# Hierarchical Modeling to Enhance Spectrophotometry Measurements—Overcoming Dynamic Range Limitations for Remote Monitoring of Neptunium

^{*}

## Abstract

**:**

_{2}

^{+}) includes many bands, which have molar absorption coefficients that differ by nearly 2 orders of magnitude. The shape, position, and intensity of these bands differ with chemical interactions and changing temperature. These challenges make traditional quantification by univariate methods unfeasible. Measuring Np(V) concentration over several orders of magnitude would typically necessitate cells with varying path length, optical switches, and/or multiple spectrophotometers. Alternatively, the differences in the molar extinction coefficients for multiple absorption bands can be used to quantify Np(V) concentration over 3 orders of magnitude with a single optical path length (1 mm) and a hierarchical multivariate model. In this work, principal component analysis was used to distinguish the concentration regime of the sample, directing it to the relevant partial least squares regression submodels. Each submodel was optimized with unique feature selection filters that were selected by a genetic algorithm to enhance predictions. Through this approach, the percent root mean square error of prediction values were ≤1.05% for Np(V) concentrations and ≤4% for temperatures. This approach may be applied to other nuclear fuel cycle and environmental applications requiring real-time spectroscopic measurements over a wide range of conditions.

## 1. Introduction

^{237}NpO

_{2}

^{+}) in nitric acid (HNO

_{3}) is essential to improve Np processing efficiency, which is an ongoing effort of the

^{238}Pu Supply Program at Oak Ridge National Laboratory where

^{238}Pu is produced through irradiating

^{237}Np targets [2]. Improved analytical time will help scale up the production of heat source plutonium oxide (PuO

_{2}) to meet NASA’s projected needs [3]. Multiple analytical techniques are available for measuring Np concentration, including alpha- and gamma-ray spectroscopy, inductively coupled plasma–mass spectrometry (ICP-MS), titrimetric analysis, and optical spectroscopy. Spectrophotometry can provide rapid feedback (e.g., 10–1000 ms intervals) and is sensitive to Np valence and concentration [2]. This method can be readily employed in hazardous environments using fiber optic cables, making it ideal for remote, online monitoring applications [4,5].

_{3}, making it the focal point of spectroscopic detection research [6]. The most intense 5f–5f electronic transition in the visible (vis)–near infrared (NIR) absorption spectrum of the aquo NpO

_{2}

^{+}ion occurs at 979 nm (ε = 395 M

^{−1}·cm

^{−1}) [7,8]. The most intense transition originating from the 5f shell for the isoelectronic plutonyl ion (PuO

_{2}

^{2+}) occurs at a shorter wavelength near 830 nm [9]. The intense Np(V) 979 nm peak and a less intense band at 616 nm (ε = 22 M

^{−1}·cm

^{−1}) have been used analytically to determine the concentration of NpO

_{2}

^{+}in solution using Beer’s law. Additional bands are also available for analysis in the spectrum with even lower molar absorptivity values (ε = 2.5 M

^{−1}·cm

^{−1}) [10]. The 979 nm absorption band is the most widely used because the intensity and position is sensitive to the coordination environment of NpO

_{2}

^{+}for most studies at relatively low Np concentrations (~1 mM) [11,12]. Quantifying Np(V) in aqueous solutions using spectrophotometry over dynamic conditions encountered during processing is challenging because of the broad range of molar extinction coefficients, nonlinear concentration responses, concentration-dependent chemical equilibria, and dynamic temperature effects [10,13,14].

## 2. Materials and Methods

#### 2.1. Materials

_{3}(70%) was purchased from Sigma Aldrich. All solutions were prepared using deionized water with a resistivity of 18.2 MΩ⋅cm at 25 °C. Oak Ridge National Laboratory provided

^{237}NpO

_{2}(t

_{½}= 2.14 × 10

^{6}years) in-house.

#### 2.2. Methodology

_{2}in 8 M HNO

_{3}and diluting to achieve a Np concentration of 210 ± 7 g L

^{−1}(0.886 M Np) in 1 M HNO

_{3}. The concentration of Np in the sample was determined using ICP-MS (iCAP Q ICP-MS, Thermo Fisher Scientific). The stock solution was used to prepare the calibration and validation samples (0.00075–0.89 M Np). Aliquots from the stock solution were taken and sequentially diluted in 1.0 M HNO

_{3}using a 1 mL volumetric flask (1.00 ± 0.01 mL) to achieve the desired total Np concentration. Calibration and validation samples used in this study are detailed in Table 1. Here, more validation samples were used than the calibration set. This is representative of the true application where it is desired to minimize the training set to minimize resources used. A small fraction of Np(VI) (≤3%) was present in the higher Np concentration samples. This oxidation state distribution is commonly observed in process solutions. No attempts were made to adjust the valence of the Np, and the models discussed in this study are for total Np concentration. Increasing the solution temperature did not change the ratio of Np(V/VI) or alter the Np(VI) band [17].

#### 2.3. Spectrophotometry

#### 2.4. Multivariate Data Analysis

#### 2.5. Statistics

_{i}is the known concentration, ${\widehat{y}}_{i}$ is the model-predicted concentration, and n is the total number of samples. The RMSE of calibration (RMSEC) is determined using the calibration set to train the data; then, the same calibration set is predicted by the model, essentially making RMSEC a measure of fit. The RMSE of cross validation (RMSECV) was determined using a fivefold approach where the calibration set was split into five random groups. Then, one group was left out as the model was built and predicted the values of the left-out group. This approach was an iterative process that proceeded until each sample was left out at least once. The deviation of predicted values was averaged into a single RMSECV metric. The RMSE of prediction (RMSEP) measures the dispersion of samples not included in a validation set (i.e., never included in model construction) around the regression line. The RMSE values are typically discussed in terms of percentages to ease comparisons [16,20,23]. The RMSE value was divided by the median of the model concentration range to produce percent RMSEP (RMSEP%). For the percentage conversions in this study, the RMSE values were divided by 0.05 for low Np concentrations, 0.40 for high Np concentrations, and 35 for temperature models. Lower RMSE values indicate improved model performance. In the following discussion, models were rated based on their predictive error: strong (RMSEP% ≤ 5%), satisfactory (5 < RMSEP% ≤ 10%), or indicative (10 < RMSEP% ≤ 15%). RMSEP% values above 15% do not offer any monitoring value and are undesirable [23].

_{pu}) proposed by Ortiz et al. that extends the IUPAC recommendations for univariate models for use in multivariate models [25]. In this work, the multivariate model was used to estimate the concentrations of the calibration sample set. The slope of these predictions versus the known values (i.e., the slope of the parity plot) was used in place of the univariate calibration curve. The LOD

_{pu}was then calculated using Equation (2):

_{pu}is the slope of the produced parity plot, var

_{pu}is the variance of the regression residuals, N is the number of calibration samples, ${\overline{y}}_{\mathrm{cal}}$ is the mean concentration of the calibration analytes, and y

_{n}is the centered analyte concentration of sample n.

## 3. Results and Discussion

#### 3.1. Np Vis-NIR Spectra

_{3}is shown as a function of Np concentration in Figure 1a. A large range in molar absorptivity values are represented. The dominating band in the spectrum is centered at 979 nm for Np(V) and has a molar absorptivity of 367 M

^{−1}∙cm

^{−1}, which agrees well with published data. Several additional absorption bands appear at 433, 476.5, 616.4, 687.0, 914.2, 1022, 1096, and 1116 nm with molar absorptivity values of 7, 22, 5, 2.5, 9, 25, and 6, respectively [10]. The asymmetric Np(VI) peak is shown in high Np concentration samples centered near 1224 nm, but the quantity is negligible. The peak near 1616 nm is convoluted with the NIR water band response centered near 1450 nm [26]. This water band is related to the first overtone of water. The broad positive (1404 nm) and negative peaks in this region (1490 nm), which result in an isosbestic point near 1440 nm, occur because of differences in the local tetrahedral structure of water owing to its temperature [27].

_{3}with temperature varied from 10–80 °C. The effect of temperature is visible in the water band (1300–1650 nm), but the inset plot provides a closer examination of how the Np(V) bands change shape and shift with temperature. These changes may appear small, but they can generate challenges when attempting to apply Beer’s Law to monitor Np(V) concentrations. For example, the Np(V) 979 nm band intensity decreases by 12%, and the peak position blue-shifts by 1.9 nm from 10–80 °C [10]. These effects necessitate the use of multivariate modeling to accurately monitor such a system with a wide range of conditions.

#### 3.2. Principal Component Analysis

#### 3.3. Hierarchical Modeling

#### 3.4. Feature Selection for Model Optimization

#### 3.5. Final PLSR Model Evaluation

_{pu}was calculated for the final low Np concentration submodel to evaluate the lowest concentration that the overall hierarchical model would be able to predict with reasonable sensitivity. Using Equation (2), the LOD

_{pu}was 0.232 mM Np. To measure lower concentrations, an alternative measurement system (e.g., larger pathlength or a more sensitive spectrometer) would be needed, but a hierarchical model similar to the one discussed in this work (Figure 6) could describe a lower concentration range.

## 4. Conclusions

^{238}Pu Supply Program. Future work will explore quantifying multiple Np oxidation states in the regression model.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

^{238}Pu Supply Program at Oak Ridge National Laboratory.

## Conflicts of Interest

## References

- Harris, D.C. Chapter 18: Fundamentals of Spectrophotometry. In Quantitative Chemical Analysis, 7th ed.; W. H. Freeman and Company: New York, NY, USA, 2007. [Google Scholar]
- Sadergaski, L.R.; Myhre, K.G.; Delmar, L.H. Multivariate chemometric methods and Vis-NIR spectrophotometry for monitoring plutonium-238 anion exchange column effluent in a radiochemical hot cell. Talanta Open
**2022**, 5, 1000120. [Google Scholar] [CrossRef] - Sadergaski, L.R.; DePaoli, D.W.; Myhre, K.G. Monitoring the caustic dissolution of aluminum in a hot cell by Raman spectroscopy. Appl. Spectrosc.
**2020**, 74, 1252–1262. [Google Scholar] [CrossRef] [PubMed] - Kirsanov, D.; Rudnitskaya, A.; Legin, A.; Babain, V. UV-Vis spectroscopy with chemometric data treatment: An option for on-line control in nuclear industry. J. Radioanal. Nucl. Chem.
**2017**, 312, 461–470. [Google Scholar] [CrossRef] - Lascola, R.; O’Rourke, P.E.; Kyser, E.A. A Piecewise Local Partial Least Squares (PLS) Method for the Quantitative Analysis of Plutonium Nitrate Solutions. Appl. Spectrosc.
**2017**, 71, 2579–2594. [Google Scholar] [CrossRef] - Ikedo-Ohno, A.; Hennig, C.; Rossberg, A.; Funke, H.; Scheinost, A.C.; Bernhard, G.; Yaita, T. Electrochemical and Complexation Behavior of Neptunium in Aqueous Perchlorate and Nitrate Solutions. Inorg. Chem.
**2008**, 47, 8294–8305. [Google Scholar] [CrossRef] [PubMed] - Matsika, S.; Pitzer, R.M.; Reed, D.T. Intensities in the Spectra of Actinyl Ions. J. Phys. Chem. A
**2000**, 104, 11983–11992. [Google Scholar] [CrossRef] - Matsika, S.; Pitzer, R.M. Electronic Spectrum of the NpO
_{2}^{2+}and NpO_{2}^{+}Ions. J. Phys. Chem. A**2000**, 104, 4064–4068. [Google Scholar] [CrossRef] - Eisenstein, J.C.; Pryce, M.H.L. Interpretation of the Solution Absorption Spectra of the (PuO
_{2})^{++}and (NpO_{2})^{+}Ions. J. Res. Natl. Bur. Stand. A**1966**, 70, 165–173. [Google Scholar] [CrossRef] - Sadergaski, L.R.; Morgan, K. Applying Two-Dimensional Correlation Spectroscopy and Principal Component Analysis to Understand How Temperatures Affects the Neptunium(V) Absorption Spectrum. Chemosensors
**2022**, 10, 475. [Google Scholar] [CrossRef] - Maiwald, M.M.; Skerencak-Frech, A.; Panak, P.J. The complexation and thermodynamics of neptunium(V) with acetate in aqueous solution. New J. Chem.
**2018**, 42, 7796–7802. [Google Scholar] [CrossRef] - Maiwald, M.M.; Sittel, T.; Fellhauer, D.; Skerencak-Frech, A.; Panak, P.J. Thermodynamics of neptunium(V) complexation with sulfate in aqueous solution. J. Chem. Thermodyn.
**2018**, 116, 309–315. [Google Scholar] [CrossRef] - Chatterjee, S.; Bryan, S.A.; Casella, A.J.; Peterson, J.M.; Levitskaia, T.G. Mechanisms of neptunium redox reactions in nitric acid solutions. Inorg. Chem. Front.
**2017**, 4, 581–594. [Google Scholar] [CrossRef] - Edelstein, N.M. Reanalysis of the Aqueous Spectrum of the Neptunyl(V) [NpO
_{2}^{+}] Ion. J. Phys. Chem. A**2015**, 119, 11146–11153. [Google Scholar] [CrossRef] [PubMed] - Dupont, F.M.; Elbourne, A.; Cozzolino, D.; Chapman, J.; Truong, V.K.; Crawford, R.J.; Latham, K. Chemometrics for environmental monitoring: A review. Anal. Methods
**2020**, 12, 4597–4620. [Google Scholar] [CrossRef] - Sadergaski, L.R.; Andrews, H.B. Simultaneous quantification of uranium(VI), samarium, nitric acid, and temperature with combined ensemble learning, laser fluorescence, and Raman scattering for real-time monitoring. Analyst
**2022**, 147, 4014–4025. [Google Scholar] [CrossRef] - Ban, Y.; Hakamatsuka, Y.; Tsutsui, N.; Urabe, S.; Hagiya, H.; Matsumura, T. Spectroscopic study of Np(V) oxidation to Np(VI) in 3 mol/dm
^{3}nitric acid at elevated temperatures. Radiochim. Acta**2014**, 102, 775–780. [Google Scholar] [CrossRef] - Bro, R.; Smilde, A.K. Principal component analysis. Anal. Methods
**2014**, 6, 2812–2831. [Google Scholar] [CrossRef] - Andrews, H.B.; Myhre, K.G. Quantification of lanthanides in a molten salt reactor surrogate off-gas stream using laser-induced breakdown spectroscopy. Appl. Spectrosc.
**2022**, 76, 877–886. [Google Scholar] [CrossRef] - Andrews, H.B.; Sadergaski, L.R.; Cary, S.K. Pursuit of the Ultimate Regression Model for Samarium(III), Europium(III), and LiCl using Laser-Induced Fluorescence, Design of Experiments, and a Genetic Algorithm for Feature Selection. ACS Omega
**2023**, 8, 2281–2290. [Google Scholar] [CrossRef] - Leardi, R.; Boggia, R.; Terrile, M. Genetic algorithms as a strategy for feature selection. J. Chemom.
**1992**, 6, 267–281. [Google Scholar] [CrossRef] - Leardi, R.; Gonzalez, A.L. Extraction of representative subsets by potential functions method and genetic algorithms . J. Chemom. Intell. Lab. Syst.
**1998**, 40, 33–52. [Google Scholar] - Andrews, H.B.; Sadergaski, L.R. Leveraging visible and near-infrared spectroelectrochemistry to calibrate a robust model for Vanadium (IV/V) in varying nitric acid and temperature levels. Talanta
**2023**, 259, 124554. [Google Scholar] [CrossRef] - McNaught, A.D.; Wilkinson, A. (Eds.) IUPAC Compendium of Chemical Terminology (the “Gold Book”), 2nd ed.; Blackwell Scientific Publications: Oxford, UK, 1997. [Google Scholar]
- Ortiz, M.C.; Sarabia, L.A.; Herrero, A.; Sánchez, M.S.; Sanz, M.B.; Giménez, D.; Meléndez, M.E. Capability of detection of an analytical method evaluating false positive and false negative (ISO 11843) with partial least squares. Chemom. Intell. Lab. Syst.
**2003**, 69, 21–33. [Google Scholar] [CrossRef] - Toney, G.K.; Delmau, L.H.; Myhre, K.G. Chemometrics and Experimental Design for the Quantification of Nitrate Salts in Nitric Acid: Near-Infrared Spectroscopy Absorption Analysis. Appl. Spectrosc.
**2021**, 75, 1155–1167. [Google Scholar] - Segtnan, V.H.; Sasic, S.; Isaksson, T.; Ozaki, Y. Studies on the Structure of Water Using Two-Dimensional Near-Infrared Correlation Spectroscopy and Principal Component Analysis. Anal. Chem.
**2001**, 73, 3153–3161. [Google Scholar] [CrossRef] [PubMed] - Chang, K.; Shinzawa, H.; Chung, H. Concentration determination of inorganic acids that do not absorb near-infrared (NIR) radiation through recognizing perturbed NIR water bands by them and investigation of accuracy dependency on their acidities. Microchem. J.
**2018**, 139, 443–449. [Google Scholar] [CrossRef]

**Figure 1.**UV-vis-NIR absorption spectrum of (

**a**) 0–0.886 M Np in 1 M HNO

_{3}at 20 °C and (

**b**) 0.0687 M Np in 1 M HNO

_{3}with temperature varied from 10 °C–80 °C. All samples were blanked in water at 20 °C. The inset plot in (

**a**) shows the Np(V) 979 nm peak saturating the detector at higher concentrations. The inset plot in (

**b**) highlights the effect of temperature on Np(V) bands. The temperature effects on the water band can be seen in the full plot (≥1300 nm).

**Figure 2.**PCA score plots comparing principal component scores: (

**a**) PC-1 vs. PC-2 colored by Np concentration; (

**b**) PC-1 vs. PC-2 colored by sample temperature; and (

**c**) PC-2 vs. PC-3 colored by sample temperature. In (

**d**), the principal component weights vs. wavelengths are provided. As seen in (

**a**), a positive PC-1 score correlates to a high Np concentration (i.e., ≥0.1 M).

**Figure 3.**Parity plots comparing known and (

**a**,

**b**) low Np concentration submodels and (

**c**,

**d**) high Np concentration submodels’ predicted values for Np concentration and temperature. The 1:1 line signifies a perfect prediction; the closer a marker to the 1:1 line, the better the prediction.

**Figure 4.**Features selected by the GA for the low Np concentration submodel to regress (

**a**) Np concentration and (

**b**) temperature, and the high Np concentration submodel to regress (

**c**) Np concentration and (

**d**) temperature.

**Figure 5.**Parity plots comparing known and predicted values for the GA filtered models: (

**a**) low Np concentration submodel concentration predictions, (

**b**) low Np concentration submodel temperature predictions, (

**c**) high Np concentration submodel concentration predictions, and (

**d**) high Np concentration submodel temperature predictions. The 1:1 line signifies a perfect prediction; the closer a marker is to the 1:1 line, the better the prediction is.

**Figure 6.**Overview of final hierarchical model design. Each GA filter prior to PLSR modeling is unique.

Sample Set | Sample Tag | Np Concentration (M) | Tested Temperatures (°C) |
---|---|---|---|

Calibration | C1 | 0.00 | 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0 |

C2 | 0.00075 | ||

C3 | 0.0069 | ||

C4 | 0.034 | ||

C5 | 0.069 | ||

C6 | 0.34 | ||

C7 | 0.52 | ||

C8 | 0.89 | ||

Validation | V1 | 0.00 | 15.0, 16.5, 24.0, 25.0, 35.0, 45.0, 48.8, 55.0, 56.7, 65.0, 71.6, 75.0 |

V2 | 0.00075 | ||

V3 | 0.0044 | ||

V4 | 0.0088 | ||

V5 | 0.017 | ||

V6 | 0.069 | ||

V7 | 0.17 | ||

V8 | 0.34 | ||

V9 | 0.64 | ||

V10 | 0.89 |

RMSE | |||||||
---|---|---|---|---|---|---|---|

Submodel | C | C% | CV | CV% | P | P% | |

Low Np concentration | Conc. | 0.0004 | 0.78% | 0.0034 | 6.89% | 0.0004 | 0.85% |

T | 0.1471 | 0.42% | 0.3838 | 1.10% | 0.9892 | 2.83% | |

High Np concentration | Conc. | 0.0032 | 0.80% | 0.0088 | 2.20% | 0.0220 | 5.49% |

T | 0.1157 | 0.33% | 0.3964 | 1.13% | 1.7967 | 5.13% |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Andrews, H.B.; Sadergaski, L.R.
Hierarchical Modeling to Enhance Spectrophotometry Measurements—Overcoming Dynamic Range Limitations for Remote Monitoring of Neptunium. *Chemosensors* **2023**, *11*, 274.
https://doi.org/10.3390/chemosensors11050274

**AMA Style**

Andrews HB, Sadergaski LR.
Hierarchical Modeling to Enhance Spectrophotometry Measurements—Overcoming Dynamic Range Limitations for Remote Monitoring of Neptunium. *Chemosensors*. 2023; 11(5):274.
https://doi.org/10.3390/chemosensors11050274

**Chicago/Turabian Style**

Andrews, Hunter B., and Luke R. Sadergaski.
2023. "Hierarchical Modeling to Enhance Spectrophotometry Measurements—Overcoming Dynamic Range Limitations for Remote Monitoring of Neptunium" *Chemosensors* 11, no. 5: 274.
https://doi.org/10.3390/chemosensors11050274