{{\rm{abs}}{\rm{.}}}} } $$
(6)
$$ \hat c_{j,test} = t_j C_{abs.} $$
(7)

Then ĉ j,test is being put into Eq. 6 as new c j,test . If the values in c j,test converge to ĉ j,test , the iterative cycle between Eqs. 6 and 7 is stopped. Brayden et al. have shown that in this way the unknown elements of the test vectors converge to the true physical values [23]. During the iterations, negative elements in c j,test are set to zero. Elements greater one are set to one. The ITT procedure determines the concentration distributions of the factors independently from each other. As an additional criterion for the creation of the concentration test vectors, we used the maximums in the concentration profile that were determined before by VARIMAX rotation. The VARIMAX rotation performs an orthogonal rotation of the basis of the multivariante factor space. Each eigenvector in C abs. contains the unknown concentration distribution of a factor in the spectra [21, 24]. This abstract concentration distribution can be interpreted qualitatively.

After the ITT procedure, the real spectra of the factors (pure chemical species) R real can be calculated using:

$$ {{\bf{R}}_{{{\rm{real}}}} = {\bf{R}}_{{{\rm{abs}}{\rm{.}}}} {\bf{T}}^{{ - 1}} } $$
(8)

The transformation matrix T is simply a combination of the transformation vectors t j , which are calculated according to Eq. 6.

In case of a mixture containing n metal complexes, the experimental EXAFS signal χ total,k (k) can be written as [25]

$$ {\chi _{{{\rm{total}},k}} {\left( {\bf{k}} \right)} = {\sum\limits_{j = 1}^n {\chi _{j} {\left( {\bf{k}} \right)}c_{{jk}} } }} $$
(9)

The term of the right side of Eq. 9 represents the sum of the contributions χ j (k) from the near-neighbor atoms of the central metal ions of the complexes j with their relative concentration distribution c jk at the k'th pH value to the measured EXAFS signal. Since the right term of Eq. 9 is equivalent to Eq. 1, eigenanalysis and ITT can be applied to EXAFS spectra. According to Eq. 2, the columns of the data matrix D with the format r×c contain the measured EXAFS spectra χ total,k (k) at r wave vectors at c pH values.

Results and discussion

EXAFS structural analysis of the raw data

In a first step, the average metrical parameters of the uranium near-neighbor surrounding in all samples were determined using conventional EXAFS data analysis. The calculations of the theoretical phase and amplitude functions were performed in the potential of a cluster consisting of 42 atoms. The coordinates of the cluster atoms were taken from the crystal structure of sodium uranyl(VI)-triacetate [26]. In all fits the coordination number (N) of the axial oxygen of the uranium(VI) moiety was held constant at two. The twofold degenerated 4-legged multiple-scattering (MS) path U-Oax(1)-U-Oax(2) within the linear Oax(1)-U-Oax(2) chain was also included in the analysis [27, 28, 29]. The metrical parameters of this MS path were linked to the corresponding variables of the U-Oax single-scattering (SS) path. The metrical parameters of the best theoretical model to the raw data for each sample are summarized in Table 1.

Table 1. EXAFS structural parameters for the uranium(VI)/PCA mixtures at different pH values
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The EXAFS spectra of all samples contain two well separated oxygen coordination shells, i.e., axial oxygen Oax and equatorial oxygen Oeq. An additional carbon shell C1 was detected for the sample at pH 4.0. An inverse relationship between the U-Oax and U-Oeq bond distances was observed (Table 1). With increasing pH, the average U-Oeq bond distance decreases from 2.46 Å to 2.36 Å. The opposite trend was observed for the U-Oax bond distance, which increases from 1.78 to 1.81 Å. The axial oxygen bond gets longer when the equatorial oxygen atoms come closer to the uranium.

A qualitative estimate of the contribution of the different species can be obtained assuming that the spectra measured at pH 4.0 and 6.8 represent two different uranium(VI) species. For a 1:1 mixture of these two species, the average U-Oeq bond distance would be approximately 2.40 Å. Such a bond distance was measured for the solution at pH 4.5. The Debye-Waller factor of the Oeq shell, which is a measure of the disorder, has its largest values at pH 4.5 and 4.8 (Table 1). Therefore, one can conclude that the two structural different uranyl species have nearly equal concentration in the pH range of 4.5 to 4.8. In the following, the EXAFS spectra of the individual components and their relative concentrations will be determined by iterative transformation FA.

Iterative transformation factor analysis of EXAFS spectra

The data matrix D contains the raw uranium LIII-edge k3-weighted EXAFS spectra of the uranium(VI)/PCA mixtures at seven different pH values. The eigenanalysis of D yields maximum seven eigenvalues λ and eigenvectors contained in C abs. and R abs., respectively. For the first four factors the eigenvalues, the corresponding real and extracted errors, and the values of the IND function are listed in Table 2. The abstract spectra of the first four factors and the abstract concentration distributions of the first two factors are shown in Fig. 2.

Table 2. Eigenanalysis results of D
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Fig. 2.
figure 2

The first four abstract spectra (eigenvectors) of the factors (left) and the abstract concentration distribution of the first two factors (right); j number of factor

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The eigenvalues measure the amplitude of the abstract spectra of the factors. Factors with large eigenvalues influence the data more than factors with small eigenvalues. The first factor has always the largest eigenvalue and is always a primary factor (Table 2). Beginning with the third eigenvalue, the eigenvalues are small and do not change significantly. This indicates that only two primary factors contribute to the variation in the data. To check whether the third or a following factor contain only the experimental error, it is instructive to look at the abstract spectra of the factors (Fig. 2, left).

Only the abstract spectra of the first two factors show EXAFS-like oscillations and contain usable information. The following factors contain the experimental noise. The IND function should reach a minimum when the correct number of primary factors is employed for the abstract data reproduction [11]. As one can see from Table 2, the IND function reaches a minimum at the second factor. The eigenvalues, the abstract spectra, and the IND function show clearly that two structural different spectral components exist in the pH range 4.0–6.8. The factor space is compressed to two primary factors and the other factors are neglected. The experimental error of the raw k3-weighted EXAFS spectra is given at n=2 with RE 2 =0.31 absorption units (Table 2). The extracted error XE 2 , which is the standard deviation between the experimental and the reproduced spectra, is 0.26 absorption units due to the factor compression. This leads to an improvement of the abstract reproduced EXAFS spectra by a factor of 1.8. Figure 3 compares the raw k3-weighted EXAFS spectra and the corresponding Fourier transforms (FTs) with their abstract reproductions, which were calculated according to Eq. 5 using the first two factors.

Fig. 3.
figure 3

Raw uranium LIII-edge k3-weighted EXAFS spectra and corresponding Fourier transforms of the aqueous U(VI)/PCA mixtures at different pH values (dotted line) and their abstract reproductions (solid line)

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The result of the VARIMAX rotation for the first two factors shows that the first factor and the second factor reach their maximum concentration at pH 4.0 and pH 6.8, respectively. Using this additional information, the ITT started with the concentration test vectors c 1,test and c 2,test given in Table 3. The two spectral components correspond to the EXAFS spectra of the two structural different uranium(VI)/PCA complexes (Eqs. 9 and 1). Therefore, the ITT results in the speciation of the uranium(VI)/PCA complexes as a function of pH (Table 3). After the ITT, the real EXAFS spectra of the two spectral components were calculated using Eq. 8.

Table 3. Result of iterative target test: The real concentration distribution ĉ 1,test and ĉ 2,testof the pure spectral components as a function of pH
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EXAFS structural analysis of spectral component 1

Figure 4 shows the best theoretical fit to the EXAFS spectra of components 1 and 2 and the corresponding FTs. The corresponding metrical parameters are summarized in Table 4. The first and the second peaks in the FT of spectral component 1 are caused by the first two oxygen coordination shells, i.e., the two axial oxygen atoms Oax of the uranium(VI) moiety and the oxygen atoms Oeq in the equatorial plane. Note that the distances in the FTs of Figs. 3 and 4 are not corrected for phase shift and appear, therefore, at a shorter distance. The average U-Oax and U-Oeq bond distances are 1.78 Å and 2.45 Å, respectively (Table 4). The shoulder of the second FT peak at 2.3 Å was modeled as a carbon coordination shell with a U-C1 bond distance of 2.88 Å (Table 4). The FT peak at 3.8 Å was modeled as a combination of the SS contribution of the distal carbon atom C2 of the carboxyl group and the per C1 atom twofold degenerated 3-legged MS path U-C1-C2 [27]. The obtained U-C2 bond distance was 4.38 Å (Table 4). Within the experimental uncertainty of 0.02 Å, the determined U-Oeq, U-C1, and U-C2 bond distances are similar to those found for uranyl(VI)-triacetate [26]. In this compound the carboxyl group coordinates in a bidentate mode to the uranium(VI). According to the EXAFS structural parameters, we identify spectral component 1 as the EXAFS spectrum of a uranium(VI)/PCA complex where the carboxyl group forms a bidentate complex with the uranium(VI) moiety (Fig. 1). This conclusion agrees with the results of our previous EXAFS investigation of aqueous uranium(VI) complexes with various lignin degradation products [8]. According to the determined coordination number for the C1 shell (Table 4), the stoichiometry of the uranium(VI)/PCA complex is in the range of 1:2 to 1:3. The formation of a 1:1 complex of uranium(VI) with PCA at pH 4 is unlikely. If four water molecules and only one carboxyl group would be attached to the uranium(VI) ion, the average U-Oeq bond distance would be much smaller than 2.45 Å and closer to the corresponding value for the aqueous uranium(VI) ion, i.e., 2.41 Å [30, 31].

Fig. 4.
figure 4

Uranium LIII-edge k3-weighted EXAFS spectra of the spectral components 1 and 2 (left) and their corresponding Fourier transforms (right). Dashed line–best theoretical fit to the data (solid line)

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Table 4. EXAFS structural parameters for the spectral components 1 and 2
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EXAFS structural analysis of spectral component 2

The U-Oax bond distance of 1.80 Å is slightly higher than the corresponding value for spectral component 1 (Table 4). A similar trend of increasing U-Oax bond distances with increasing pH was also observed in our previous investigation of uranium(VI) complexes with PCA [8]. The short U-Oeq bond distance of 2.36 Å indicates that the coordination of uranium(VI) occurs via the neighboring phenolic OH groups of the PCA under formation of a five-member ring (Fig. 1). The detection of carbon backscattering atoms C1 at a distance of 3.26 Å supports this interpretation (Table 4). The EXAFS spectrum and the metrical parameters of the Oax and Oeq shells of spectral component 2 are similar to those observed for an aqueous uranium(VI)/PCA solution at pH 10.0 [8]. From this we deduce that the o-diphenolic uranium(VI)/PCA complex exists in the pH range of 6.8 to 10.0.

The stoichiometry of the o-diphenolic complex, which could not be derived from the EXAFS measurements, was studied by UV-vis spectroscopy. Only a summary of these measurements is given here. A more detailed description is subject of a forthcoming publication [32]. UV-vis spectra of a 0.1 mM PCA solution at pH 11 were measured in the spectral range of 220–350 nm. In these carbonate-free solutions with an ionic strength of 0.01 M NaClO4, the uranium(VI) concentration was varied from 0 to 0.21 mM.

The UV-vis spectra of fourteen different samples were analyzed by iterative transformation FA. As a result of this analysis, the average ratio of uranium(VI) to PCA in the complex was determined as 1:1.96±0.04. This allows to conclude that a 1:2 uranium(VI)/PCA complex exists at pH 11.0. Due to the similarity of the EXAFS structural parameters of the uranium(VI)/PCA complexes at pH 6.8 and 10.0, it can be assumed that the 1:2 stoichiometry of the o-diphenolic complex exists in the pH range 6.8–11.0

Summary

The complexation of uranium(VI) with the lignin decay product protocatechuic acid (PCA) was investigated in the pH range of 4.0 to 6.8 using EXAFS spectroscopy. The EXAFS spectra corresponding to two different uranium(VI)/PCA complexes were extracted from a series of EXAFS measurements using iterative transformation factor analysis. At pH 4.0 the carboxyl group of two or three PCA molecules binds to the uranium(VI) ion in a bidentate fashion (Fig. 1). The metrical parameters of the uranium(VI)/PCA complex at pH 6.8 are similar to those observed previously at pH 10.0 [8]. In this pH range the coordination occurs via the two neighboring phenolic OH groups of PCA under formation of a five-member ring (Fig. 1). The stoichiometry of this uranium(VI)/PCA complex is 1:2 according to UV-vis measurements at pH 11.0 [32]. The relative concentration of these two uranium(VI) species is given in the two columns on the right of Table 3. Note that this speciation is based solely on the structural differences in the near-neighbor surrounding of the uranium atoms that could be observed by EXAFS. Already at pH 4.5–4.8 nearly fifty percent of the uranium forms an o-diphenolic 1:2 complex with PCA. The sterical arrangement of the two phenolic OH groups is the reason for the strong complexation capability of PCA toward uranium(VI).

Although eigenanalysis has been applied previously to X-ray absorption spectra [21, 33, 34, 35, 36, 37, 38], our algorithm allowed to extract the spectral components contained in a series of EXAFS measurements for the first time. For the implementation of the proposed factor analysis algorithm, we wrote a computer code in the programming language FORTRAN90. It was shown that the number of spectral components and the abstract spectra and abstract concentrations of the spectral components can be determined using eigenanalysis. The VARIMAX rotation gave the abstract concentration profile of the spectral components in the mixtures. In the following step, the result of the VARIMAX rotation and other chemical input were used to construct concentration test vectors as input for the ITT. The real concentration distribution of the spectral components is the result of the ITT, i.e., chemical species, and their EXAFS spectra. Once the EXAFS spectra of each species were isolated, the metrical parameters for the uranium near-neighbor surrounding could be determined by conventional EXAFS analysis. By comparing the measured U-Oeq bond distances with those of reference compounds, the molecular structure of the uranium(VI)/PCA complexes could be determined (Fig. 1). The iterative transformation FA is a valuable tool for the analysis of spectroscopic data of samples that contain several spectroscopically active species simultaneously. This approach can be applied to EXAFS spectroscopy, X-ray absorption near-edge structure (XANES) spectroscopy, UV-vis spectroscopy, time-resolved laser-induced fluorescence spectroscopy (TRLFS), thermal lensing spectroscopy, photoacoustic spectroscopy etc.