In Situ Monitoring and Kinetic Analysis of the Extraction of Nitric Acid by Tributyl Phosphate in N-Dodecane Using Raman Spectroscopy

ABSTRACT Understanding the fundamental rates of transfer and complex formation is crucial in maintaining optimal efficiency and effectivity in solvent extraction. Methodologies to analyze solvent extraction systems are lacking in that they are commonly performed off-line in subsequent experiments. Thus, a method to proficiently investigate solvent extraction systems in a Lewis cell using in situ Raman spectroscopy paired with chemometric modeling has been developed to allow for on-line analysis and monitoring. Forward and reverse interfacial transfer coefficients for the extraction of nitric acid by tributyl phosphate, a process crucial to used nuclear fuel reprocessing, were measured by spectroscopic monitoring of both phases simultaneously in a two-phase solvent extraction system. Concentration data was derived from the chemometric modeling using Raman spectra. The concentration data was fit to a nonlinear least squares regression model to allow for the calculation of the transfer coefficients in the system. The reverse interfacial transfer coefficient, kr, was determined along with the parameter 95% confidence intervals and 95% prediction intervals. The forward interfacial transfer coefficient, kf, was then back calculated from kr and the aqueous phase and organic phase equilibrium concentrations. The average calculated values of kr and kf were 2.56 (± 0.50) × 10−5 m s−1 and 4.75 (± 1.13) × 10−6 m s−1, respectively. The information obtained regarding solvent extraction parameters and transfer can be applied in the study of systems of higher complexity, involving complex formation and their transfer across a liquid:liquid interface.


Introduction
[3] SX exploits the partitioning of solutes between two immiscible liquids to drive solute separation, where interfacial transfer is usually rapid enough that net extraction rates are controlled by molecular diffusion to the interface.Typically, direct quantification of analytes as they transfer across an aqueous:organic interface is difficult due to the inherent asymmetry of competitive hydrophobic-hydrophilic forces at the interfacial boundary, giving rise to interfacial tension. [4]reviously, direct measurement of interfacial tension was used to investigate the liquid-liquid interface, [5] but this method does not provide molecular insights into the behavior of chemically reactive species at the interface or the influence of reactivity on interfacial transfer.
Methods that reveal quantitative information about the interfacial transfer of chemically reactive species during SX are usually indirect and off-line.Changes in concentrations of the reactive analytes in one or both of the immiscible phases can be measured by subsampling. [6]Experimental SX processes can be performed using a rotating diffusion cell, [7] Lewis cell, [8,9] , centrifugal contactor, [10] the single drop method, [11] Nitsch cell (a prototype of a stirred cell), [12,13] and the rotating membrane cell (RMC). [14]Within a Lewis cell, the transport process is generally divided into the diffusive process to the interface and the subsequent mass transfer process across the interface.While the Lewis Cell does provide many experimental benefits, the sample volume required per experiment is quite high, which is problematic especially when working with samples in harsh environments. [15]Secondly, the interfacial area available in a Lewis Cell is typically small, which can cause slow mixing and slow rates of reaction (depending on the system of interest), resulting in long experimental times. [15]Most reports from the 1980's and earlier relied on monitoring changes in an analyte in only one of the immiscible phases. [6]Mass transfer coefficients and extraction rates were obtained, however, results were often empirical and uncertainties were higher than desired due to operational hydrodynamic issues. [15]arge-scale processing of nuclear materials has historically been achieved by SX using the welldocumented Plutonium Uranium Reduction EXtraction (PUREX) process. [16]During the Cold War, target materials were irradiated to produce plutonium (Pu) for nuclear weapons.Plutonium was first dissolved in concentrated nitric acid (HNO 3 ), and then was extracted into organic diluents by complexation with tributyl phosphate (TBP).Following the end of the Cold War, nuclear materials processing has shifted to the recycling of uranium (U) and Pu via commercial SX technologies such as COEX TM (CO-EXtraction of actinides). [2,17]COEX also relies on the use of TBP and other complexants to extract both U and Pu out of HNO 3 solutions containing dissolved, irradiated fuels.The design, operational safety, and safeguarding of these processes relies on the ability to monitor the transfer of reactants and other analytes in situ.[20][21][22][23][24][25] In addition, second harmonic generation (SHG) monitoring is a useful tool to monitor local interfaces at the molecular level. [4][29][30] In the extraction process studied here, HNO 3 and TBP form a 1:1 adduct HNO 3 •TBP, [9,[28][29][30] as shown in Equation ( 1), below: This can be simplified to: The extent of HNO 3(aq) transferred into the organic phase depends on the chemical activity of HNO 3(aq) in the aqueous phase.The low solubility of TBP in the aqueous phase (≈ 10 −3 M) [8,26] indicates that minimal amounts of TBP can enter the aqueous phase, thus it can be assumed that the total TBP concentration in the organic phase is not changing.First, the uncomplexed, undissociated acid is transported by convection in the aqueous phase to the aqueous:organic interface.At the interfacial region, the HNO 3 •TBP adduct is formed, and the adduct is then transported away from the interfacial region into the bulk organic phase.Initial computational studies (Servis, M., McCue, A., Clark, A., Personal communication, 2017), indicate that the interfacial region between the organic and aqueous phase in this system exists more as an undefined region of both organic and aqueous phase moieties.These preliminary results show that due to the nature of this intermediate region, the transport of the formed adduct is hindered and slowed in this region before fully transferring to the bulk organic phase.Thus, the transfer of the HNO 3 •TBP adduct from the interfacial region into the organic bulk phase is the rate controlling factor in this system. [9]][33] At high nitric acid concentrations it has been shown that significant amounts of a 2:1 complex of (HNO 3 ) 2 •TBP forms. [34]However, work by Davis [35] shows that this species does not form as a major component until the HNO 3 concentration is greater than 7 M, while Orekhov found the threshold was around 9 M. [30] While the authors agree that a 2:1 complex is justified at higher concentrations, only the 1:1 complex will be focused on for this work due to the PUREX relevant concentrations (3 M HNO 3 ) studied.This 1:1 adduct is thought to be hydrogen-bonded to form a bridge between the HNO 3 proton and the phosphoryl group of TBP in the form of Figure 1. [27]he solubility of TBP in HNO 3 is low (≈10 −3 M) [8,26] suggesting that only small amounts of TBP can enter the aqueous phase and extract HNO 3 back into the organic phase.Two-film theory of mass transfer, [30] however, assumes that both HNO 3 in the aqueous phase and TBP in the organic phase can each diffuse across their own interface into a thin film on each side of the interface and react with one another at or close to the interfacial region.Lawson et al. [7] assumed a two-film model in the extraction process of HNO 3 from the aqueous phase whereby TBP could migrate into the aqueous phase, react with HNO 3 to form the adduct, and then diffuse back into the organic phase.Thus, the reaction was assumed to occur in the aqueous film in that scenario.While many agree that the reaction is occurring at or very close to the interface [9,26,[36][37][38] no agreement in literature currently exists which explains the exact location of the reaction within the two phases.
The extent of transfer of HNO 3 into the organic phase (HNO 3(org) ) depends on the chemical activity of HNO 3 present in the aqueous phase (HNO 3(aq) ). [30]The transfer of HNO 3 across the interface requires complexation with TBP.The "free" TBP concentration in the organic phase, or the uncomplexed TBP, is the difference between the known total TBP concentration (also the initial concentration) in the organic phase and the HNO 3 •TBP (org) adduct concentration in the organic phase.HNO 3 •TBP (org) can be determined by measuring the extracted HNO 3(org) concentration or calculated from a mass balance on the HNO 3(aq) concentration.
The expected concentration of HNO 3(org) , i.e. the concentration of the adduct HNO 3 •TBP (org) , can be determined as a function of the HNO 3 chemical activity a HNO 3 aq ð Þ in the aqueous phase and the initial TBP molar concentration [27] and an equation can be derived of the form, [27] HNO 3 org The molecular activity coefficient of the undissociated acid was used, as opposed to the dissociated acid, as the intact HNO 3 molecule is being extracted into the organic phase to form the HNO 3 •TBP adduct.Therefore, for calculations pertaining to Equation (2), values for the molecular activity coefficients of the undissociated acid, HNO 3 , were used here. [39]ollowing mathematically modeling the interfacial transfer of HNO 3 , as described using Equation (2), and measuring the transfer experimentally, we utilized an on-line, in situ methodology to monitor the extraction of HNO 3 by TBP in n-dodecane in the Lewis cell.The on-line monitoring technique used here was Raman spectroscopy coupled with chemometric modeling.On-line monitoring coupled with chemometric analysis has been successfully used previously on a microfluidic platform to characterize PUREX relevant SX conditions in a microfluidic device. [40]Batch experiments performed in this work were modeled based on the PUREX process, with the region of process technical interest of 20 ≤ TBP ≤ 35% (v/v) and 1 ≤ HNO 3 ≤ 11.6 M. The Lewis cell extraction experiments, however, were only performed at PUREX relevant concentrations of 3 M HNO 3 and 30% (v/v) TBP in n-dodecane.The Lewis cell design provided simultaneous, continuous, on-line monitoring of the species of interest (HNO 3 ) in both phases using Raman spectroscopy.

Materials
Tributyl phosphate (TBP, purity 98%) and n-dodecane (purity 99+%) were purchased from Alfa Aesar and used to prepare organic phase solutions.Nitric acid (HNO 3 , ACS reagent grade, 70%) was obtained from Sigma-Aldrich, and was used in aqueous phase solutions.Sodium hydroxide (NaOH pellets, 98%) was purchased from Alfa Aesar and used to prepare NaOH solution for titrations to determine HNO 3 concentration.Distilled deionized water (DDI) used in this study was purified using a Barnstead E-Pure Ultrapure Water Purification System with a resistivity of 18.2 MΩ cm −1 .All materials were used without further purification.

Solution preparation
The organic phase was comprised of TBP diluted in n-dodecane (20≤ TBP ≤ 35% (v/v)).Each dilution was made by measuring TBP, by volume, into a calibrated volumetric flask and diluting with n-dodecane to the final target TBP concentration.The TBP molarity was calculated according to Equation (3): where ρ TBP is the density of TBP, and square brackets represent concentration (mol/L).
The aqueous phase was comprised of 1-11.6 M HNO 3 and was prepared in calibrated volumetric flasks by pipetting volumes of stock HNO 3 and diluting to the final concentration with DDI.The HNO 3 concentrations in the aqueous phases were measured by automated titration (905 Titrando and 778 Sample Processor with tiamo™ software, version 2.4, Metrohm).

Batch extractions
Equal volumes of the organic and aqueous phases were used to prepare batch extraction samples.Samples of varying aqueous and organic concentrations were prepared by contacting 12.4 mL of HNO 3 (1 M to 11.6 M) with 12.4 mL of TBP in n-dodecane (20% (v/v) to 35% (v/v) TBP in n-dodecane) in 50 mL polypropylene centrifuge tubes (Corning).Samples were mixed using a vortex mixer (Scientific Industries Vortex Genie 2) at 2350 rpm for 15 min.Immediately following mixing, phases were centrifuged (Damon/IEC Division, IEC HN-SII centrifuge).The aqueous and organic phases were then manually separated for further analysis.Pre-and post-contact HNO 3 concentrations (where subscripts denote the aqueous (aq) and organic (org) phase) were determined by auto-titration with NaOH; HNO 3(org) concentrations were calculated from the difference between the starting and ending HNO 3(aq) concentration.

Raman training set for chemometric modeling
A Raman training set was collected from batch extraction samples to build the chemometric model.The training set is used to calibrate the chemometric model to recognize concentrations and complexes in solution.Raman spectra of the separated phases from batch extractions were collected using an RS2000 Raman spectrometer (InPhotonics, Inc.) containing a thermoelectrically cooledcharge coupled device detector.A focused fiber-optic InPhotonics RamanProbe, operating at -54°C, with a 670 nm laser and a 150 mW visible diode laser probe as the source, was operated in a 180°back reflection mode.Each spectrum acquisition had an integration time of 1 s, and 10 acquisitions were collected per sample.

Chemometric modeling
Chemometric models for the quantitative measurement of species were constructed from samples with known concentrations of HNO 3(aq) and TBP (org) solutions.Samples were prepared in the same manner as described for the batch extractions, and pre-and post-contact phases were both analyzed.A total of 65 organic and aqueous phase extraction experiments were analyzed by Raman spectroscopy to develop the model and incorporate the phase transfer of HNO 3 from the aqueous to the organic phase.Aqueous solutions varied in concentration from 0 M to 4 M HNO 3 , while the organic phase measurements varied in concentration from 0% (v/v) TBP to 35% (v/v) TBP in n-dodecane.Post-contact organic phase samples contained varied concentrations of HNO 3 (0 M to 1.04 M HNO 3 ) as a consequence of the transfer.The raw spectra files were input into a matrix database in MATLAB (version 7.9, Mathworks Inc., Natick, MA, USA).
Commercial software (PLS Toolbox, version 6.2.1, Eigenvector Research Inc., Wenatchee, WA, USA) was used to develop the partial least squares (PLS) models where spectral data was correlated to concentration data in order to develop a quantitative model.The PLS method has been widely utilized, [41,42] including in the modeling of spectroscopic data. [21,24,43]By selecting areas in the spectra that contain analyte chemical information, while eliminating those that do not contain such information, the PLS regression model can be improved. [42,44]Models were evaluated using external validation sets in addition to cross validation of the training sets.The method of preprocessing used depended on the phase analyzed (aqueous or organic).In the case of the aqueous phase, standard normal variate scaling was used to normalize for laser power fluctuations, and the baseline was corrected by applying a 1st derivative.The organic phase preprocessing involved applying a 1st derivative and mean centering the spectral data.An example of a parity plot comparing the chemometrically measured concentration of HNO 3 to the titrated concentration of the training set in the aqueous phase is shown in Figure 2. The 1:1 correlation indicates the model is accurately measuring concentrations.

Lewis cell design
The Lewis cell was manufactured specially for Pacific Northwest National Laboratory (PNNL) based loosely on the ARMOLLEX (ARgonne MOdified Lewis cell for Liquid-liquid EXtraction kinetic measurements) design by Danesi et al. [45,46] A schematic of the set-up, showing the placement of the extraction cell in relation to the stirring and stabilization apparatus, is shown in Figure 3.
The extraction cell consisted of many components including: stainless steel cylindrical inserts (including mesh and external rings), a 1 L water jacketed vessel to control extraction temperature, and a Teflon lid to maintain temperature and prevent evaporation.The mechanical design of the stainless steel cylindrical assembly within the interior of the Lewis cell has been described and characterized previously. [46]Briefly, the water jacketed cell is a custom made 1 L Pyrex glass water jacketed beaker that connects to a programmable temperature-controlled water re-circulator (Cole-Parmer Polystat) using Tygon tubing (0.79 cm inner diameter).
The organic and aqueous phase are independently stirred by magnetic stir bars (Bel-Art Double Spinfin Magnetic Stirring Bar [2.54 cm × 1.91 cm]).The aqueous phase stir bar was rotated via a stir plate (Thermo Scientific Super-Nuova Multi-Place Stirring Hotplate), while the organic phase stir bar was attached to a custom spindle with adjustable height that was rotated by a modified Parr stirrer (Parr Instruments Series 4843 Reaction Vessel, custom spindle fabricated at PNNL).Both the Parr stirrer and the stir plate had a digital readout for spin speed (rpm).Each rotated in a clockwise manner, allowing fluid to flow convectively, as in the Danesi et al. design. [45]It has been previously shown that stir speeds for the two phases do not need to match exactly, [45] justifying the use of two different stir mechanisms.
The organic and the aqueous phase each contained independent Raman probes connected to spectrometers to allow for in situ measurement of both the organic and aqueous phase (described in full in the following section).The probes were run simultaneously on separate computers using MoleCue software (InPhotonics, Inc., version 1.82), and were mechanically held in place in the cell.

Lewis cell extraction experiments
Lewis cell extraction experiments were performed with concentrations of the organic and aqueous phase that were industrially relevant in the PUREX process. [16,47]Thus, extractions were performed with 3 M HNO 3 as the aqueous phase and 30% (v/v) TBP in n-dodecane as the organic phase.Once assembled, water was circulated through the water-jacketed Lewis cell and allowed to come to both chemical and thermal equilibrium at 25°C.Following the addition of 365 mL of 3 M HNO 3 , the bottom stir bar was activated.In order to not disturb the aqueous phase, 255.5 mL of H 2 O washed n-dodecane was slowly added to the cell and, once the addition was complete, the top stir rod was spun at an identical rate to that of the bottom stir bar.The Teflon lid was secured and the cell was jacketed with foil to reduce cosmic ray interference in the Raman collection.The Raman probes were activated to collect spectra concurrently from the two phases.Spectra were measured at 5 s intervals with a 1 s acquisition time.The cell was run for 2 h to establish the background spectra of the aqueous and organic phase and allow thermal and chemical equilibrium to be achieved before the extractant, TBP, was added.After 2 h of equilibration, 109.5 mL of TBP (corresponding to a final solution concentration of 30% (v/v) TBP in n-dodecane) was quickly added (< 2 min duration), but carefully, so as not to disturb the aqueous:organic interface.The extraction ran for an additional 4 h, with spectra collection as stated above, for a total experimental time of 6 h.Upon completion, the aqueous and organic phases in the Lewis cell were immediately separated for analysis, and the aqueous phase was titrated as previously described to confirm the final HNO 3(aq) concentration.

Lewis cell stir speed dependence experiments
The dependence of stir speed on extractions was measured using the same experimental set up as described in the Lewis cell extraction experiments.Analyses were performed at equal stir speeds of 125, 200, 275, 330, 375, 400, and 425 rpm for each phase.Beyond 425 rpm the interface between the two phases began to become unstable and significant mixing began to occur which was undesirable for the purpose of this work.Therefore, stir speeds of ≤ 425 rpm were used here.

Mathematical analysis of kinetics data
The rate of extraction of HNO 3(aq) to HNO 3 •TBP (org) was determined using the Lewis cell.Equation (2) describes the transfer of the HNO 3 (org) from HNO 3(aq) immediately adjacent to the aqueousorganic interface.Using the Lewis cell for the experiments allows the assumption that the bulk organic and aqueous phases are homogenous in composition and that any concentration gradients that exist occur near the interface. [48]The rate coefficients for interfacial transfer between the aqueous and organic phases for the reaction defined in Equations (5A, B) were defined as k f and k r , for the forward and reverse transfer coefficients respectively.These transfer coefficients include both the mass transfer effects and the molecular kinetics effects.The rate equations together with their initial conditions for the interfacial transfer coefficient are: [15,[48][49][50] where A is the interfacial area of the interface (calculated as 79.15 cm 2 ); V aq and V org are the volumes of the aqueous and organic phases, respectively; t is time in minutes; and square brackets indicate molar concentrations.This set of equations presumes that no side reactions occur at the interface or in the well-mixed bulk solutions, and that the initial HNO 3(org) concentration in the organic phase is 0. Equations (4A, B) can be solved by integrating over time and then applying the initial conditions to get, in the case where V aq = V org = V = 365 mL, which reduce to, at long times, where the eq subscript denotes that the system has come to equilibrium.Finally, Equations (6A, B) can be expressed in the form, in preparation for parameter estimation by nonlinear least squares regression, where D is defined as the distribution ratio between the respective phases such that, Equations (6A, B) are equivalent to the linearized equations obtained by Heller et al. [46] Together Equations (8A, B) are used to estimate k f and k r from experimental data.

Nonlinear regression and statistical analysis
The reverse transfer coefficient was determined by fitting the experimentally monitored HNO 3 concentration in the aqueous phase and the adduct concentration in the organic phase to Equations (8A,B) using MATLAB R2017a.Nonlinear least squares regression of multiple data sets with shared fitting parameters was performed using the MATLAB function, nlinmultifit.mdeveloped by Alvinadav. [51]The regression was based on minimizing the sum of squares of the following objective function (Z), where the subscripts exp and model indicate the experimental data and the model predictions, respectively.The best-fit reverse transfer coefficient for each of the three data sets at a stir speed of 400 rpm are shown in Table 1.
The forward transfer coefficient was then calculated from Equation ( 9) since the concentrations of HNO 3 in the aqueous phase and the concentration of adduct in the organic phase at equilibrium were determined as described previously.The 95% parameter confidence intervals for k r were then calculated using the MATLAB function nlparci.m.These calculated values are also given in Table 1.In addition, 95% prediction intervals (PI) for a new observation for each fit were estimated according to the methods by Ryan, [52] and modified by Bhattarai et al. [53] such that, where y model,i is the aqueous phase or organic phase model data, i.e. fit, t α/2,DOF is the Student's t-inverse cumulative distribution function for 100(1-α)% confidence interval for each phase, α equals 0.05 for a 95% confidence interval, DOF is the degrees of freedom for each phase, σ is the standard error for each phase, c ii is the ith diagonal element of the covariance matrix, and J is the Jacobian matrix which is evaluated at the parameter's best-fit value.The latter two values were obtained directly from MATLAB's nlinmultifit.m [51]function as a result of the nonlinear least squares regression analysis.
Table 1.Kinetic results for extraction analysis at a stir speed of 400 rpm for three trials.The nonlinear regression was based on k r and the associated 95% confidence intervals are given.
TBP % (v/v) (± 0.2%) [HNO 3(aq) ] 0 (± 0.02 M) [HNO 3(aq) ] eq (± 0.04 M) rate of mass transfer.All remaining experiments, unless otherwise noted, were performed at 400 rpm in each phase, to maintain a kinetically limited regime for the transfer of HNO 3 from the aqueous phase to the organic phase within the Lewis cell.

Lewis cell extractions
Representative Raman spectra from the Lewis cell extractions of 3 M HNO 3 by 30% (v/v) TBP in n-dodecane are provided in Figure 4 for both the aqueous and organic phases.The system was equilibrated for ≈ 2 h in the absence of extractant, thus t 0 occurs at 122.5 min, the time at which the extractant, TBP, was added to the system.The Raman spectra of the aqueous phase Figure 4 (A) shows a 12% decrease in the intensity of the NO 3 − peak at 1046 cm −1 (which compares well with the value of 1047 cm −1 , ν 1s NO 3 , in literature [56,57] ) after the addition of TBP from t 0 to t eq .This corresponds to the transfer of HNO 3 across the interface into the organic phase as a consequence of HNO 3 •TBP adduct formation.Accordingly, during the same time frame an increase in Raman intensity is observed for the NO 3 − peak at 950 cm −1 Figure 4b in the organic phase, signaling an increase in the concentration of the adduct in the organic phase (ν N-(OH), 955 cm −1 in literature [56,57] ).
The concentration decrease in the aqueous phase and resulting increase in the organic phase is quantified by correlating the Raman spectra using chemometric modeling of the concentration of HNO 3 in the respective phases.The concentration values for both phases as a function of time are shown in Figure 5.In this figure, the time was corrected to reflect time 0 as the time when the TBP extractant was added to the  9) using the equilibrium concentrations.As a result, the forward and reverse interfacial transfer coefficients from each experiment were determined.These values, the initial HNO 3 concentration, the equilibrium concentrations, k r 's 95% parameter confidence intervals (CIs) from the nonlinear least squares regression, and the propagated error on k f are reported in Table 1, along with the average k r and k f values from the three trials.
The triplicate calculated constants of k f and k r agree well with each other.In the kinetic plateau regime, the first-order average k f and k r values were 4.75 (± 1.13) × 10 − [6] m s −1 and 2.56 (± 0.50) × 10 − [5] m s −1 , respectively.The resulting chemometric model of the change in concentration of the organic and aqueous phase matched well with the known concentration from automated titration pre-and post-extraction (Fig. S4).The concentrations versus time plot in Figure 5 verifies the appearance of HNO 3 in the organic phase and the disappearance of HNO 3 in the aqueous phase.However, there was more background noise and scattering in the aqueous phase.The reason for this larger ratio is likely due to two reasons: a) the Raman instrument recorded some background and fluorescence from the glass on the bottom of the Lewis cell, adding to a higher background and higher uncertainty in the measurements, and/or b) the Raman instrument collected sporadic signal from the water flowing within the water jacket.Nevertheless, calculations were performed to compare the k f and k r calculated using the chemometric model from both phases.The model predictions and their respective 95% prediction intervals fit well to the aqueous phase experimental data.However, the model fit is in less agreement to the organic phase experimental data, especially between time points 0 seconds to 5000 seconds.The modeled curves show that the decrease in HNO 3(aq) is not mirrored by the HNO 3 •TBP (org) increase, showing that there is a discrepancy in the chemometric modeling of the organic data that is not fully understood at this point.Future work involves the improvement of the model, especially in the organic phase, by further studying transient species that may be affecting the spectra, as previously observed in the same Lewis cell by Heller. [58]n any case, the in situ Raman spectroscopic analysis and subsequent chemometric model allowed for measurements of concentration in the organic and aqueous phases simultaneously.As mentioned previously, the quantification of analytes as they transfer phases is quite difficult to observe, but this work validates a methodology in which HNO 3 was monitored as it transferred from the aqueous to the organic phase via adduct formation at the interfacial region.
Pandey et al. [26] presented kinetic results in a constantly stirred cell for a chemical system similar to that presented here.Burger [8] also presented kinetic results for a constantly stirred cell with similar chemical systems, which were interpreted by Olander et al. [9] in the context of the cell volume and interfacial area.In the case of the data treatment by Pandey et al. [26] the mathematical model used to treat the data was fundamentally different than the model used here.Pandey assumed three models for the experimental data: (1) a very slow reaction regime that is mass transfer independent, (2) a diffusion controlled regime, and (3) a fast reaction in the thin film near the interface. [26]Experimental results ruled out the presence of any of these three regimes, and an intermediate regime between a slow and fast reaction was instead proposed. [26]In the model proposed by Olander et al., [9] experimental results reflected a diffusion controlled mechanism.The model assumed that the complexing reaction was reversible, and that the mass transfer and equilibrium chemical reaction occurred in the organic phase. [9]Model assumptions affect the kinetic results calculated, and unless all assumptions and models are identical, results are not comparable.Data presented in this paper was modeled from a kinetically controlled regime.Thus, these fundamental differences mean the parameters calculated here cannot be compared to those presented by Olander et al. [9] or Pandey et al. [26] However, our organic phase experimental data fits reasonably well to data from Pandey et al., [26] as shown in Fig. S5, despite the difference in forward and reverse transfer coefficients that cannot be compared.This indicates that the theoretical model and the assumptions made are important aspects of this work going forward.
Values determined in this system help in the understanding of kinetic rates of HNO 3 extraction in this Lewis cell setup.The k f and k r values allow for the examination of a more complex extraction process using this novel and effective system of combining Lewis cell testing with chemometric modeling.The chemometric model can be expanded to more complex systems in future analysis to provide on-line, in situ monitoring of product formation and interfacial transfer.Future work includes, but is not limited to, the study of the formation of degradation and hydrolysis products typical in PUREX reprocessing.

Conclusions
A methodology was developed and tested to allow for on-line concentration measurements of species of interest in a two phase Lewis cell system.Raman spectra collected can give a greater understanding of the complexation and species formed in a biphasic system, and the resulting transfer between phases.Batch extractions of HNO 3 by TBP dissolved in n-dodecane were examined and the proposed model of HNO 3 extraction was found to be consistent with the experimental data.The results suggest that HNO 3 distribution to the organic phase, particularly in the region of industrial interest in the PUREX process at 20 ≤ TBP ≤ 35% (v/v) and ≈ 1 to 11.6 M HNO 3 concentrations, can be well modeled by assuming a 1:1 stoichiometric ratio of HNO 3 and TBP reaction to form the HNO 3 •TBP adduct.The chemical equilibrium model developed was best represented by using the chemical activity of molecular HNO 3 in the aqueous phase and the assumed ideal behavior of the TBP and extracted HNO 3 , as the free TBP and the HNO 3 •TBP adduct, in the organic phase.
The forward and reverse rate constants of interfacial transfer for the transfer of HNO 3 to the organic phase, forming the HNO 3 •TBP adduct, were accurately determined using a novel Lewis cell coupled with Raman spectroscopy and subsequent chemometric modeling.The experimental data for both phases was fit by nonlinear least squares regression that included 95% parameter confidence intervals and 95% prediction intervals.The results presented here can be used to aid in the determination and understanding of the complexation and the transfer kinetics of additional species moving across the aqueous:organic interface by using the rate constants determined.This work can be expanded on to monitor the interfacial transfer of more advanced systems.

Figure 1 .
Figure 1.The adduct formation between the HNO 3 proton and the phosphoryl group from the TBP.

Figure 2 .
Figure 2. (A) A parity plot illustrating the chemometrically measured concentration of HNO 3 in comparison to the titrated HNO 3 in the aqueous phase; (B) Collected Raman spectra showing the Raman intensity from the NO 3 − band as a function of concentration, where a solid line represents a pre contact sample and the corresponding dotted line of the same color represents a post contact sample.

Figure 3 .
Figure 3.A schematic illustration of the experimental set up of the Lewis cell with the included spectroscopic probes showing the placement for in situ analysis.

Figure 4 .
Figure 4. Representative Raman spectra of the (A) full spectra of the aqueous phase, with the decrease in the NO 3 − peak at 1046 cm −1 , and (B) the area of NO 3 − peak growth in the organic phase (950 cm −1 ).

Figure 5 .
Figure 5.The HNO 3 concentration, modeled using chemometric analysis of the aqueous (•) and organic (•) phase from the Raman spectra in Figure 4, plotted as a function of extraction time.The best-fit (solid lines) and the upper and lower 95% prediction intervals (dashed lines) are also shown for each phase.