# A Fast and Robust Third-Order Multivariate Calibration Approach Coupled with Excitation–Emission Matrix Phosphorescence for the Quantification and Oxidation Kinetic Study of Fluorene in Wastewater Samples

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−1}and 45.5 min for free-interference water and 0.017 min

^{−1}and 40.0 min for wastewater, respectively. Research results show that SWAQLD coupled with EEMP allows the quantification and kinetic monitoring of FLU in analytical conditions of different complexities with excellent robustness to the choice of the number of model components.

## 1. Introduction

^{2}-DAD) [19], and two-dimensional liquid/gas chromatography–mass spectrometry (LC

^{2}/GC

^{2}-MS) [20]. Various research works clearly show that modeling third-order data using third-order multivariate calibration methods can achieve a more accurate quantification, but this is without taking into account the sometimes-difficult choice of the number of factors to consider in the model [1,7,10,20]. The evaluation of the chemical rank of the model in these approaches is, therefore, crucial. It is in this sense that we propose, in this work, an algorithm that is potentially faster and more robust to the choice of the number of factors to consider for qualification.

## 2. Theory of Third-Order Multivariate Calibrations

#### 2.1. The Quadrilinear Model

**N**-way data array

**X**n, each element x

_{ijklm…}it contains can be expressed in a general way, as follows, given a number of factors F:

**N**= 4, each element of the four-way data array can be represented in the following form,

_{if}, b

_{jf}, c

_{kf}, and d

_{lf}are the elements of excitation spectrum matrices

**A**(sized I × F), elements of emission spectrum matrices

**B**(sized J × F), elements of the kinetic matrices

**C**(sized K × F), and elements of the sample matrices

**D**(sized L × F), respectively. Regarding e

_{ijkl}, they are elements of the residual four-way data array

**E**q (sized I × J × K × L) with the following equation:

**X**

_{L×IJK}is the stretched matrix of four-way data array

**X**q along the lth direction; and

**A**

^{(m)},

**B**

^{(m)},

**C**

^{(m)}, and

**D**

^{(m)}are the mth updated matrices of

**A**,

**B**,

**C,**and

**D**, respectively. In the following sections, we introduce the algorithms that allow us to do this type of decomposition.

#### 2.2. The Four-way PARAFAC Algorithm

**Z**

^{+}denotes the Moore–Penrose generalized inverse of a matrix

**Z**, and the sign ‘⊙’ corresponds to the Khatri–Rao product.

#### 2.3. The AQLD Algorithm

#### 2.4. SWAQLD, the Proposed Algorithm

**D,**with

**A**,

**B,**and

**C**being fixed; minimizes σ(i) to obtain

**A,**with

**B**,

**C,**and

**D**being fixed; minimizes σ(j) to obtain

**B,**with

**C**,

**D,**and

**A**being fixed; and minimizes σ(k) to obtain

**C,**with

**D**,

**A,**and

**B**being fixed. We have, thus,

**X**..

_{i},

**X**..

_{j},

**X**..

_{k}, and

**X**..

_{l}are slices of the pseudo-fully stretched three-way data array

**X**

_{J×KL×I},

**X**

_{K×LI×J},

**X**

_{L×IJ×K}and

**X**

_{I×JK×L}with the ith, jth, kth, and lth directions being respectively fixed. An iterative process for the SWAQLD algorithm is, therefore, defined by the following steps:

- (1)
- Estimation of chemical ranks for the considered four-way data set;
- (2)
- Random initialization of matrices
**A**,**B,**and**C**; - (3)
- Matrix
**D**calculation applying Equation (24); - (4)
- Matrix
**A**calculation applying Equation (25) and then scaling it to be column-wise normalized; - (5)
- Matrix
**B**calculation applying Equation (26) and then scaling it to be column-wise normalized; - (6)
- Matrix
**C**calculation applying Equation (27) and then scaling it to be column-wise normalized; - (7)
- Update the
**D**matrix applying Equation (24); - (8)
- Update matrices
**A**,**B**, and**C**according to steps (4) to (7) until the stopping criteria are reached (Equation (28)):

^{−6}. SWAQLD alternatively minimized four different objective functions related to the quadrilinear model, which not only has all the interesting properties of AQLD, such as fast convergence, insensitivity to excess factors, and second-order advantage, but can also improve the resolution ability for complex four-way data, which we demonstrate in the results. The MATLAB code for SWAQLD can be provided free of charge on request by email to the corresponding authors.

## 3. Material and Methods

#### 3.1. Generation of a Simulated Excitation (EX)–Emission (EM)–Kinetic Phosphorescence Data Array

**A**(:, 1),

**A**(:, 2), and

**A**(:, 3) were produced by the following equations:

**A**(i, 1) = gs(0.5, 14, 30, i) + gs(1, 32, 58, i);

**A**(i, 2) = gs(1, 18, 43, i) + gs(1, 16, 50, i);

**A**(i, 3) = gs(2, 40, 54, i) + gs(0.5, 20, 160, i);

_{0}, i) denotes the value at i of a Gaussian peak with the peak height of h and the peak width of w at the center of x

_{0}, i.e.,

**B**(j, 1) = gs(1, 12, 48, j) + gs(1, 20, 16, j) + gs(1, 31, 60, j);

**B**(j, 2) = gs(1, 6, 24, j) + gs(0.5, 40, 84, j);

**B**(j, 3) = gs(1, 52, 65, j) + gs(1, 40, 70, j);

**C**(k, 3) = gs(2.2, 18, 32, k) + gs(1, 16, 50, k);

_{1}= 0.10; and a

_{2}= 0.05. The concentration matrix of the 12 samples containing three contributions was randomly generated, as indicated below, using Matlab notations:

**D**(:, :)= rand(12, 3);

**D**(1:7, 3) = zeros(7, 1);

#### 3.2. Sample Preparation and EX–EM–Kinetic Data Arrays Acquisition

#### 3.2.1. Reagents and Chemicals

_{2}SO

_{3}compounds were purchased from Hunan Hui-hong Reagent Co. Ltd. (Changsha, China). Methanol (HPLC-grade, ≥99.9%) for analytical standards dissolution was obtained from Aladdin. Other solvents including ethanol, cyclohexane, acetone, acetonitrile, and n-hexane were provided by Hunan Hui-hong Reagent Co. Ltd. (Changsha, China).

#### 3.2.2. Sample Preparation

^{−1}was first prepared by dissolving the compound in methanol. A 2.0 mol.L

^{−1}KI solution and a 0.5 mol.L

^{−1}Na

_{2}SO

_{3}solution were prepared by dissolving the corresponding substances in ultrapure water. An 8.0% acetonitrile–aqueous solvent was also prepared using ultrapure water. The wastewater samples were immediately filtrated. All these solutions were stored at 4.0 °C.

^{−1}KI, 1.5 mL 0.5 mol L

^{−1}Na

_{2}SO

_{3}, 2.5 mL 8.0% acetonitrile–aqueous solvent, and appropriate quantities of FLU solution to reach the final concentrations of 1.52, 2.28, 3.04, and 3.80 μg.mL

^{−1}, respectively. The six validation samples were prepared in the same way to obtain the reference concentrations given in the leftmost column of Table 1. Then, a wastewater set, including four calibration samples and five wastewater samples (W01–W05), was prepared in the same way as the free-interference water set, except that additional concentrated wastewater solutions were transferred into these five samples. The leftmost column of Table 2 provides the reference concentrations of FLU in these five wastewater samples. Three blank wastewater samples (i.e., not spiked with FLU) were also considered in order to estimate the limit of detection (LOD) and the limit of quantification (LOQ).

#### 3.2.3. Spectroscopic Acquisition

## 4. Results and Discussion

#### 4.1. Analysis of the Simulated Data Sets

**A**, 8.2 for

**B**, 12.3 for

**C,**and 3.0 for

**D**, respectively, indicating well-conditioned matrices [32]. Homoscedastic noise was first introduced into the simulated four-way data array, considering four noise levels of 0.02%, 0.2%, 2%, and 20%. The SWAQLD, PARAFAC, and AQLD algorithms were then applied to investigate their convergence behavior and their robustness to noise.

^{−6}, and a maximum number of iterations of 3000. It can be seen that SWAQLD has a faster convergence than PARAFAC, regardless of noise level. The mean iteration number and the mean calculation time of SWAQLD are 80 and 6.6 s, respectively, much less than those of PARAFAC (281 and 443.8 s, respectively). However, AQLD holds the fastest convergence in the simulated data, whose iteration number and computation time, on average, are only 6 and 0.6 s, respectively. Table 4 allows us to go further in this evaluation, as it presents correlation coefficients for the different modes, root mean square error of prediction (RMSEP) values of the two compounds, and predicted constant rate k for different noise levels when PARAFAC, AQLD, and SWAQLD are considered. Regarding the correlation coefficients, we observe excellent results for the three methods studied, and this is independent of the level of homoscedastic noise. When the noise level is small (i.e., lower than 0.2%), three or four factors can be used to fit the simulated data set by the three methods. All of correlation coefficients for four modes provided by three methods are identical to 1.0000, RMSEPs of two analytes are less than 0.0003, and predicted k values are larger than 0.0992 (the reference value of 0.1000). When the noise level is higher than 2%, four factors are necessary to decompose the simulated data by the three methods, according to the results of the core consistency diagnostic (CORCONDIA) [33] and alternating weighted quadrilinear decomposition incorporating Monte Carlo simulation (AWQLD-MCS) [34] (Supplementary Figure S1). If we look at the RMSEP values, we observe good results for the three algorithms when the noise level is as high as 2%. On the other hand, we notice a significant amplification of the error for the AQLD algorithm at 20% noise, where the PARAFAC and SWAQLD algorithms are relatively unaffected. Regarding the prediction of the constant rate k, we naturally find the same trends with large errors observed for the AQLD method at high noise levels, for example, as high as 20%. In parallel, we observe fairly stable prediction results for the PARAFAC and SWAQLD algorithms, although the latter presents slightly better ones. The same figures of merit have been evaluated, this time considering different levels of heteroscedastic noise for the three considered algorithms. As can be seen, the conclusions about the convergence behavior of the three methods are consistent with those of homoscedastic noise (Supplementary Table S1). However, heteroscedastic noise has no impact on the quality of the predictions, in general (Supplementary Table S2).

#### 4.2. Data Analysis of Real Data Sets

#### 4.2.1. Finding Optimal Experimental Conditions

_{2}SO

_{3}were used as heavy atom perturber and deoxygenator, respectively, for the phosphorescence measurement. Then, two suitable concentrations of KI (0.6 mol L

^{−1}) and Na

_{2}SO

_{3}(0.03 mol L

^{−1}) were obtained by investigating the effect of their concentrations on the FLU phosphorescence intensity at room temperature. The influence of organic solvents, such as ethanol, cyclohexane, acetone, acetonitrile, and n-hexane were also studied. Thus, it was found that a 0.8% acetonitrile–aqueous solvent could strengthen the phosphorescence intensity of FLU.

^{−1}), acetonitrile–aqueous solvent (0.8%), KI (0.6 mol L

^{−1}), and Na

_{2}SO

_{3}(0.03 mol L

^{−1}). It was found that a temperature of 40 °C could provide a gradually decreasing and measurable phosphorescence intensity of FLU in water systems within 120 min, which was quite satisfactory for our case.

#### 4.2.2. Global Analysis of the FLU Kinetic

_{2}SO

_{3}is added as a deoxygenator. Therefore, it could be deduced that FLU is very likely to be oxidized in the experimental condition. Figure 2 shows excitation–emission matrix phosphorescence (EEMP) plots of the calibration sample C4 with initial concentrations of 3.80 μg mL

^{−1}of FLU, 0.8% acetonitrile–aqueous solvent, 0.6 mol L

^{−1}KI, and 0.03 mol L

^{−1}Na

_{2}SO

_{3}acquired at five different times. It is, thus, easy to see that the intensity of the FLU phosphorescence gradually decreased with the duration of the reaction. The FLU phosphorescence decrease is very likely due to the oxidation of FLU to 9-fluorenone in water systems, and its product does not emit phosphorescence in the pH 10.6 mixed solution [38,39].

#### 4.2.3. Spectral Characteristics of Samples

#### 4.2.4. Analysis of FLU in Free-Interference Water Samples

^{−1}. However, we should not lose sight of the fact that these differences are very small. Therefore, it is difficult to say whether these three methods are statistically different when free-interference water samples are considered. Figure 4 also shows the oxidation kinetic profiles of FLU resolved (solid lines) by the three methods for the two considered ranks N = 3 and 4. As can be seen from the figure, the phosphorescence intensity of FLU decreases slowly and steadily, which is quite consistent. Considering that the FLU oxidation reaction follows a first-order kinetic model, its concentration follows the following equation as a function of time:

^{−1}for the three methods, respectively. Half-lives of FLU are 45.9, 45.0, and 46.2 min for the three methods, respectively. These values remain fairly stable for the SWAQLD and AQLD methods when the rank is overestimated, which are 0.0154 min

^{−1}for rate constant and 45.2 min for half-life, on average. Although the experimental conditions can be considered simple with these free-interference water samples, we can see that the SWAQLD and AQLD methods are the most robust to the choice of rank both in terms of FLU quantification and estimation of kinetic parameters.

#### 4.2.5. Analysis of FLU in Wastewater Samples

^{−1}for N = 3, are obtained for the SWAQLD method. This same method also shows a stability of this prediction error when faced with a change in rank, which is less the case for the AQLD one. This is due to the poor profile extracted in the previous section. We also observe that for a given method, the best sensitivity is always obtained for a rank of three. Obviously, this parameter is very sensitive to the change in model rank. Finally, with regard to the LOD and LOQ values, only the SWAQLD method proposes fairly stable values in the face of rank change. In view of all these observations, we can, therefore, say that the SWAQLD method is the most robust to the size of the models, which is an important advantage in an analytical implementation for the characterization of complex samples where interfering molecules are omnipresent.

^{−1}and a half-life of 40.0 min. At first glance, it may seem surprising to find different values from those calculated for free-interference water samples. We must simply consider that inorganic or organic species present in the wastewater system potentially speed up the FLU oxidation reaction.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Escandar, G.M.; Muñoz de la Peña, A. Multi-way calibration for the quantification of polycyclic aromatic hydrocarbons in samples of environmental impact. Microchem. J.
**2021**, 164, 106016. [Google Scholar] [CrossRef] - Shang, F.K.; Wang, Y.T.; Wang, J.Z.; Zhang, L.; Cheng, P.F.; Wang, S.T. Determination of three polycyclic aromatic hydrocarbons in tea using four-way fluorescence data coupled with third-order calibration method. Microchem. J.
**2019**, 146, 957–964. [Google Scholar] [CrossRef] - Sánchez-Barragán, I.; Costa-Fernández, J.M.; Pereiro, R.; Sanz-Medel, A.; Salinas, A.; Segura, A.; Fernández-Gutiérrez, A.; Ballesteros, A.; González, J.M. Molecularly imprinted polymers based on iodinated monomers for selective room-temperature phosphorescence optosensing of fluoranthene in water. Anal. Chem.
**2005**, 77, 7005–7011. [Google Scholar] [CrossRef] - Chen, J.C.; Wu, H.L.; Wang, T.; Dong, M.Y.; Chen, Y.; Yu, R.Q. High-Performance Liquid Chromatography–Diode Array Detection Combined with Chemometrics for Simultaneous Quantitative Analysis of Five Active Constituents in a Chinese Medicine Formula Wen-Qing-Yin. Chemosensors
**2022**, 10, 238. [Google Scholar] [CrossRef] - Baroudi, F.; Al-Alam, J.; Chimjarn, S.; Delhomme, O.; Fajloun, Z.; Millet, M. Conifers as environmental biomonitors: A multi-residue method for the concomitant quantification of pesticides, polycyclic aromatic hydrocarbons and polychlorinated biphenyls by LC-MS/MS and GC–MS/MS. Microchem. J.
**2020**, 154, 104593. [Google Scholar] [CrossRef] - Araújo, A.S.; Castro, J.P.; Sperança, M.A.; Andrade, D.F.; de Mello, M.L.; Pereira-Filho, E.R. Multiway calibration strategies in laser-induced breakdown spectroscopy: A proposal. Anal. Chem.
**2021**, 93, 6291–6300. [Google Scholar] [CrossRef] - Wu, H.L.; Wang, T.; Yu, R.Q. Recent advances in chemical multi-way calibration with second-order or higher-order advantages: Multilinear models, algorithms, related issues and applications. Trends Anal. Chem.
**2020**, 130, 115954. [Google Scholar] [CrossRef] - Anzardi, M.B.; Arancibia, J.A.; Olivieri, A.C. Processing multi-way chromatographic data for analytical calibration, classification and discrimination: A successful marriage between separation science and chemometrics. Trends Anal. Chem.
**2021**, 134, 116128. [Google Scholar] [CrossRef] - Pérez-Cova, M.; Jaumot, J.; Tauler, R. Untangling comprehensive two-dimensional liquid chromatography data sets using regions of interest and multivariate curve resolution approaches. Trends Anal. Chem.
**2021**, 137, 116207. [Google Scholar] [CrossRef] - Mazivila, S.J.; Bortolato, S.A.; Olivieri, A.C. MVC3_GUI: A MATLAB graphical user interface for third-order multivariate calibration. An upgrade including new multi-way models. Chemom. Intel. Lab. Syst.
**2018**, 173, 21–29. [Google Scholar] [CrossRef] - Yin, X.L.; Gu, H.W.; Liu, X.L.; Zhang, S.H.; Wu, H.L. Comparison of three-way and four-way calibration for the real-time quantitative analysis of drug hydrolysis in complex dynamic samples by excitation-emission matrix fluorescence. Spectrochim. Acta Part A
**2018**, 192, 437–445. [Google Scholar] [CrossRef] [PubMed] - Osorio, A.; Toledo-Neira, C.; Bravo, M.A. Critical evaluation of third-order advantage with highly overlapped spectral signals. Determination of fluoroquinolones in fish-farming waters by fluorescence spectroscopy coupled to multivariate calibration. Talanta
**2019**, 204, 438–445. [Google Scholar] [CrossRef] [PubMed] - Carabajal, M.D.; Arancibia, J.A.; Escandar, G.M. Excitation-emission fluorescence-kinetic third-order/four-way data: Determination of bisphenol A and nonylphenol in food-contact plastics. Talanta
**2019**, 197, 348–355. [Google Scholar] [CrossRef] [PubMed] - Goicoechea, H.C.; Yu, S.; Moore, A.F.T.; Campiglia, A.D. Four-way modeling of 4.2K time-resolved excitation emission fluorescence data for the quantitation of polycyclic aromatic hydrocarbons in soil samples. Talanta
**2012**, 101, 330–336. [Google Scholar] [CrossRef] [PubMed] - Lenardon Vinciguerra, L.; Carla Böck, F.; Pires Schneider, M.; Alejandra Pisoni Canedo Reis, N.; Flores Silva, L.; Christina Mendes de Souza, K.; Crivellaro Guerra, C.; de Araújo Gomes, A.; Maria Bergold, A.; Flôres Ferrão, M. Geographical origin authentication of southern Brazilian red wines by means of EEM-pH four-way data modelling coupled with one class classification approach. Food Chem.
**2021**, 362, 130087. [Google Scholar] [CrossRef] - Fu, H.Y.; Wu, H.L.; Yu, Y.J.; Yu, L.L.; Zhang, S.R.; Nie, J.F.; Li, S.F.; Yu, R.Q. A new third-order calibration method with application for analysis of four-way data arrays. J. Chemom.
**2011**, 25, 408–429. [Google Scholar] [CrossRef] - Cabrera-Bañegil, M.; Valdés-Sánchez, E.; Muñoz de la Peña, A.; Durán-Merás, I. Combination of fluorescence excitation emission matrices in polar and non-polar solvents to obtain three- and four-way arrays for classification of Tempranillo grapes according to maturation stage and hydric status. Talanta
**2019**, 199, 652–661. [Google Scholar] [CrossRef] - Lozano, V.A.; Muñoz de la Peña, A.; Durán-Merás, I.; Espinosa Mansilla, A.; Escandar, G.M. Four-way multivariate calibration using ultra-fast high-performance liquid chromatography with fluorescence excitation–emission detection. Application to the direct analysis of chlorophylls a and b and pheophytins a and b in olive oils. Chemom. Intel. Lab. Syst.
**2013**, 125, 121–131. [Google Scholar] [CrossRef] - Bailey, H.P.; Rutan, S.C. Comparison of chemometric methods for the screening of comprehensive two-dimensional liquid chromatographic analysis of wine. Anal. Chim. Acta
**2013**, 770, 18–28. [Google Scholar] [CrossRef] - Arancibia, J.A.; Damiani, P.C.; Escandar, G.M.; Ibañez, G.A.; Olivieri, A.C. A review on second- and third-order multivariate calibration applied to chromatographic data. J.Chromatogr. B
**2012**, 910, 22–30. [Google Scholar] [CrossRef] - Gao, Z.W.; Mou, L.; Xue, S.F.; Tao, Z.; Zeng, X. Cucurbit[8] urils-induced room temperature phosphorescence of phenanthrene and fluorene. Spectrosc. Spectral Anal.
**2010**, 30, 1026–1029. [Google Scholar] [CrossRef] - Guo, J.; Yang, C.; Zhao, Y. Long-lived organic room-temperature phosphorescence from amorphous polymer systems. Accounts Chem. Res.
**2022**, 94, 5190–5195. [Google Scholar] [CrossRef] [PubMed] - Arif, S.; Al-Tameemi, M.; Wilson, W.B.; Wise, S.A.; Barbosa, F.; Campiglia, A.D. Low-temperature time-resolved phosphorescence excitation emission matrices for the analysis of phenanthro-thiophenes in chromatographic fractions of complex environmental extracts. Talanta
**2020**, 212, 120805. [Google Scholar] [CrossRef] [PubMed] - Pulgarin, J.A.M.; Molina, A.A.; Sanchez-Ferrer, I. Determination of propranolol and naproxen in urine by using excitation-emission matrix phosphorescence coupled with multivariate calibration algorithms. Curr. Pharm. Anal.
**2012**, 8, 83–92. [Google Scholar] [CrossRef] - Muñoz de la Peña, A.; Mora Diez, N.; Bohoyo Gil, D.; Cano Carranza, E. Second-order data obtained by time-resolved room temperature phosphorescence. A new approach for PARAFAC multicomponent analysis. J. Fluoresc.
**2009**, 19, 345–352. [Google Scholar] [CrossRef] - Arancibia, J.A.; Escandar, G.M. Room-temperature excitation–emission phosphorescence matrices and second-order multivariate calibration for the simultaneous determination of pyrene and benzo[a]pyrene. Anal. Chim. Acta
**2007**, 584, 287–294. [Google Scholar] [CrossRef] - Arancibia, J.A.; Boschetti, C.E.; Olivieri, A.C.; Escandar, G.M. Screening of oil samples on the basis of excitation−emission room-temperature phosphorescence data and multiway chemometric techniques. Introducing the second-order advantage in a classification study. Anal. Chem.
**2008**, 80, 2789–2798. [Google Scholar] [CrossRef] - Goicoechea, H.C.; Yu, S.; Olivieri, A.C.; Campiglia, A.D. Four-way data coupled to parallel factor model applied to environmental analysis: Determination of 2,3,7,8-tetrachloro-dibenzo-para-dioxin in highly contaminated waters by solid−liquid extraction laser-excited time-resolved Shpol’skii spectroscopy. Anal. Chem.
**2005**, 77, 2608–2616. [Google Scholar] [CrossRef] - Qing, X.D.; Wu, H.L.; Yan, X.F.; Li, Y.; Ouyang, L.Q.; Nie, C.C.; Yu, R.Q. Development of a novel alternating quadrilinear decomposition algorithm for the kinetic analysis of four-way room-temperature phosphorescence data. Chemom. Intel. Lab. Syst.
**2014**, 132, 8–17. [Google Scholar] [CrossRef] - Harshman, R.A. Foundation of the PARAFAC procedure: Models and conditions for “explanatory” multimodal factor analysis. UCLA Work. Pap. Phon.
**1970**, 16, 1–84. Available online: https://www.psychology.uwo.ca/faculty/harshman/wpppfac0.pdf (accessed on 1 December 2022). - Wu, H.L.; Shibukawa, M.; Oguma, K. An alternating trilinear decomposition algorithm with application to calibration of HPLC–DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons. J. Chemom.
**1998**, 12, 1–26. [Google Scholar] [CrossRef] - Chen, Z.P.; Wu, H.L.; Jiang, J.H.; Li, Y.; Yu, R.Q. A novel trilinear decomposition algorithm for second-order linear calibration. Chemom. Intel. Lab. Syst.
**2000**, 52, 75–86. [Google Scholar] [CrossRef] - Bro, R.; Kiers, H.A.L. A new efficient method for determining the number of components in PARAFAC models. J. Chemom.
**2003**, 17, 274–286. [Google Scholar] [CrossRef] - Qing, X.D.; Li, Y.; Wen, J.; Shen, X.Z.; Li, C.Y.; Liu, X.L.; Xie, J. A new method to determine the number of chemical components of four-way data from mixtures. Microchem. J.
**2017**, 135, 114–121. [Google Scholar] [CrossRef] - Wang, X.M.; Dong, M.J.; Li, Z.J.; Wang, Z.P.; Liang, F.S. Recent advances of room temperature phosphorescence and long persistent luminescence by doping system of purely organic molecules. Dyes Pigments
**2022**, 204, 2–12. [Google Scholar] [CrossRef] - Machicote, R.G.; Bruzzone, L. Simultaneous determination of carbaryl and 1-naphthol by first-derivative synchronous non-protected room temperature phosphorescence. Anal. Sci.
**2009**, 25, 623–626. [Google Scholar] [CrossRef] [Green Version] - Liu, L.L.; Yang, B.; Zhang, H.Y.; Tang, S.; Xie, Z.Q.; Wang, H.P.; Wang, Z.M.; Lu, P.; Ma, Y.G. Role of Tetrakis(triphenylphosphine)palladium(0) in the degradation and optical properties of fluorene-based compounds. J. Phys. Chem. C
**2008**, 112, 10273–10278. [Google Scholar] [CrossRef] - Wang, Y.S.; Yang, J.; Tian, Y.; Fang, M.M.; Liao, Q.Y.; Wang, L.W.; Hu, W.P.; Tang, B.Z.; Li, Z. Persistent organic room temperature phosphorescence: What is the role of molecular dimers? Chem. Sci.
**2020**, 11, 833–838. [Google Scholar] [CrossRef] [Green Version] - Liu, L.L.; Tang, S.; Liu, M.R.; Xie, Z.Q.; Zhang, W.; Lu, P.; Hanif, M.; Ma, Y.G. Photodegradation of polyfluorene and fluorene oligomers with alkyl and aromatic disubstitutions. J. Phys. Chem. B
**2006**, 110, 13734–13740. [Google Scholar] [CrossRef]

**Figure 2.**The kinetic evolution contour plots of excitation–emission matrix phosphorescence for calibration sample C4 at specific times (0, 12, 24, 36, and 42 min).

**Figure 3.**Excitation–emission matrix phosphorescence corresponding to samples of (

**a**) a 3.80 μg mL

^{−1}FLU sample, (

**b**) a free-interference water sample, and (

**c**) a wastewater one.

**Figure 4.**Resolved excitation, emission, and kinetic profiles, normalized to unit length obtained from PARAFAC, AQLD, and SWAQLD for the analysis of four-way phosphorescence data of free-interference water samples with a rank N = 3 (

**a**) or 4 (

**b**). The black dotted lines denote the FLU reference profiles. The red, blue, and green solid lines represent the FLU-resolved profiles obtained from PARAFAC, AQLD, and SWAQLD, respectively. Other extracted profiles represent additional extracted components.

**Figure 5.**The plot of the natural logarithm of reciprocal of relative concentration (Ln(1/[FLU]

_{t})) versus time (t) for PARAFAC, AQLD, and SWAQLD in the case of free-interference water samples and a rank of 3 (

**a**) or 4 (

**b**).

**Figure 6.**Resolved excitation, emission, and kinetic profiles, normalized to unit length obtained from PARAFAC, AQLD and SWAQLD for the analysis of four-way phosphorescence data of wastewater samples with a rank N = 3 (

**a**) or 4 (

**b**). The black dotted lines denote the FLU reference profiles. The red, blue, and green solid lines represent the FLU-resolved profiles obtained from PARAFAC, AQLD, and SWAQLD, respectively. Other extracted profiles represent additional extracted components.

**Figure 7.**The plot of the natural logarithm of reciprocal of relative concentration (Ln(1/[FLU]

_{t})) versus time (t) for PARAFAC, AQLD, and SWAQLD in the case of wastewater samples and a rank of 3 (

**a**) or 4 (

**b**).

**Table 1.**Statistical figures of merit concerning the fluorene quantification in free-interference water samples by using third-order calibration methods (PARAFAC, AQLD, and SWAQLD) with different rank values.

Sample No. | Reference Concentration (μg.mL ^{−1}) | Recovery (%) | ||||
---|---|---|---|---|---|---|

PARAFAC | AQLD | SWAQLD | ||||

N = 3 | N = 3 | N = 4 | N = 3 | N = 4 | ||

V01 | 1.71 | 117.8 | 117.3 | 115.8 | 111.2 | 113.2 |

V02 | 2.09 | 101.8 | 91.3 | 93.6 | 95.5 | 96.3 |

V03 | 2.47 | 97.7 | 88.5 | 89.6 | 96.6 | 96.2 |

V04 | 2.85 | 100.4 | 102.1 | 100.4 | 99.5 | 101.7 |

V05 | 3.23 | 100.0 | 112.7 | 111.4 | 100.4 | 105.6 |

V06 | 3.61 | 94.1 | 95.9 | 98.6 | 93.6 | 97.3 |

AR ^{a} (%)SDR ^{b} (%) | 101.9 5.3 | 101.3 9.4 | 101.6 8.0 | 99.5 4.2 | 101.7 5.1 | |

RMSEP ^{c} (μg.mL^{−1}) | 0.17 | 0.28 | 0.24 | 0.15 | 0.15 |

^{a}AR: average recovery.

^{b}SDR: standard deviation of recovery.

^{c}Root mean square error of prediction (RMSEP) is calculated by $\mathrm{RMSEP}={\left[\frac{1}{\mathrm{I}-1}\sum {\left({\mathrm{c}}_{\mathrm{ref}}-{\mathrm{c}}_{\mathrm{pred}}\right)}^{2}\right]}^{1/2}$, where c

_{ref}and c

_{pred}are the reference and predicted values, respectively.

**Table 2.**Statistical figures of merit concerning the fluorene quantification in wastewater samples by using third-order calibration methods (PARAFAC, AQLD, and SWAQLD) with different rank values.

Sample No. | Reference Concentration (μg mL ^{−1}) | Recovery (%) | ||||
---|---|---|---|---|---|---|

PARAFAC | AQLD | SWAQLD | ||||

N = 3 | N = 3 | N = 4 | N = 3 | N = 4 | ||

W01 | 2.09 | 121.4 | 122.7 | 108.1 | 113.6 | 118.8 |

W02 | 2.47 | 86.5 | 91.7 | 97.8 | 92.9 | 93.9 |

W03 | 2.85 | 93.8 | 96.9 | 84.8 | 92.8 | 94.6 |

W04 | 3.23 | 89.5 | 94.9 | 84.1 | 90.0 | 88.4 |

W05 | 3.61 | 103.0 | 105.5 | 91.6 | 93.6 | 97.3 |

AR | 98.8 | 102.3 | 93.3 | 96.6 | 98.6 | |

SDR | 10.7 | 9.4 | 7.7 | 6.8 | 8.1 | |

RMSEP (μg mL^{−1}) | 0.34 | 0.29 | 0.38 | 0.28 | 0.30 | |

SEN (mL μg^{−1}) ^{a} | 12.98 | 41.33 | 8.03 | 18.71 | 1.98 | |

LOD (μg mL^{−1}) ^{b} | 0.21 | 0.13 | 0.04 | 0.10 | 0.11 | |

LOQ (μg mL^{−1}) ^{c} | 0.64 | 0.40 | 0.11 | 0.29 | 0.34 |

^{a}SEN: sensitivity.

^{b}LOD: limit of detection = 3.3σ

_{0}, where σ

_{0}is the standard deviation of the FLU-predicted concentration in three blank samples.

^{c}LOQ: limit of quantification = 10σ

_{0}.

**Table 3.**The convergence property of PARAFAC, AQLD, and SWAQLD for simulated excitation–emission–kinetic four-way phosphorescence data with four levels of homoscedastic noise.

Noise_{homo} (%) | Iteration Number (Computation Time (s)) | ||||||||
---|---|---|---|---|---|---|---|---|---|

PARAFAC | AQLD | SWAQLD | |||||||

Min | Max | Average ^{a} | Min | Max | Average | Min | Max | Average | |

0.02 | 162 (250.9) | 1951 (2756.9) | 281 (443.8) | 5 (0.4) | 10 (1.0) | 6 (0.6) | 52 (4.3) | 183 (13.3) | 80 (6.6) |

0.2 | 118 (191.4) | 1921 (3113.2) | 235 (375.9) | 5 (0.4) | 10 (0.9) | 6 (0.6) | 24 (1.8) | 168 (11.6) | 66 (4.6) |

2 | 135 (165.7) | 2132 (4230.5) | 756 (1156.6) | 5 (0.4) | 13 (1.1) | 7 (0.7) | 29 (1.8) | 227 (16.0) | 58 (3.9) |

20 | 91 (123.1) | 882 (1473.3) | 252 (412.6) | 8 (0.8) | 68 (5.0) | 13 (1.1) | 29 (2.0) | 256 (15.4) | 47 (3.1) |

^{a}These values are average results for 100 runs with random initialization.

**Table 4.**The influence of homoscedastic noise levels (ɑ

_{homo}) on correlation coefficients, RMSEPs, and k values predicted by PARAFAC, AQLD, and SWAQLD, respectively, for simulated four-way data.

Mode | PARAFAC | AQLD | SWAQLD | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0.02% | 0.2% | 2% | 20% | 0.02% | 0.2% | 2% | 20% | 0.02% | 0.2% | 2% | 20% | ||

A | a_{1} | 1.000 ^{a} | 1.0000 | 1.0000 | 0.9998 | 1.0000 | 1.0000 | 1.0000 | 0.9988 | 1.0000 | 1.0000 | 1.0000 | 0.9997 |

a_{2} | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 | 0.9998 | 1.0000 | 1.0000 | 1.0000 | 0.9998 | |

a_{3} | 1.0000 | 1.0000 | 1.0000 | 0.9998 | 1.0000 | 1.0000 | 1.0000 | 0.9976 | 1.0000 | 1.0000 | 1.0000 | 0.9998 | |

B | b_{1} | 1.0000 | 1.0000 | 1.0000 | 0.9994 | 1.0000 | 1.0000 | 1.0000 | 0.9986 | 1.0000 | 1.0000 | 1.0000 | 0.9994 |

b_{2} | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 | 0.9984 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | |

b_{3} | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 | 0.9952 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | |

C | c_{1} | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9991 | 1.0000 | 1.0000 | 1.0000 | 0.9997 |

c_{2} | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9997 | 1.0000 | 1.0000 | 1.0000 | 0.9999 | |

c_{3} | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9996 | 1.0000 | 1.0000 | 1.0000 | 0.9997 | |

D | d_{1} | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9920 | 1.0000 | 1.0000 | 1.0000 | 0.9999 |

d_{2} | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9997 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

d_{3} | 1.0000 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 | 0.9902 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

RMSEP | Analyte 1 | 0.0000 | 0.0002 | 0.0005 | 0.0026 | 0.0000 | 0.0001 | 0.0007 | 0.0546 ^{c} | 0.0000 | 0.0003 | 0.0006 | 0.0049 |

Analyte 2 | 0.0000 | 0.0001 | 0.0006 | 0.0032 | 0.0000 | 0.0001 | 0.0010 | 0.0093 | 0.0000 | 0.0002 | 0.0003 | 0.0023 | |

Predicted k ^{b} | 0.0999 | 0.0992 | 0.1005 | 0.0941 | 0.0999 | 0.0996 | 0.0940 | 0.0367 | 0.0999 | 0.0992 | 0.1000 | 0.0997 |

^{a}All values in the first 12 rows of this table correspond to the correlation coefficient between the profiles predicted by the different methods and the reference profiles.

^{b}The chosen constant rate of the analyte in the simulated data set is 0.1000.

^{c}Bold characters are used to highlights the worst results.

**Table 5.**The influence of factor numbers (N) on correlation coefficients, RMSEPs, and k values predicted by PARAFAC, AQLD, and SWAQLD, respectively, for simulated four-way data with ɑ

_{homo}= 0.02%.

Mode | PARAFAC | AQLD | SWAQLD | |||||||
---|---|---|---|---|---|---|---|---|---|---|

N = 3 | N = 4 | N = 10 | N = 3 | N = 4 | N = 10 | N = 3 | N = 4 | N = 10 | ||

A | a_{1} | 1.0000 | 1.0000 | 0.9964 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

a_{2} | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

a_{3} | 1.0000 | 1.0000 | 0.9919 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

B | b_{1} | 1.0000 | 1.0000 | 0.9122 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

b_{2} | 1.0000 | 1.0000 | 0.9638 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

b_{3} | 1.0000 | 1.0000 | 0.9397 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

C | c_{1} | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

c_{2} | 1.0000 | 1.0000 | 0.9995 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

c_{3} | 1.0000 | 1.0000 | 0.9813 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

D | d_{1} | 1.0000 | 1.0000 | 0.9891 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

d_{2} | 1.0000 | 1.0000 | 0.9196 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

d_{3} | 1.0000 | 1.0000 | 0.9967 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |

RMSEP | Analyte 1 | 0.0000 | 0.0000 | 0.0679 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0001 |

Analyte 2 | 0.0000 | 0.0014 | 0.2455 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Predicted k | 0.0999 | 0.1000 | 0.0640 | 0.0999 | 0.0999 | 0.1000 | 0.0999 | 0.1000 | 0.1001 |

Regression Equation | Correlation Coefficient | Rate Constant (min ^{−1}) | Half Life (min) | |
---|---|---|---|---|

PARAFAC (N = 3) | y = 0.0151x + 0.7655 | 0.9962 | 0.0151 | 45.9 |

AQLD (N = 3) | y = 0.0154x + 0.7600 | 0.9889 | 0.0154 | 45.0 |

AQLD (N = 4) | y = 0.0148x + 0.7698 | 0.9980 | 0.0148 | 46.8 |

SWAQLD (N = 3) | y = 0.0150x + 0.7687 | 0.9928 | 0.0150 | 46.2 |

SWAQLD (N = 4) | y = 0.0159x + 0.7526 | 0.9931 | 0.0159 | 43.6 |

**Table 7.**Regression equation, correlation coefficient, rate constant, and half-life of the oxidation reaction of FLU in wastewater samples.

Regression Equation | Correlation Coefficient | Rate Constant (min ^{−1}) | Half Life (min) | |
---|---|---|---|---|

PARAFAC (N = 3) | y = 0.0172x + 0.7321 | 0.9981 | 0.0172 | 40.3 |

AQLD (N = 3) | y = 0.0173x + 0.7310 | 0.9908 | 0.0173 | 40.1 |

AQLD (N = 4) | y = 0.0169x + 0.7374 | 0.9954 | 0.0169 | 41.0 |

SWAQLD (N = 3) | y = 0.0179x + 0.7219 | 0.9978 | 0.0179 | 38.7 |

SWAQLD (N = 4) | y = 0.0174x + 0.7288 | 0.9977 | 0.0174 | 39.8 |

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## Share and Cite

**MDPI and ACS Style**

Qing, X.-D.; Zhang, X.-H.; An, R.; Zhang, J.; Xu, L.; Duponchel, L.
A Fast and Robust Third-Order Multivariate Calibration Approach Coupled with Excitation–Emission Matrix Phosphorescence for the Quantification and Oxidation Kinetic Study of Fluorene in Wastewater Samples. *Chemosensors* **2023**, *11*, 53.
https://doi.org/10.3390/chemosensors11010053

**AMA Style**

Qing X-D, Zhang X-H, An R, Zhang J, Xu L, Duponchel L.
A Fast and Robust Third-Order Multivariate Calibration Approach Coupled with Excitation–Emission Matrix Phosphorescence for the Quantification and Oxidation Kinetic Study of Fluorene in Wastewater Samples. *Chemosensors*. 2023; 11(1):53.
https://doi.org/10.3390/chemosensors11010053

**Chicago/Turabian Style**

Qing, Xiang-Dong, Xiao-Hua Zhang, Rong An, Jin Zhang, Ling Xu, and Ludovic Duponchel.
2023. "A Fast and Robust Third-Order Multivariate Calibration Approach Coupled with Excitation–Emission Matrix Phosphorescence for the Quantification and Oxidation Kinetic Study of Fluorene in Wastewater Samples" *Chemosensors* 11, no. 1: 53.
https://doi.org/10.3390/chemosensors11010053