Triborate Formation Constants and Polyborate Speciation under

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Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

Triborate Formation Constants and Polyborate Speciation under Hydrothermal Conditions by Raman Spectroscopy using a Titanium/ Sapphire Flow Cell Swaroop Sasidharanpillai, Hugues Arcis, Liliana Trevani,† and Peter R. Tremaine* Department of Chemistry, University of Guelph, 50 Stone Road W., Guelph, Ontario, Canada N1G 2W1

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S Supporting Information *

ABSTRACT: Solvent-corrected reduced isotropic Raman spectra of aqueous boric acid + sodium borate solutions have been obtained from perpendicular and parallel polarization measurements in a novel custom-made titanium flow cell with sapphire windows over the temperature range 25 to 300 °C at 20 MPa using the perchlorate anion, ClO4−, as an internal standard. The reduced isotropic spectra of solutions yielded the first reported quantitative speciation results for polyborate ions in equilibrium with boric acid and borate in high-temperature aqueous solutions above 200 °C. The spectra obtained from solutions at low sodium/boron ratios, −1 ST 0 < mST Na/mB < 0.254, displayed well-defined bands at 880, 747, 615, and 532 cm , corresponding to the species B(OH)3 > − − − [B(OH)4] > [B3O3(OH)4] ≫ [B5O6(OH)4] , respectively. The triborate ion, [B3O3(OH)4]−, was found to be the major polyborate species in these boric acid-rich solutions in the range 25 to 300 °C. Thermodynamic formation constants for the triborate species, [B3O3(OH)4]−, calculated from the peak areas, are in agreement with the literature values reported by Mesmer et al at 50, 100, and 200 °C to within the combined experimental uncertainties. At 300 °C, the value for the formation constant, log Kb31,m= 2.259 ± 0.060, is larger than the value extrapolated from the results of Mesmer et al. by a factor of ∼3.

1. INTRODUCTION The chemistry of aqueous boron solutions under hydrothermal conditions1 is of scientific interest due to their complexity relative to other acid−base equilibria and to the important role of borate and polyborate species in geochemistry and industrial chemistry. In the nuclear industry, boron-containing compounds are added to the primary coolant systems of pressurized water reactors (PWRs)2 in order to control the neutron flux. An ability to understand and model polyborate speciation in hightemperature water chemistry is needed to control the pH and to predict the onset of under- and in-deposit borate precipitation reactions on fuel surfaces that can reduce the reactor’s operating efficiency. At least 10 different borate and polyborate species are known to exist in aqueous boric acid solutions at different conditions. Various spectroscopic techniques including UV− visible spectroscopy,3 dielectric relaxation spectroscopy,4 infrared spectroscopy,5,6 Raman spectroscopy,5,7−11 X-ray diffraction,12 and NMR13 have been used to study aqueous boron species, both to determine the formation constants of polyborate species and to deduce their structures. Boric acid (B(OH)3), borate ([B(OH)4]−), and the major polyborate species are shown below as reactions 1 to 5. B(OH)3 + OH− F [B(OH)4 ]− 2B(OH)3 + OH− F [B2(OH)7 ]− © XXXX American Chemical Society

3B(OH)3 + OH− F [B3O3(OH)4 ]− + 3H 2O

(3)

4B(OH)3 + 2OH− F [B4 O5(OH)4 ]− + 5H 2O

(4)

5B(OH)3 + OH− F [B5O6 (OH)4 ]− + 6H 2O

(5)

The complexity in the speciation due to the presence of so many polyborate species and the experimental challenges associated with measuring quantitative thermodynamic speciation data under high-temperature, high-pressure conditions pose serious problems in formulating chemical equilibrium models for boron speciation. Raman spectroscopy has proven to be a powerful tool for identifying the structures of the major equilibrium polyborate species. Raman spectra and band assignments for several of these species near ambient conditions have been reported by a number of workers.5,7−11,14 Applegarth et al.14 reported quantitative reduced isotropic Raman spectra of boric acid ST solutions over a range of sodium to boron ratios, 0 < mST Na/mB < 2.0 at 25 and 80 °C from which the scattering coefficients with respect to the perchlorate ion could be determined. The only Raman study in the literature under hydrothermal conditions was reported by Schmidt et al.8 who studied aqueous boron

(1) Received: April 1, 2019 Revised: May 13, 2019

(2) A

DOI: 10.1021/acs.jpcb.9b03062 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B species up to 600 °C and 2 GPa. However, they were not able to quantify the equilibrium concentrations of the different polyborate species. The application of Raman spectroscopy to determine quantitative chemical equilibrium constants under hydrothermal conditions has been limited by the considerable experimental challenges in determining accurate solution compositions from Raman spectra. Quantitative equilibrium constants can be determined at near ambient conditions by measuring reduced isotropic spectra with appropriate solvent subtraction methods over a range of concentrations.14,15 The development of high-pressure fused silica capillary cells by Chou and his co-workers16 allowed Raman methods to be applied to determine formation constants in hydrothermal solutions under acidic and neutral conditions.17 However, previous studies in this laboratory18,19 have shown that fused silica capillary techniques cannot be used to study borate and polyborate solutions under hydrothermal conditions because the silica walls are quickly corroded. This study presents reduced isotropic Raman spectra for boric acid/borate buffer solutions in which triborate is the predominant polyborate species at temperatures up to 300 °C at 20 MPa. The spectra were measured using a newly designed titanium alloy high-pressure flow cell with sapphire windows, one of the first to be reported in the literature for quantitative Raman spectroscopy. The relative scattering coefficient reported by Applegarth et al.14 for the major vibrational bands were used to calculate accurate concentrations of the boron species from which formation constants of the triborate species, [B3O3(OH)4]−, were determined. Structures for B(OH)3, [B(OH)4]−, and [B3O3(OH)4]− are shown in Figure 1. The

sealed polypropylene Nalgene bottles until use. Stock solutions of ∼1 mol·kg−1 sodium hydroxide were prepared from the 50% w/w aqueous solution and standardized by triplicate titrations using KHP. Boron-containing solutions were prepared by first diluting the ∼1 mol·kg−1 sodium hydroxide stock solution and then adding the mass of boric acid required to obtain the desired boric acid molality in the final solution. Sodium perchlorate was added by mass to all solutions studied, as an internal reference standard (0.1 mol·kg−1), and the band at 936 cm−1 was used as the internal reference peak. Aqueous polyborate solutions were prepared with five different stoichiometric ratios of NaOH to B(OH)3, 0 < mST Na/ −1 NaClO4 was added as an mST B < 1.02, to which ∼0.1 mol·kg internal standard. The buffer ratio, RBuffer = (mNaTotal − mClO−4 )/ mBTotal, refers to the stoichiometric molality ratio of NaOH to ST B(OH)3 used to make the solutions, mST NaOH and mB(OH)3. Thus, −1 RBuffer = 0 and mB = 0.80 mol·kg refer to a pure boric acid −1 solution with mST and mST B(OH)3 = 0.80 mol·kg NaOH = 0.00 mol· −1 −1 kg , and RBuffer = 1.0 and mB = 1.0 mol·kg refer to an aqueous −1 solution of sodium borate with mST and B(OH)3 = 1.00 mol·kg ST −1 mNaOH = 1.00 mol·kg . 2.2. Custom-Built Titanium and Sapphire Optical Flow Cell. A custom-made titanium flow cell with sapphire windows was constructed for the experiment. The cylindrical titanium (Grade 7) body (31 mm o.d. × 16 mm thickness) contained a sample chamber of 4 mm i.d. and ∼40 mm3 internal volume. The top and bottom surfaces of the cell body included a machined recess on the outward-facing side with polished seats for the sapphire windows (10 mm diameter × 2 mm thickness). Annealed gold disks (0.25 mm thickness) on each side of the windows provided a pressure seal. The windows were held in place by titanium disks, secured by six bolts with Belleville or lock-type spring washers. Details of the cell are shown in Figure 2. Solutions were carried into and out of the cell through titanium tubing (VICI Valco, Grade 2, 1.6 mm o.d., 0.3 mm i.d.) laser-welded in place (microlaser wielding). The cell was mounted inside an aluminum block (11.6 cm × 7.6 cm × 1.7 cm), which was heated using a set of two cartridge heaters (Omega Model CSH-202200/120 V) whose temperature was controlled to ±1 °C by an Omega controller (model CNi3243). The 35 cm-long inlet tube was wrapped several times around a cylindrical aluminum post inside the block to preheat the solution before it entered the cell. The aluminum block containing the cell and cartridge heaters was thermally insulated from its surroundings by a ceramic liner that was fitted into an aluminum housing. The external aluminum housing was cooled using a circulating glycol temperature bath, which maintained the contact surface with the Raman microprobe stage at 18 °C. The whole assembly was mounted on a Teflon cell holder, held in a fixed position on the translation stage of the confocal microscope. The cell was pressurized with ultrapure water using an ISCO high-pressure liquid chromatography syringe pump (model 260D) in constant flow mode. PEEK (polyether ether ketone) tubing with an internal diameter of 0.05 mm (pressure rating of 5000 psi) was used to connect the pump to the titanium inlet tubing. Stainless steel tubing (316) with a similar internal diameter was used to connect the titanium outlet tube to the back-pressure regulator. Cell temperatures were measured using a thermocouple placed inside the titanium body of the cell and controlled with an Omega CNi3243 controller. The cell pressure was controlled using a back pressure flow control

Figure 1. Structures of aqueous boric acid, borate, and triborate.

experimental formation constants are compared to those in recent critically evaluated thermodynamic databases for boric acid,20−22 which are based on extrapolated values for the polyborate species above 200 °C. The implications of the new data on speciation calculations from the two chemical equilibrium databases used by the nuclear industry23−25 are discussed. To our knowledge, these are the first quantitative Raman spectra reported in the literature for boric/borate solutions under hydrothermal conditions and the first direct comparisons of experimental polyborate speciation measurements with chemical equilibrium model predictions at PWR reactor coolant temperatures.

2. EXPERIMENTAL SECTION 2.1. Chemical and Sample Preparation. Boric acid (B(OH)3; Purotronic, 99.9995% metal basis grade), sodium hydroxide (NaOH, 50% (w/w) aqueous solution), and anhydrous sodium perchlorate (NaClO4; ACS reagent grade, 99%+) were used as received from Alfa Aesar. Potassium hydrogen phthalate (KHP) (Fisher Scientific, 99.95%) was dried at 110 °C to constant mass before use. All solutions were prepared by mass (±0.5%) using ultrapure water from a Millipore Direct-Q5 water purification system and stored in B


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The Journal of Physical Chemistry B

Reduced isotropic Raman spectra of aqueous boric acid solutions and buffer solutions with three different stoichiometric Na/B ratios were obtained at temperatures from 25 to 300 °C at 20 MPa using the confocal Raman microscope. The 532 nm laser beam was focused onto the flowing sample through the sapphire window with a 20× objective lens (Olympus SLMPlanN 20×/0.25). The Raman signals were collected using the 360° back-scattering geometry. The slit width was set to 500 μm. The sample focusing was achieved by first focusing the laser onto the sapphire window to get Raman scattering for the sapphire window and then focusing into the solution underneath the window in order to minimize the sapphire signal and maximize the Raman signal from the sample. Each Raman spectra was obtained from an average of eight runs to reduce the background noise. Isotropic Raman spectra, IIso(ν̅), were obtained from the parallel (||) and perpendicular (⊥) polarized spectra using the following equation14,26 IIso(ν ̅ ) = I (ν ̅ ) −

4 I⊥(ν ̅ ) 3

(6)

where ν̅ is the Raman frequency in wavenumbers (cm−1). Calibration using solvent peaks with known depolarization ratios for CCl4 (l) showed that the 4/3 factor should be substituted with 1.167 ± 0.001 for measurements using the optics in our confocal microscope, and 1.167 was used instead of 4/3. The isotropic spectra thus-obtained include contributions from Rayleigh wing scattering and the thermal excitations of low-frequency modes as given by the expression ÅÄÅ ÑÉ Å (ν − ν ̅ )3 ÑÑÑ Sij ÑÑ IIso(ν ̅ ) = C InstrÅÅÅÅ 0̅ ÑÑ B(ν ) ÅÅÅ ν̅ ÑÑÖ (7) ̅ Ç É ÅÄÅ i −hcν ̅ yzÑÑÑÑ Å zzÑÑ B(ν ̅ ) = ÅÅÅ1 − expjjj ÅÅÇ (8) k kT {ÑÑÖ Here, the parameter CInstr is a constant that is dependent on the instrument response, slit-width, solid collection angle, laser frequency, and absorption due to color, νo is the absolute frequency of the exciting laser in wavenumbers, ν̅ is the frequency shift of the Raman band with respect to the excitation frequency, B is the Boltzmann distribution for the thermal population of low frequency vibrational excited states, and Sij is the intrinsic molar scattering activity for a Raman scattering process associated with species j over the ith Raman band. To remove the contributions from the Rayleigh scattering and low frequency excited states, we used the reduced isotropic form of the spectrum, Riso,

Figure 2. (a) Schematic cross section of the titanium sapphire window flow cell and its assembly. (b) Titanium sapphire window flow cell and its thermal regulating system. (c) Schematic of the Raman flow experiment setup with the six-port valve in position B in which the sample loop is introduced into the flow path. In position A, the loop is bypassed.

valve (TESCOM model no. 26-1722-24) in the flow path after the cell. The samples were injected using a 24 mL injection loop and a Rheodyne six-port valve. A flow rate of 0.5 cm3/min at constant pressure (20 MPa) was maintained throughout the experiment. 2.3. Raman Spectroscopy. Polarized Raman spectra were recorded on a custom-made Horiba Jobin Yvon LabRAM HR 800 spectrometer equipped with a fiber-optic-coupled Olympus confocal microscope and a macrochamber. A 532 nm, Torus200 diode-pumped solid-state (DPSS) laser with an output power of 250 mW was used as the excitation source in these experiments. The Raman scattered light from the sample was passed through an edge filter with a Stokes edge of less than 120 cm−1 for Rayleigh rejection, a rotating polarizer for selecting the Raman polarization, and a polarization scrambler before entering the 800 mm focal length spectrograph with a 1800 line/mm holographic grating and a Peltier-cooled (−70 °C) 1024 × 256 pixel CCD detector.

RIso(ν ̅ ) = IIso(ν ̅ )

ν̅ B (ν ̅ ) (νo − ν ̅ )3

(9)

3. RESULTS 3.1. Reduced Isotropic Raman Spectra. 3.1.1. Boric Acid Spectra. The reduced isotropic Raman spectra of a 0.8 m aqueous solution of boric acid (RBuffer, = 0, mB = 0.776 mol·kg−1) −1 in which sodium perchlorate (mST NaClO4 = 0.087 mol·kg ) was added as an internal standard were measured from 25 to 300 °C at p = 20 MPa. The spectrum for boric acid at 25 °C and the spectrum for sodium borate presented in the following section are shown in Figure 3. The temperature-dependent spectra of boric acid are plotted in Figure 4, in which each spectrum is normalized with respect to the height of the perchlorate internal C


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Figure 4 also shows the change in Raman frequency with temperature for both boric acid and the perchlorate ion peaks. 3.1.2. Triborate Spectra. The reduced isotropic Raman spectra of three aqueous solutions with buffer ratios RBuffer = 0.130 and mB = 0.847 mol·kg−1 (solution 1), RBuffer = 0.254 and mB = 0.964 mol·kg−1 (solution 2), and RBuffer = 0.129 and mB = 0.806 mol·kg−1 (solution 3) to which sodium perchlorate −1 (mST NaClO4 ≈ 0.1 mol·kg ) was added as an internal standard were measured from 25 to 300 °C at p = 20 MPa. These buffer ratios were chosen to yield triborate as the major polyborate species in solution. The spectra for solution 1 (RBuffer = 0.130 and mB = 0.847 mol·kg−1) at temperatures from 25 to 300 °C at 20 MPa are plotted in Figure 5. The spectra clearly show four peaks at all

Figure 3. Reduced isotropic Raman spectra of a 1 mol·kg−1 aqueous solution of sodium borate and a 0.8 mol·kg−1 aqueous solution of boric acid with sodium perchlorate present as an internal standard at t = 25 °C and p = 20 MPa.

Figure 5. Reduced isotropic Raman spectra normalized with respect to the peak areas of the perchlorate internal standard for solution 1 from t = 25 to 300 °C at p = 20 MPa. The region between 500 and 800 cm−1 is enlarged in the inset, to show the presence of [B(OH)4]−, [B3O3(OH)4]−, and [B5O6(OH)4]−.

temperatures: two large peaks at 880 and 936 cm−1 for boric acid B(OH)3 and the perchlorate ClO4− internal standard and two small peaks at 615 and 747 cm−1 for triborate [B3O3(OH)4]− and borate [B(OH)4]−, respectively.9,14 A fifth peak at 532 cm−1, corresponding to the pentaborate ion [B5O6(OH)4]−, indicates that this species was present in solution up to 150 °C. The inset in Figure 5 shows that the triborate and borate peaks at 615 and 747 cm−1 were present at all temperatures. The normalized reduced isotropic spectra for solution 2 (RBuffer = 0.254 and mB = 0.964 mol·kg−1) at temperatures from 25 to 300 °C at 20 MPa are shown in Figure 6. The spectra clearly indicate the presence of three major boron species: triborate ([B3O3(OH)4]−), borate ([B(OH)4]−), and boric acid (B(OH)3) at all temperatures. The two very small peaks at frequencies lower than that of the triborate band indicate the presence of the tetraborate and pentaborate species, [B4O5(OH)4]2− and [B5O6(OH)4]−, at temperatures below 100 °C. The inset shows the shifts in frequencies of the triborate and borate bands with temperature. The triborate peak shifted from 615 cm−1 at 25 °C to 608 cm−1 at 300 °C, whereas the borate peak shifted from 747 cm−1 to 736 cm−1 when the temperature was increased from 25 to 300 °C. The values are tabulated in Table 1. Unless otherwise stated, the frequencies used to identify the bands in the discussion below refer to 25 °C. Spectra for solution 3 (RBuffer = 0.129 and mB = 0.806 mol· kg−1) were also acquired at higher temperatures, but the triborate and borate peaks at this composition were too small to

Figure 4. Reduced isotropic Raman spectra normalized with respect to the peak areas of the perchlorate internal standard for an aqueous solution with RBuffer = 0 and mB = 0.776 mol·kg−1 from t = 25 to 300 °C at p = 20 MPa. The inset shows the shifts in the B(OH)3 and ClO4− peaks with temperature.

standard peak. All spectra show the characteristic B(OH)3 peak at ∼880 cm−1 with no bands other than the ∼936 cm−1 peak of the perchlorate ion. It is evident from the figure that both bands shift to lower energy with increasing temperature. The frequency of the B(OH)3 peak at 25 °C was 880 cm−1 but by 300 °C had shifted to 872 cm−1. Similarly, the perchlorate peak shifted from 936 cm−1 at 25 °C to 934 cm−1 at 300 °C. The peak heights for the boric acid band were observed to decrease with increasing temperatures, while the width of the peak increased proportionately, so the ratio of the area of the boric acid band to that of the perchlorate at all temperatures remained constant to within the experimental uncertainty. Metaboric acid, HBO2, which has a symmetric vibrational band at 785 cm−1,8,18 was postulated by Wang et al.23 to be a significant species in equilibrium with B(OH)3 above ∼200 °C. This prediction is not supported by the Raman spectra since no band was observed at 785 cm−1 in the spectra of the 0.8 m B(OH)3 solutions at temperatures up to 300 °C. The inset of the D


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triborate with respect to the perchlorate internal standard were 10% or less. In the discussion that follows, the scattering coefficient of boron species i relative to perchlorate is represented as Sri = Si/SClO−4 . The scattering coefficients reported by Applegarth et al.14 were used to calculate the molalities of the boron species in this study. These are based on reduced isotropic Raman spectra measured at 25 and 80 °C over a very wide range of molalities and are consistent with the mixed solvent electrolyte (MSE) activity coefficient model and critically evaluated database reported by Wang et al.,23 which is considered accurate over the entire concentration range at temperatures below 125 °C. To test the validity of the values reported by Applegarth et al.,14 relative Raman scattering coefficients for boric acid B(OH)3 with respect to perchlorate were calculated from the spectra of the 0.8 m aqueous solution of boric acid (RBuffer, = 0 and mB = 0.776 mol·kg−1), with the assumption that no other boron species were present at any of the temperatures studied, as is evident from the spectra in Figure 3. The results are tabulated in Table 1. The mean value for the relative scattering coefficient of boric acid, SrB(OH)3 = 0.221 ± 0.011, is in good agreement with the value reported by Applegarth et al.,14 SrB(OH)3 = 0.222 ± 0.003. A comparison of the scattering coefficients calculated from this work and those reported by Applegarth et al.14 is given in Table 1. It was not possible to measure the relative scattering coefficient of the borate ion, SrB(OH)4−, at temperatures above ∼25 °C because of the presence of polyborate species.23 A value could be determined from the 25 °C reduced isotropic Raman spectrum of the 1 m aqueous solution of sodium borate of buffer ratio RBuffer = 0.98 with mB = 1.019 mol·kg−1, shown in Figure 3. The relative scattering coefficient for [B(OH)4]− with respect to the perchlorate internal standard was SrB(OH)4− = 0.139 ± 0.009, in agreement with the value reported by Applegarth et al.,14 SrB(OH)4− = 0.147 ± 0.003, to within the combined experimental uncertainties. The molality and the relative scattering coefficients of triborate were calculated from the spectra for solution 2, using the following procedure. First, the molalities of B(OH)3, mB(OH)3, and [B(OH)4]−, m[B(OH)4]−, were calculated from the areas of the B(OH)3, [B(OH)4]−, and perchlorate bands using the relative scattering coefficients reported by Applegarth et al.,14 as cited above. The molality of triborate, m[B3O3(OH)4]−, was

Figure 6. Reduced isotropic Raman spectra normalized with respect to the peak areas of the perchlorate internal standard for solution 2 from t = 25 to 300 °C at p = 20 MPa. The region between 500 and 800 cm−1 is enlarged in the inset, to show the presence of [B(OH)4]−, [B3O3(OH)4]−, [B4O5(OH)4]2−, and [B5O6(OH)4]−.

determine quantitative values of the integrated areas at temperatures above 150 °C. 3.2. Relative Scattering Coefficients. The equilibrium concentrations of each boron species i in each solution at each temperature were calculated from the integrated areas of each band relative to that of the perchlorate internal standard (IS) according to the equation:14

jij mi zyz jij Si zyz jij Ai zyz jj z·j z = j z j mIS zz jj SIS zz jj AIS zz (10) k {k { k { Here, the terms Si and SIS are the scattering cross sections, mi and mIS are the molalities of species i and the internal standard, and Ai and AIS are the areas of peaks for species i and the internal standard, respectively. Peak fitting to integrate the area under each band was done with a Voigt function using the curve fitting function in Origin Pro 2016. The deconvolution of the spectra used to calculate the peak areas and scattering coefficients for solutions 1 and 2 is shown in Figures 7 and 8. The sum of the areas of the two peaks at ∼935 and ∼920 cm−1 was used in the calculation of the total area of the perchlorate band. These have the lowest and highest relative concentrations of triborate species, respectively. The standard errors in the relative areas for

Table 1. Experimental Peak Positionsa, ν̅, and Relative Scattering Coefficients to Perchlorate, Sri , for Aqueous Boric Acid, Borate, and Triborate from 25 to 300 °C [B(OH)4]−

B(OH)3 t (°C)

ν̅ (cm−1)

SrB(OH)3

ν̅ (cm−1)

Sr[B(OH)4]−

25 75 150 200 250 275 300 this work (mean) Applegarth et al.14

879.6 877.9 875.9 874.5 873.0 872.3 871.5

0.237 ± 0.011 0.232 ± 0.012 0.229 ± 0.014 0.217 ± 0.007 0.211 ± 0.003 0.213 ± 0.006 0.208 ± 0.008 0.221 ± 0.011 0.222 ± 0.003

747.4 746.3 745.4 742.1 738.8 737.8 736.4

0.139 ± 0.009 NA NA NA NA NA NA 0.139 ± 0.009 0.147 ± 0.003

[B3O3(OH)4]− ν̅ (cm−1) 614.9 614.5 614.0 613.5 611.2 608.3 608.8

Sr[B3O3(OH)4]− NA NA NA 0.120 ± 0.010 0.073 ± 0.007 0.079 ± 0.008 0.116 ± 0.017 0.097 ± 0.024 0.105 ± 0.003

High temperature frequencies for [B(OH)4]− and [B3O3(OH)4]− were taken from spectra from solution 2.

a

E


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Figure 7. Reduced isotropic Raman spectra for solution 1 showing peaks deconvoluted at t = 300, 250, 150, and 75 °C and p = 20 MPa. Peaks and corresponding peak fitting in the 500−800 cm−1 regions is zoomed in for clarity and presented as insets at each temperature.

then calculated by subtracting the equilibrium molalities of B(OH)3 and [B(OH)4]− from the total molality of boron species. Once the molality of triborate species was known, eq 10 was used to determine its relative scattering coefficient, S[Br 3 O 3 (OH) 4]− . The molalities and the relative scattering coefficients of the triborate species were calculated using the reduced isotropic spectra shown in Figure 6, which correspond to the temperature range 200 to 300 °C. The mean value for the relative scattering coefficient was Sr[B3O3(OH)4]− = 0.097 ± 0.024, which is comparable to the value Sr[B3O3(OH)4]− = 0.105 ± 0.003 reported by Applegarth et al.14 Small but significant equilibrium concentrations of tetraborate and pentaborate prevented the calculation of molality of triborate using mass balance from the spectra of solutions from 25 to 150 °C. The experimental scattering coefficients for the triborate ion are tabulated in Table 1. 3.3. Equilibrium Molalities and Triborate Formation Quotients, Qb31,m. The experimental molalities of B(OH)3, [B(OH)4]−, and [B3O3(OH)4]− were determined from the peak areas in the reduced isotropic Raman spectra using the scattering coefficients in Table 1 and are listed in Table 2. The equilibrium constant for triborate formation, Kb31,m, according to reaction 3 is given by the expression b b b K31, m = Q 31, mQ γ ,31, m

b Q 31, = m

m[B3O3(OH)4 ]− 3

(mB(OH)3) mOH−

and Q γb,31, m =

γ[B O (OH) ]− 3 3

4

(γB(OH) )3 γOH− 3

(12)

Here, Qb31,mis the experimental equilibrium quotient obtained from molalities calculated from the Raman spectra, Qγ,31,m is the activity coefficient quotient, and γi is the activity coefficient of species i. In these boric acid-rich solutions, the relative molalities of hydroxide, mOH−, required to calculate experimental equilibrium formation quotients, Qb31,m, were found to be too small to be calculated accurately by charge and mass balance. Instead, they were calculated from the molalities of B(OH)3 and [B(OH)4]− and the ionization constant of boric acid, mOH− =

b m[B(OH)4 ]− Q γ ,11, m

mB(OH)3

b K11, m

(13)

using the expressions for Kb11,mand Qbγ,11,mreported by Palmer et al.21 These have been shown to be accurate to ionic strengths 0 < I (mol·kg−1) < 1.0 at temperatures up to and above 300 °C at pressures from steam saturation to 20 MPa.18 Mass balance and charge balance constraints were not imposed. The discrepancies in boron mass balance and charge balance, listed in the Supporting Information (Table S1), were typically less than 5% and no more than 10%. The resulting experimental formation quotients, Qb31,m, are tabulated in Table 2.

(11)

where F


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Figure 8. Reduced isotropic Raman spectra for solution 2 showing peaks deconvoluted at t = 300, 250, 150, and 75 °C and p = 20 MPa. Peaks and the corresponding peak fits in the 500−800 cm−1 regions expanded for clarity and presented in the inset at each temperature.

Table 2. Experimental Temperature, Solvent Densities, Equilibrium Molalities of Boric Acid, Borate, Triborate, and Hydroxide, Ionic Strength, and Equilibrium Triborate Formation Quotients at p = 20 MPa for Solutions 1, 2, and 3 t (°C)

ρw (kg·m3)

mB(OH)3 (mol·kg−1)

m[B(OH)4]−(mol·kg−1)

m[B3O3(OH)4]−(mol·kg−1)

mOH−·106 (mol·kg−1)

I (mol·kg−1)

log Qb31,m

1.21 10.6 174 377 897 695 1796

0.223 0.222 0.231 0.202 0.206 0.195 0.208

5.816 ± 0.058 4.780 ± 0.058 3.521 ± 0.047 2.876 ± 0.048 2.471 ± 0.052 2.501 ± 0.075 2.186 ± 0.060

3.52 40.0 442 1238 1928 2011 3512

0.340 0.358 0.326 0.339 0.301 0.295 0.305

6.234 ± 0.034 5.090 ± 0.041 3.593 ± 0.034 3.057 ± 0.036 2.537 ± 0.043 2.492 ± 0.045 2.240 ± 0.048

2.01 17.6 150

0.217 0.216 0.210

5.608 ± 0.045 4.663 ± 0.058 3.579 ± 0.061

−1

25 75 150 200 250 275 300

1005.80 983.48 927.69 877.97 816.09 778.71 734.71

0.480 ± 0.016 0.527 ± 0.017 0.554 ± 0.016 0.558 ± 0.010 0.580 ± 0.012 0.594 ± 0.030 0.599 ± 0.027

25 75 150 200 250 275 300

1005.80 983.48 927.69 877.97 816.09 778.71 734.71

0.299 ± 0.005 0.342 ± 0.011 0.418 ± 0.008 0.463 ± 0.012 0.498 ± 0.014 0.5191 ± 0.015 0.544 ± 0.020

25 75 150

1005.80 983.48 927.69

0.484 ± 0.011 0.502 ± 0.019 0.555 ± 0.019

Solution 1, RBuffer = 0.130,mB = 0.847 mol·kg 0.039 ± 0.004 0.087 ± 0.007 0.033 ± 0.004 0.094 ± 0.006 0.055 ± 0.004 0.099 ± 0.007 0.044 ± 0.002 0.049 ± 0.005 0.056 ± 0.004 0.052 ± 0.005 0.035 ± 0.004 0.046 ± 0.005 0.078 ± 0.004 0.059 ± 0.006 Solution 2, RBuffer = 0.254,mB = 0.964 mol·kg−1 0.075 ± 0.004 0.161 ± 0.009 0.086 ± 0.004 0.197 ± 0.012 0.108 ± 0.004 0.126 ± 0.008 0.125 ± 0.005 0.140 ± 0.008 0.106 ± 0.005 0.082 ± 0.006 0.091 ± 0.005 0.087 ± 0.007 0.142 ± 0.007 0.098 ± 0.007 Solution 3, RBuffer = 0.129,mB = 0.806 mol·kg−1 0.066 ± 0.004 0.093 ± 0.007 0.053 ± 0.005 0.102 ± 0.008 0.047 ± 0.004 0.097 ± 0.009

The presence of tetraborate and pentaborate was evident in the spectra obtained from solutions 1 and 2 at temperatures up to 120 °C, as shown in Figures 5 and 6. The small equilibrium concentrations of pentaborate and tetraborate observed in these

solutions were not considered in the calculations. Approximate estimates showed that their relative concentrations were less than the uncertainties. The uncertainty associated with omitting them was less than 10%. G


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Table 3. Experimental Temperature, Solvent Densities, Ionic Strength, Equilibrium Triborate Formation Quotients, Boric Acid Ionization Constants, and Activity Coefficient Quotients as Calculated from Palmer et al.,21 Equilibrium and Fitted Triborate Formation Constants Using Models I and II, and Triborate Formation Constants from Wang et al.23 at p = 20 MPa for Solutions 1, 2, and 3 log Kb31,m

experimental parameters log t (°C)

Qb31,m

exp

a

I

ref 21, p = 20 MPa

mol·kg

−1

log

Kb11,m

25 75 150 200 250 275 300

5.816 4.780 3.521 2.876 2.471 2.501 2.186

0.223 0.222 0.231 0.202 0.206 0.195 0.208

4.792 3.737 2.719 2.289 2.001 1.904 1.834

25 75 150 200 250 275 300

6.234 5.090 3.593 3.057 2.537 2.492 2.240

0.340 0.358 0.326 0.339 0.301 0.295 0.305

4.792 3.737 2.719 2.289 2.001 1.904 1.834

25 75 150

5.608 4.663 3.579

0.217 0.216 0.210

4.792 3.737 2.719

model 1, p = 20 MPa

Qbγ,11,m

exp

model 2, p = 20 MPa

p = psat

p = 20 MPa

fit

ref 21

ref 23

(5.692) (4.663) 3.410 2.782 2.382 2.418 2.102

6.592 5.012 3.498 2.845 2.409 2.271 2.197

6.657 5.171 3.613 2.855 2.246 1.985 1.747

6.615 5.309 3.791

(6.052) (4.912) 3.443 2.913 2.415 2.377 2.129

6.592 5.012 3.498 2.845 2.409 2.271 2.197

6.657 5.171 3.613 2.855 2.246 1.985 1.747

6.615 5.309 3.791

(5.487) (4.549) 3.477

6.592 5.012 3.498

6.657 5.171 3.613

6.615 5.309 3.791

fit

a

exp

Solution 1, RBuffer = 0.130, mB = 0.847 mol·kg−1 −0.041 (5.775) 6.599 −0.039 (4.741) 5.060 −0.037 3.484 3.575 −0.031 2.844 2.928 −0.030 2.441 2.488 −0.028 2.473 2.343 −0.028 2.158 2.259 Solution 2, RBuffer = 0.254, mB = 0.964 mol·kg−1 −0.061 (6.173) 6.599 −0.059 (5.031) 5.060 −0.050 3.543 3.575 −0.048 3.009 2.928 −0.041 2.496 2.488 −0.038 2.453 2.343 −0.037 2.203 2.259 Solution 3, RBuffer = 0.129, mB = 0.806 mol·kg−1 −0.040 (5.568) 6.599 −0.038 (4.625) 5.060 −0.034 3.545 3.575

a

a

Standard uncertainty u(log Kb31,m) = 0.14. The standard uncertainty of log Qb31,mcalculated from models 1 and 2 decreases from 0.14 to 0.08 as the ionic strength is increased from I = 0 to 0.3 mol kg −1.The values in parenthesis were not included in the fit.

Mesmer’s values were re-fitted by Palmer et al.21 to yield the following expressions for the thermodynamic ionization constant, Kb11,m, a[B(OH)4 ]− b log K11, m = aB(OH)3aOH− p = p1 + 2 + p3 log T + (p4 + p5 T )log ρw (16) T

Methods used to estimate the activity coefficient quotient, are discussed in the following section. 3.4. Activity Coefficient Models for Boric Acid Ionization Constants and Calculation of Triborate Formation Constants, Kb31,m. Raman spectroscopy cannot distinguish between sodium borate ion pairs, [NaB(OH)4]0, and the borate ion, [B(OH)4]−,14 so that the peak at 747 cm−1 corresponds to the sum of the aqueous [NaB(OH)4]0 and [B(OH)4]− species. As a result, the contribution of the ion pair must either be calculated from ion-pair formation constants determined by other methods or included in the activity coefficient term, Qbγ,31,m. The treatment in this study is based on the activity coefficient model derived by Palmer et al.,21 which was fitted to boric acid ionization constants measured in KCl solutions by potentiometric titrations with a hydrogen concentration cell from 25 to 290 °C at steam saturation pressures.27 In Palmer’s model, [KB(OH)4]0 was not included as a species, and ion-pair formation was treated as an activity coefficient effect. Details are discussed below. As noted above, experimental values for the ionization quotient of boric acid according to reaction (1) were reported by Mesmer et al.27 as a function of ionic strength in aqueous KCl Qbγ,31,m,

b b b K11, m = Q 11, mQ γ ,11, m =

m[B(OH)4 ]−

where the terms p1 = − 36.261, p2 = 3645.18, p3 = 11.6402, p4 = 16.4914, and p5 = − 0.0239 are adjustable parameters fitted to experimental values and ρw is the density of water in g·cm−3. The activity coefficient quotient, Qbγ,11,m, is given by the expression γ[B(OH) ]− 4 log Q γb,11, m = γB(OH) γOH− pI i y = −jjjjp6 I + 7 f (I ) + p8 I 2 log ρw zzzz T k { 3

where the terms p6 = 0.11902, p7 = 36.3613, and p8 = 0.72132 are adjustable parameters fitted to experimental values, f(I) is the Pitzer formulation for the Debye−Hückel limiting law,

γ[B(OH) ]− 4

mB(OH)3mOH− γB(OH) γOH− 3

f (I ) =

(14)

where b Q 11, = m

(17)

1 − (1 + 2 I )e−2 2I

I

(18)

and I is the ionic strength n

m[B(OH)4 ]− mB(OH)3mOH−

I= (15) H

1 ∑ mizi2 2 i=1

(19) DOI: 10.1021/acs.jpcb.9b03062 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B Here, mi is the molality of the ith ion and zi is its charge. The sign of the term in eq 17 is incorrectly reported as positive by Palmer et al.21 Palmer’s model treated ion association with potassium as an activity coefficient effect and did not consider the [K(BOH)4]0 ion pair as a distinct species. The model is valid over the temperature range 0 ≤ t ≤ 300 °C, at steam saturation pressures and ionic strengths 0 ≤ I ≤ 1 mol·kg−1. The calculation of triborate formation constants, Kb31,m, from b the experimental reaction quotients, Q31,m , requires an expression for the activity coefficient quotient. γ[B O (OH) ]− 3 3 4 Q γb,31, m = (γB(OH) )3 γOH− (20)

along with the values reported in the critically compiled databases reported by Wang et al.23 and Palmer et al.21 at p = 20 MPa and p = psat, respectively. The formation constants derived from the experimental reaction quotients, Qb31,m, using activity coefficients from Model I at temperatures above 100 °C are in better agreement with those obtained from the recent conductivity study by Ferguson et al.28 than those from model II. At temperatures below 125 °C, the values of Kb31,mfrom both models deviate significantly from those reported by Wang et al.,23 which were based on critically evaluated literature data measured by a variety of techniques over a very wide range of concentrations. The formation quotients reported in Table 2 are based on the Raman scattering coefficients reported by Applegarth et al.,14 which were derived from Wang’s lowtemperature formation constants and MSE activity coefficient parameters. Except for the small pressure effect, the Raman results below 100 °C must, by definition, be consistent with Wang’s formation constants, and the discrepancies with the values derived from models I and II, in Table 3, may be due to a breakdown in the activity coefficient assumptions on which models I and II were based. These assumptions are known to be valid at temperatures above 125 °C and increasingly less valid at temperatures approaching ambient conditions.24,29 A second source of error may be the small equilibrium concentrations of pentaborate and tetraborate observed in our solutions at temperatures up to 120 °C, which were not considered in the mass balance calculations. As noted above, the uncertainty associated with omitting them was less than 10 percent. Finally, the values for the formation constants for the pentaborate and (possibly) tetraborate species selected by Wang et al.23 are not consistent with the results of Mesmer et al.27 and Applegarth et al.14 These values may cause the borate concentrations calculated from the MSE model to be too low at the solution compositions reported in this paper. At higher temperatures, the formulations for Kb31,min the databases of both Wang et al.23 and Palmer et al.21 are based largely on the single formation quotient reported by Mesmer et al.27 at 200 °C in 1 mol·kg−1 KCl (aq). Standard uncertainties based on these considerations and on the standard errors in the Raman peak areas are listed in Table 2. The values for Kb31,m reported by Wang et al. are most accurate at temperatures below 125 °C, while the values derived from models I and II are considered to be more accurate at higher temperatures. The standard uncertainties for the values of log Qb31,mwere taken to be u(log Qb31,m) = 0.08 at ionic strengths of 0.2 < I (mol·kg−1) < 0.3, based on the standard errors listed in Table 2, which are largely independent of temperature. The standard uncertainties of log Kb31,mwere estimated to be u(log Kb31,m) = 0.14 based on differences between models I and II and the standard uncertainty of log Qb31,m. The experimental formation constants from model I at temperatures from 150 to 300 °C at 20 MPa and the values from Wang et al. at 25 and 80 °C at 0.1 MPa were fitted with a density model of the form

3

Two methods were adopted, both based on the application of Palmer’s model for the excess properties of the boric acid ionization constant, Qbγ,11,m(eqs 14 to 20). Model I is based on the assumption proposed by Palmer et al.21 that the activity coefficient effect in both boric acid ionization and triborate formation reactions can be attributed to the borate and polyborate ionic species and that they are equal γ[B O (OH) ]− γ[B(OH) ]− 3 3 4 4 = = Q γb,11, m ; and γB(OH) = 1 3 γOH− γOH− (21)

Qbγ,31,m=

Qbγ,11,m.

so that Thus, the extrapolation to zero ionic strength in model I was based on the expression b b b log K31, m = log Q 31, m + log Q γ ,11, m

pI i y b = log Q 31, − jjjjp6 I + 7 f (I ) + p8 I 2 log ρw zzzz m T k { (22)

Model II was based on the assumption that ionic activity coefficients at elevated temperatures depend only on charge. For the boric acid ionization reaction, this corresponds to the expression γ[B(OH) ]− 1 4 = 1; so that γB(OH) = b 3 γOH− Q γ ,11, m (23) The corresponding expressions for the formation constant of triborate are γ[B O (OH) ]− 1 4 Q γb,31, m = = (Q γb,11, m)3 ; where 3 3 3 γOH− (γB(OH) ) 3

=

γ[B(OH) ]− 4

γOH−

=1 (24a)

and b b b log K31, m = log Q 31, m + 3log Q γ ,11, m

pI i y b = log Q 31, − 3jjjjp6 I + 7 f (I ) + p8 I 2 log ρw zzzz m T k {

b log K31, m = a +

(24b)

The experimental values of the triborate formation constants obtained from models I and II are tabulated in Table 3 along with the activity coefficient quotients used to calculate them. 3.5. Comparison of Triborate Formation Constants, Kb31,m, with Other Studies. Values of the triborate formation constants from models I and II at 20 MPa are listed in Table 3

b c + log ρw T T

(25)

where a, b, and c are the fitting parameters, T is the temperature in Kelvin, and ρw is the density of water in g·cm−3. The nonlinear regression yielded parameters, which are listed together with standard errors in Table 4. A plot of the triborate formation constants as a function of inverse temperature, log Kb31,mversus 1/ I


Article


speciation to form metaboric acid, HBO2, or polyborates in this temperature and concentration range. The spectra in Figure 3 are of higher quality than those reported in ref 18 and more clearly show the absence of polyborate species in the region from 600 to 850 cm−1, which was obscured by bands from dissolved silica from the capillary cell used by Arcis et al.18 4.2. Stability and Structure of the Triborate Ion. Together with the diamond anvil cell results from Schmidt et al.,8 the Raman spectra presented in Figures 5 to 8 are the first direct spectroscopic confirmation of the triborate ion as an equilibrium species in aqueous solutions at temperatures above 80 °C, as reported in the literature. The lack of other bands shows that B(OH)3, [B(OH)4]−, and [B3O3(OH)4]− persist as the predominant boron species in these boric acid-rich buffer solutions at temperatures up to 300 °C. Moreover, the agreement between the high-temperature scattering coefficients listed in Table 1 and those reported by Applegarth et al.14 below 100 °C confirms that the values for SrB(OH)3 and Sr[B3O3(OH)4]− are independent of temperature as required for the thermodynamic calculations presented above. The symmetric stretching bands of all three species were shifted to lower frequencies at elevated temperatures. This effect, which has been observed in other oxyacids and oxyanions, is thought to arise because water is more strongly hydrogen bonded to their oxygen moieties due to the breakdown in hydrogen bonding in high-temperature liquid water.19,30,31 4.3. Comparisons with Industrial Chemical Equilibrium Models. The implications of the new data for modelling nuclear reactor coolant chemistry were examined by comparing the experimental results with speciation calculations from the two chemical equilibrium databases used by the nuclear industry, the OLI Analyzer Studio 9.2.1 software23 and the EPRI MULTEQ software (ChemWorks 4.2, MULTEQ database version 8.0).24,25 These models are based on two different activity coefficient models and self-consistent sets of critically evaluated equilibrium constants. The EPRI MULTEQ chemical equilibrium model is based on a thermodynamic representation of multiphase chemical equilibria where the non-ideality of the aqueous phase is determined by a non-flexible activity coefficient model parametrized on sodium chloride. The mean activity coefficient for aqueous electrolytes is calculated with the simple Meissner 2 equation24,32 through the relationship γi = (γ±,NaCl)zi . Speciation calculations were carried out with the chemical equilibrium model MULTEQ software (version 8.0) using the EPRI chemical modeling software, ChemWorks (version 4.2). The OLI Analyzer Studio model is based on the mixed solvent electrolyte (MSE) treatment of excess properties reported by Anderko et al.33 and the Helgeson−Kirkham−Flowers−Tanger (HKFT) equation34,35 for the standard-state properties of aqueous species. In this work, we used the critically evaluated database recently reported by Wang et al.,23 and speciation calculations were carried out with OLI Analyzer Studio 9.2.1 software (OLI Systems Inc.). We note that the scattering coefficients reported by Applegarth et al.14 were based on this model, which is considered accurate for the solutions studied here from 25 up to 125 °C. Wang’s database includes parameters for metaboric acid, HBO2, and a pentaborate species, [B5O6(OH)6]3−, whose existence was not confirmed by our previous Raman studies14 but was instead found to be [B5O6(OH)4]−. These are minor species under the experimental conditions of the present study.

Table 4. Fitted Parameters for Equilibrium Triborate Formation Constants According to the “Density Model” (Eqs 25 and 26) a −5.194 ± 0.677 −5.599 ± 0.719 −6.495

b (K)

c (K)

log Kb31,m (model 1) 3530 ± 200 −5539 ± 1773 log Kb31,m (model 2) 3650 ± 212 −6111 ± 1882 log Kb31,m (Palmer et al.21) 3219.1 NA

d NA NA 0.95186

T, is presented as Figure 9. Figure 9 also includes values calculated from the expression developed by Palmer et al.,21

Figure 9. Equilibrium triborate formation constant, log Kb31,m, from t = 25 to 300 °C: red open circle and red solid circle, this work at p = 20 MPa (model I); black solid down triangle, Wang et al.23 at p = 20 MPa; black solid tilted square, Mesmer et al.27 at psat; red line, this work (eq 25) at p = 20 MPa; black line, Palmer’s density model21 (eq 26) at p = 20 MPa (dashed curve indicates extrapolation). The experimental values below 100 °C do not agree with the values of Wang et al. from which the scattering coefficients were derived because the activity coefficient models are not consistent with Wang’s more accurate treatment at these near-ambient temperatures. b log K31, m = − 6.495 +

3219.1 + 0.95186 log T T

(26)

which yields nearly identical values to those reported by Wang et al.23 Both eqs 25 and 26 yield values of log Kb31,m between 75 and 200 °C that agree to within the combined experimental uncertainties of this work and that of Mesmer et al.27 Extrapolations to higher temperatures using eq 26 underpredict the stability of triborate to a significant degree, relative to the experimental results from this study. At 300 °C, the b experimental value of log K31,m is higher than Palmer’s extrapolated value by a factor of ∼3. This exceeds the effect of the pressure difference between the present study at p = 20 MPa and Mesmer’s study at psat, predicted by eq 25. The effect of increasing the pressure from psat to p = 20 MPa on log Kb31,m is 0.129 log K units for model I and 0.143 log K units for model II, while the difference between eqs 25 and 26 at psat and 300 °C is 0.641 and 0.593 log K units for models I and II, respectively.

4. DISCUSSION 4.1. Boric Acid Speciation under Hydrothermal Conditions. The consistency of the calculated relative scattering coefficient for B(OH)3 at all temperatures confirms the preliminary finding of Arcis et al.18 that there is no boric acid J


Article


formation constant, Kb31,m= 2.259 ± 0.060 (model I) is larger than the extrapolated value by a factor of ∼3. This discrepancy and the absence of detectable concentrations of the diborate ion in the Raman spectra of these solutions above 150 °C suggest that more accurate values for the formation constants of other polyborates may lead to improvements in chemical equilibrium models used to predict aqueous boron chemistry and “hideout” reactions with metal oxides and ferrites under reactions under primary coolant operating conditions in PWR nuclear reactors. Raman spectroscopy has proven to be a very effective way to “see” different species in aqueous solution under hydrothermal conditions8,38−40 and can be effective in identifying different species in solution when combined with computational calculations for predicting structure and vibrational frequencies of the molecules.8−10,31,38,39,41 The techniques used to measure and analyze the structure and equilibrium concentrations of inorganic complexes in hydrothermal solutions were pioneered by D. E. Irish at the University of Waterloo, M. H. Brooker at Memorial University, and E. U. Franck at Karlsruhe University, among others. The methods used here are based on the use of polarized Raman measurements to obtain the reduced isotropic Raman spectra, which yield the concentration of each Ramanactive equilibrium species in solution.26,39,40 More recently, advances in the development of confocal Raman microscopes allowed Raman spectroscopy to be coupled with hydrothermal diamond anvil cells42 (HDAC) and with high-pressure optical capillary (HPOC) cells by Chou at the U.S. Geological Survey and others.43,44 However, these techniques have limitations. Diamond anvils cells are difficult to load without affecting solution concentrations and are not designed to operate under isobaric conditions. The capillaries used in HPOC cells restrict the experimental conditions to acidic and neutral solutions. Only a few hydrothermal flow cells for Raman spectroscopy have been reported in the literature.45−48 The cell described here incorporates some of the features of these cells modified for a back-scattering geometry and to enable continuous sample injection for quantitative Raman measurements. The sapphire windows used in the flow cell reported here have been found to be inert at concentrations of base up to 1 mol·kg−1 at 300 °C. Moreover, in future studies, the flow configuration will provide a means of studying systems in which the spectrum of the internal standard overlaps with the bands of interest, by allowing an external reference standard to be injected in series with the solutions to be studied. To the authors’ knowledge, this is the first application of flow techniques to obtain quantitative reduced isotropic Raman spectra under alkaline hydrothermal conditions.

The predicted chemical speciation results from the two models for each of the three solutions are listed in Supporting Information, Table S2 along with the experimental results in Table 2. The upper detection limits of tetraborate and pentaborate, [B4O5(OH)4]2− and [B5O6(OH)4]−, were determined by estimating the minimum detectable peak area at the known peak positions reported by Applegarth et al.14 and assuming scattering coefficients equal to those of [B 3 O 3 (OH) 4 ] − . The detection limits for diborate, [B2O(OH)5]−, whose spectrum has not been reported in the literature, were estimated from the standard uncertainties of the boric acid and borate molalities, assuming that the diborate peak could lie in these bands. Both models underpredicted the degree of hydrolysis of boric acid to form borate and polyborate species in these solutions by ∼5 to ∼10% at temperatures up to 200 °C. The differences increased to ∼15% at 275 and 300 °C. As expected, the equilibrium molalities for triborate listed in Table 2 are consistent with the predictions from both models up to 200 °C. Above this temperature, the models underpredicted the concentration of [B3O3(OH)4]− so that at 300 °C, the discrepancies between the model predictions and the experimental results were ∼30%. The OLI model predicted minor concentrations of tetraborate ([B4O5(OH)4]2−), pentaborate ([B5O6(OH)4]−), and diborate ([B2O(OH)5]−) as equilibrium species near ambient conditions. Although the predicted tetraborate and pentaborate concentrations decreased with increasing temperature, the diborate concentrations increased and became approximately equal to the triborate concentration at temperatures above 250 °C. The predictions from MULTEQ were similar, except that pentaborate is not included in the database, and the diborate species is written as [B2(OH)7]−. The predicted diborate concentrations are at or below the detection limit of the experimental reduced isotropic Raman spectra if its most intense peak lies in the boric acid band. The experimental results showed that triborate is the major polyborate species in these solutions at all temperatures, with diborate as the only other possibly significant polyborate ion at temperatures above 150 °C. Both models underpredicted the equilibrium concentration of the hydroxide ion by a factor of ∼3 relative to the experimental value, as calculated from eq 13. Finally, we note that pH estimates based on the values tabulated in Table S2 would yield significant discrepancies between the MULTEQ and OLI models, because of the different equations of state used to calculate the water ionization constant, Kw. The MULTEQ model uses the Marshall and Franck36 expression for Kw, while the OLI model is based on the treatment by Tanger and Helgeson.34 The impact of the formulation used for Kw is discussed in more detail in our recent lithium borate study.37

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5. CONCLUSIONS This work reports the very first quantitative Raman measurements on aqueous solutions of polyborate at temperatures above 80 °C. Experiments were performed under hydrothermal conditions, at moderately low ionic strengths (0.2 < I (mol· kg−1) < 0.3), using a novel sapphire window flow cell to yield formation constants for the triborate ion from 25 to 300 °C at 20 MPa. The experimental formation constants are consistent with the formulation for polyborates developed by Palmer et al.21 (eq 26) up to 200 °C, the limit of the experimental data on which they were based,27 to within the combined experimental uncertainties. At 300 °C, the experimental value for the

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.9b03062. Tables of mass and charge balance calculation results and comparisons of the experimental speciation with the predictions from OLI and MULTEQ chemical equilibrium modelling industrial software and isotropic Raman spectra of the solution with RBuffer = 0.40 and mB = 0.80 mol·kg−1 at different temperatures (5−120 °C) without the perchlorate internal standard (PDF) K


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(10) Zhu, F. Y.; Fang, C. H.; Fang, Y.; Zhou, Y. Q.; Ge, H. W.; Liu, H. Y. Structure of Aqueous Potassium Metaborate Solution. J. Mol. Struct. 2014, 1070, 80−85. (11) Zhu, F. Y.; Fang, C. H.; Fang, Y.; Zhou, Y. Q.; Ge, H. W.; Liu, H. Y. Structure of Aqueous Potassium Pentaborate Solution. J. Mol. Struct. 2015, 1083, 471−479. (12) Fang, C. H.; Zhu, F. Y.; Fang, Y.; Zhou, Y. Q.; Tao, S.; Xu, S. Structure of Aqueous Potassium Tetraborate Solutions by X-Ray Scattering. Phys. Chem. Liq. 2013, 51, 218−232. (13) Ishihara, K.; Nagasawa, A.; Umemoto, K.; Ito, H.; Saito, K. Kinetic Study of Boric Acid-Borate Interchange in Aqueous Solution by 11 B NMR Spectroscopy. Inorg. Chem. 1994, 33, 3811−3816. (14) Applegarth, L. M. S. G. A.; Pye, C. C.; Cox, J. S.; Tremaine, P. R. Raman Spectroscopic and Ab Initio Investigation of Aqueous Boric Acid, Borate, and Polyborate Speciation from 25 to 80 °C. Ind. Eng. Chem. Res. 2017, 56, 13983−13996. (15) Applegarth, L. M. S. G. A.; Corbeil, C. R.; Mercer, D. J. W.; Pye, C. C.; Tremaine, P. R. Raman and Ab Initio Investigation of Aqueous Cu(I) Chloride Complexes from 25 to 80 °C. J. Phys. Chem. B 2014, 118, 204−214. (16) Chou, I. M.; Burruss, R. C.; Lu, W. A New Optical Capillary Cell for Spectroscopic Studies of Geologic Fluids at Pressures up to 100 MPa. In Advances in High-Pressure Technology for Geophysical Applications; Chen, J.; Wang, Y.; Duffy, T. S.; Shen, G.; Dobrzhinetskaya, L. F., Eds. Elsevier: Amsterdam, 2005, pp 475−485. (17) Alcorn, C.; Applegarth, L. M. S. G. A.; Cox, J. S.; Tremaine, P. R. An Investigation of Uranyl Sulfate Complexation under Hydrothermal Conditions by Quantitative Raman Spectroscopy and Density Functional Theory. Submitted to J. Phys. Chem. B. (18) Arcis, H.; Ferguson, J. P.; Applegarth, L. M. S. G. A.; Zimmerman, G. H.; Tremaine, P. R. Ionization of Boric Acid in Water from 298K to 623K by AC Conductivity and Raman Spectroscopy. J. Chem. Thermodyn. 2017, 106, 187−198. (19) Applegarth, L. M. S. G. A.; Alcorn, C.; Bissonette, K.; Noël, J.; Tremaine, P. R. Non-Complexing Anions for Quantitative Speciation Studies Using Raman Spectroscopy in Fused Silica High-Pressure Optical Cells under Hydrothermal Conditions. Appl. Spectrosc. 2015, 69, 972−983. (20) Bassett, R. L. Critical evaluation of the thermodynamic data for boron ions, ion pairs, complexes, and polyanions in aqueous solution at 298.15 K and 1 bar. Geochim. Cosmochim. Acta 1980, 44 (8), 1151− 1160. (21) Palmer, D. A.; Benezeth, P.; Wesolowski, D. J. Boric Acid Hydrolysis: A New Look at the Available Data. PowerPlant Chem. 2000, 2, 261−264. (22) Wang, P.; Anderko, A.; Young, R. D. A Speciation-Based Model for Mixed-Solvent Electrolyte Systems. Fluid Phase Equilib. 2002, 203, 141−176. (23) Wang, P.; Kosinski, J. J.; Lencka, M. M.; Anderko, A.; Springer, R. D. Thermodynamic Modeling of Boric Acid and Selected Metal Borate Systems. Pure Appl. Chem. 2013, 85, 2117. (24) Lindsay, W. T., Jr. Chemistry of Steam Cycle Solutions : Principles. In The ASME Handbook on Water Technology for Thermal Power Systems; Cohen, P., Ed.; American Society of Mechanical Engineers: New York, 1989, pp 341−544. (25) Lindsay, W. T., Jr. In MULTEQ: What It Is and What It Can Do, Control of Corrosion on the Secondary side of Steam Generators; Staehle, R. W.; Gorman, J. A.; Mcllree, A. R., Eds.; Nat. Assoc. Corrosion Eng. (NACE): Houston, TX, United States, 1996. (26) Brooker, M. H.; Nielsen, O. F.; Praestgaard, E. Assessment of Correction Procedures for Reduction of Raman Spectra. J. Raman Spectrosc. 1988, 19, 71−78. (27) Mesmer, R. E.; Baes, C. F.; Sweeton, F. H. Acidity Measurements at Elevated Temperatures. VI. Boric Acid Equilibriums. Inorg. Chem. 1972, 11, 537−543. (28) Ferguson, J. P. Aqueous Boric Acid Chemistry under Pressurized Water Reactor Coolant Conditions by AC Conductivity. PhD Thesis, University of Guelph, Guelph, Canada, 2018.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Swaroop Sasidharanpillai: 0000-0002-2372-1973 Hugues Arcis: 0000-0002-2683-8560 Peter R. Tremaine: 0000-0002-9722-9180 Present Address †

Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe Street N., Oshawa, Ontario, Canada L1G 0C5

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Electric Power Research Institute (EPRI, Project 10006135) and by PT’s NSERC Discovery Grant. The authors thank OLI Systems Inc. (Edison, N.Y.) for donating their software package OLI Analyzer Studio 9.2.1 to the Hydrothermal Chemistry Laboratory at the University of Guelph and Dr. Peiming Wang (OLI) for help and advice with the database and software. We are grateful to Dr. Don Palmer (ORNL, ret.) for insights on polyborate thermodynamics and on published thermodynamic models. Mr. Ian Renaud and Mr. Case Gielen provided capable electronic and machine-shop support, particularly in constructing the titanium flow cell. The authors express their deep gratitude to Dr. Daniel Wells, EPRI, for providing technical advice, many fruitful discussions, and steadfast support on this project. Dr. Jenny Cox contributed to refinements of the flow cell design with assistance from Ph.D. student Jacy Conrad. We also thank Dr. Cox and Ph.D. student Jane Ferguson for carrying out the OLI and MULTEQ chemical equilibrium calculations and for many suggestions and technical discussions related to polyborate thermodynamics.

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REFERENCES

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Triborate Formation Constants and Polyborate Speciation under

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