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A Comparative Study of the Application of Fluorescence Excitation-Emission Matrices Combined with Parallel Factor Analysis and Nonnegative Matrix Factorization in the Analysis of Zn Complexation by Humic Acids

The main aim of this study was the application of excitation-emission fluorescence matrices (EEMs) combined with two decomposition methods: parallel factor analysis (PARAFAC) and nonnegative matrix factorization (NMF) to study the interaction mechanisms between humic acids (HAs) and Zn(II) over a wide concentration range (0–50 mg·dm−3). The influence of HA properties on Zn(II) complexation was also investigated. Stability constants, quenching degree and complexation capacity were estimated for binding sites found in raw EEM, EEM-PARAFAC and EEM-NMF data using mathematical models. A combination of EEM fluorescence analysis with one of the proposed decomposition methods enabled separation of overlapping binding sites and yielded more accurate calculations of the binding parameters. PARAFAC and NMF processing allowed finding binding sites invisible in a few raw EEM datasets as well as finding totally new maxima attributed to structures of the lowest humification. Decomposed data showed an increase in Zn complexation with an increase in humification, aromaticity and molecular weight of HAs. EEM-PARAFAC analysis also revealed that the most stable compounds were formed by structures containing the highest amounts of nitrogen. The content of oxygen-functional groups did not influence the binding parameters, mainly due to fact of higher competition of metal cation with protons. EEM spectra coupled with NMF and especially PARAFAC processing gave more adequate assessments of interactions as compared to raw EEM data and should be especially recommended for modeling of complexation processes where the fluorescence intensities (FI) changes are weak or where the processes are interfered with by the presence of other fluorophores.

Introduction
Humic acid (HA) is a complex mixture of degraded organic compounds formed by complex, biochemical processes. HA plays an essential role in the environment by improving the air-water interactions, porosity, viscosity, compaction and buffering properties of soils. HA is also a key source of energy for the activity of microflora and -fauna of soils and take part in the regulation of oxidation-reduction processes [1]. However, the most important functions of HA result from its high reactivity and great sorption capacity, in the range of 500-1200 cmol/kg [2]. HA strongly interacts with metals and as a consequence controls chemical speciation, bioavailability, toxicity, and mobility of heavy metals in the biosphere [3][4][5][6][7].

HAs Chemical Characterization
HAs were isolated from well-humified A-horizons of five different soils in order to compare Zn complexation with the compounds of varied properties like humification degree, elemental composition or functional group content. Type of soils and sampling location data are presented in Table 1.
Their physicochemical properties were extensively discussed elsewhere [31]. The extraction of HAs was performed according to the procedure recommended by the International Humic Substances Society (IHSS) [32]. Purified HAs were characterized to assess their chemical properties. The nitrogen (N) as well as carbon (C) content, expressed as weight percent, was determined using a CHN 2400 analyzer (Perkin Elmer, MA, USA), and then the atomic ratio of N/C was calculated. The surface charge at pH 6.00 (Q6), which describes the amount of negatively charged functional groups, was estimated from potentiometric titration curves (Titrino 702 SM, Metrohm AG, Herisau, Switzerland) according to Boguta and Sokołowska [1]. The UV-VIS spectral ratio E254/E436 provides information on structure aromaticity, aliphaticity, molecular weight and maturity of organic particles. This parameter was calculated on the basis of absorbance values measured for HA solutions of 40 mg·dm −1 in 0.05 M NaHCO 3 at wavelengths of 254 and 436 nm (UV-VIS spectrometer, Jasco V-520, Jasco, Tokyo, Japan). Each analysis was performed in triplicate and the results averaged. The content of COOH and OH functional groups as well as humification parameters E4/E6 and ∆logK were determined as described in detail in previous studies [33]. Table 1. Chemical properties of the studied HA samples (in part previously reported in Boguta and Sokołowska [33]

Fluorescence Measurements in HA-Zn(II) Systems
Five stock solutions of HAs were prepared by dissolving of 50 mg of each lyophilized sample in 1 dm 3 of deionized water. The pH of the solutions was adjusted to 8 by adding small amounts of 0.1 M NaOH. A stock solution of Zn ions (1000 mg·dm −3 ) was obtained by dissolving analytical grade zinc chloride in deionized water. For each HA sample, a series of solutions with increasing Zn concentrations was prepared by mixing of constant volumes (40 cm −3 ) of the sample HA stock solution with appropriate volumes of Zn stock solution and deionized water. Thus, each series contained 50 cm −3 solutions with constant HAs concentration of 40 mg·dm −3 and an increasing amount of Zn(II) ions: 0, 1, 2, 3,4,5,6,7,8,9,10,12,15,20,30,40 and 50 mg·dm −3 . The pH of each sample in the series was adjusted to 6.00 ± 0.1. All the samples were left on a magnetic stirrer under N 2 atmosphere for 24 h in order to avoid interferences from sorption of small amount of CO 2 from the air. Afterward, the pH was readjusted to 6.00 ± 0.1 and emission-excitation fluorescence 3-D matrices (EEM) were recorded for all prepared HA-Zn series using a F-7000 FL luminescence spectrometer (Hitachi, Tokyo, Japan). Emission and excitation slits were set at 10 nm and scan speed adjusted to 12,000 nm·min −1 . Samples were excited from 250 to 500 nm in increments of 5 nm, whereas emissions were measured at each excitation wavelength from 300 to 600. All measurements were performed at 25 • C to ensure complexation equilibrium and minimize. The fluorescence spectrometer was calibrated. Fluorescence intensity was calibrated using fluorescence intensity of quinine sulphate (λ ex = 350 nm and λ em = 450 nm. Spectral corrections were performed for the instrument using solution of Rhodamine B [34,35].

Fluorescence Data Pre-Processing
Scatter signal on EEM spectra is often large and therefore should be deleted before modeling [35]. All fluorescence maps/landscapes were processed via a MATLAB protocol designed to remove first-and second-order Rayleigh peaks ( Figure 1). Peaks were removed using simple binary thresholding based on magnitudes of gradients of the fluorescence data. Gradient magnitudes were computed from directional orthogonal gradients, G x and G y , with respect to the x-axis and y-axis (defined along the columns and rows of the data matrix, respectively). The threshold level was expressed as the percentage of maximum value of gradient magnitude. Regions of gradient map with values above the threshold value were selected for removal. The binary mask resulting from thresholding operation was dilated using a disk-structuring element with an arbitrarily chosen radius.

Fluorescence Data Pre-Processing
Scatter signal on EEM spectra is often large and therefore should be deleted before modeling [35]. All fluorescence maps/landscapes were processed via a MATLAB protocol designed to remove first-and second-order Rayleigh peaks ( Figure 1). Peaks were removed using simple binary thresholding based on magnitudes of gradients of the fluorescence data. Gradient magnitudes were computed from directional orthogonal gradients, Gx and Gy, with respect to the x-axis and y-axis (defined along the columns and rows of the data matrix, respectively). The threshold level was expressed as the percentage of maximum value of gradient magnitude. Regions of gradient map with values above the threshold value were selected for removal. The binary mask resulting from thresholding operation was dilated using a disk-structuring element with an arbitrarily chosen radius. Corrupted data indicated by the binary mask was removed by an inpainting procedure where each marked region of original data was filled using an iterative process based on two-dimensional convolution using a Gauss kernel. At the very beginning, selected regions were uniformly filled with values equal to the global average from the original fluorescence data (Figure 1c). The next operation involved smoothing using the Gauss kernel. The part of the smoothed map indicated by binary mask was preserved while the rest of the image was replaced with original data. This process was repeated and at each iteration, the regions of corrupted data were gradually filled in with smoothed data from the neighboring regions.

Fluorescence Data Unmixing
All fluorescence maps were decomposed into two separate components using the PARAFAC and NMF algorithms. A scheme of the decomposition is shown in Figure 2. Then, local maxima searches were performed using the original pre-processed EEM maps (simply marked as RAW data) and all component maps (designated as PARAFAC and NMF data). Searching was based on the local neighborhood defined by a circle with an arbitrarily chosen radius. Corrupted data indicated by the binary mask was removed by an inpainting procedure where each marked region of original data was filled using an iterative process based on two-dimensional convolution using a Gauss kernel. At the very beginning, selected regions were uniformly filled with values equal to the global average from the original fluorescence data (Figure 1c). The next operation involved smoothing using the Gauss kernel. The part of the smoothed map indicated by binary mask was preserved while the rest of the image was replaced with original data. This process was repeated and at each iteration, the regions of corrupted data were gradually filled in with smoothed data from the neighboring regions.

Fluorescence Data Unmixing
All fluorescence maps were decomposed into two separate components using the PARAFAC and NMF algorithms. A scheme of the decomposition is shown in Figure 2. Then, local maxima searches were performed using the original pre-processed EEM maps (simply marked as RAW data) and all component maps (designated as PARAFAC and NMF data). Searching was based on the local neighborhood defined by a circle with an arbitrarily chosen radius. The goal of NMF is to decompose an M by N data matrix A into the products of two factor matrices W and S of reduced size, and can be written as: The rank value K describes the largest collection of linearly independent components of the data matrix. For fluorescence data sets, K is interpreted as the number of pure chemical components in the sample. In this study, the number of rows M corresponds to the number of excitation wavelengths, while the number of columns N to the number of emission wavelengths. The resulting W matrix is interpreted as the matrix of excitation profiles for individual components. Similarly, the S matrix consists of the emission profiles of components. The multiplication of K-th column of W by corresponding row of S gives the M by N fluorescent map of K-th component.
Usually NMF algorithms need an estimation of the number of components in the system. In this study, such estimations were provided by the Singular Value Decomposition algorithm (SVD). The rank value K was determined by examination of the non-zero singular values of the singular matrix resulting from SVD decomposition of matrix A. The goal of NMF is to decompose an M by N data matrix A into the products of two factor matrices W and S of reduced size, and can be written as: The rank value K describes the largest collection of linearly independent components of the data matrix. For fluorescence data sets, K is interpreted as the number of pure chemical components in the sample. In this study, the number of rows M corresponds to the number of excitation wavelengths, while the number of columns N to the number of emission wavelengths. The resulting W matrix is interpreted as the matrix of excitation profiles for individual components. Similarly, the S matrix consists of the emission profiles of components. The multiplication of K-th column of W by corresponding row of S gives the M by N fluorescent map of K-th component.
Usually NMF algorithms need an estimation of the number of components in the system. In this study, such estimations were provided by the Singular Value Decomposition algorithm (SVD). The rank value K was determined by examination of the non-zero singular values of the singular matrix resulting from SVD decomposition of matrix A.
In this study, the factors W and S were chosen to minimize the root-mean-squared residual between A and WS by means of a multiplicative update algorithm. The algorithm used in this study was developed in MATLAB and is based on build-in implementation of the NMF algorithm.

Parallel Factor Analysis Model (PARAFAC)
A PARAFAC model of a three-way array is given by three loading matrices, A, B, and C with elements a in , b jn , and c kn . The model was independently proposed by Harshman [36] and by Carroll and Chang [37]. The trilinear model is found to minimize the sum of squares of the residuals, e ijk in the model: where x ijk is the measured value of emission intensity of the i-th fraction of the k-th sample measured at the j-th excitation wavelength; a in , b jn and c kn represent the parameters to estimate; r ijk are the residuals; and C is the number of factors/components extracted. In this solution each component consists of one score vector and two loading vectors. Using the model it is possible to resolve the data into meaningful components corresponding to individual analytes. The loading matrices A, B and C are estimated in a least squares sense. In this study, two-way arrays were processed as input, therefore the third mode of the model was interpreted as a one-dimensional mode. Also, non-negativity constraints were put on the loadings of the different modes. Calculations were performed using the N-way PARAFAC toolbox (version 3.30) for MATLAB R2013A (MathWorks, Natick, MA, USA) [38]. Scheme of the decomposition process is showed in Figure 2.

Calculation of Binding Parameters
Binding parameters were estimated for pre-processed, original RAW data sets as well as for decomposed data (PARAFAC and NMF) at each maximum. Fluorescence intensities (FI, arbitrary units) of the found peaks (designated when possible as α, β, γ or ω), which changed markedly as a function of Zn(II) concentration, were used in the Ryan and Weber quenching model for quantification of complexation process [39]. As a result, the conditional stability constant of HA-Zn(II) complexes (logK), binding capacity of HAs (C L ) and I ML values (the FI signal at which no more decrease of FI was observed during Zn addition) were estimated by solving equation of the model: where I 0 is the fluorescence intensity of HA without addition of Zn and C M is a metal concentration.

Chemical Properties of Humic Acids
The studied samples exhibited a wide diversity in term of their chemical properties. Results of analyses that might have any effect on the binding processes of Zn(II) ions are presented in Table 1. As noted above, methods for determining the concentration of oxygen-containing functional groups, E4/E6 and ∆logK ratios, as well as further discussion of these results is presented in more detail in Boguta and Sokołowska [33]. Briefly, the content of COOH groups was the highest for HA3 whereas the total amount of COOH + OH reached the highest value for HA2. These functional groups constitute a major part of all reactive structures in HA particles so their high concentrations indicated, to some extent, a higher reactivity, sorption and buffering capacity of HA2 and HA3 in comparison to the other samples [1]. Results of ∆logK coefficient showed that HA3 belonged to the samples with the lowest stage of humification (R-type), whereas all remaining HAs demonstrated a weak degree (B-types) of humification [41]. The values of the E4/E6 ratio decreased in the order: HA3 > HA4 > HA2 > HA1 > HA5 which suggested increasing molecular weight, humification degree, and increasing presence of condensed aromatic structures (highest in HA5, lowest in HA3). The highest value of E4/E6 for HA3 indicated much more quantities of aliphatic structures in comparison to the other samples [42]. Results obtained in these studies showed that E4/E6 order was almost duplicated in the E254/E436 ratios which were ordered as follows: HA3 > HA4 > HA2 > HA5 > HA1 revealing the highest content of unsaturated compounds, conjugated quinones and ketones and large molecular size for sample HA1 and the lowest one for HA3. The highest amount of nitrogen was found in the HA1 sample, whereas the lowest content was measured in HA4. High N concentration indicated an early stage of biological transformation and a higher amount of this element in functional groups like amines and amides or in heterocyclic compounds. The nitrogen-containing structures exhibit abilities for improving HA sorption properties due to their donor electron properties [9]. The highest content of C was measured for HA4 while the lowest one for HA2. These amounts influenced atomic N/C ratio which was the highest for HA1 and the lowest for HA4. All range of calculated N/C ratios was typical for soil HAs. This parameter might be considered as indicator of humification. High values showed also lower degree of organic substance transformation [43]. The value of Q6 was the highest for HA1, which indicated the highest concentration of all negatively charged functional groups (not only COOH + OH), however, limited to the structures dissociating below pH 6.00 (the pH of the present experiments on HA-Zn systems). The results showed that this parameter did not correspond with the number of COOH and COOH + OH groups, which indicated a contribution of other functional groups to Q6 values and dissociation of COOH and OH partly above a pH of 6.00.
It should be noted that the process of extraction, purification and drying of HA can have slight effect on chemical and physical properties of HA. However these procedures are necessary when interactions with metals are performed as well as when abilities of HAs from different sources are compared. Modification of the structure can be minimized by using well designed procedures as in case recommended by IHSS [32].

RAW Data
Direct analysis of the EEM RAW data showed the presence of two or three local maxima of fluorescence, depending on the HA sample. Results are depicted in Table 2 (ex/em coordinates of the peaks) and in Figure 3 (HAs without Zn ions: column A, rows: 1-5) where the local maxima are marked as α, β and γ. All of the α, β and γ signals corresponded with the presence of various kinds of humic type structures [4,14,44]. The α signals, placed at excitation/emission wavelengths 270-275 nm/490-505 nm were visible in all studied HAs with the highest FI signal for HA1 and HA2, which indicated a higher amount of electron-donating substituents like hydroxyl or methoxy groups for these samples [40]. According to the literature, the α area was related to terrestrial HA derived from lignin [7,45] and might reflect simple structural components of low molecular weight, low content of conjugated and aromatic groups and low humification degree [6,46,47]. The activity of β area was visible at wavelengths 360-365 nm/490-500 nm (partly overlapped by the α peak) with the strongest signal for HA1 and the weakest one for HA4. Fluorescence of this maximum could be attributed to the presence of moderately humified structures, simple phenols, coumarins, alkaloids, semiquinones and hydroquinones [47,48]. Only HA5 did not demonstrate a fluorescence maximum at β site. The γ area was applied to maximum placed at 435-445 nm/505-525 nm which could be ascribed to the presence of unsaturated bonds, high molecular weight and high humification degree as well as to linearly-condensed aromatic rings formed mainly from lignin oxidation [11,16,46]. These sites were clearly seen for all HAs except for HA3. The lowest FI of this site for HA3 and HA4 could indicate a great concentration of electron-withdrawing groups like carbonyls [16,40].

PARAFAC and NMF Processing
Decomposition of EEM matrices to the two components using PARAFAC and NMF algorithms revealed the presence of additional local maxima as well as improved resolution of the peaks found in analysis of RAW data. Two-component analysis was also recognized in previous studies by Mounier et al. [49] and Santos et al. [45] as sufficient for separation of binding sites. Example EEM-PARAFAC and EEM-NMF matrices for the HA1 (the strongest FI) and HA4 (the lowest FI) are depicted in Figures 4 and 5 (column A).
Maxima of component 1 corresponded in terms of excitation wavelength λex with the peaks found for RAW data in the α, β and γ areas (Figure 3: Column A), whereas both the PARAFAC and NMF decomposition revealed slight changes in the λem of the α, β and γ areas toward longer wavelengths. The PARAFAC and NMF decomposition processes uncovered a noticeable γ peak for HA3, which was invisible during the RAW data evaluation. Component 2 obtained via PARAFAC and NMF processing revealed the presence of a whole new maximum (marked as ω) of low intensity, located in the short wavelengths: 260-275 nm/430-470 nm (see Table 2-Detailed coordinates). Fluorophores similar to ω were also confirmed by Mounier et al. [49] in two-component decomposition. This activity could be attributed to some contents of carbohydrates and electron-withdrawing carboxylic functional groups, which may be

PARAFAC and NMF Processing
Decomposition of EEM matrices to the two components using PARAFAC and NMF algorithms revealed the presence of additional local maxima as well as improved resolution of the peaks found in analysis of RAW data. Two-component analysis was also recognized in previous studies by Mounier et al. [49] and Santos et al. [45] as sufficient for separation of binding sites. Example EEM-PARAFAC and EEM-NMF matrices for the HA1 (the strongest FI) and HA4 (the lowest FI) are depicted in Figures 4 and 5 (column A).
Maxima of component 1 corresponded in terms of excitation wavelength λ ex with the peaks found for RAW data in the α, β and γ areas (Figure 3: Column A), whereas both the PARAFAC and NMF decomposition revealed slight changes in the λ em of the α, β and γ areas toward longer wavelengths.
The PARAFAC and NMF decomposition processes uncovered a noticeable γ peak for HA3, which was invisible during the RAW data evaluation.      Component 2 obtained via PARAFAC and NMF processing revealed the presence of a whole new maximum (marked as ω) of low intensity, located in the short wavelengths: 260-275 nm/ 430-470 nm (see Table 2-Detailed coordinates). Fluorophores similar to ω were also confirmed by Mounier et al. [49] in two-component decomposition. This activity could be attributed to some contents of carbohydrates and electron-withdrawing carboxylic functional groups, which may be responsible of the small fluorescence intensity [16,46] as well as to structures of low humification and molecular weight, with natures more similar to derivatives of amino acids and other heterocyclic compounds [47].
Both γ (for HA3) as well as ω peaks (for all HAs) were concealed in the original EEM spectra, which was likely caused by overlapping signals of neighboring fluorophores. PARAFAC and NMF algorithms enabled better separation of the above maxima for their further elaboration. The total number of local maxima found via the PARAFAC method was the same as for NMF and the differences in their locations were negligible. FI values of the peaks in component 1 were higher for PARAFAC than NMF but the reverse for component 2.

RAW Data
The addition of increasing concentration of Zn(II) ions caused a gradual quench of fluorescence in the areas marked as α, β and γ, which indicated the presence of metal complexation by HAs particles [6,27,40]. Example EEM-RAW spectra displaying the changes of fluorescence intensities of the above peaks under the influence of Zn are shown in Figure 3.
It is notable that the increasing Zn concentration also caused an apparent shift of the λ em of the maximum to shorter wavelengths (blue shift), which could result from: (1) more localization of the π-electron system, (2) branching of the aromatic system [50], (3) a decrease in conjugated double bonds [47], or (4) the presence of a few groups of fluorophores in one area with various affinity to Zn(II) binding. In this case, the structures of the area active at longer wavelengths could be more strongly complexed than the structures active at shorter λ em , therefore the maximum of the entire area could be shifted to shorter wavelengths. Similar suppositions were also reported by Hernández et al. [6] and Plaza et al. [16] in studies of copper interactions with humic acids. This process was evidently seen for α binding sites. In turn, the addition of Zn(II) ions did not cause significant changes in λ ex of the analyzed fluorescence maxima.
More detailed information on the mechanism of Zn(II) binding was obtained by fitting experimental RAW data, i.e., changes of FI values at α, β and γ sites, under increasing Zn(II) concentrations, to the mathematical, quenching model of Ryan and Weber which enabled to calculate binding parameters [39]. These fits are presented in Figure 6 as percent changes (I/I 0 × 100), where I and I 0 are the fluorescence intensities with and without Zn(II), respectively. Binding parameters estimated from the model are displayed in Table 2.
Results showed that the decrease in FI was the most intensive at the lowest Zn(II) concentrations. This trend likely resulted from the presence of a significant amount of free, available reactive sites on the HA ligands. Metal binding was additionally facilitated at pH 6.00 due to a high degree of functional group dissociation and in the consequence due to a high value of the negative charge (Q6) on the HA surface, which made it easier for positive cations to be attracted to the coordination sphere [1,51]. The decrease of FI was progressively weaker and weaker with increasing Zn dose, until a point above which further metal addition did not cause a significant drop of the FI value, which indicated saturation of available reactive sites by metal ions [39]. It should be noted that the fluorescence signal was not completely quenched in any case even at the highest Zn concentrations. The values of residual fluorescence (IML) calculated from the Ryan and Weber model are presented in Table 2 (α, β, γ-RAW data).
Plaza et al. [16] have reported that uncompleted quenching could result from some steric effects occuring at partly complexed ligands during complexation. Functional groups that bind Zn(II) ions could weaken reactivity of neighboring structures. Incomplete saturation of the functional groups could also be related with spatial conformation of the structures of HA particles. The structures could be partly presented in form of coils hampering access of metal to ligands. It is known that linear and spatial development of the polymeric HA structure increases with increasing pH and reaches a maximum in strongly alkaline conditions [1]. Dissociation degree is the highest at these alkaline pHs and the generated negative surface charge is able to repulse particular chains and prevents spherical structure formation. These studies were conducted at pH 6.00, at which point functional groups of weakly acidic nature like carboxylic or phenolic are not dissociated completely, which can be a reason for partial aggregation of the particles and hampered metal complexation. This supposition was in agreement with the Q6 values, which were lower than value of COOH + OH and lower even in most cases than the content of COOH. The influence of pH on metal binding was also confirmed in previous studies [51,52], which showed an increased proton-binding competition at lower pHs.
Sensors 2016, 16, 1760 12 of 20 This supposition was in agreement with the Q6 values, which were lower than value of COOH + OH and lower even in most cases than the content of COOH. The influence of pH on metal binding was also confirmed in previous studies [51,52], which showed an increased proton-binding competition at lower pHs. The highest relative drop of FI (from I0 to IML), expressed as f was observed for all HAs at γ binding sites, which reflected a preferential binding of Zn(II) ions by strongly humified structures with high molecular weight and condensation of aromatic units. The lowest f values were determined for α areas, which indicated a lower contribution of weakly humified and low molecular weight structures in the process of Zn(II) complexation. Considering the studied HAs, the highest The highest relative drop of FI (from I 0 to I ML ), expressed as f was observed for all HAs at γ binding sites, which reflected a preferential binding of Zn(II) ions by strongly humified structures with high molecular weight and condensation of aromatic units. The lowest f values were determined for α areas, which indicated a lower contribution of weakly humified and low molecular weight structures in the process of Zn(II) complexation. Considering the studied HAs, the highest drop of FI was observed for HA1 and HA5, whereas the lowest was for HA3, which suggested these had the strongest and the weakest affinities of Zn(II) ions, respectively.
Values of complexation capacity (C L ) estimated from the model on the basis of RAW data demonstrated wide diversity within the individual fluorescence area as well as in the group of all studied HAs. At the α and γ maxima, the C L was the highest for HA1, whereas at β sites, the C L was highest for HA3. However, it should be emphasized that the C L parameter showed strong sensitivity even to slight deviations of experimental points from the model curve. In our opinion, the parameter that was much more stable for assessment of complexing degree was the f index described in the previous paragraph.
The stability of HA-Zn complexes (logK) calculated from the model at the α and γ binding sites was the highest for HA1, whereas at β sites the stability was highest for HA3. According to the literature, significant stability of HA-Zn binding can suggest the forming of chelates with participation of aromatic rings, highly humified structural units as well as structures containing nitrogen atoms as an electron donor greater than oxygen donor atoms [9,16]. On the other hand, the studies of Garcia-Gil et al. [5] report that low values of logK could be ascribed to stronger aliphatic character and small degree of aromatic polycondensation and humification.
A very good fit of the model to the experimental data ( Table 2) was confirmed by its high correlation coefficient (R > 0.92). However the model was not applicable for RAW data at α-sites of HA3. This was probably due to very low changes of fluorescence in α area under increasing Zn doses.

PARAFAC and NMF Processing
Fluorescence local maxima found by means of PARAFAC and NMF processing (α, β, γ in component 1, and new maximum ω in component 2) were quenched with increase in Zn ions concentrations. This process differed for studied HAs as well as for analyzed fluorescent peaks, which was typical for the different origin, properties and components of HAs [7,12,18]. FI changes of decomposed EEM spectra in components 1 and 2 under example Zn doses are shown for PARAFAC and NMF algorithms in Figures 4 and 5. The changes in FI were more pronounced on EEM spectra for the datasets decomposed by PARAFAC and NMF (better resolving of the peaks) than in case of RAW data.
The experimental points from the PARAFAC and NMF methods were applied to the quenching model for quantification of complexation process. High values of R coefficients (Table 2) confirmed a good fit of the obtained models, which showed also similar results when compared with the RAW data. In more detail, for peaks in α and β areas fits were good for RAW and PARAFAC data, showing slightly lower performance for NMF data. In the case of ω and γ fluorescence sites R coefficients were the highest and on similar level for RAW, PARAFAC and NMF data, which indicated the best reliability of the model was for both processing methods in case of ω and γ structures.
Trends in the modeled PARAFAC and NMF data were similar to the RAW data ( Figure 6). Such that, the most intensive drop of the FI signal took place at first in the lowest metal concentrations, which was evidence of extensive complexation processes. An Increase in Zn concentration caused FI to decrease until a plateau was reached, indicating saturation of the HA structure by metal ions.
It was interesting that both PARAFAC and NMF decomposition of the experimental EEM data enabled the fitting o model curves to the HA3 data at the α site. The model was not applicable for RAW data of this sample at the α area, due to very low changes of FI under increasing concentrations of Zn. Moreover, as was described in Section 3.3.1, the maximum at the α site of the RAW data was probably due to fluorophores of different kinds. Part of these were complexed and their fluorescence was quenched whereas others remained without any changes, which could be revealed in RAW data as changes in the maximum location of whole area and in consequence could hamper application of the model. Decomposition of the data enabled the separation of neighboring maxima and analysis of the changes only for fluorophores taking part in Zn complexing. Furthermore, the decomposition of the HA3 (α site) data remolded the rectilinear character of FI changes into nonlinear ones with a visible point of inflection, which allowed the use of the model to quantify Zn binding (see Figure 6). These results showed that NMF and especially PARAFAC processing (higher R coefficients) can be recommended for modeling of complexation processes of weak intensity, where the changes of FI are too slight or for processes that are interfered with by the presence of other fluorophores.
PARAFAC and NMF processing also enabled separation of the maximum for HA3 at the γ-area, which was impossible in the analysis of the RAW data. Experimental points of this area after PARAFAC and NMF treatment fit well to the model with high R-values of 0.96 for these two methods. This was possible due to better resolving of the fluorescent sites neighboring γ and β. In analysis of Zn complexation in the RAW data, fluorescence at β areas was much more intensive than at γ, and probably part of the signal from β sites could interfere with analysis of changes at γ sites. PARAFAC and NMF decomposition eliminated this problem.
A positive feature of the application of the PARAFAC and NMF algorithms was the opportunity of analysis of Zn interactions in the newly found ω area. This fluorescent site was hidden in the RAW data. This peak was confirmed by Santos et al. [45] as being partly covered by neighboring fluorophores. The ω structures attributed to very low humification and groups of low molecular weight [47], demonstrated a tendency for complexation of Zn ions, which was visible as quenching of the FI with increasing metal concentration. The drop in FI with increasing Zn concentration for each HA at the ω area was lower than at α, β and γ sites, which could indicate a lower importance of ω structures with simple units, low molecular weight and aromaticity in comparison to highly humified and condensed structures with large molecular mass. The ω data fit very well to the model despite the low FI of this area as well as weak changes when Zn ions were increased. The only case in these studies when model curve could not be fit to experimental data of ω sites after treatment by the PARAFAC and NMF algorithms was related to the HA3 sample. However, it should be emphasized that Zn complexation degree expressed by fluorescence changes was negligible in this case.
The stability constants (logK) of individual HAs at α, β and γ areas estimated using the PARAFAC and NMF methods showed some differences when compared to logK values calculated from RAW data. The lowest discrepancies occurred between the values of γ sites. Higher differences were found between logK at α and β, which indicated that the decomposition process could affect more experimental data of above areas in comparison to γ fluorescent sites. This probably was due to partial interference of α with β and α with ω fluorescent areas. Decomposition of the EEM matrices caused better separation of these maxima, which could be translated into higher differences in logK values in comparison to the RAW data. Therefore, it might be assumed that logK values from NMF and especially PARAFAC processing (higher R indices) had higher accuracy than from RAW data. Despite these differences, the highest stability constants for both RAW, PARAFAC and NMF calculations were demonstrated by HA1, which was due to its greater nitrogen content; N-containing functional groups are considered to be ligands with strong affinity to metals [11,53]. HA1 data revealed also the highest value of Q6 and the lowest E245/E436 ratio, which could also substantially determine the stability of these complexes. This reflected that it has a greater concentration of negatively charged functional groups and the highest content of unsaturated compounds, such as conjugated quinones and ketones, which might be of key importance in Zn binding. It should be stressed that all studied HAs showed the lower logK values for ω structures than other areas, which pointed out weaker complexing properties of the lowest humified and low-molecular groups and, in the consequences, formation of clearly weaker complexes.
The degree of quenching (f) calculated for PARAFAC and NMF data was similar to the values obtained from RAW data and showed the highest values for HA1 and HA5 at each fluorescent area. These samples were characterized by the highest concentration of nitrogen (N) and value of negative charge at pH 6.00 (Q6) as well as by the greatest humification degree, molecular weight and content of unsaturated structures (expressed by the lowest E4/E6 and E254/E436), which could have a dominant influence on the amount of bounded Zn ions. According to He et al. [40] large quenching degrees can also be associated with the presence of electron-donating groups. Comparing the particular fluorescent areas of PARAFAC and NMF data, it might be noted that the lowest degree of quenching by Zn(II) was attributed to ω binding sites. This insight together with low logK confirmed weak affinity of ω structures to Zn(II) ions.

Summary of the PARAFAC and NMF Performance
In this study two supporting methods-parallel factor analysis (PARAFAC) and nonnegative matrix factorization (NMF)-were applied for decomposition of the EEM spectra into independent, well-resolved groups of fluorophores. The EEM data analysis showed that NMF algorithm has a potential use as an alternative method to the PARAFAC decomposition. In terms of the qualitative performance of decomposition the NMF algorithm showed comparable results with the PARAFAC-by constraining the model to two components we obtained the same number of peaks with similar excitation-emission coordinates. Both sets of the EEM decomposed maps shown in Figures 4 and 5 reveal similar features for the two components, with only slight different intensities for peaks from sites β and ω. This lower performance of the NMF algorithm was reported in terms of quantitative representation of individual fluorescence sources, especially in terms of overlapping of signals. This is clearly visible when we compare quenching profiles for α and ω sites obtained by means of the PARAFAC and NMF. The peak at the ω site was previously not visible at raw EEM maps. It's presence was successfully revealed as a separate signal belonging to the second component by both applied methods. However due to presence of neighboring peak at the α site the unmixing process performed by means of the NMF algorithm in some cases led to suboptimal solution. The less stable unmixing process, resulted in a wider spread of data points used to build quenching profiles. Better performance of the NMF algorithm can be achieved by tightening the termination tolerance on change in size of the residual or increase in the maximum number of iterations. Another possibility is to change the algorithm which minimized the root-mean-squared residual. The applied multiplicative algorithm is more sensitive to initial values of the resolved system (which by default were randomly chosen), while the alternating least squares algorithm is known to converge faster and more consistently.

Influence of Chemical Properties of HAs on the Complexation Process of Zinc(II) Ions
Statistical analysis confirmed a significant influence of the chemical properties of HAs on the process of Zn(II) complexation at pH 6.00. Correlation coefficients found between selected properties and parameters describing complexation, i.e., logK and f values at α, β, γ and ω are shown in Table 3.
Degree of quenching (f) did not show in any case a significant relationship to the content of COOH and COOH + OH functional groups. This indicated that oxygen-containing groups did not exhibit a dominant influence on the amount of bounded metal. The reason could be found in partially protonated COOH and OH groups at pH 6, at which proton-binding competition can hamper interaction with the total number of COOH and COOH + OH functional groups. Previous studies have shown that full dissociation takes place at higher pHs, even at alkaline conditions in case of OH groups [51,52]. On the other hand, the f parameter displayed negative correlations in the α, β and γ areas with E4/E6, E254/E436, and ∆logK. A number of these significant correlations with the f-parameters was higher in PARAFAC and NMF data than with parameters estimated from RAW data. The negative direction of the these relationships confirmed a high affinity of Zn ions to HAs characterized by high humification, molecular weight, aromaticity and great content of unsaturated structures, which was also reported by Plaza et al. [16].
The stability of HA-Zn(II) complexes was determined by the nitrogen content, which was confirmed by positive correlations of logK with N for structures at α sites of RAW data, as well as at α and β binding sites in the PARAFAC data (Table 3, data with asterisks). These results can be explained by strong electron donor properties of nitrogen atom, stronger even than oxygen atoms [9,53]. Moreover, the presence of nitrogen in form of side chain functional groups including mainly moieties of amines, amides, amino sugars or peptides involved in linkages between the aromatic groups favors formation of chelates in which metal is built into the ring [53][54][55]. Such types of compounds reveal exceptionally high stability. This fact may justify statistical significance of the relationship with N and simultaneously its absence in relationship to content of COOH and COOH + OH. Above relationship between stability of complexes and nitrogen was also confirmed by positive correlations with N/C atomic ratio which can be considered as the relative abundance of N. Directions and values of R-coefficients were similar to R values of correlations with nitrogen however one more statistically significant correlation was found for the NMF data in case of N/C ratio. The stability constants of HA-Zn(II) complexes of γ structures significantly increased with the decrease in E4/E6 and E254/E436 ratios, which indicated formation of the strongest bindings with the highly humified structures of high molecular weight, rich in unsaturated bonds and linearly-condensed aromatic rings. However, it should be noted that these correlations were not found in evaluation of the data from PARAFAC and NMF processing. Plaza et al. [15] reported that logK was negatively correlated with the content of COOH and total number of COOH and OH groups in case of interaction with copper. Lack of this dependency in our studies may suggest a high selectivity of complexation process by HA. Stability of the complexes of ω structures did not show significant relationships with any analyzed chemical properties of HAs, probably due to fact of low importance of these structures in Zn binding.

Conclusions
To summarize, results obtained in these studies showed that EEM fluorescence matrices combined with PARAFAC or NMF processing as well as with data modeling can be considered a promising approach to provide better insight into the mechanisms of metal complexation by specific structural units of HAs.
Elaboration of RAW data enabled finding three and in some cases only two fluorescent peaks, which corresponded with binding sites of HAs. Maxima of the lowest intensities for the moderately and strongly humified structures of β and γ areas were in some samples invisible because of overlapping by neighboring stronger signals. The model was not applied in such cases and the binding parameters could not be estimated. Combination of EEM fluorescence analysis with one of the proposed decomposition methods, PARAFAC or NMF, enabled better separation of the overlapped binding sites and yielded more accurate calculations of the binding parameters. The results showed that PARAFAC and NMF processing worked even for low intensity data and allowed finding binding sites for β and γ areas, which was impossible in the analysis of a few RAW data sets. Both PARAFAC and NMF processing also enabled the observation of a new local maximum (ω), which was attributed to the very simple structures of the lowest humification and molecular weight with the chemical nature similar to derivatives of amino acids and other heterocyclic compounds. Data obtained using PARAFAC and NMF techniques fit very well with the applied complexing model at the γ and ω areas and slightly better for PARAFAC than NMF with the data from the α and β peaks.
Detection of fluorescence changes due to Zn addition demonstrated high sensitivity and this, in turn, provided the possibility for observation of influence of various HAs properties on the Zn complexation process. EEM combined with PARAFAC and NMF methods gave a higher number of statistically significant relationships of the above properties with binding parameters in comparison to RAW data, indicating better preparation of the data for further calculations. As a result, EEM-PARAFAC and EEM-NMF methods showed an increase in quenching degree of fluorescence under increasing concentrations of Zn ions with increase in humification, aromaticity, molecular weight and amount of unsaturated bonds of HAs. EEM-PARAFAC analysis revealed also that the most stable compounds were formed by the HAs containing the highest amounts of nitrogen, which was especially seen for the α and β binding sites. The content of COOH and COOH + OH functional groups did not significantly influence the binding parameters, mainly due to partial protonation of these groups and higher competition of metal cation with protons. The area designated as ω was not clearly affected by analyzed properties of HAs, probably due to its low importance in Zn(II) binding processes. In our opinion, decomposition of EEM spectra by PARAFAC or NMF can be recommended for modeling of complexation processes of weak intensity, where the changes of FI are slight or for processes that can be interfered with by the presence of other fluorophores. PARAFAC and NMF processing coupled with EEM spectra gave more reliable and adequate assessment of HA-Zn interactions as compared to RAW, mainly due to possibility of identifying and quantifying contributions of the each unique structural area associated with HAs.
Author Contributions: P.B. conceived and designed the experiments; P.B. performed the experiments; P.B. and P.M.P. analyzed the data; P.B. and Z.S. contributed reagents/materials/analysis tools; P.B. and P.M.P. wrote the paper.


Determination of trace uranium (VI) using its self-assembly with a tetradentate–monodentate ditopic ligand by resonance light scattering

ABSTRACT We describe here a resonance light scattering (RLS) method for uranium (VI) detection by using phosphorylethanol-amido-salophen (PAS) as optical probe. PAS is a tetradentate–monodentate ditopic ligand in which the tetradentate and monodentate ligands are salophen moiety and phosphate group, respectively. PAS can chelate uranyl with its salophen moiety. The chelated uranyl can connect phosphate group in another PAS through coordination reaction. This causes the self-assembly of PAS with uranyl to form a metallo-supramolecular polymer, resulting in a production of strong RLS signal. The RLS method was established based on the self-assemble. The RLS intensity is linearly related to the concentration of uranium (VI) in the 0.8–32 ng mL−1 range, with a detection limit of 0.24 ng mL−1 detection limit under optimal conditions. The method was successfully applied to determine uranium (VI) in environmental water samples with the recoveries between 97.1% and 102.6%.

Introduction
Uranium is the most important source in nuclear energy generation. Identification and isolation of uranium from various resources are of great significance due to the worldwide demand. Uranium is also a highly toxic metal element with the severe damage to human health and environment. Therefore, it is of importance to determine uranium in water and environment. Several analytical methods have been applied to determine uranium, including gamma ray absorption [1], atomic emission spectrometry [2], inductively coupled plasma-mass spectrometry (ICP-MS) [3], neutron activation analysis [4], surface-enhanced Raman spectroscopy [5], fission track registration technique [6], fluorimetry/laser fluorimetry [7,8], cathodic stripping voltammetry [9] and kinetic phosphorescence [10]. However, these methods often are unsuitable for the routine analysis because they need high running cost with expensive equipments. Although spectrophotometry [11,12] is not costly, it often needs pre-concentration procedure for the determination of trace uranium. Therefore, it is significant to study new analytical methods for the routine determination of uranium.
Ditopic ligands are a type of important ligands. They can self-assemble with metal ions to form various metallo-supramolecular polymers (MSPs). MSPs have various and tunable properties and can be used in many fields by utilising these properties, such as they can be used to determine various target analytes by utilising their spectroscopic and electrochemical properties [13][14][15][16], and can be used to separate substances by utilising the self-assembly properties. Up to date, most of ditopic ligands used to assemble MSPs contain two same ligands. The two same ligands usually are tridentate ligands or bidentate ligands since the coordination numbers of metal ion usually are six or four. The ditopic ligands containing two different ligands also can be used to assemble MSPs. However, the study on this type of ditopic ligands and the corresponding MSPs as well as their application have less been reported.
Resonance light scattering (RLS) methods are a type of spectroscopic analytical methods [17]. They are based on the assembly or aggregation of the molecules and/ or particles which result in the enlargement of particle size. The assembly and aggregation reactions include the self-assembly of ions [18][19][20][21], the aggregation of nanoparticles [22][23][24][25], the combination of antigens with antibodies [26], and the binding of small molecules with DNA and proteins [27][28][29][30]. RLS methods have the advantages of simplicity, rapidness and high sensitivity, and have been used to determine various target analytes, including ions [19,20,24], organic and biological molecules [18,[21][22][23], medicines [27][28][29][30], as well as antigens and antibodies [25,26]. The self-assembly of ditopic ligands with metal ions to form MSPs also causes the enlargement of particle size and can result in an enhanced RLS signal. Therefore, a type of RLS analytical methods can be developed based on this self-assembly.
Uranyl ion is a linear cation. It can react with ligands to form planar complexes with typical coordination number of five. Salophen and its derivatives are Schiff base type tetradentate ligands. They can chelate uranyl to form stable uranyl-salophen complexes. In these complexes chelated uranyl leaves one site open for the coordination with another monodentate ligand. Previous studies have demonstrated that uranyl-salophen complex can bind monodentate ligand phosphate group with strong affinity and high selectivity to form stable phosphate-uranyl-salophen sandwich-type structure [31,32]. Hence uranium has been separated and determined by utilising the formation of the sandwich-type structure [33,34].
In recent years, based on the formation of phosphate-uranyl-salophen sandwichtype structure and the further formation of MSPs, a series of RLS methods for the determination of uranium, fluoride, ATP and fructose 1,6-bisphosphate have been developed [35][36][37][38]. These RLS methods have the advantages of high sensitivity, good selectivity and low cost. However, these RLS methods need two different ditopic ligands or a tritopic ligand for the formation of MSP, which results in the need of multi-step operations or a complicated reaction for the determination. Therefore, it is significative to develop new simpler RLS methods in which the formation of MSP needs only one ditopic ligand and one-step reaction for the determination of uranium and other target analytes.
Herein, we aimed to prepare a ditopic ligand that contains a tetradentate ligand and a monodentate ligand so as to assemble a MSP of uranyl for the determination of uranium by RLS method. The tetradentate and monodentate ligands are salophen moiety and phosphate group, respectively. This tetradentate-monodentate ditopic ligand is phosphorylethanol-amido-salophen (PAS). It can be synthesised by utilising the condensation reaction of carboxylated salophen with phosphorylethanolamine. We anticipated that PAS can self-assemble with uranium (VI) or uranyl cation to form a MSP of uranium (VI), resulting in a production of strong RLS signal. Thus, a new RLS method for the direct determination of uranium (VI) can be established. The method should have the advantages of simple operation and high sensitivity because it uses only one ditopic ligand and one-step operation for the formation of MSP, and RLS methods are highly sensitive.
The standard stock solution of uranium (10.00 mg mL −1 ) was prepared by dissolving 2.123 g uranyl nitrate hexahydrate into water with the total volume of 100 mL. The concentration of the standard stock solution was verified by Davies and Gray method using iron (II) sulphate as reductant and potassium dichromate as titrant [39]. The working standard solutions were prepared by diluting the standard stock solution with water.
RLS spectra were recorded with a Hitachi F-4500 spectrofluorometer.

Synthesis of carboxylated salophen
Carboxylated salophen was synthesised and characterised following literature procedure [40]. Briefly, 2.28 g of 3,4-diaminobenzoic acid and 3.66 g of salicylaldehyde were dissolved in 75 mL of anhydrous ethanol. The mixture was stirred for 90 min under reflux, then cooled to room temperature. The solid mass was filtered, and the product, N, N-bis (salicylidene)-4-carboxy-o-phenylenediamine (carboxylated salophen), was recrystallised from ethanol.  Figure S1 in Supplementary Material). For ESI-MS, m/z = 482 (M-H + ). The UV absorption spectrum of PAS in water shows that the strong absorption bands are at 216 nm, 250 nm and 327 nm, respectively (see Figure S2 in Supplementary Material).

Procedure of uranium detection
One millilitre of 10.0 μmol L −1 PAS solution and 1.0 mL of pH 7.0 Tris-HCl buffer were added into a 10 mL volumetric flask. Then 5.0 mL of uranium (VI) calibration solution or sample solution and 2 mL of 5.0 mmol L −1 diethylentriamine penta-acetic acid (DTPA) was added. The total solution volume was fixed at 10 mL with water. The solution was mixed thoroughly and was then incubated at room temperature for 25 min. After that, the RLS spectra of the solution were recorded on the spectrofluorometer. A calibration curve of the RLS intensity versus uranium (VI) concentration was plotted. The procedure of detecting uranium is also illustrated in Figure 1. 3. Results and discussion 3.1. RLS spectral characteristics Figure 2 shows the RLS spectra of 1.0 μmol L −1 PAS solution in the presence of different concentrations of uranium (VI). It can be seen that the RLS intensity of PAS solution is weak in the absence of uranium. The RLS intensity of uranium (VI) solution is also weak in the absence of PAS. When uranium coexists with PAS, there is a distinct enhancement in the RLS intensity, which indicates that a molecular self-assembly reaction has occurred. PAS is a tetradentate-monodentate ditopic ligand. When a uranyl ion is chelated by the tetradentate ligand salophen moiety in a PAS molecule, the chelated uranyl can combine further a monodentate ligand phosphate group in another PAS molecule. Thus, the self-assembled reaction of PAS with uranyl to form MSP can occur through the coordination reaction of uranyl with salophen moiety and phosphate group, resulting in the production of strong RLS signal. The maximum scattering wavelength in the RLS spectra is at 368 nm. We found that at this wavelength, there is a linear relationship between the enhanced RLS intensity and the uranium concentration under a certain condition. Therefore, a RLS method for the determination of uranium (VI) can be developed by using the self-assembled reaction of PAS with uranyl to form MSP. Thus, the RLS intensity at 368 nm was selected for the determination of uranium.

Optimisation of reaction conditions
This RLS assay for uranium (VI) is based on the enhancement in the RLS intensity caused by the self-assembled reaction of PAS with uranyl. The main factors influencing the selfassembled reaction are PAS concentration, media pH, reaction time and temperature. To make this method reproducible and highly stable, we have investigated the effect of these parameters. The effect of PAS concentration on the RLS intensity was investigated by using 24 ng mL −1 of uranium (VI) at pH 7.0 for the test. The results shown in Figure 3 demonstrate that in the absence of uranium (VI), the RLS intensity of PAS solution is very low and hardly change with the increase of PAS concentration. While in the presence of uranium (VI), the enhanced RLS intensity is dependent on the concentration of PAS. When PAS concentration is less 0.3 nmol mL −1 , the RLS intensity of the solution is low and becomes stronger gradually with the increase of PAS concentration. When PAS concentration is higher than 0.3 nmol mL −1 , the RLS intensity keeps constant and reaches the maximum, indicating that uranium (VI) has reacted completely with PAS. Thus, 1.0 nmol mL −1 of PAS was selected for the determination experiment.
The effect of media acidity or pH was investigated by using 24 ng mL −1 of uranium (VI) and 1.0 nmol mL −1 of PAS for the test. The results are shown as an inset in Figure 3. It can be seen that in the presence of uranium (VI), the RLS intensity of PAS solution increases at first and then decreases with the increase of pH, and reaches maximum in the pH range of 6.5-7.5. The results indicate that the self-assembly reaction needs to be carried out in a neutral solution. The reason maybe that in acidic solution, the phosphate group and salophen moiety in PAS are protonated, resulting in the reduction of their binding affinity to uranyl. While in basic solution, the binding affinity of uranyl to phosphate group and salophen moiety in PAS is also reduced due to the combination of uranyl with hydroxyl ion. Thus, we used Tris-HCl as buffer to control the solution acidity at pH 7.0 for the self-assembly reaction.
The effect of reaction time shown in Figure 4 demonstrates that when the reaction time is more than 20 min, the RLS intensity reaches the maximum and keeps constant. Thus, the selected reaction time was 25 min. The effect of reaction temperature shown as an inset in Figure 4 demonstrate that in the temperature range of 20-30°C, the RLS intensity reaches the maximum. Thus, the selected reaction temperature was room temperature 25°C.

Analytical parameters for the determination of uranium (VI)
Under optimal conditions the analytical figures of merit for the determination of uranium (VI) was tested with different amounts of uranium (VI) according to the general procedure. The calibration curve demonstrates that there is a good linear relationship between RLS intensity (I RLS ) and uranium (VI) concentration (c) in the range of 0.8-32.0 ng mL −1 . The linear regression equation is I RLS = 13.6 c (ng mL −1 ) +19.4 with a correlation coefficient of r 2 = 0.9984. The detection limit of the method was determined to be 0.24 ng mL −1 calculated from three times the standard deviation through 11 parallel blank tests. The relative standard deviation of six parallel determinations for 2.0 and 32.0 ng mL −1 uranium (VI) were 2.7% and 2.2%, respectively. Table 1 shows the comparison of the analytical linear range and detection limit of our method with that of other available methods used for the determination of uranium in aqueous solution. It can be seen that the detection limit of our method is lower than that of arsenazo-III spectrophotometry. The analytical linear range and detection limit of our method are approach that of laser fluorimetry and cathodic stripping voltammetry. Although the analytical range and detection limit of kinetic phosphorescence are wider and lower than that of our method, this method demands strict conditions for the determination.

Influences of coexistent ions
The effect of several coexistent ions on the determination of 4 ng mL −1 uranium (VI) was investigated. The effect of each ion was examined individually by adding a relatively high concentration of this ion into the uranium (VI) solution. When the error is less than 5%, it can be considered that there is no interference in the determination.

Analysis of real samples
In order to test the validation of this method for real samples, we collected three uranium slag heap drainages, two river water samples and two distilled water samples for the analysis. Each uranium slag heap drainage was diluted with water to a 100 times dilution sample and was then analysed by this method. The river water samples and distilled water samples were analysed directly analysed by this method. The recovery experiment of adding standard uranium (VI) concentrations was carried out for evaluating the applicability and reliability of this method. The samples were also analysed with the control experiment of ICP-MS method for comparison. All results are summarised in Table 2. It can be observed that the recoveries vary from 97.1% to 102.6%. It also can be observed that the analytical results obtained from our method show good agreement with that obtained from ICP-MS method. These results demonstrate that the new method developed in this study can be successfully applied to real samples. 8.04 ± 0.15 100.5 a Samples 1, 2 and 3 are 100 times dilution samples of uranium slag heap drainages. Samples 4 and 5 are river water samples. Samples 6 and 7 are distilled water samples. b Mean ± SD, were mean is mean value of six measurements, SD is standard deviation.

Conclusions
In this study, we synthesised tetradentate-monodentate ditopic ligand PAS and developed a new RLS method for the determination of uranium (VI) by utilising the selfassembly reaction of PAS with uranium (VI) to form MSP. The method is simple and convenient with only one operation step. The RLS method based on the self-assembly reaction using only one ditopic ligand and only one operation step may open new strategy for the determination of targets.


s2fieldsofstudy: Chemistry Physics

text:
Orbital-selective single molecule excitation and spectroscopy based on plasmon-exciton coupling

The electronic excitation of molecules triggers diverse phenomena such as luminescence and photovoltaic effects, which are the bases of various energy-converting devices. Understanding and control of the excitations at the single-molecule level are long standing targets, however, they have been hampered by the limited spatial resolution in optical probing techniques. Here we investigate the electronic excitation of a single molecule with sub-molecular precision using a localised plasmon at the tip apex of a scanning tunnelling microscope (STM) as an excitation probe. Coherent energy transfer between the plasmon and molecular excitons is discovered when the plasmon is located in the proximity of isolated molecules, which is corroborated by a theoretical analysis. The polarised plasmonic field enables selective excitation of an electronic transition between anisotropic frontier molecular orbitals. Our findings have established the foundation of a novel single-molecule spectroscopy with STM, providing an integrated platform for real-space investigation of localised excited states.

SUMMARY PARAGRAPH:
The electronic excitation of molecules triggers diverse phenomena such as luminescence and photovoltaic effects, which are the bases of various energy-converting devices. Understanding and control of the excitations at the single-molecule level are long standing targets [1][2][3][4] , however, they have been hampered by the limited spatial resolution in optical probing techniques. Here we investigate the electronic excitation of a single molecule with sub-molecular precision using a localised plasmon at the tip apex of a scanning tunnelling microscope (STM) 5 as an excitation probe. Coherent energy transfer between the plasmon and molecular excitons 2,6-8 is discovered when the plasmon is located in the proximity of isolated molecules, which is corroborated by a theoretical analysis. The polarised plasmonic field enables selective excitation of an electronic transition between anisotropic frontier molecular orbitals. Our findings have established the foundation of a novel single-molecule spectroscopy with STM, providing an integrated platform for realspace investigation of localised excited states.
Single-molecule spectroscopy employing luminescence and Raman scattering has been established [9][10][11][12] and become indispensable in various research fields such as quantum physics, physical chemistry, and biophysics. The single-molecule sensitivity in luminescence and Raman spectroscopies relies on the fact that these processes involve energy conversions, so the spectroscopic signals can be separated from the excitation source. This is not the case for absorption spectroscopy [1][2][3][4] which is the primary technique to directly investigate the excitation process. Because absorbance is measured as attenuation of the incident light at a given frequency, the absorption signal competes with the huge shot-noise of the incident photons 13 .
This signal isolation problem and the limited spatial resolution in absorption spectroscopy makes it particularly difficult to investigate the excitations at the single molecule level.
In contrast to the conventional techniques using external light sources, scanning tunnelling luminescence (STL) spectroscopy, where luminescence is induced by the atomically localised tunnelling current of STM, provides a unique way to investigate local optical properties of matters 5,12,[14][15][16][17][18][19] . A previous STL study reports that the energy of the localised plasmon in the tunnelling junction of an STM is absorbed by molecules located close to the STM tip 20 . Although the number of molecules interacting with the plasmon was not determined in the study, the pioneering work showed that the near-field excitation of molecules is possible in the STM, opening up an opportunity for revealing the molecular excitations with an unprecedented precision. Figure 1a illustrates the design of the experiment to investigate the detail of near-field interaction between the localised plasmon and molecular excitons. The tunnelling current of the STM excites the localised plasmon which then interacts with the molecule through the plasmon-exciton coupling, and the photons emitted from this coupled system are detected. The strength of the plasmon-exciton coupling is finely tuned by changing the lateral distance between the molecule and the location of the localised plasmon with the angstrom precision. Figure 1b shows a topographic STM image of the sample. Since the electronic decoupling of a molecule from a metallic substrate is necessary to identify the intrinsic optical properties of the molecule 11 , free-base phthalocyanine (H2Pc) was deposited on an ultrathin NaCl(100) film 21 grown on Ag(111) (results of scanning tunnelling spectroscopy measurement are shown in Supplementary Fig. 1). We define the coordinates around the molecule as shown in Fig. 1c.
A series of luminescence spectra induced by the tunnelling current were obtained near an H2Pc/NaCl as a function of the lateral distance of the STM tip from the molecular centre (Fig. 1d). When the tip is placed far from the molecule ( ≥ 4 nm, # 1, 2), the luminescence spectrum is dominated by a broadband emission, which is attributed to the radiative decay of the localised plasmon 5 . Remarkably, dip structures emerge at 1.81 and 1.92 eV in the broad spectrum when the tip is positioned close to the molecule (r = 1.4-3 nm, # 3-11), and the spectral features becomes prominent as the tip is closer to the molecule. When the STM tip reaches at the edge of the molecule where direct excitation of the molecule by carrier injection turns into possible, intensive molecular luminescence is observed (Fig. 1e). The luminescence peaks at 1.81 and 1.92 eV are attributed to transitions from the first and second singlet excited states of H2Pc, so-called the Qx and the Qy states 22-25 , respectively (detailed peak assignment is given in Supplementary Fig. 3). Figure 2a shows two representative STL spectra measured with tip positions far from and close to the molecule. We define the STL spectrum measured with the tip located far from the molecule as the excitation source spectrum I0, and that measured close to the molecule as I(r,θ). As shown in Fig. 2b, the ratio spectrum I/I0 clearly reveals the change in the spectral shape resulting from the plasmon-exciton coupling.
The larger dip at 1.81 eV has an asymmetric feature, and the smaller dip at 1.92 eV has a more complex shape.
The origin of the dip structures is investigated based on the theory of STL using the nonequilibrium Green's function method 7,8 . Figure 2c shows calculated STL spectra with the plasmon-exciton coupling ℏg of 0 and 10 meV, and Fig. 2d displays the I/I0 spectrum. When ℏg = 10 meV, the energy of localised plasmons is absorbed by the electronic transitions of the molecule through the plasmon-exciton coupling, which leads to the dip structures at 1.81 and 1.92 eV. The asymmetric spectral profile is explained by a quantum mechanical interference effect 2,6-8 . The energy of localised plasmons is absorbed by the molecule, and then the energy of the excited molecule is re-emitted into localised plasmons. These processes interfere with each other, and the constructive and destructive interference of these processes leads to enhancement and suppression of the energy transfer, resulting in asymmetric spectral shapes 7,8 . These dynamic processes in the coupled plasmon-exciton system are schematically summarised in Fig. 2e. Figure 3a shows the θ dependence of the excitation I/I0 signal (θ is defined in Fig. 1c). When the STM tip is on the x-axis (θ = 0º), the spectrum only shows the Qx dip at 1.81 eV and a small dip at 1.90 eV (indicated by an arrow). This is reminiscent of a typical absorption spectrum having a mirror symmetry with the corresponding luminescence spectrum 24 . Indeed, the small dip at 1.90 eV can be attributed to the transition from the ground state to a vibrationally excited state of the Qx state, because the dip is located at the symmetric position about the band origin of the Qx state (1.81 eV) with the small vibronic peak at 1.72 eV observed in the electroluminescence spectrum (Fig. 1e). When θ = 90º, the Qx dips disappear and the spectrum displays only the Qy dips around 1.92 eV with a rather complicated dip structure. The congested spectral feature has been explained by state-mixing between the Qy state and vibrationally excited Qx state [22][23][24] . If the tip is placed between the xand y-axes (θ = 45º), both the Qx and Qy dips appear. transition is the major component of the second (first) singlet excited state, inversely 25 . This remarkable assignment is fully consistent with our results. As shown in Fig. 3a, the second singlet excited state (the Qy state) is exclusively detected when the direction of ∥ ⃗⃗⃗⃗ ( ) is aligned with the y-axis of H2Pc (θ = 90º), in which only the electric dipole transition between the HOMO and LUMO is allowed by the selection rule. In addition, the HOMO−LUMO transition in the x-direction is prohibited by the selection rule. This is because both MOs have the same (odd) parity in x (Fig. 3b), and the Qy state is never detected when ∥ ⃗⃗⃗⃗ ( ) is aligned with the x-axis (θ = 0º).
We note that the I/I0 spectrum reproduces the following features seen in the typical absorption spectrum of H2Pc 21,23,29,30 : the signal at 1.81 eV (Qx) is stronger than that at 1.92 eV (Qy), and the energy separation of 110 meV between the two dips agrees with the reported value (106-126 meV which varies depending on the environment surrounding H2Pc) 24 measured at low temperature with the matrix isolation method.
Therefore, it is concluded that the I/I0 spectrum allows us to measure the excitation or absorption characteristics of a single molecule with a molecular scale (~2 nm) spatial resolution.
One important requirement for a spectroscopy is the capability to differentiate molecules. Figure 4a shows an STM image, where H2Pc and magnesium phthalocyanine (MgPc) are co-deposited on a 3ML-NaCl film on Ag(111). The adsorption structures of MgPc and H2Pc on the NaCl film were previously investigated and reported elsewhere 27 . I spectra of MgPc and H2Pc as well as an I0 spectrum on 3ML-NaCl were measured using the same STM tip (Fig. 4b), and analysed to provide the I/I0 spectra (upper curves in Fig. 4c and 4d). The I/I0 spectra of MgPc shows only one doubly-degenerate molecular resonance at 1.89 eV (Q state), which is between the Qx (1.81 eV) and Qy (1.92 eV) states of H2Pc. This observation is consistent with the four-fold molecular symmetry and the previously results of conventional spectroscopy 28 . The apparently symmetric dip structure in the I/I0 spectrum of MgPc is reasonable in the coupled plasmonexciton system 2,6-8 where the interference condition depends on the relative energy of the plasmon and exciton 6 .
The STL spectra measured on the molecules are also presented in Fig. 4c and 4d (lower curves). While the I/I0 spectra of the two molecules have similar signal intensities, the intensity of STL fluorescence of MgPc is surprisingly weak; the integrated photon intensity of the Q fluorescence peak of MgPc is almost one-order weaker than that of Qx fluorescence peak of H2Pc. The similar intensities in the I/I0 spectra are straightforward to understand. Since the Q state of MgPc and the Qx state H2Pc have similar magnitudes of transition dipole moment ⃗ 29 , the strengths of the plasmon-exciton coupling ⃗ • ⃗⃗ which dominate the I/I0 spectrum should also be similar. In contrast, precise explanation for the very different intensities in STL fluorescence is not an easy task. This is because the fluorescence intensity is determined by several factors including the probability of creating an exciton by a tunnelling electron, and the rates of fluorescence and competing non-radiative processes. Thus, it can be concluded that I/I0 spectrum provides fundamental information about the molecular excitations and STL fluorescence spectrum reflects the complicated energy and charge dynamics in the excited states.
We have revealed the details of plasmon-exciton coupling and demonstrated the direct analysis of singlemolecule excitation. As shown in Supplementary Fig. 4, the energy of the localised plasmon is tunable from the near-infrared to the visible range, thus our method is expected to be widely applicable to various molecules, clusters, and local defects, even including non-luminescent objects. More importantly, the developed technique in combination with STL has established the foundation of an absorption/emission spectroscopy with the unprecedented sensitivity and spatial resolution, which will certainly expand our Preparation of the sample and the tip.
The Ag(111) surface was cleaned by repeated cycles of Ar + ion sputtering and annealing. The deposition of NaCl was performed using a home-made evaporator heated to 850 K onto Ag(111) held at room temperature. H2Pc and MgPc were deposited onto the NaCl-covered Ag(111) at 4.7-10 K cooled in the STM head using a commercial three-cell evaporator (Kentax) heated to 575 K for H2Pc and 625 K for MgPc.
The STM tips were prepared by electrochemical etching of a silver wire and conditioned by controlledindentation and voltage pulse on the Ag(111) surface.

STL measurement.
The STM stage was designed to be equipped with two optical lenses (each covered a solid angle of about 0.5 sr). The emitted light was collimated with the lens and directed out of the UHV chamber, where it was refocused onto a grating spectrometer (Acton, SpectraPro 2300i) with a charge-coupled-device photon detector (Princeton, Spec10) cooled with liquid nitrogen. All the optical spectra (except for figures in Supplementary Information) were measured using a grating with 300 gr/mm, and the spectral resolution of the optical system was better than 1 nm, which corresponds to an energy resolution better than 0.003 eV at 1.80 eV. The peak energies presented in this paper are rounded to two decimal places. The STL spectra are not corrected for the optical throughput of the detection system.

Theoretical calculations.
We


s2fieldsofstudy:
Chemistry
Materials Science

text:
A study on reduction processes of elements in the system V2O5-Si

The calculation of parameters of elements reduction in the system V2O5-C-Si was made at temperatures of metallurgical processes by the method of thermodynamic simulation. Dependences of vanadium reduction from its oxides with carbon and silicon oxides separately with each reducing agent, as well as in combination, on the temperature and reducing agents consumption were considered. The obtained results led to the conclusion that the vanadium reduction from vanadium pentoxide in combination with carbon and silicon takes place with the predominant formation of vanadium compounds: vanadium carbide and vanadium silicides, the main reductant is carbon.

Introduction
Currently, the actual problem is a complex usage of primary and secondary raw materials in the iron and steel industry. Extraction of components -valuable alloying additives from such materials can improve the production efficiency and at the same time the products quality. Among the most needed alloying elements, the introduction of which can significantly increase the metal performance properties, is vanadium [1][2][3]. The basic alloying material in the manufacture of vanadium-containing steels is high-priced ferrovanadium. For the further expansion of production and competitiveness assurance of vanadium-containing steels the alloying method, based on the metal processing by oxide vanadium-containing materials including a converter vanadium slag, has a special importance, while ensuring the conditions for vanadium reduction from these materials.
Currently, aluminum, silicon, calcium of high value are used as reducing agents. In this regard, the development of steel processing technology by converter vanadium slag with application of silicon and carbon as reducing agents is an urgent task. Low value of carbon application would significantly reduce the cost of steel products. However, to determine the optimal parameters for carbon-silicon thermal reduction of vanadium from converter vanadium slag the comprehensive examination of processes, including reduction of vanadium pentoxide with carbon and silicon, should be performed. The aim of this study was to consider the processes taking place during vanadium reduction with carbon and silicon, as well as vanadium pentoxide reduction with each reducing agent separately and in combination. Currently, thermodynamic simulation is widely used to study elements reduction from the oxide systems [4][5][6]. The problem solution targeting determination of conditions for vanadium reduction in the system V 2 O 5 -nС -mSi was performed with the use of methods of thermodynamic modeling based on the equilibrium conditions calculation in the model thermodynamic systems. While implementing the thermodynamic simulation, a ready software complex "Terra", developed in Moscow State Technical University, was used. On the basis of maximum entropy principle it finds the equilibrium composition of a multicomponent heterogeneous thermodynamic system for high temperature conditions [7].

Research and results
The process research was carried out by solving model problems for determination of the conditions for vanadium reduction in the systems, the input flow of which consists of a combination of elements V-O-C-Si, represented by a group of substances V 2 O 5 -nС -mSi, where n and m -mass of carbon and silicon per 1 kg of vanadium pentoxide. The initial composition of the system was formed by specific values of the parameters n, m.
At the first stage of calculations the possible compositions and the boundaries of concentration areas of reduction processes flow were identified, as well as the temperature influence on these parameters. The list of substances, that can be formed from the given elemental composition of the mixture for temperature range from 1573 to 2273 K, were determined by numerical simulation using the software package "Terra". Thermodynamically the possible quantity of substances, generated from the indicated elements for a selected temperature range, was approximately 20. All concentration values of the substances in the final state were divided into significant and insignificant with a difference threshold 10-4 mol/kg of the mixture. The significant substances were the condensed phase consisting of С, V, VC, VO, V 2 O 4 , V 2 O 3 , V 2 O 5 , Si, SiO 2 , SiC and vanadium silicides and a gas phase consisting of CO, CO 2 , SiO.
To investigate the temperature influence on vanadium reduction process in the system V 2 O 5 -С -Si the calculations of equilibrium states at temperatures from 1673 K to 2273 K were made. The minimum and maximum temperatures were conditioned by the temperature values characteristic to the out-of-furnace steel treatment, and vanadium melting point 2173 K. The calculation results are presented in Figure 1.
Analysis of the results showed that the vanadium reduction process from its oxides does not dependent on the temperature in the range from 1673 to 2073K. The total mass of vanadium oxides in the reaction products at a temperature below 2073 K goes to zero during the increase in the carbon consumption from 0 to 0.5 kg/kg V 2 O 5 , during increase of silicon consumption from 0 to 0.7 kg/kg V 2 O 5 . The vanadium reduction process from vanadium pentoxide in the system V 2 O 5 -C ends at a specific carbon consumption 0.5 kg/kg V 2 O 5 , and the system V 2 O 5 -Si -at a specific silicon consumption 0.7 kg/kg V 2 O 5 .
Condensed and gas phases were selected for a better study of the vanadium reduction in the process products. The analysis of these phases was performed.
The composition of the condensed phase comprises vanadium oxides, carbide and vanadium silicides, silicon carbide, silicon dioxides, metallic vanadium, carbon and silicon. The gas phase, formed during the vanadium oxides reduction, consists of reaction products of vanadium oxides reduction with carbon and silicon (CO, CO 2 , SiO) and dissociation product of vanadium oxides -O 2 .
Results of thermodynamic calculations for the system V 2 O 5 -С -Si are shown in Figures 2 and 3. From these dependences it follows that the mass of the condensed phase ( Figure 2a) increases with the increase of silicon consumption and decreases with the increase of carbon consumption. For the gas phase ( Figure 2b) the relationship is reverse.
As can be seen from the curves in Figure 3 the basic component of the gas phase is carbon monoxide. Its mass increases with the increase of carbon consumption and decreases with the increase of silicon consumption. SiO mass increases with the increase of carbon consumption, while at the increase of silicon consumption at first goes up (at a specific silicon consumption not more than 0.3 kg/kg V 2 O 5 ) and then decreases. CO 2 mass does not exceed 0.00003 kg, O 2 mass does not exceed 0.03 kg with the reducing agents mass is zero, further in the gas phase it is present in the form of tracks.  From the data obtained it can be concluded that in the system V 2 O 5 -С -Si system the direct reduction of vanadium pentoxide with carbon takes place. In addition, carbon reduces the formed silica.
The calculation results of reduction products masses for the system V 2 O 5 -С -Si given in Figures 4, 5 and 6, showed that vanadium, reduced from the vanadium pentoxide during carbon-silicon thermal reduction, is mainly found in the form of vanadium carbide and vanadium silicides.
The results of thermodynamic calculations of the vanadium coreduction with carbon and silicon for the system V 2 O 5 -С -Si shows that vanadium reduction from vanadium pentoxide is initially occurs with formation of vanadium carbide (Figure 4), and further as the silicon consumption increases more than 0.3 kg / kg V 2 O 5 , vanadium silicides VSi 2 , V 5 Si 3 and V 3 Si ( Figure 5) are also formed.
The mass of the metallic vanadium according to the calculated data is insignificant and does not exceed 8% of the reduced vanadium mass. With the increase in the specific consumption of silicon this value decreases due to the formation of vanadium silicides ( Figure 6).
Thermodynamic modeling showed that carbon is a predominant reducing agent during carbonsilicon thermal reduction of vanadium from pentoxide vanadium.  The performed thermodynamic calculations showed that in the examined system the reduction products contain silicon carbide formed from SiO 2 in the reaction: SiO 2 + 3С = SiС + 2СO.