B(OH)4- hydration and association in sodium metaborate solutions by X-ray diffraction and empirical potential structure refinement.

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Cite this: DOI: 10.1039/c7cp05107g

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B(OH)4 hydration and association in sodium metaborate solutions by X-ray diffraction and empirical potential structure refinement† Yongquan Zhou, ab Souta Higa,b Chunhui Fang,a Yan Fang,a Wenqian Zhanga and Toshio Yamaguchi *b X-ray diffraction is used to study the structure of aqueous sodium metaborate solutions at salt concentrations of 1, 3, and 5 (oversaturated) mol dm3. The X-ray structure factors are subjected to empirical potential structure refinement (EPSR) modelling to extract the individual site–site pair correlation functions, the coordination numbers, and the spatial density functions (three-dimensional structure) of ion hydration and association as well as solvent water in the borate solutions. The sodium ion is surrounded on average by (5.4 0.7), (4.6 1.0), and (3.7 1.2) water molecules at 1, 3, and 5 mol dm3, respectively, with the Na–O (H2O) distance of 2.34 Å. The decrease in hydration number of the sodium ion is compensated by direct binding of the oxygen atom of the borate ion, B(OH)4, with the average coordination number of (0.2 0.5), (1.0 0.8), and (2.1 1.3) at the Na–O(B) distance of 2.34 Å to keep the octahedral hydration shell of the sodium ion. The average number of water molecules around the borate ion is (13.9 1.8), (14.2 1.8), and (16.1 2.4) per borate ion with increasing salt concentration with the B–O(H2O) distance of 3.72 Å. The number of nearest-neighbour water molecules around a central water molecule in a solvent decreases as (4.8 1.2), (3.8 1.1), and (2.8 1.1) with an increase in salt concentration with the O(H2O)–O(H2O) distance of 2.79 Å. The Na+– B(OH)4 ion association is characterized by the Na–O(B) and Na–B pair correlation functions. The Na–B interactions are observed at 3.00 Å as a shoulder and 3.57 Å as a main peak in the site–site pair correlation function, suggesting two occupancy sites of Na+ with one for the edge-shared bidentate

Received 28th July 2017, Accepted 28th September 2017 DOI: 10.1039/c7cp05107g

bonding and the other for the corner-shared monodentate bonding. The total number of Na–B interactions at 3.00 and 3.57 Å is consistent with that of the Na–O(B) interactions. The detailed three-dimensional structure of the ion hydration and association is visualized as a function of salt concentration. The structure and stability of [NaB(OH)4(H2O)6]0 clusters are further investigated by DFT calculations, and the

rsc.li/pccp

most likely structure is proposed and cross-checked.

1 Introduction Aqueous borate solutions are ubiquitous in sea water, salt lakes, underground brine and geothermal water, and are used in many related industry fields, such as wood preservation, flame retardance, and nuclear electric power,1,2 etc. Borate ion hydration and association in an aqueous solution directly affect the borate mineral sedimentation and crystallization process,1,3,4 significantly influence the abilities of wood preservation and fire retardancy,5 and impact the fuel performance of pressurized

a

Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China Department of Chemistry, Faculty of Science, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka 814-0180, Japan. E-mail: [email protected]; Fax: +81-91-865-6030; Tel: +81-92-871-6631 ext. 6224 † Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp05107g b

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water nuclear reactors (PWRs).6,7 Borate ion hydration has also been proved to be critical for borate dissociation and polymerization.8 The boric acid–borate equilibrium in sea water even shows some potential effects on dioxide equilibrium and global climate change.9,10 Recently, due to the excellent performance of H2 storage materials of borohydride (NaBH4), aqueous sodium metaborate solutions have drawn new attention regarding their application in direct borohydride fuel cell (DBFC) technologies.11,12 Aqueous borate solutions are much more complicated than many other aqueous inorganic salt solutions.1,13 Various techniques including conductometric and potentiometric titrations, 11B NMR, IR, Raman and mass spectroscopy were used to unravel the polyborate distribution in solution.1,13–15 To date, the polyborate distribution and solid–liquid equilibrium prediction in aqueous borate solutions are barely satisfactory.16,17 As the ‘‘simplest’’ member of hydroxyl-hydrated borate, more than 95% of the

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borate ions are in the B(OH)4 form (ESI,† Fig. S1) in sodium metaborate (NaB(OH)4) solutions over a wide range of salt concentrations.15 Much supporting evidence of the ion association in an aqueous NaB(OH)4 solution has so far been reported.6,7,18–20 However, no clear atomic/molecular level information about the borate ion association is available. Theoretical studies on small size [B(OH)4(H2O)n] hydration clusters were reported by OI et al.21 and Rustad et al.22 who mainly focused on the isotopic fractionation of B(OH)4 hydration. The hydration of B(OH)4,23 ion association in LiB(OH)4 solutions,24 and hydration and acid dissociation mechanism of B(OH)38 were studied by DFT or by Car–Parrinello molecular dynamics simulation. Compared with theoretical studies, experimental reports are relatively scarce. Feng et al.25 studied [NaBO2(H2O)n]0, n = 0–4 clusters by photoelectron spectroscopy and ab initio calculations in the gas phase, and the initial step of dissolution of NaBO2 was suggested. Duffin et al.26 measured the near-edge X-ray absorption fine structure (NEXAFS) spectra at the boron K-edge for aqueous borate solutions using liquid microjet technology. The boron K-edge NEXAFS spectrum of the aqueous borate solutions was proved to be insensitive to the borate ion hydration. Raman and X-ray scattering measurements were implemented on aqueous sodium metaborate solutions with the salt concentration of 2.8 to 5.4 mol L1. However, the structural information was limited to one-dimensional time- and space-averaged structures of the borate ion and association.27 Empirical potential structure refinement (EPSR) modelling has been developed by Soper28–31 as one of the versatile methods to analyze the one-dimensional X-ray and neutron scattering data of liquid and amorphous materials. EPSR has been proved to be very successful in extracting the site–site partial distribution function, coordination number distribution, angle distribution, and spatial density function (SDF), which is a three-dimensional structure, for various liquids and solutions under various conditions.32–35 In the present work, X-ray diffraction data of aqueous sodium borate solutions over a wide salt concentration were collected. The X-ray data were subjected to EPSR modelling to extract the detailed structural information about bulk water, hydrated sodium ions, hydrated metaborate ions, and ion association in an aqueous sodium metaborate solution as a function of salt concentration. Furthermore, the structure of [NaB(OH)4(H2O)6]0 clusters was investigated by DFT at the B3LYP/Aug-cc-pVDZ basis level to serve as supporting evidence for distinguishing the different ion pairs in the solution. The effect of salt concentration on borate hydration and association is discussed from the structural point of view.

2 Experimental and theoretical methods 2.1

Sample preparation and analysis

Commercially available NaB(OH)42H2O of analytical reagent was recrystallized from distilled water. The sample solutions were prepared by mass using double-distilled water. The concentrations of boron in the sample solutions were determined


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by the mannitol method.36 The density of all the solutions was measured with a DMA48 vibrating densitometer (Anton Paar) which had been calibrated with dried air and distilled water at 298 0.5 K with the reproducibility of 0.1%. The composition (c), density (d), linear absorption coefficient (m), and stoichiometric volume (V) containing one water molecule for the sample solutions are listed in Table 1. 2.2

X-ray diffraction measurements

¨ller) Each of the solutions was sealed in a glass capillary (W. Mu of 2 mm diameter and 0.01 mm wall thickness. The X-ray scattering intensities of the empty capillary and the sample solutions were measured under ambient conditions (T = 298 1 K) with an X-ray diffractometer (DIP301, Bruker AXS) and a curved imaging plate detector. The X-rays were generated by a rotating Mo anode operated at 50 kV and 200 mA and then monochromatized with a flat graphite crystal to obtain Mo Ka radiation (l = 0.7107 Å). A double-hole type collimator, whose hole-diameters are 0.5 mm, was used to obtain the parallel X-ray beam. The exposure time was 3600 s for each measurement.37 The scattering angle range of the measurements spanned over 21 r 2y r 1401, corresponding to a range of the scattering vector Q (Q = 4p sin y/l) of 0.31 Å1 r Q r 16.62 Å1. 2.3

Structure function and RDF extraction

The two-dimensional diffraction pattern of the samples recorded on an imaging plate was integrated to one-dimensional intensities with a 2DP program (Rigaku). After the absorption correction of the sample and the capillary, the intensity of an empty glass capillary was subtracted from those of the sample. Then the subtracted intensities were normalized to an electron unit by comparing the asymptote of the experimental data with the calculated coherent intensity at large scattering vector (Q 412.0 Å1). The normalizing factor was further checked by the Krogh-Moe and Norman integration methods. The values from both the methods agreed with each other within 2%. The details about the X-ray data treatment can be found elsewhere.38 The structural function i(Q) of a solution was calculated by subtracting the independent scatterings from all the atoms in the solution from the normalized intensity as i X h 2 iðQÞ ¼ KI cor ðQÞ ni f 2i ðQÞ þ Df 00i þ I inc (1) i ðQÞ Here, K is the normalization factor, Icor(Q) is the corrected experimental intensity, ni is the number of the ith atom in the stoichiometric volume V containing one water molecule, fi(Q) is Table 1

Composition and properties of the sample solutions

No

c/mol dm3

d/g cm3

m/cm1

V/Å3

Water B1N1 B1N2 B1N3a

— 0.966 2.765 5.436

0.997 1.069 1.186 1.337

1.12 1.23 1.43 1.70

30.005 30.822 33.077 38.198

c, molarity; d, density; m, linear absorption factor; V, stoichiometric volume containing one water molecule. a A supersaturated sample with the degree of oversaturation of 0.238.


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the atomic scattering factor of atom i corrected for the real part of the anomalous dispersion, and Dfi00 is the imaginary part which was taken from the literature.39 Iiinc(Q) presents the incoherent scattering intensity corrected for the Breit-Dirac recoil factor for atom i cited from Cromer’s paper.40 The Q-weighted structure function Qi(Q) was Fourier-transformed to the radial distribution function (RDF) ð 2r Qmax 2 DðrÞ ¼ 4pr r0 þ Q iðQÞ MðQÞ sinðQrÞdQ (2) p 0 where r0 indicates the average electron density of the sample . P r0 ¼ ½ ni f i ð0Þ2 V . The modification function M(Q) is

factors; gij(Q) is the site-site radial distribution function for all of the atoms present in the sample. The total radial distribution functions (G(r)) are calculated as eqn (8): XX GðrÞ ¼ ci cj fi ðQÞfj ðQÞ gij ðrÞ 1 (8) i

ji

Initial structures for an EPSR simulation are generated by placing the appropriate number of molecules into a box to give the required density. The potential of the simulation box is calculated as eqn (9). " # ! X qi qj sij 12 sij 6 U tot ¼ U intra þ 4eij þ þ U EP rij rij 4pe0 rij ij

expressed as

(9)

MðQÞ ¼

1 eij ¼ ei ej 2 ;

X h 2 i.X h 2 2 i ni f i ðQÞ þ Df 00i exp kQ2 ni f 2i ð0Þ þ Df 00i (3)

The constant k is a damping factor to be chosen as 0.01 Å2 to minimize the truncation error of the Fourier transformation. The spurious ripples were removed from RDF by calculating the peak shape of the intramolecular structure of a water molecule and performing inversed Fourier transformation.41 Then, the coherent scattering intensity Icoh(Q) used for the subsequent EPSR modelling was calculated as eqn (4) X I coh ðQÞ ¼ KI cor ðQÞ ni I incoh ðQÞ (4) i All the corrections and treatments for diffraction data were performed with the program KURVLR.42 2.4

EPSR Modelling

EPSR utilizes a Monte Carlo style approach to minimize the difference between experimental diffraction data and those generated from the simulation of the structure. The experimental total normalized structure factor used in the EPSR is defined as eqn (5) coh P I ðQÞ ni f i2 ðQÞ exp P F ðQÞ ¼ (5) ½ ni f i2 ðQÞ The simulated Fsim(Q) is calculated as eqn (6) and compared with the experimental data. F sim ðQÞ ¼

XX i

, i hX ci f i2 ðQÞ 2 dij ci cj f i ðQÞf j ðQÞ Aij ðQÞ 1

ji

1 sij ¼ ðsi þ si Þ 2

(10)

where Uintra is described by using a series of harmonic potentials, eij and sij are the Lennard-Jones parameters for the potential well depth and effective atom size, respectively, e0 is the vacuum permittivity, and rij is the interatomic spacing; qi is the atomic charge; UEP is the empirical potential, which is calculated from the difference between the experimental scattering pattern and that generated by the simulated structure. The Monte Carlo (MC) simulations in EPSR were done in the conventional MC way. This additional empirical perturbation term (UEP) serves to drive the simulated structure as close as possible to the scattering data, without violating the constraints imposed on the atomic overlap, van der Waals forces, and hydrogen bonding.29–31 The potential parameters used in the EPSR modelling are listed in Table 2. The parameters used to describe the molecules in the simulations are detailed in Table S1 (ESI†). The EPSR simulations were set up using a cubic box containing 1000 water molecules, the number of Na+ and B(OH)4 ions corresponding to the salt concentration. Details about the composition of the simulation box are found in Table S2 of the ESI.† 2.5

NaB(OH)4(H2O)6 DFT calculations

The structure and stability of the [NaB(OH)4(H2O)6]0 clusters were investigated using the B3LYP method,45 on searching for the local minimum energy of all possible initial configurations in the aqueous phase. For all the atoms, Dunning’s correlation consistent basis sets were employed, that is, Aug-cc-pVDZ.46 In order to consider the long-range electrostatic effect of a solvent, a single-point polarized continuum model (PCM) was employed in the calculation of hydration energy for all the configurations.

(6) ð1 sin Qr dr Aij ðQÞ 1 ¼ 4pr r2 gij ðrÞ 1 Qr 0

Table 2

where Fsim(Q) is the total scattering structure factor; ci and cj are the atomic fractions of atom types i and j; fi(Q) and fj (Q) are the Q dependent ‘electron form factors’ of atom types i and j; dij is the Kronecker function to avoid double counting pairs of atoms of the same type; Aij(Q) is the Faber–Ziman partial structure


Potential parameter values used in EPSR modelling

(7) 1

e (kJ mol ) s (Å) Mass Chargea

Ow36

Hw36

Na+ 43

BB44

OB

HB

0.65 3.16 16.00 0.8476

0.00 0.00 1.00 0.4238

0.514 2.29 22.99 1.000

0.397 3.581 10.81 1.14

0.720 3.120 16.00 0.715

0.00 0.00 1.00 0.180

a The charge parameters of B(OH)4 are the Mulliken charge from DFT calculation at B3LYP/Aug-cc-pVDZ.


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Various possible isomer clusters were optimized at the B3LYP/ 6-31G(d) level, and the lowest energy structures obtained were considered for further geometry optimizations at the B3LYP/ Aug-cc-pVDZ level. Vibrational frequency calculations were performed at the same level to ascertain the nature of the stationary points (no virtual frequency). The basis set superposition error (BSSE) correction in the present work was made by partitioning the cluster into three fragments, i.e. Na+, B(OH)4, and (H2O)n. The interaction energies pertinent to [NaB(OH)4(H2O)6]0 could be considered as the total solvation energy. More details about the DFT calculations can be found elsewhere.24 All the geometry optimizations and frequency analyses were done with the Gaussian 09 software package.47

3 Results and discussion 3.1

X-ray structure functions and RDFs

The experimental structure functions are shown in Fig. 1a. The changes in a Q-range of 2–4 Å1 reflect some structural difference in solution with salt concentration. The corresponding RDFs are shown in Fig. 1b. The main peak at about 2.8 Å can be ascribed to the O(W)–O(W) hydrogen bonds of solvent water.37,48 The first peak at around 0.95 Å can be assigned to the intramolecular O–H interactions in the H2O molecules. The peak at around 1.45 Å is due to the intra-ionic O–B distance within B(OH)4 as suggested by the crystal structure data.49–51 This interaction increases steadily with an increase in concentration. The concentration proportional shoulder peak at around 2.4 Å can be ascribed to the Na+–O(W) interactions within the first hydration shell of hydrated Na+ ions on the basis of the crystal structure of Na(BOH)42H2O46 and the previous findings,52,53 tallying with the sum of the ionic radius of Na+ (0.95 Å) and the size of a water molecule (1.4 Å). This peak can also be partly ascribed to the intra-O–O interactions in the tetrahedral B(OH)4 according to (8/3)1/2 1.45 = 2.40 Å.49–51 The peak at 3.30 Å is strongly concentration dependent, mainly suggesting the octahedral vertexes of hydrated Na+ according to (2)1/2 2.4 = 3.30 Å. Other peaks over 3.50 Å may be assigned to the B–O(W) interactions of

Fig. 1 Experimental structure functions (a), and the D(r) 4pr 2r0 radial distributions functions (b) for sample solutions B1N1, B1N2, and B1N3, with that of pure water for comparison.


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the hydrated B(OH)4, the interaction of the contact ion pair (CIP) of Na+ and B(OH)4, etc., which are difficult to classify qualitatively. A more detailed analysis of the structure is made in the subsequent EPSR modelling. 3.2

EPSR modelling

Fig. 2 shows the experimentally determined and EPSR simulated F(Q) and G(r) for the aqueous NaB(OH)4 solutions. There are good agreements between the experimental data and the EPSR fitting down to about 1.0 Å1 in the F(Q) and 2.0 Å in the G(r) except for B1N3, indicates that the simulation structures are close to the real solutions. The small differences between the two functions in the low Q range may be due to the finite size of the simulation box.35 In the concentrated solution (B1N3), a small discrepancy is seen, which might be caused by a few other coexisting polyborates in this system (Fig. S1 in the ESI†). In fact, the EPSR calculations were not converged satisfactorily with only B(OH)4 as the borate species. 3.2.1 Bulk water. The pair radial distribution functions of O(W)–O(W) in pure water and aqueous NaB(OH)4 solutions are shown in Fig. 3a. The first-neighbour O(W)–O(W) peak in pure water is observed at around 2.80 Å, which is well consistent with the literature.34,54 The position of the first O(W)–O(W) peak remains at B2.79 Å, and the peak sharpens slightly with increasing concentration. On the other hand, a drastic shift of the second peak is observed from 4.5 Å for water to 3.5 Å for B1N3, i.e. Na+ and B(OH)4 perturb the tetrahedral structure of the solvent. This feature in the local structure of bulk water is similar to that in pure water under pressure, which has been observed by many other researchers.43 The effect of ions on the bulk water structure is unquestionable to compress the local ordering water. Fig. 3b shows the distribution of coordination numbers CN(I) and CN(II) of the first-neighbour and the second-neighbour O(W)–O(W) interactions, respectively, which were calculated by eqn (11). CN ¼ 4prj

ð rmax

gij ðrÞr2 dr

(11)

rmin

Fig. 2 Experimentally obtained (points) and EPSR simulated (solid line) F(Q) (a) and G(r) (b) for the aqueous sodium metaborate solutions.


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Fig. 3 The pair distribution functions (a) and the coordination number distributions (b) of O(W)–O(W) under various concentrations obtained from EPSR modelling.

Here, rj is the number density of atom j, and rmin and rmax denote the minimum and maximum distances, respectively, to define the coordination number. Both the values are summarized in Table 3. As seen in Fig. 3b, the peak positions of both first-neighbour and second-neighbour O(W)–O(W) interactions shift to the lower coordination number with increasing salt concentration. The average coordination number of CN(I) and CN(II) for O(W)–O(W) decreases from 4.9 1.1 to 2.8 1.1 and from 19.8 2.2 to 10.9 2.3 with an increase in concentration (Table 3). This finding shows that at higher concentrations bulk water is unable to form the discrete tetrahedral structure due to a lack of free water molecules and incorporates into the hydration shells of ions. To confirm this, the SDFs were calculated, which shows the location of neighbouring molecules or portions of molecules relative to a central ion or molecule. By averaging over the orientation of the neighbouring molecules derived from a spherical harmonic expansion of the pair correlation function in the modelling box, SDF provides a three-dimensional view of the liquid structure.55 The SDFs of the neighbouring water molecule around a central water molecule in pure water and aqueous NaB(OH)4 solutions are shown in Fig. 4 where the range for each shell is defined as the first minimum of the O(W)–O(W) pair distribution functions. Details about the SDFs for the water molecules for the first shell, the second shell, and

both the first and second shells can be found in Fig. S2 in the ESI.† As Fig. 4 shows, when concentration increases the first shell of the water molecule keeps the tetrahedral coordination, accompanied by no obvious changes in the distribution range, indicating the tendency for keeping a tetrahedron structure independent of salt concentration. However, the greyish blue and semitransparent lobes of the second sphere diffuse to a significant extent, compared with those of pure water. This indicates that the tetrahedral ordering of the second shell becomes more disordered. The structure breaking property14 of Na+ and B(OH)4 becomes effective only for the second hydration sphere. 3.2.2 Hydrated Na+ ion. The hydration of Na+ has been extensively studied.56 In the present work, we can see from gNa–O(W)(r) (Fig. 5a) that the hydration shell is not very sensible to the concentration. Especially, the position of the first peak does not change at all, while the peak intensity changes and the number of hydration water molecules decreases from 5.4 0.7 to 3.7 1.2 (Fig. 5b and Table 3), consistent with the previous work.43 The second hydration sphere of Na+ can be defined in a range from 3.1 to 5.4 Å. The peak position tends to shift to a shorter distance with increasing concentration, while their hydration number decreases from 17.1 2.3 to 12.2 2.5 (Fig. 5b and Table 3).

Table 3 The positions and the average coordination number of the atom pairs in aqueous NaB(OH)4 solutions. r(I,peak) and r(II,peak) denote the peak positions of the first and second shells, respectively. CN(I) and CN(II) represent the average coordination number of the first and second shells, respectively

Atom pair

No.

r(I,peak)/Å

r-Range(I)/Å

CN(I)

O(W)–O(W)

Water B1N1 B1N2 B1N3 B1N1 B1N2 B1N3 B1N1 B1N2 B1N3 B1N1 B1N2 B1N3 B1N1 B1N2 B1N3

2.82 2.79 2.79 2.76 2.34 2.34 2.34 3.72 3.72 3.72 2.34 2.34 2.34 3.57 3.57 3.57

2.34–3.45 2.31–3.42 2.31–3.27 2.31–3.15 2.01–3.09 2.01–3.09 2.01–3.09 2.91–5.16 2.91–5.31 2.91–5.40 2.04–3.03 2.04–3.03 2.04–3.03 2.01–4.35 2.01–4.35 2.01–4.35

4.9 4.8 3.8 2.8 5.4 4.6 3.7 12.9 13.2 15.6 0.2 1.0 2.1 0.2 1.0 2.1

Na–O(W) B–O(W) Na–O(B) Na–B


1.1 1.2 1.1 1.1 0.7 1.0 1.2 1.8 1.8 2.4 0.5 0.8 1.3 0.4 0.7 1.0

r(II,peak)/Å

r-Range(II)/Å

CN(II)

4.53 4.50 3.84 3.54 4.46 4.46 4.46

3.48–5.7 3.5–5.4 3.3–5.1 3.2–5.0 3.12–5.40 3.12–5.40 3.12–5.40

19.8 16.2 12.3 10.9 17.1 15.2 12.2

2.2 2.3 2.2 2.3 2.3 2.3 2.5


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Fig. 4 Spatial density functions of the neighbouring water molecules around a central water molecule. The dark blue lobes represent the first sphere and the greyish blue and semitransparent lobes represent the second sphere. The red and white ball in the centre represent O and H atoms of H2O, respectively.

As the angle distribution of +O(W)–Na–O(W) in the first sphere shows (Fig. 5c), there are two peaks at around 901 and 1801, which may indicate an octahedral hydration geometry around Na+ in the solution. Fig. 6 shows the SDFs of the first neighbouring water oxygen atoms around a central Na+ with different concentrations. We can see the first hydration of Na+ in an approximately octahedral hydration sphere. With an increase in concentration, the tendency for maintaining an octahedral hydration sphere does not change, while we can find a remarkable difference that one of the ‘‘vertices’’ of the octahedron diminishes in the oversaturated solution. This indicates a strong ion association in the concentrated solution, in which one of the octahedral sites may be superseded by another receptor such as the oxygen atom in B(OH)4. 3.2.3 Hydrated B(OH)4. As Andrew et al.26 noted, the presence of hydroxide moieties on boron compounds implies strong hydrogen bonds with water. There are four hydroxide moieties around the central boron atom in B(OH)4,13,57 so strong hydration can be anticipated. As gB–O(W)(r) (Fig. 7a) shows, there is a single broad peak with a similar peak position at 3.72 Å. It should be noted that hydration numbers derived from these broad pair distribution functions are highly cut-off distance sensitive. By using the local minima as the cut-off distances of gB–O(W)(r), the hydration number ranges from 12.9 1.8 to 15.6 2.4 (Table 3), corresponding to about 3 or 4 water molecules hydrated with one hydroxide on average. This result is consistent with the optimized lowest-energy structures of the aqua-B(OH)4 [B(OH)4 (H2O)12] at the B3LYP/aug-cc-pVDZ level (ESI,† Fig. S3). It indicates that the water network structure is broken and that more

Fig. 6 Spatial density functions of the neighbouring water molecules around a central Na+. The lobes represent the water molecules for the first shell from 1.0 to 3.1 Å, and the purple ball in the centre represents Na+.

free water molecules enter into the first sphere of B(OH)4, and most of those water molecules may be shared by B(OH)4 and Na+ in the concentrated solution. The SDFs of the neighbouring water molecules around a central B(OH)4 are shown in Fig. 8. The details can be found in ESI,† Fig. S4. In the blue grid transparent lobes encompassing the B(OH)4, corresponding to disperse zones, the water molecule arrangement is relatively random around the B(OH)4 without a very particular geometry. With increasing concentration, a lower density of water molecules around the tetrahedral corner of B(OH)4 with four ‘‘holes’’ can be found. It is most likely that these ‘‘holes’’ are caused by the ion association. 3.2.4 Ion associations. Ion-association between Na+ and B(OH)4 is palpable in an aqueous NaB(OH)4 solution. Firm evidence for ion association is supported by the vapour pressure method, conductivity, or dielectric spectroscopy18–20 etc. A typical ion association in aqueous NaB(OH)4 solution at 298.15K and

Fig. 5 The pair distribution functions (a), the coordination number distributions (b), and the +O(W)–Na–O(W) distributions (c) of Na–O(W) under various concentrations obtained from EPSR modelling.



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Fig. 7 The pair distribution functions (a) and the coordination number distributions (b) of B–O(W) under various concentrations obtained from EPSR modelling.

Fig. 8 The SDF surfaces showing the top 25% probability density for correlations of hydrated water molecules to the central B(OH)4 within the cutoff distance of 5.0 Å (blue and transparency grid); the top 35% probability density for correlations of Na+ to the central B(OH)4 within the cutoff distance of the local minima of gNa–B(r), the tetrahedral-edge-shared bidentate ion pairs (red lobes) and tetrahedral-corner-shared monodentate ion pairs (green and semitransparent lobes). The pink, red, and white balls in the centre represent B, O, and H atoms of B(OH)4, respectively.

1 atm is shown in ESI,† Fig. S5. Ion association increases with increasing concentration, with around 30% of the Na+ and B(OH)4 forming ion association pairs in a concentrated solution. Noteworthily, ion association based on physicochemical properties is usually expressed as an apparent and synthetic form such as NaB(OH)4. However, different kinds of ion association forms are deducible in the micro-aspect view, and these different ion association forms may affect the macro-properties such as crystal nucleus formation and solid–liquid equilibria. The ionic aggregates can be observed through gNa–O(B)(r) and gNa–B(r). The Na–O(B) distance (2.34 Å) in gNa–O(B)(r) (Fig. 9a) is the same as that of Na–O(W), and the peak intensity increases steadily with increasing concentration. The coordination number of Na–O(B) (Table 3) increases from 0.2 0.5 in B1N1 to 2.1 1.0 in the supersaturated solution (B1N3), which indicates a very strong ion

Fig. 9

association tendency between Na+ and B(OH)4. It is notable that the total interaction number of Na+, i.e. the total of Na–O(W) and Na–O(B), is around 6.0. The sharpening first peak of gNa–O(B)(r) also indicates a strong ion association in solution. More detailed information about Na+ and B(OH)4 ion pairs can be seen from the Na–B pair distribution functions gNa–B(r) shown in Fig. 9b. In gNa–B(r), we can find a bifurcated peak with peak positions at 3.00 Å and 3.57 Å. In order to assign them in a well-founded way, the structure, and stability of NaB(OH)4(H2O)6 clusters were investigated by DFT at the B3LYP/Aug-cc-pVDZ basis level. The most stable clusters for each kind of association form are shown in Fig. 10. Their energy bond parameters can be found in Table S3 of the ESI.† The Na+ and B(OH)4 may constitute the contact ion pairs (CIPs) in three forms based on the chemical intuition, i.e. the

The pair distribution functions of Na–O(B) (a) and Na–B (b) under various concentrations obtained from EPSR modelling.



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Fig. 10 Optimized lowest-energy structures of aqua-NaB(OH)4 clusters [(NaBOH)4(H2O)6] at the B3LYP/Aug-cc-pVDZ level. The green, pink, blue, and white balls represent O and H atoms of H2O, respectively.

tetrahedral-corner-shared monodentate (CIPM), the tetrahedraledge-shared bidentate (CIPB), and the tetrahedral-face-shared tridentate (CIPT). In addition, solvent-shared ion pairs (SIPs) and solvent separated ion pairs (SSIPs) may exist in the solution.24 As Fig. 10 shows, Na+ and B(OH)4 form monodentate ion pairs (CIPM-A to CIPM-C), bidentate ion pairs (CIPB-A to CIPB-C), and solvent-shared ion pairs (SIP-A to SIP-C), while the CIPT and SSIP are not stable under this condition. The CIPT form cluster may occur in some small hydrated clusters, and the SSIP may occur in some big ones. In Fig. 10, the solvent-shared SIP-A is relatively more stable, with an interaction energy 11.77 kJ mol1 lower than that of the most stable CIPM-A and 32.30 kJ mol1 more stable than CIPB-A. It should be noted that since the DFT calculation was made in a single-point polarized continuum solvent model the SIP-A or the SIP form may not be the exclusive or dominant cluster in the solution system. In a real sodium metaborate solution system, all those clusters should coexist, and their relative contents would vary with the salt concentration. The DFT calculations show that the distances between the Na+ and the B atom of B(OH)4 in CIPB and CIPM are around 3.0 Å and 3.5 Å, respectively, and the separation between the Na+ and B atoms of B(OH)4 in the SIP clusters ranges from 4.1–4.7 Å. The detailed bond parameters can be found in Table S4 of the ESI.† These results can be used as the indicator distances to distinguish the contacted ion pairs in the solution. Based on the conclusions from the DFT calculations, the shoulder peak at B3.00 Å can be ascribed to the interaction of CIPB ion pairs,


whereas the peak at B3.57 Å can be specified as the CIPM in gNa–B(r). The broad peak at 4.1–5.4 Å may be contributed by both SIP and SSIP. As gNa–B(r) shows (Fig. 9b) with an increase in concentration, the fractions of CIPB and CIPM increase whereas those of SIP and SSIP decrease, which means a more serious ion association in more concentrated solutions. The occurrence of contact ion pairs in solution is regularly increased as the coordination number increases from 0.2 0.4 in B1N1 to 2.1 1.0 in B1N3, which are well consistent with that from the Na–O(B) interactions (Table 3). The ion association features can be reconfirmed from the SDFs of the neighbouring Na+ around a central B(OH)4 (Fig. 8). In the 3D visualized ion pairs, two different ion association forms can be designated from the SDF surfaces. There are 6 blue lobes around the intersection angle zone by two O atoms of B(OH)4, which can be ascribed to the tetrahedral-edge-shared bidentate Na+–B(OH)4 clusters. Besides those 6 blue lobes, Na+ also aggregates around the 4 vertices of tetrahedral B(OH)4, which can be ascribed to the tetrahedral-corner-shared monodentate Na+–B(OH)4 clusters and this feature intensifies as the concentration increases. Noteworthily, a none aggregation lobe for the tetrahedral-face-shared tridentate can be found. The conclusions from the SDFs are consistent with the results from DFT. In a diluted solution, water hydrates B(OH)4 directly with relatively small ‘‘holes’’ in the SDFs of water molecules around a central B(OH)4 (Fig. 8), and Na+ associates with B(OH)4


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unsymmetrically in both the tetrahedral-corner-shared and tetrahedral-edge-shared forms. The directly hydrated distance of B(OH)4 (B–O(W)) is 3.1–5.0 Å and the tetrahedral-edgeshared Na+ distance (Na–B) ranges from 2.5 to 3.1 Å. The hydrated water molecules of B(OH)4 encompass the tetrahedral-edge-shared Na+. Noteworthily, the water hydrates the tetrahedral-edge-shared Na+ (and does not hydrate B(OH)4 directly) with a B–O(W) distance of around 3.8 Å (as Fig. S6 shows in ESI†) which runs into the first hydration sphere of B(OH)4 (3.1–5.0 Å). This also indicates why the gB–O(W)(r) has such a broad peak (Fig. 7a). Using local minima in gB–O(W)(r) as the cut-off distances overrates the hydration number of B(OH)4, leading to the atypical feature that the hydration number increases with increasing concentration (Table 3). The tetrahedral-corner-shared Na+ has a Na–B distance ranging from 3.2 to 4.3 Å, which overlaps with the hydration distance of B(OH)4 (3.1–5.0 Å). The steric-hinerance effect indicates a competition interaction between B(OH)4 hydration and B(OH)4– Na+ ion association. As Fig. 8 shows, the tetrahedral-corner-shared Na+ occupies the positions of hydrated water molecules, which generates the ‘‘holes’’ in the SDFs of water around a central B(OH)4. The competition between B(OH)4 hydration and ion association is conspicuous.

4 Conclusions Solution structures, especially B(OH)4 hydration and B(OH)4– Na+ association, and the effect of bulk water in aqueous sodium metaborate solutions with concentrations of 1–5.4 mol dm3 were studied by X-ray diffraction and empirical potential structure refinement modelling. For hydrated Na+ ions, Na+ is surrounded by around six water molecules in an octahedral geometry in a diluted solution. The octahedral hydrated geometry is kept stable, while some of the water molecules are replaced by the oxygen from B(OH)4 to form CIPs with increasing concentration. About 12 water molecules surround the B(OH)4 without specific coordination sites and hydration geometry. For the bulk solvent water, Na+ and B(OH)4 compress the local water order as pressurization, and the structure breaking property of NaB(OH)4 becomes effective for the second hydration sphere only from the microscopic view. Both X-ray diffraction and DFT calculations of NaB(OH)4(H2O)6 clusters indicate that there are two forms of contact ion pairs between Na+ and B(OH)4 in aqueous sodium metaborate solutions, i.e. tetrahedraledge-shared bidentate and tetrahedral-corner-shared monodentate with Na+–B distances of 3.06 and 3.57 Å, respectively.

Conflicts of interest There are no conflicts to declare.

Acknowledgements This work was financially supported by the NSFC (21503051, 21573268), Youth Innovation Promotion Association, CAS (2017467) and the China Scholarship Council. We also acknowledge computing resources and time at the supercomputing center of CAS.


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