Raman Spectroscopic and ab Initio Investigation of Aqueous Boric

Article pubs.acs.org/IECR

Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX-XXX

Raman Spectroscopic and ab Initio Investigation of Aqueous Boric Acid, Borate, and Polyborate Speciation from 25 to 80 °C Lucas M. S. G. A. Applegarth,† Cory C. Pye,‡ Jenny S. Cox,† and Peter R. Tremaine*,† †

Department of Chemistry, University of Guelph, Guelph, Ontario, Canada N1G 2W1 Department of Chemistry, Saint Mary’s University, Halifax, Nova Scotia Canada B3H 3C3

‡

ABSTRACT: Temperature-dependent Raman studies of the aqueous speciation of boric acid and sodium borate have been carried out at 25 and 80 °C. Normalized solvent-corrected reduced isotropic Raman spectra were obtained from perpendicular and parallel polarization measurements using perchlorate anion, [ClO4]−, as an internal standard. The intensity variations of these bands with concentration and temperature provided strong evidence that these arise from boric acid B(OH)3, borate [B(OH)4]−, and the polyborate species [B3O3(OH)4]−, [B4O5(OH)4]2−, and [B5O6(OH)4]−. A very weak high frequency shoulder on the borate band may indicate the presence of the diborate species [B2O(OH)5]−. Temperature- and concentration-independent quantitative Raman molar scattering coefficients (S) for the symmetric vibrational bands of boron-containing species were calculated, consistent with the mixed solvent electrolyte model reported by Wang et al. (Pure Appl. Chem. 2013, 85, 2117−2144) up to approximately 100 °C. The band assignments and scattering parameters reported here provide a framework for using reduced isotropic Raman spectroscopy as a research tool for measuring quantitative speciation of boric acid/polyborate solutions under conditions relevant to nuclear reactor primary coolant circuits and spent fuel bays, among other applications.

1. INTRODUCTION Aqueous boron systems are of broad interest to earth sciences and geochemistry1−6 as well as a range of emerging industrial applications such as fuel cells,7 hydrogen storage,8 and nanotechnology.9 In the nuclear industry, boron solutions are used as a chemical shim to control the neutron flux in the primary coolant of pressurized water reactors (PWRs),10,11 which typically operate at temperatures from 250 to 310 °C. Under sub-nucleate boiling conditions, borates can concentrate on fuel cladding under thin oxide and ferrite fuel deposits, where they can cause significant losses in neutron flux. Boric acid is used as a neutron absorber in spent fuel bays and in the moderators of the proposed Canadian Supercritical Water-Cooled (SCWR) reactor and the Indian Advanced Heavy Water reactor, which operate in the range 25 to 80 °C. It is also injected at high concentrations into reactor containment buildings to suppress radiation in the event of a nuclear reactor loss-of-coolant accident. Accurate thermodynamic properties are needed for these applications, to model the transport of boron-containing compounds by dissolution and precipitation reactions, and the effects of aqueous boron species on pH, mineral and corrosion product solubility, and the colligative properties of water. The development of accurate chemical equilibrium models for aqueous boric acid systems is particularly challenging because of their complex speciation in solution, including the formation of polyborates and polyborate−metal complexes, and the ability to precipitate a number of solid phases.12,13 © XXXX American Chemical Society

The structure, hydration, and thermodynamic properties of borate ions have been studied by conductivity;14 potentiometry;15−19 densimetry;20,21 vapor−pressure osmometry;22 UV− visible spectroscopy;23,24 NMR;25 dielectric relaxation spectroscopy;26 X-ray scattering;27 infrared spectroscopy;28 and Raman spectroscopy.5,29−31 Several of these experimental studies have reported thermodynamic models for calculating the speciation of aqueous borates as a function of temperature and pressure.17,22,23,33 Although boric acid speciation has been studied over a broad range of temperatures and pressures, the identity and structure of certain polyborates are still the subject of active investigation. Recently, Wang et al.13 compiled a critically evaluated comprehensive thermodynamic database for aqueous borate species covering an expansive range of temperatures and pressures which were then implemented into the Mixed Solvent Electrolyte (MSE) activity coefficient model of OLI Studio (OLI Systems, Inc.).34,35 Their model includes the following reactions of boric acid, to form the borate ion and four polyborate species: B(OH)3 + 2H 2O ⇌ [B(OH)4 ]− + H3O+

(R1)

Received: August 10, 2017 Revised: October 27, 2017 Accepted: October 28, 2017

A

DOI: 10.1021/acs.iecr.7b03316 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Table 1. Stoichiometric Concentrations of Boric Acid/Sodium Borate Solutions solution no.

m(B(OH)3), mol·kg−1

m(NaOH), mol·kg−1

m(NaClO4), mol·kg−1

buffer ratio mNa/mB

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.7971 0.7866 0.7661 0.7156 0.6434 0.5680 0.5101 0.8148 1.015 1.503 2.001 1.043 1.315 1.450 1.748 1.988 2.272

0.0034 0.0293 0.0843 0.1616 0.2714 0.4183 0.5073 0 2.026 2.026 2.026 0.9568 0.9568 0.9568 0.9568 0.9568 0.9568

0.0934 0.1021 0.1018 0.1052 0.1046 0.1033 0.0988 0.1055 0.0996 0.0996 0.0996 0.1082 0.1082 0.1082 0.1082 0.1082 0.1082

0.0043 0.0372 0.1100 0.2258 0.4218 0.7364 0.9945 0 1.997 1.348 1.013 0.9178 0.7279 0.6599 0.5474 0.4814 0.4212

2B(OH)3 + H 2O ⇌ [B2O(OH)5 ]− + H3O+

(R2)

3B(OH)3 ⇌ [B3O3(OH)4 ]− + H 2O + H 2O+

(R3)

4B(OH)3 ⇌ [B4 O5(OH)4 ]2 − + H 2O + 2H 2O+

(R4)

5B(OH)3 ⇌ [B5O6 (OH)6 ]3 − + 3H3O+

species measured by potentiometric titration were assigned to the species [B2O(OH)7]−, but its formula and structure were not confirmed. Ab initio calculations using density functional theory (DFT) have proven useful in identifying structures of stable species, which can then be compared to vibrational spectra.31,36 The recent study by Zhou et al.31 reported optimized geometries, energies, and vibrational frequencies of the metaborate, borate, and polyborate species and used them to interpret Raman spectra in both gaseous and aqueous phases from their own measurements and those of other authors.29,30 These results are consistent with more recent computational studies on gas phase polyborate anions by Beckett et al.32 Although their work confirmed that the triborate and tetraborate species shown in reactions (3) and (4) do exist in concentrated solutions, Zhou et al.31 interpreted their Raman spectra for concentrated solutions of K2B4O7 as containing the pentaborate species [B5O6(OH)4]−, rather than the species [B5O6(OH)6]3− proposed by Mesmer et al.17 The structures for these species, as determined from the computational studies in the present study, are presented and discussed below in Section 3.3. The goal of the present study was to determine quantitative Raman spectra and Raman scattering coefficients for boric acid, borate, and the polyborates, which can be used as tools to study speciation and to develop a self-consistent chemical equilibrium model that is valid over a wide range of temperatures and pressures. The study was initiated on the premise that the comprehensive MSE model developed by Wang et al.13 is accurate near ambient temperatures. The model was tested by using polarized Raman spectroscopy to measure the reduced isotropic spectra of sodium borate solutions over a very wide range of compositions and concentrations at 25 and 80 °C. Comparisons of the Raman spectra with predictions using density functional theory were first used to identify the polyborate species in solutions, in order to confirm Wang et al.’s selection of the tri- and tetraborate species, and to resolve the controversy about the nature of the pentaborate. The concentration-dependent spectra were then used to determine accurate reduced isotropic Raman scattering coefficients, consistent with this MSE model. The novelty of this work lies in the experimental difficulty of obtaining quantitative reduced isotropic Raman spectra for these species; the identification of the structure of the pentaborate ion;

(R5a)

31

Recently, Zhou et al. reported evidence for a monovalent pentaborate species B5O6(OH)4−, based on Raman measurements at room temperature. The ionization reaction to form this pentaborate from boric acid may be represented as 5B(OH)3 ⇌ [B5O6 (OH)4 ]− + 4H 2O + H3O+

(R5b)

In addition to the neutral boric acid species, B(OH)3, Wang et al.13 also reported statistically significant formation constants for aqueous metaboric acid, HBO20, and B2O30 by regressing high temperature solubility data. The model thus includes the condensation reactions of boric acid and borate to form aqueous metaborate and polyborate species: B(OH)3 ⇌ HBO2 + H 2O

(R6)

2[B(OH)3 ] ⇌ B2O3 + 3H 2O

(R7)

It should be noted that no direct measurements of the formation constants for reactions 6 and 7 have been reported in the literature. Although the ionization constants for polyborate formation reported by Wang et al. are largely consistent with the accurate high-temperature values reported by Mesmer et al.,17 later refitted by Palmer et al.,33 the stoichiometries were determined by regression of the MSE activity coefficient model to a much larger set of experimental data. Mesmer’s high temperature ionization constants were measured by potentiometry in a stateof-the-art hydrogen concentration cell, and the boron stoichiometry and charge of each species was determined by nonlinear regression of a large matrix of concentrationdependent pH data. Their method was unable to resolve which of the tetraborate or pentaborate species were present, since both had similar statistical significance. Potentiometric titrations are similarly unable to distinguish between borate, metaborate, and polyborate species having the same boron stoichiometry and charge. Formation constants for the singly charged diborate B


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pressure tested in an oven at a temperature 25 °C above the experimental temperature to ensure mechanical integrity. Stokes Raman spectra of solutions in quartz cells were collected at 90° scattering angle geometry, with slit widths of 1000 μm, at both parallel and perpendicular polarizations relative to the exciting monochromatic lasing line. A schematic diagram of the optical setup is shown in Figure 1. For each polarization

and the self-consistent, quantitative agreement between the Raman band assignments, temperature-dependent formation constants, and ab initio structures for these important species. The equilibrium speciation of hydrothermal boron solutions is of considerable interest to chemists, geochemists, and materials scientists who are carrying out basic research in nuclear reactor chemistry, nuclear waste management, and ore body formation. Together with recently reported high pressure capillary cell methods,37 the quantitative scattering coefficients reported below provide a means of using Raman spectroscopy to determine the quantitative speciation of aqueous polyborates over a range of temperatures.

2. EXPERIMENTAL METHODS 2.1. Chemicals and Solution Preparation. Boric acid (99.9995%), anhydrous sodium perchlorate (99.3%), and sodium hydroxide aqueous solution (50% w/w) were purchased from Alfa Aesar. Potassium hydrogen phthalate (KHP, 99.95%) was purchased from Fisher Scientific. Two stock solutions of NaOH (1 and 2 mol kg−1) were prepared from the 50% w/w aqueous solution and standardized by triplicate titrations against KHP. All solutions were prepared by mass (±0.5%) and stored in sealed Nalgene bottles. Solutions with sodium/boron mole ratios 0 < mNa/mB < 1 were prepared from aqueous ∼0.8 mol kg−1 stock solutions of boric acid by adjustment with 2 mol kg−1 NaOH to various pH values between 3.73 to 11.45 (Solutions 1 to 8 and 12 to 17). Solutions with higher Na/B mole ratios, 1 < mNa/mB < 2, were prepared by adding solid boric acid to aliquots of the 1 or 2 mol kg−1 stock solutions of NaOH (Solutions 9 to 11). These solutions were calculated to be supersaturated with respect to precipitation of solid phases, according to the thermodynamic calculations presented below, however the spectra were reproducible to within ±2% throughout the runs and a careful examination of our solution containers and spectroscopic cells before and after the measurements showed no sign of precipitates. A small amount of solid sodium perchlorate was then added by mass into each solution, in order to provide a noncomplexing internal reference standard for Raman measurements. Solution compositions are listed in Table 1. 2.2. Raman Instrumentation. The Raman spectra were recorded with a custom-made Horiba Jobin Yvon LabRAM HR800 spectrometer constructed with both a microprobe and a large macrochamber. The instrument is equipped with an 800 mm focal length spectrograph; a 532 nm/250 mW Torus-200 diode-pumped solid-state (DPSS) laser; an edge filter with a Stokes cutoff of less than 120 cm−1; a 1024 × 256 pixel CCD detector that is Peltier-cooled to −70 °C; an 1800 line/mm holographic grating; a polarizer; and a scrambler. The measurements were carried out in the macrochamber, using a sample cell holder equipped with a calibrated Peltier heater/cooler element. Cell temperatures were measured by a resistance temperature detector (RTD) located inside the thermostatted copper compartment of the sample holder, and LabView VM software was used to control the cell temperature to a thermal stability of ±0.10 °C. Solutions for study by Raman spectroscopy were sealed in cells constructed from commercially available quartz tubing (Quartz Scientific Inc., OH, U.S.A.), 5.0 mm OD × 3.0 mm ID. The tubing was sealed on one end under an oxygen-gas torch, loaded with the solutions to a solution level of ∼50 mm in height, and then sealed on the other end to form a cell. Filled cells were sealed to a height of no less than 100 mm. The sealed cells were

Figure 1. Schematic of the 90° geometry setup of the Raman spectrometer, where Ez is the polarization of the incident laser beam on the sample and Iz and Iy are the intensities of parallel and perpendicular polarized Raman signal from the sample with respect to the incident laser beam.

orientation, nine spectra were taken and averaged to minimize the background noise. Spectra of both the internal reference standard (0.1001 mol·kg−1 NaClO4) and pure solvent (H2O) were recorded daily before sample collection to provide the baseline corrections required for quantitative spectral analysis. The spectrum of the internal reference standard was also recorded after the experiment to measure the instrument drift throughout the day. The spectra of the internal standard showed the instrument response to be stable to within ±5% over 16 h. The reproducibility of the peak areas in spectra from cells that were removed and reinserted into the temperature controller was typically within ±2%. 2.3. Raman Spectra. Quantitative baseline-corrected Raman spectra from the parallel and perpendicular polarizations, I∥(ω) and I⊥(ω), were successfully measured at 25 and 80 °C. An example of a solution of 0.8148 mol kg−1 boric acid at 25 °C is shown in Figure 2, displaying the polarized spectra of I∥(ω) and I⊥(ω), and the subsequent isotropic spectrum IIso(ω), with a boric acid band at 878 cm−1. Following the approach used by Brooker et al.38 and others,39,40 I∥(ω) and I⊥(ω) were combined to yield the isotropic spectrum IIso(ω): IIso(ω) = I∥(ω) −

4 I⊥(ω) 3

(1)

The isotropic spectra and the reduced isotropic spectra derived from them below consist only of bands arising from symmetric vibrational modes and do not contain contributions from asymmetric vibrations and librations. For the borate and polyborate species considered here, these spectra typically consist of only one or two strong bands from symmetric stretching vibrations and ring breathing modes. C


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Spectra of a solution of the internal standard, 0.1001 mol kg−1 NaClO4, were taken at the beginning and end of each day, to ensure that the detector response was stable, typically within 2%. A second spectrum of water solvent was also taken. The contribution of the water solvent was first subtracted from each reduced isotropic spectra between the frequency nodes 160 and 1100 cm−1, with no intensity adjustments. These water subtracted spectra were then normalized to the perchlorate peak area (AIS) and concentration (mIS) in the solution as shown in eq 5, ⎛ ISpectrum ⎞ RIso,Normalized = ⎜ ⎟mIS ⎝ AIS ⎠

The solvent subtracted reduced isotropic Raman spectra of the solutions were further corrected by the subtraction of the spectrum of the normalized reference internal standard solution, 0.1001 mol kg−1 NaClO4, between the frequency nodes 160 and 1100 cm−1, with no intensity adjustments. The initial spectrum recorded at the beginning of the experiment was used. Due to the varying peak intensities of each species, the subtracted baseline-reduced isotropic Raman spectra were divided into three segments in order to optimize the integrated peak areas. This permitted smaller weak peaks to be deconvoluted without being suppressed by the more intense peaks. The segments are related to the corresponding windows where the following speciation occurs: (1) tri-, tetra-, and pentaborate speciation from 450−675 cm−1, (2) borate and “diborate” speciation from 670−835 cm−1, and (3) boric acid from 830−915 cm−1. Each division overlapped by 5 cm−1, and divisions were the same throughout each analyzed spectrum. The segments were further baseline corrected by subtracting a straight line between the beginning and the end of each window (i.e., across the nodes). To maintain self-consistency, the same nodes were used for all the spectra throughout the study. This permitted peak deconvolution analysis to be obtained by fitting each band to a Voigt function, using the curve fitting program in OriginPro v9.0 with default convergence criteria (threshold >20% of the baseline noise). 2.4. Chemical Equilibrium Model for Spectral Analysis. The comprehensive thermodynamic mixed-solvent electrolyte (MSE) speciation model reported by Wang et al.13 and implemented in OLI Studio 9 was used in the quantitative

Figure 2. Isotropic, parallel, and perpendicular spectra for 0.8148 mol· kg−1 B(OH)3 in water (Solution 8) at 25 °C.

The isotropic spectrum IIso(ω) also contains contributions from Rayleigh-wing scattering and the thermal excitation of low frequency modes. These are described by the expressions, IIso(ω) = C Instr(ωo − ω)3 ω−1B−1Sj

(2)

⎡ ⎛ −hcω ⎞⎤ ⎟ B = ⎢1 − exp⎜ ⎝ kT ⎠⎥⎦ ⎣

(3)

where CInstr is a constant which depends on the instrument response, slit-width, solid collection angle, and absorption due to color; ωo is the absolute frequency of the incident laser, in wavenumber units; ω is the frequency dif ference of the scattered radiation (i.e., the Raman shift); B is the Boltzmann distribution for the thermal population of low frequency excited states; and Si is the intrinsic molar scattering activity for a Raman scattering process associated with species j. The exponent of the (ωo − ω) term is cubic for photon-based CCD detection systems and quartic for energy based detectors.38−40 To remove these effects, our data treatment is based on the reduced isotropic form of the spectrum, RIso(ω), RIso(ω) = IIso(ω)(ωo − ω)−3 ωB

(5)

(4)

The reduced isotropic Raman spectra RIso(ω) were calculated from IIso(ω) using eqs 3 and 4, using code written on the Wolfram Mathematica 5.0 platform.

Table 2. Equilibrium Constants of Boron Species from Wang et al.13 equilibrium constants Kxa

Kb

speciesc

reaction

25 °C

80 °C

25 °C

80 °C

[B(OH)4]− [B2O(OH)5]− [B3O3(OH)4]− [B4O5(OH)4]2− [B5O6(OH)6]3− HBO2(aq) B2O3(aq) [NaB(OH)4]0 [LiB(OH)4]0

1 2 3 4 5 6 7 8 9

1.05201 × 10−11 2.54832 × 10−10 2.61921 × 10−6 3.22128 × 10−15 7.67095 × 10−26 1.03974 × 10−2 6.14138 × 10−3 1.05368 × 102 7.23825 × 100

1.91730 × 10−11 9.95431 × 10−10 1.84735 × 10−6 1.44243 × 10−15 5.42232 × 10−26 1.87030 × 10−2 1.92603 × 10−2 1.39932 × 102 5.56523 × 101

5.83445 × 10−10 2.54683 × 10−10 4.72063 × 10−8 5.88844 × 10−17 1.38038 × 10−27 1.03992 × 10−2 1.10662 × 10−4 1.89845 × 100 1.30407 × 10−1

1.064143 × 10−9 9.95405 × 10−10 3.32660 × 10−8 2.63027 × 10−17 9.77237 × 10−28 1.87068 × 10−2 3.46737 × 10−4 2.52116 × 100 1.00260 × 100

a Reported K values from OLI Studio 9/Wang et al. are the Raoult’s law standard state mole-fraction values (Kx) to the number of significant figures output by the program. bMolality-based values (K) calculated from OLI Studio values using log Km = log Kx + Δn log(55.50826) where Δn is the change in number of moles in reaction (water excluded). For example, for 2H2O = H3O+ + OH−, Δn = 2. cAt 25 °C and 1 bar, the values for the dissociation constant of water are Kwx = 3.04638 × 1017; at 80 °C 1 bar, Kwx = 1.23985 × 1016.

D


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Table 3. Standard Partial Molar Gibbs Energy of Formation, Entropy, and Parameters of the HKF Equation of State for Standard Partial Molar Thermodynamic Properties αHKF1,...,4, cHKF1,...,2, and ω for Individual Ionic and Neutral Boron Speciesa from Wang et al.13 species

Δf G°, kJ·mol−1

S°, kJ·K−1·mol−1

αHKF1

αHKF2

αHKF3

αHKF4

cHKF1

cHKF1

ω

B(OH)3 [B(OH)4]− [B2O(OH)5]− [B3O3(OH)4]− [B4O5(OH)4]2− [B5O6(OH)6]3− B2O3(aq) HBO2(aq) NaB(OH)40(aq)b LiB(OH)40(aq)c

−968.674 −1153.15 −1882.59 −2389.85 −3070.49 −3978.53 −1193.63 −720.176 −1416.62 −1440.70

157.3548 92.90074 216.4256 182.077 79.72733 86.81227 77.91252 74.25244 164.0128 196.9522

1.594831 −7.196197 −4.434878 0.341374 1.192614 1.821451 0 1.594831 0.626 −7.19857

−1116.716 21141.18 13226.81 0 0 0 0 −1116.716 751.0 21134.28

−55.30091 526.1382 34.78676 107.2192 0 0 0 −55.30091 2.8 537.7182

108097 −1430320 0 0 0 0 0 108097 −30900 −1458080

40.61506 41.31961 11.02683 8.693543 −57.1699 −84.92186 0 40.61506 73.5 58.78995

−98866.36 −131414 48925.48 74500.7 511476 327528 0 −98866.36 189000 −137181

5372.18 76730.88 0.1 0.1 0.1 0.1 0 5372.18 0 125351

a

Parameters were reproduced from the study by Wang et al.13 unless otherwise stated. bValues taken from Pokrovski et al. (1995).54 cIn the study of Wang et al.,13 Δf G° and S° were adjusted and αHKF1,...,4, cHKF1,...,2, and ω were estimated using values for Li+ and [B(OH)4]−.

3. RESULTS

analysis of our spectra. The model is based on the MSE treatment of excess properties reported by Wang et al.41 and the Helgeson− Kirkham−Flowers−Tanger (HKF) equation42,43 for the standard-state properties of aqueous species. The database for boron species in Wang et al.13 was derived from a comprehensive critical evaluation of literature values for the speciation, solubility, and vapor−liquid equilibrium of the aqueous boron systems (MnO + B2O3 + H2O), where M ≡ Li, Na, Ca, or Mg, and their mixtures with chlorides (LiCl, NaCl, and HCl) over a wide range of temperature, pressure, and composition. The equilibrium constants and HKF parameters used in the model for the species corresponding to reactions R1 to R5 are reported in Tables 2 and 3, respectively. Speciation calculations using the MSE model were carried out using the OLI Analyzer Studio 9.0.13 software (OLI Systems, Inc.). Experimental solutions were observed to be single phase despite calculations indicating they were metastable with respect to solids, so calculations were carried out with the suppression of solid phases. 2.5. Computational Chemistry. Calculations were performed using Gaussian 03 software, and the MP2 calculations used the frozen core approximation. The geometries were optimized using a stepping stone approach, in which the geometries at the levels HF/6-31G*, HF/6-31+G*, HF/6311+G*, B3LYP/6-31G*, B3LYP/6-31+G*, B3LYP/6311+G*, MP2/6-31G*, MP2/6-31+G*, and MP2/6-311+G* were sequentially optimized, with the geometry and molecular orbital reused for the subsequent level. Default optimization specifications were normally used. After each level, where possible, a frequency calculation was performed at the same level, and the resulting Hessian was used in the next optimization. Zmatrix coordinates constrained to the appropriate symmetry were used as required to speed up the optimizations. Because frequency calculations are done at each level, any problems with the Z-matrix coordinates would manifest themselves by giving imaginary frequencies corresponding to modes orthogonal to the spanned Z-matrix space. The Hessian was evaluated at the first geometry (Opt = CalcFC) for the first level in a series in order to aid geometry convergence. Solvation effects were taken into account by explicit incorporation of three and four water molecules for boric acid and borate, respectively, but were shown to be minor ( 0.05 mol kg−1 and m[B4O5(OH)4]2− > 0.1 mol kg−1, respectively. The mean values and standard errors were S([B3O3(OH)4]−) = 0.105 ± 0.005 and S([B4O5(OH)4]2−) = 0.158 ± 0.005. Reduced isotropic scattering coefficients S were calculated for the diborate and pentaborate bands using the methods described above. There was significant scatter in these results, particularly at low concentrations. For both species, the values of S from the lowest concentrations were omitted from the data set until the non-weighted average value had the lowest standard error. This corresponded to concentrations of m[B2O(OH)5]− > 0.006 mol kg−1 and m([B5O6(OH)4]−) > 0.0075 mol kg−1. The mean value and standard errors are S([B2O(OH)5]−) = 0.266 ± 0.090 and S([B5O6(OH)4]−) = 0.058 ± 0.019. In the discussion of ab initio results that follows, it will be shown that the pentaborate species on which these calculations are based, [B5O6(OH)6]3−, is not the correct species, and that the band at ∼530 cm−1 in Figures 4 and 5 corresponds to [B5O6(OH)4]−. As a result, the calculated scattering coefficients for the pentaborate species only apply to the incorrectly defined species in the MSE model of Wang et al.,13 over the narrow concentration range for which they were measured. They are not included in the tables or plots and are not considered further in the discussion. The scattering coefficients reported above are listed in Table 5. Figure 7 presents a plot of these scattering coefficients, as a function of the number of boron−oxygen (B−O bonds, nB−O, in each species. The correlation for the relative scattering coefficients of the boric acid, borate, triborate, and tetraborate species, S([B(OH)3]), S([B(OH)4]−), S([B3O3(OH)4]−), and

Table 5. Overall Temperature and Concentration Independent Reduced Raman Molar Scattering Coefficients Si/SClO4−a for Boric Acid, Borate, and Polyborate Species Relative to Perchlorate species

average S ratio (Si/SClO4−)a

B(OH)3 [B(OH)4]−b [B2O(OH)5]− [B3O3(OH)4]− [B4O5(OH)4]2− [B5O6(OH)6]3−

(2.22 ± 0.03) × 10−1 (1.47 ± 0.03) × 10−1 (2.66 ± 0.90) × 10−1 (1.05 ± 0.05) × 10−1 (1.58 ± 0.05) × 10−1 NAc

⎡ A ij ⎤1 The formula is as follows: Si/SClO4− = ⎢⎣ A ·mIS⎥⎦ m . bThe Raman IS j scattering coefficient for total borate species [B(OH)4]−Total = [B(OH)4]− + [NaB(OH)4]0. The least-squares fit of scattering coefficients of individual borate species, [B(OH)4]− and [NaB(OH)4]0, from eq 10, gives scattering coefficients of (1.47 ± 0.12) × 10−1 and (1.48 ± 0.07) × 10−1, respectively. cThe scattering coefficient for the pentaborate species obtained from the chemical equilibrium model reported by Wang et al.13 is based on the formula B5O6(OH)63−. Our ab initio results show that the correct formula is [B5O6(OH)4]−. As a result the pentaborate scattering coefficients are not reported in this table. a

mean value and standard error are S([B(OH)3]) = 0.222 ± 0.003. The borate ion is known to exist as both free borate, [B(OH)4]−, and the sodium ion pair, [NaB(OH)4]0. Although the Raman spectra of contact ion pairs of oxyanions and hydroxy anions usually appear as a high frequency shoulder on the M−O symmetric stretching band,45,46 the Raman spectra of the two species could not be distinguished in our spectra (see Figure 3). In an attempt to determine independent scattering coefficients for the hydrated borate ion and the ion pair, the peak area of the borate peak and the concentrations of [B(OH)4]−total were treated as the sum of the two contributions of both species, yielding a scattering coefficient of the total combined band, Stotal: A S([B(OH)−4 ]total ) = total mtotal =

m[B(OH)4 ]− S([B(OH)4 ]− ) mtotal +

m[NaB(OH)4 ] S([NaB(OH)4 ]) mtotal (10)

−

0

mtotal = m[B(OH)4 ] + m[NaB(OH)4 ]

(11)

The values of S for the two borate species were optimized using the nonlinear regression program implemented in SigmaPlot 9.0 (Systat Software Inc.), omitting the lowest concentrations from the data set until the regressed mean value for Stotal and the values for S([B(OH)4]−) and S([NaB(OH)4]0) showed no significant improvement in their standard errors. The overall peak where scattering coefficient values showed no significant improvement was m([B(OH)4]−)total > 0.325 mol kg−1. The mean value and standard error was S([B(OH)4]−)total = (0.147 ± 0.003). The calculated scattering coefficients of each individual species that contribute to the overall peak were S([B(OH)4]−) = (0.147 ± 0.012) and S([NaB(OH)4]0) = (0.148 ± 0.003). These values are identical to within the statistical uncertainties.

Figure 7. Experimental scattering coefficients, of boric acid, borate, and polyborate species relative to perchlorate, S/SClO4−(◆), plotted as a function of the number boron−oxygen bonds (B−O). The tentatively assigned diborate species [B2O(OH)5]− (◇) is shown but not included in the linear regression. The dashed line corresponds to the fitted eq 12. H


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Industrial & Engineering Chemistry Research S([B4O5(OH)4]2−), is approximately linear and was fitted using the expression Si = 0.21 − 6.50 × 10−3·nB − O SClO−4

The structure of diborate ions in solution, [B2O(OH)x]4−x, x = 4−6, is not known. The anion with x = 6 exists in solid form in nature as the mineral pinnoite,48a Mg[B2O(OH)6], as well as the mineral pentahydroborite,48b CaB2O(OH)6·2H2O. The equilibrium diborate ion species observed in aqueous solutions below 200 °C by potentiometric titrations was postulated to be [B2(OH)7]− by Mesmer et al.17 However, Palmer et al.33 and Wang et al.13 chose to use the condensed diborate species, [B2O(OH)5]−, in fitting the MSE activity coefficient model to a wider range of data, including high temperature solubility measurements. Both species were considered in the computational studies reported in this study. The B3LYP and MP2 calculations yielded two symmetric stretching bands for [B2(OH)7]−, at ∼690 ± 10 cm−1 and ∼870 ± 10 cm−1. The former is primarily a B−O−B stretch, while the latter is primarily a B−(OH)3 stretching mode. At the low relative concentrations of diborate predicted by Wang et al.’s model (B2/BTotal < 3 mol %), the high frequency band would be obscured by the boric acid at 878 cm−1. The value predicted for the low frequency mode, ∼690 ± 10 cm−1, is much lower than that observed for the weak shoulder on the borate band at 773 cm−1. The condensed diborate species [B2O(OH)5]− was found to occur in one of 8 conformations with no symmetry. The calculated B3LYP and MP2 symmetric stretching band for [B2O(OH)5]− is at ∼710 ± 6 cm−1. This value is well below the experimental band observed at 773 cm−1 or the computational value of 674(697) cm−1 and 783(793) cm−1 reported by Zhou et al.31 at B3LYP/aug-ccpVDZ (scaled by 1.0233, comparable to the B3LYP/6-31+G* results presented here). The omission of waters of hydration from all these calculations is known to cause the symmetric stretching frequencies to be too low. For borate, the MP2/6-311+G* calculation on the unhydrated ion underestimated the frequency by 15 cm−1, and it would be expected to be the same for diborate [B2O(OH)5]−. Thus, the corrected value for [B2O(OH)5]− would be expected to be ∼731 cm−1. These values are lower than the value of 785 cm−1 reported by Zhou et al.31 The structure of Zhou et al. corresponds to a C1 conformation, which is approximately 75 kJ/mol higher in energy than the minimum energy of the C1 form shown in Figure 8, and is therefore unlikely to be the stable species. Neither is a good match for the experimental band observed at 773 cm−1, which had been initially assigned to [B2O(OH)5]− based on Zhou’s result. The cyclic triborate in solution, [B3O3(OH)4]−, can exist in one of several C2 and C1 forms, which are competitive in energy. The predicted vibrational mode for the symmetric B−O stretch at 615 cm−1 is underestimated by 20−30 cm−1 (except at Hartree−Fock, where it is overestimated by 10−15 cm−1). A second mode, at 732−740 cm−1, could possibly correspond to the experimental band seen at 773 cm−1. Metaboric acid, [B3O3(OH)3]0, which occurs as the trimer of HBO2, occurs as both a C3h and a Cs form, analogous to orthoboric acid. Its most intense fully symmetric vibrational mode is lower, but within 10 cm−1, of the anion. A second mode at 792−803 cm−1 may correspond to the experimental band at 773 cm−1. The tetraborate anion, [B4O5(OH)4]2−, has several forms of C2v, C2, Cs, and C1 symmetry. Of the two possibilities, those in which the bridgehead borons are tetrahedral are the most stable. In this case, the Hartree−Fock values (573−576 cm−1) are quite close to the experimental value at 569 cm−1, whereas the correlated calculations underestimate by about 20−30 cm−1.

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to a standard error of 0.05. The value for the diborate species S([B2O(OH)5]−)/SClO4− is shown but was not included in the regression. 3.3. Ab Initio Calculations. Selected structures obtained from the ab initio calculations are shown in Figure 8a,b. A more

Figure 8. a. Lowest energy calculated structures of boric acid, borate, and polyborates. b. Calculated structures of postulated pentaborate species.

detailed account may be found elsewhere.47a,b The predicted symmetric Raman bands of the model species are given in Table 6, along with the experimental Raman peaks assigned to these bands. Boric acid, B(OH)3, can occur as either the highly symmetric C3h or a higher-energy Cs structure, in which one of the hydroxyl groups has rotated. It is well-known that Hartree−Fock theory overestimates the vibrational frequencies of covalent bonds such as B−O and that the frequencies get slightly smaller as the basis set improves. However, the B3LYP and MP2 frequencies were in good agreement (869−879 cm−1 compared to 878 cm−1 experimentally). Because boric acid is only weakly hydrated, addition of an explicit first hydration shell of three water molecules (C3 structure) only marginally improves the frequencies. The borate anion, [B(OH)4]−, occurs as a symmetric S4 structure. The Hartree−Fock frequencies are overestimated, and the B3LYP and MP2 frequencies are underestimated (721− 732 compared to 745 cm−1), for the totally symmetric B−O stretching mode. This is not due to hydration, as the addition of four water molecules to the first hydration sphere only increases the frequencies by 2−5 cm−1, which is about a third of the difference (16 cm−1) between the unhydrated ion at MP2/6311+G* and experimental values. I


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Industrial & Engineering Chemistry Research Table 6. Ab Initio Calculated and Experimental Frequencies of Borate Species frequency (cm−1) calculated symmetry

basis set

HF

B3LYP

MP2

B(OH)30

aqueous species

C3h

B(OH)3(H2O)30

C3

B(OH)4−

S4

B(OH)4(H2O)4−

S4

B2O(OH)5−

C1

B2(OH)7−

C1

6-31G* 6-31+G* 6-311+G* 6-31G* 6-31+G* 6-311+G* 6-31G* 6-31+G* 6-311+G* 6-31G* 6-31+G* 6-311+G* 6-31G* 6-31+G* 6-311+G* 6-31G*

927 923 919 929 927 922 775 774 770 776 776 774 760 756 755 741 919 736 913 736 908 631 792 628 791 627 792 620 873 619 872 618 877 576 574 573 546 822 544 820 543 823 609 636 766

877 871 869 882 874 871 728 724 721 726 726 725 710 707 705 688 861 684 851 683 847 590 732 585 734 584 734 585 803 582 801 582 804 547 541 538 513 758 510 756 509 757 597 698 708 750

6-31+G*

601 623 768

6-311+G*

600 621 766

500b 553 570 700 710 744 547 577 692 712 722

879 872 873 881 871 875 732 725 729 728 728 734 719 713 716 699 880 699 865 706 869 593 737 586 738 590 740 583 796 580 792 583 800 547 541 536b 512 754 510b 752 511 757 554 596 703 713 736 548 583 700 715 733

6-31+G* 6-311+G* B3O3(OH)4−

C1

6-31G* 6-31+G* 6-311+G*

B3O3(OH)30

C3h

6-31G* 6-31+G* 6-311+G*

B4O5(OH)42−

C2

B5O6(OH)4−

D2d

6-31G* 6-31+G* 6-311+G* 6-31G* 6-31+G* 6-311+G*

B5O6(OH)63−

C2

6-31G*

J

experimental 878

745

(773)a

(773)a

615 (773)

615 (773)

569

530 (773)a

530

522 557 591 700 710 DOI: 10.1021/acs.iecr.7b03316 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Table 6. continued frequency (cm−1) calculated aqueous species

symmetry

ClO4−

basis set

Td

HF

6-31G* 6-31+G* 6-311+G*

B3LYP

MP2

816

729 817 971 944 942

975 958 948

851 818 805

experimental

970

The weak shoulder at 773 cm−1 is tentatively assigned to the diborate species B2O(OH)5− or the pentaborate species B5O6(OH)4−. bThe structure has at least one small imaginary frequency. See refs 47a,47b.

a

Table 7. Raman Scattering Coefficients from Hartree-Fock ab Initio Calculationsa Si/SClO4−

Raman activity symmetry

frequency (cm−1)

HF/6-31G

B(OH)30 [B(OH)4]− [B2O(OH)5]− [B2(OH)7]−

C3h S4 C1 C1

[B3O3(OH)4]−

C1

B3O3(OH)3

C3h

[B4O5(OH)4]2− [B5O6(OH)4]−

C2 D2d

ClO4−

Td

∼927 ∼775 ∼760 ∼740 ∼910 ∼631 ∼792 ∼620 ∼873 ∼576 ∼546 ∼822 ∼960

3.81 3.72 3.10 4.13 1.60 3.37 0.813 3.52 4.04 4.96 4.22 2.84 20.9

aqueous species

a

a

HF/6-31+G 5.37 4.48 3.94 4.55 3.18 5.01 0.780 5.01 4.93 6.18 6.30 2.96 32.0

a

HF/6-311+G 5.01 4.50 3.44 4.48 3.06 4.78 0.692 4.76 4.38 6.49 6.20 2.37 30.5

a

HF/6-311+Ga 0.164 0.148 0.113 0.147 0.100 0.157 0.023 0.156 0.144 0.213 0.203 0.078 1

Calculated for a 90° scattering angle, where Raman activity = 1 − (4/3 × depolarization ratio).

The calculated structures for the monovalent and trivalent pentaborate ions are shown in Figure 8b. The monovalent pentaborate anion, [B5O6(OH)4]−, can exist as one of several D2d, C2v, C2, Cs, or C1 forms. The D2d form shown in Figure 8b is the most stable. The correlated calculations underestimate the observed band at 530 cm−1 by about 20 cm−1, whereas the Hartree−Fock calculations overestimate by about 15 cm−1. There are no other predicted polarized modes of significant intensity (HF) within 200 cm−1 of this band. In addition, a band is predicted at 754−758 cm−1 which might correspond to the band observed at 773 cm−1. The highly charged trivalent pentaborate ion used in Wang et al.’s model,13 [B5O6(OH)6]3−, can also exist as one of several C2v, C2, Cs, or C1 structures. Of these the C2 form shown in Figure 8b is the most stable. However, there would be several predicted polarized bands of comparable intensity in the same frequency region 430−630 cm−1. These were not observed in the spectra obtained in this study or by other workers.29−31 Therefore, this structure was ruled out, and it was concluded that the pentaborate anion is [B5O6(OH)4]−. Absolute Raman scattering factors for 90° geometry were calculated from eq 1 using the Hartree−Fock depolarization ratios. The values for the HF/6-31G*, HF/6-31+G*, and HF/6311+G* levels for each species are listed in Table 7, along with values for the relative scattering coefficients, Si/SClO4−, calculated from them. The values of Si/SClO4− are plotted as a function of B− O bond number in Figure 9, for comparison with the experimental scattering coefficients in Figure 7. While the scattering coefficients do show similar patterns, the Hartree− Fock values for the well-defined polyborate species,

Figure 9. Hartree−Fock 6-311+G* scattering coefficients, of boric acid, borate, and polyborates relative to perchlorate in Table 7, S/SClO4−, plotted as a function of the number boron−oxygen bonds (B−O). The solid line corresponds to the fitted eq 12, shown in Figure 7. The dashed line corresponds to the linear least-squares regression to the HF values, eq 12, shown in Figure 7.

[B3O3(OH)4]− and [B4O5(OH)4]2−, are significantly higher than the experimental values and well outside their standard uncertainties. The values for [B(OH)3]0 and [B(OH)4]− are in better agreement. Raman activities and relative scattering coefficients from Hartree−Fock calculations are known to be less accurate than higher levels of theory. Although these results do show that the computational results for the species shown in Figure 8 are qualitatively consistent with the experimental scattering coefficients, quantitative predictions will require a K


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the spectroscopic and ab initio studies reported above, we conclude that [B2O(OH)5]− is a plausible structure for the diborate ion, still unconfirmed, and that it is consistent with Wang’s MSE model and the scattering coefficients listed in Table 5. However, because diborate is a minor species in our experimental solutions, the possibility that [B2(OH)7]− or some other monovalent diborate anion is, in fact, the equilibrium species in solution under ambient conditions cannot be definitively ruled out. 4.3. Pentaborate Ion. In their state-of-the-art high-temperature study of boric acid hydrolysis constants, Mesmer et al.17 proposed two models to fit their potentiometric data which extended from 25 to 200 °C over a wide range of concentrations. Both models incorporated boric acid, B(OH)3, borate, [B(OH)4]−, the diborate ion [B2O(OH)5]−, and the triborate ion [B3O3(OH)4]−. However, the first model used [B4O5(OH)4]2− as the third polyborate species, while the second model used the trivalent pentaborate ion, [B5O6(OH)6]3−. The Raman spectra in Figures 4 and 5 clearly show that both the tetra- and pentaborate species are present at equilibrium, and the ab initio studies reported above confirm that this species is the monovalent pentaborate anion [B5O6(OH)4]−. This conclusion is supported by the recent NEXAFS study reported by Duffin et al.49 As a consequence of this finding, the database for Wang’s MSE model13 should be modified to replace [B5O6(OH)6]3− with parameters for [B5O6(OH)4]−. Although their MSE model includes an incorrect pentaborate ion, it is unlikely that the calculated concentrations of the other borate and polyborate species will be affected because the concentration of [B5O6(OH)6]3− is significantly lower. 4.4. Sodium Borate Ion Pairs. The formation constants of the ion pair [NaB(OH)4]0 have been previously measured by conductivity,14,52a,b densitometry,16 UV−visible spectroscopy,23,24 dielectric relaxation spectroscopy (DRS),26,46 NEXAFS,49 and potentiometric methods.17,21 The differences in the values of the scattering coefficients for the free borate ion and ion-paired borate, from the calculations reported above, were not statistically significant. As a result, Raman spectroscopy cannot measure the degree of sodium borate ion pairing. Dielectric relaxation spectroscopy (DRS) measurements on B(OH)3/ NaOH/H2O systems by Buchner et al.26 showed only water relaxation processes. The lack of detectable solute relaxation processes was interpreted to mean that ion pair lifetimes are even shorter than the water relaxation time, possibly due to rapid proton exchange between the boric acid/borate hydroxide groups and water. Similar results were observed in near-edge Xray scattering studies by Duffin et al.,49 which showed that associated sodium ions had almost no effect on the NEXAFS spectra. Molecular dynamics simulations carried out in part of the study suggested that the sodium ion did in fact form contact ion pairs with borate. The NEXAFS spectra showed that water is arranged isotropically around both boric acid and borate, without forming strong hydrogen bonds to the boron hydroxides. For boric acid, this effect is thought to be due to the trigonal conformation which allows intramolecular hydrogen bonding. For borate, the sodium cation was postulated to displace water from the primary solvation sphere and to facilitate the formation of intramolecular hydrogen bonds between the hydroxide groups on the borate ion. It is not clear why this would not be reflected in the Raman spectrum of the borate ion. Although the studies cited above suggest that hydrogen bonding between water and boric acid or borate is weak, the water−boric acid interactions in the vapor phase are strong.53 Conductivity studies by Arcis et al.52a,b

higher level of theory and, quite possibly, a treatment of hydration effects.

4. DISCUSSION 4.1. Boric Acid, Borate, Triborate, and Tetraborate Species. The quantitative reduced isotropic Raman spectra shown in Figures 2−5 confirm the presence of boric acid, B(OH)3, the borate ion [B(OH)4]−, and the vibrational bands for three polyborate species. Two of these can be assigned unambiguously to the triborate and tetraborate, [B3O3(OH)4]− and [B4O5(OH)4]2−, based on ab initio calculations in this study and experimental studies by other workers.29−31 The spectrum of the third species is not consistent with the pentaborate species [B5O6(OH)6]3− postulated by Mesmer et al.17 from potentiometric titrations but is consistent with the monovalent pentaborate species [B5O6(OH)4]−. Figures 4 and 5 include expanded views of the region from 500 to 650 cm−1, where the bands for the polyborates appear. In the solutions with the lowest buffer ratio (Solutions 1−8), the spectra indicate the presence of polyborates, with evidence for three species: [B3O3(OH)4]−, [B4O5(OH)4]2−, and [B5O6(OH)4]−. The triborate species is the dominant polyborate at both temperatures, followed by the tetraborate and then pentaborate. Increasing the temperature from 25 to 80 °C destabilizes the higher polyborates relative to the triborate species. The spectra for more concentrated solutions with higher buffer ratios (Solutions 12−17) show that the formation of [B4O5(OH)4]2− at 25 °C is more favored under these conditions, and that its concentration exceeds that of the [B3O3(OH)4]−. Again, the increase in temperature to 80 °C caused the equilibrium to shift toward the less charged triborate anion, [B3O3(OH)4]−. The pentaborate ion was not observed in the spectra of Solutions 12−17. The formulas and structures of boric acid, borate, triborate, and tetraborate ions presented above are species postulated by Mesmer et al.17 to interpret their potentiometric titration results and are the species used in the MSE database developed by Wang et al.13 These species are consistent with the ab initio predictions and experimental Raman bands tabulated in Table 4, and with recent results from near-edge X-ray absorption spectroscopy (NEXAFS) studies.49 The agreement between the Raman scattering coefficients at 25 and 80 °C, over such a wide range of solution compositions, is powerful evidence that these species are correct and that the MSE model, its database, and the scattering coefficients are all self-consistent to within the stated uncertainties. 4.2. Diborate Ion. Figure 6 shows the region from 680 to 820 cm−1, with the borate band at ∼745 cm−1, and the weak shoulder at ∼773 cm−1 which has been tentatively assigned to the diborate species [B2O(OH)5]−. The shoulder was present in all the solutions and decreased slightly with temperature. To the best of our knowledge, no spectroscopic evidence for the structure of the aqueous diborate ion [B2O(OH)5]− has been reported in the literature. Its structure has been inferred from the structures of hydrated crystalline polyborates50,51 and from the ab initio calculations cited above. The potentiometric titration studies by Mesmer et al.17 have confirmed that a monovalent diborate anion is an important species at elevated temperatures and that it is present as a minor species at 25 °C, consistent with the results reported here. The formation constants for reaction R2 adopted in the MSE model by Wang et al.13 for the condensed diborate species [B2O(OH)5]− are those reported by Mesmer et al.,17 as re-evaluated by Palmer et al.,33 but written as [B2(OH)7]−. From L


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Industrial & Engineering Chemistry Research are consistent with strong “structure-making” behavior by the borate ion near ambient conditions, possibly due to strong hydrogen bonding. These conductivity studies also show that the degree of [NaB(OH)4]0 increases at elevated temperatures and that the fraction of solvent-separated ion pairs also increases.

electronics shop and machine shop in the College of Physical and Engineering Science at the University of Guelph, for their very considerable expertise in maintaining and modifying the instrument and its data acquisition system, and to Dr. Swaroop Sasidharanpillai for many insightful comments and discussion. The authors express their deep appreciation to OLI Systems Inc. (Edison, NY) for donating their software package OLI Studio 9 to the Hydrothermal Chemistry Laboratory at the University of Guelph. CCP thanks ACEnet for computational support. This research was supported by the Electrical Power Research Institute (Project EP-P43257/C18781).

5. CONCLUSIONS One of the objectives of this work was to use polarized Raman spectroscopy to obtain quantitative spectra that would allow the measurement of boron speciation in aqueous solutions as a function of temperature, to determine structural information, and to measure reduced isotropic scattering coefficients relative to the perchlorate reference ion. Reduced isotropic Raman spectra of NaOH−B(OH)3 solutions have been measured at temperatures of 25 and 80 °C, over a wide range of concentrations and mNa/mB ratios. The relative scattering coefficients have been determined for the four most predominant ions present in solution under these experimental conditions: boric acid, [B(OH)3]0; borate [B(OH)4]−; and the polyborates [B3O3(OH)4]− and [B4O5(OH)4]2−. These values are consistent with ab initio calculations and with the formation constants and MSE activity coefficients reported by Wang et al.,13 up to temperatures of ∼100 °C. Because they are temperature independent, the scattering coefficients can be used at higher temperatures to determine speciation and formation constants for these species from reduced isotropic Raman spectra to test the accuracy of such models under PWR primary coolant conditions. Less accurate spectra and scattering coefficients, consistent with the formation constants of Wang et al.,13 have been determined for the diborate species [B2O(OH)5]−. However, these are not as well supported by the ab initio calculations and should be regarded as tentative. The data presented here in this study are believed to be the first reduced isotropic scattering coefficients for these species to be reported in the literature. The spectra show, for the first time, that the triborate, tetraborate, and pentaborate anions are all present as equilibrium species in solutions near ambient conditions. The spectra and ab initio calculations confirm the observation by other studies which reported the pentaborate species as the monovalent anion, [B5O6(OH)4]−, rather than the trivalent ion, [B5O6(OH)6]3−. Finally, the band assignments and scattering parameters reported here provide a framework for using reduced isotropic Raman spectroscopy as a research tool for measuring quantitative speciation of boric acid/polyborate solutions under hydrothermal conditions.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*(P.R.T.) E-mail: [email protected]. ORCID

Cory C. Pye: 0000-0002-3253-6913 Peter R. Tremaine: 0000-0002-9722-9180 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors express deep gratitude to Dr. Dennis Hussey, EPRI, for defining the scientific mission, and to Dr. Daniel Wells, EPRI, for providing technical advice, many fruitful discussions, and steadfast support on this very challenging project over the past four years, part of which was the research presented here. We are also grateful to Mr. Ian Renaud and Mr. Case Gielen of the M


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Raman Spectroscopic and ab Initio Investigation of Aqueous Boric

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