Hydrolysis mechanism of double six–membered ring pentaborate anion

Journal Pre-proofs Research paper Hydrolysis mechanism of double six–membered ring pentaborate anion Hong-Xia Zhou, Fa-Yan Zhu, Hong-Yan Liu, Wen-Qian Zhang, Yong-Quan Zhou, Chun-Hui Fang, Hai-Bei Li PII: DOI: Reference:

S0009-2614(19)30911-X https://doi.org/10.1016/j.cplett.2019.136930 CPLETT 136930

To appear in:

Chemical Physics Letters

Received Date: Revised Date: Accepted Date:

6 August 2019 1 November 2019 2 November 2019

Please cite this article as: H-X. Zhou, F-Y. Zhu, H-Y. Liu, W-Q. Zhang, Y-Q. Zhou, C-H. Fang, H-B. Li, Hydrolysis mechanism of double six–membered ring pentaborate anion, Chemical Physics Letters (2019), doi: https://doi.org/10.1016/j.cplett.2019.136930

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Hydrolysis mechanism of double six–membered ring pentaborate anion Hong-Xia Zhoua, Fa-Yan Zhub,*, Hong-Yan Liub, Wen-Qian Zhangb, Yong-Quan Zhoub, Chun-Hui Fangb, Hai-Bei Lic,*

a

Qinghai Provincial Key Laboratory of New Light Alloys, Qinghai Provincial Engineering Research Center of High Performance Light Metal Alloys and Forming, Qinghai University, Xining 810016, China

b

Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lakes, Chinese

c

School of Ocean, Shandong University, Weihai 264209, People’s Republic of China

Academy of Sciences, Xining 81008; Key Laboratory of Salt Lake Resources Chemistry of Qinghai province, Xining 81008

ABSTRACT DFT-based calculations show that B5O6(OH)4- forms B5O5(OH)6- intermediate during the first step of hydrolysis. Then, the hydrolysis pathways are divided to principal and secondary reactions. In the principal reaction, hydrolysis occurs at the bridge position between the six-membered ring and branch BO3 units to form B(OH)3 and B3O3(OH)4-. B3O3(OH)4- hydrolyzes in dilute solution to B(OH)3 and B(OH)4-. In the secondary reaction, hydrolysis of B5O5(OH)6- occurs at the bridge position in the ring to form a "network-chain" structure B5O4(OH)8-. Then, hydrolysis occurs at the bridge atoms, each BO3 unit is converted to B(OH)3, and BO4 unit is finally converted to B(OH)4-. Keywords: Hydrolysis mechanism

Pentaborate anion

Polymerization

Distribution map of borate

species

1. Introduction Boron and borate compounds have important applications in fields such as biology (ribonucleic acid, metabolism), industry (nonlinear optical materials, ceramics, and detergents), and agriculture (boron plant fertilizer) [1–3]. Solid boron resources are scarce due to the heavy use. Therefore, finding new boron–containing resources is a viable way to solve the current shortage of boron resources. In addition to solid boron resources, borate compounds can be drived from salt lake brine and seawater using extraction methods such as acidification, solvent extraction, and ion adsorption. Therefore, understanding the interaction between water molecules, borate ions, and other chemical species is the key to developing and utilizing of boron resources in brine and seawater. Various techniques such as conductance/potential titration [4–7],

11B

NMR [8–11], IR

[11–13], and Raman spectroscopies [14–20], X–ray diffraction [19–25], and extended X–ray absorption fine structure (EXAFS) [26,27] have been used to investigate the interaction between water molecules and borate ions. In early research, it was shown that the main species are B(OH)3, B(OH)4–, B2O(OH)5–, and B3O3(OH)52– at low total boron concentrations, the main species become B3O3(OH)4–, B4O5(OH)42–, and B5O6(OH)63– at higher total boron concentrations [4–7]. An empirical relationship between the chemical equilibrium constant *Corresponding author. E-mail address: [email protected] (F.-Y. Zhu); [email protected] (H.-B. Li)

of borate ions and temperatures has been built using pH measurements [6]. Researchers have also examined the transformation between borate species using various spectroscopic techniques. For example, Momii, Smith, et al. used NMR to study the chemical transformation and formation constants of borate species in an alkaline metal borate solution [8–10]. Using Raman spectroscopy, Maya et al [15–16]. studied the symmetric stretching vibration frequency (vsym) of borate ions in aqueous borate solution and reported the vsym of tetraborate (570 cm–1), pentaborate (550 cm–1), and triborate ions (620 cm–1), and boric acid molecules (820 cm–1). Recently, Fang and co–workers [19,21–26] studied the relationship between borate species and concentration over a wide concentration range. We also studied the structural parameters of borate solutions such as hydration number, hydration distance of hydrated ions and ion pairs using X–ray diffraction and EXAFS. The above studies give us an important idea about borate solutions and have motivated this study to investigate their specific properties. In such solutions, many different boron–containing species coexist, and several factors such as concentration, counter–ions, temperature, and pH determine which borate species are present. Such coexistence is attributed to the equilibrium between polymerization and hydrolysis reactions among borate ions. Water molecules not only participate in the hydration and dehydration processes which typically occur in aqueous solutions, but also in hydrolysis and polymerization reactions. When a concentrated solution is diluted, polyborate ions undergo hydrolysis and form monoborate ions B(OH)4– and/or polyborate ions with fewer monomers. However, there is limited information about the hydrolysis mechanism of borate ions. The hydrolysis details of polyborate anions have not understood until now. Quantum mechanical (QM) calculations provide a powerful method to study reaction mechanisms, and they have been used to report several results regarding the hydrolysis and oligomerization mechanisms of silicate and aluminate solutions. Trinh et al. [28–29] studied different anionic bond formation pathways during the oligomerization and hydrolysis of siliceous oligomers in silicate solutions. Zhang et al. [30] studied the effect of pH on the formation of silicate polymers and reported that a near–neutral pH favors linear growth, while a higher pH facilitates ring closure. Pereira et al. [32] studied the condensation mechanism of Si(OH)4, and found that the calculated activation energies closely matched the experimentally–determined value for silica condensation in sol–gel systems. For the condensation and hydrolysis of aluminate solutions, Cheng et al. [32–33] studied the condensation and hydrolysis reactions of monomer, dimers, and trimers of Al(OR)3 and suggested that the first–order hydrolysis of monomer and oligomers is energetically

2

favorable in both alkaline and neutral solutions. Xiang et al. [34] studied the mechanisms of aluminophosphate oligomerization and found that the most favorable dimerization pathway is a Lewis acid–base reaction. They also proposed a dimerization mechanism by varying the proticity and hydration of phosphorus and aluminum monomers. The literature results above show that quantum chemical calculations are an excellent method to study reaction mechanisms. They not only support all possible oligomerization and hydrolysis reaction pathways in the studied systems, but also provide information about the structures, energy, and spectral properties during these reactions. The pentaborate ion B5O6(OH)4– composes of two six–membered rings which share a BO4 unit. According to the ternary system phase diagram of K2O–B2O3–H2O, potassium pentaborate crystals are homogeneous, but liquid–phase B5O6(OH)4– have also been reported. Raman spectra [17,18] and distribution maps [19,20,26] have shown that a limited amount of B5O6(OH)4– is present in borate solutions. This has motivated the current study, which examines the processes that occur during the hydrolysis of pentaborate crystals using density functional theory (DFT). The structure and energy of different hydrolysis sites at each step of the reaction were studied in detail, and the hydrolysis mechanism, especially the formation of trimers, pentamers, monoborate ions, and H3BO3, were fully investigated. Finally, two pathways for “water–rich” and “water–poor” hydrolysis were proposed. A distribution map of borate species of the pentaborate solution was given and briefly discussed using hydrolysis reaction mechanisms. 2. Molecular modeling calculations DFT has been widely used to study hydrolysis–polymerization mechanisms [28,32] and is an excellent method for predicting properties such as bond dissociation energies, geometries, and potential energy surfaces of aluminosilicates [33–35]. Moreover, the structure and properties of borate ion–pairs has also been studied using B3LYP function [20,22,25,38,39]. The long–range corrected hybrid functional, M06–2X [40] not only contains the advantages of B3LYP function, but also performs very well for describing dispersion interaction and long range correlations. Therefore, M06–2X and a standard Pople–style basis set 6–311++G(2df, 2pd) [41] were used for geometry optimization and saddle point searching in this study. The solvation effect was included using a polarizable continuum model (PCM) [42,43]. Frequency calculations were also performed using the same basis set to obtain the zero–point energies (ZPE) and to identify all stationary points as either minima (0 imaginary frequency) or transition states (1 imaginary frequency). Transition states were further validated using intrinsic reaction coordinate (IRC)

3

calculations [44,45]. All energies were corrected using ZPE and basis set superposition error (BSSE) methods using the same method and basis set. The Gaussian 09 program package was used for all calculations [46]. Wave function analysis including Mulliken atom population, electrostatic potentials, quantitative analysis of molecular surfaces, and localized orbital locator analysis were performed using Multiwfn 3.6 (dev) program [47]. 3. Results and discussions 3. 1. First two hydrolysis steps of B5O4(OH)8– As seen in Fig. 1, the pentaborate ion (B5O6(OH)4–) contains two six–membered rings with four, three–coordinate BO3 units and one, four–coordinate BO4 unit with the D2d point group. The B–O distance is 1.366 Å in BO3 and 1.469 Å in BO4. Four–coordinate boron atoms, such as B(1), are unable to participate in hydrolysis because they are coordinatively saturated with oxygen atoms. During the hydrolysis process, the hydrogen atom abstracted from water only bonds with the bridge oxygen atom to form OH and cannot bond with a terminal oxygen atom. To confirm the hydrolysis position in B5O6(OH)4–, the electrostatic potential (ESP) distribution [48] and Mulliken charges [49] of B and O were calculated using Multiwfn [47]. The ESP results of B5O6(OH)4– in Fig. 1 show that the minimum negative ESP value is located near the oxygen atoms of BO4. Table 1 shows that the four boron atoms of B5O6(OH)4– have the same Mulliken charge, and the bridge–oxygen atoms have two Mulliken values (–0.935 and –0.965 e). This suggests that the hydrogen atom from water prefers to bond with O(BO4), while the OH from water tends to bond with B(BO3). Therefore, two hydrolysis pathways were identified when B5O6(OH)4– hydrolyzed with one water molecule.

16 5

4

2

3

12 14

13

15

1

8

7

9 10

18

Fig. 1. The structure diagram and the electrostatic potential distribution diagram of B5O6(OH)4-. The blue, red, white balls represent B, O, and H atom, respectively.

4

Table 1 Mulliken charges (MK, e) of the atoms in the species during the hydrolysis B5O6(OH)4-

B5O5(OH)6-

B4O4(OH)5-

B3O3(OH)4-

B5O4(OH)8-

B4O3(OH)7-

B(2)

1.179

B(2)

1.024

B(2)

1.076

B(9)

1.246

B(2)

1.382

B(3)

1.122

B(7)

1.179

B(7)

1.075

B(9)

1.308

B(10)

1.246

B(6)

1.107

B(8)

1.093

B(12)

1.179

B(12)

1.413

B(10)

1.208

O(1)

-0.904

B(10)

1.184

B(9)

1.231

B(13)

1.179

B(13)

1.044

O(3)

-0.764

O(4)

-0.904

B(11)

1.299

O(4)

-1.029

O(3)

-0.935

O(3)

-1.143

O(4)

-0.936

O(6)

-0.934

O(3)

-1.463

O(10)

-1.081

O(4)

-0.965

O(4)

-0.902

O(11)

-0.979

O(7)

-1.022

O(11)

-1.236

O(8)

-0.935

O(8)

-0.929

O(12)

-1.005

O(12)

-1.154

O(9)

-0.965

O(14)

-0.777

O(13)

-1.262

O(14)

-0.935

O(15)

-1.082

O(15)

-0.935

These two hydrolysis pathways are shown in Fig. 2. In pathway A, a hydrolytic reaction occurs near B(7)–O(8) to form an intermediate (A–IM1) when the total energy decreases to – 20 kJ/mol as seen in potential energy surface (PES) diagram in Fig. 4. The O–H bond length and∠HOH of water in A–IM1 are respectively 0.972 Å and 105.9°, which are slightly higher than the values 0.960 Å in a free water molecule. After absorbing 117 kJ/mol energy, the A– IM1 reaches the transition state, A–TS1 ([B5O6(OH)4...H2O]–). The O–H bond length of water increases to 1.202 Å, and the B(7)…O(20) and O(8)…H(21) bond distances decrease to 1.238 and 1.636 Å, respectively, which indicates that bonds are formed between B(7)…O(20) and O(8)…H(21). After the transition state formation, the energy continually decreases until A–TS1 completely converts to A–IM2 (B5O5(OH)6–). The B(7)–O(8) distance is 1.572 Å, which is smaller than 1.6 Å, implying that the six–membered ring structure is still present at this step. The localized orbital locator (LOL) diagram of A–IM2 (Supporting Information, Fig. S1) shows a stronger covalent interaction between B(7)–O(8), although this interaction is not as strong as B(7)–O(9). Therefore, the H and OH of water simply bonds with an oxygen atom and boron atom in B5O6(OH)4– and does not break the six–membered ring in pathway A. Moreover, the six–membered ring contains an OH group in bridge oxygen, and this type of borate anion has not been previously reported, either in solid borate crystals or liquid borate solutions [17,22,39]. Therefore, there is a low probability that the first–step in the hydrolysis of B5O6(OH)4– occurs via pathway A. In pathway B, the dissociated OH of a water molecule forms a B–OH bond with B(7), and H forms an O–H bond with O(9) when the transition state B–TS1 forms, as shown in Fig. 2. The B(7)…O(9) distance gradually increases from 1.387 Å (B5O6(OH)4–) to 1.391 Å (B–IM1), 1.686 Å (B–TS1), and 2.811 Å (B–IM2) during each step of the hydrolysis reaction. This indicates 5

that one of the six–membered rings is broken in pathway B. By comparing the PES of these two pathways in Fig. 4, although pathway B requires 20 kJ/mol more energy than pathway A to form the transition state, the broken six–membered ring favors hydrolysis and preferentially forms borate ions with low degrees polymerization. Therefore, it is more likely that the first–step hydrolysis occurs via pathway B.

1.3 87

2.639

9

7

1.343

16

5

87 1.3

3

2

13

15 1

4

10

14

12

21

0.962

8 1.5

72

22

9

5

20

1.45

8

14

12

7

20 1.436

10

10

18

18

A-IM2

A-TS1

A-IM1

H2O

21 13

1.434

.3 73

18 104.6

1

4

9

8 1.343 17

14

15

3

1

16 13

22

2.639 0.972

3

2

1.37

15

2.979

3

4 12

60 0.9

21

2

A

5

0.972 20

2.979

22

5

1

9

3

2

18

22

5

4 5

2

16

-

B

3

4

[B5O6(OH)4 ]

68

0.9

5

20

1 12

14

15

13

8

7

1.341 1.3 7

18

4

21

16 9 10

2

91 1.3

1.558

18

B-IM1

14

20

15

1

12

8

18

1.233

22

3

4

7

0 1.37 6 1.39

21 1.197

12

13 9 16

10

B-TS1

14

7

8

82

1.3

2

3

11

10

9

1

4

86

1.6

20

22

11

15

12

2.8

13

14

47

8

1.3

1.339

2.242

7

2.696

1.3 87

73 1.3

10

21

0.959

15

5

13 16

B-IM2

Fig. 2. Hydrolysis pathway diagram of B5O6(OH)4-. The blue, red, white balls represent B, O, and H atom, respectively.

The main difference between these two hydrolysis pathways is the bonding location between the hydrogen atom of water and oxygen atom in the six–membered ring. In pathway A, the hydrogen atom bonds with oxygen atom shared between BO4 and BO3 units, whereas the hydrogen atom bonds to the oxygen atom shared between two BO3 units. The reason that the B(7)–O(8) bond is not broken in pathway A may be the stronger ESP near B(8) than B(9), as seen in the ESP distribution diagram in Fig. 1 (right panel). The energy of B-IM2 is 9 kJ/mol lower than that of A-IM2 which shows that the A-IM2 does not stable and changes to other structures such as B-IM2 during the hydrolysis process. B–IM2 (B5O5(OH)6–) contains a six–membered ring and two BO3 units by sharing the bridge oxygen atom between the BO4 and BO3 units, as seen in Fig. 2 and Fig. 3. There are two regions that can participate in hydrolysis, i.e., the six–membered ring and the branch position, when a second water molecule hydrolyzes B–IM2. Both B(2) and B(12) positions can accept an OH group from water, while, the Mulliken charge on B(12) is larger than that of B(2). Therefore, the B(12) region is easier to hydrolysis in the six-membered ring area. In a similar way, B(7) region is easier to hydrolysis in the branch position. When the hydrolysis reaction occurs at the branch position, the hydrolysis process is labelled as pathway C. Therefore, two representative pathways (C and D) are considered in this process.

6

18

0.9 62

2.4 11

1.353

7

1.377

1.497

7

20

13

12 1.4

15

10

15

20

8

8

1

74 1.3

16

10

3 2 12 4 18

5

+

23 0.96

7 10

14

1

1.34

3

1 3.60

2

12 4

20

18

7

72 1.3 1.389

10

1.403 1.571 23

14 12

8 15 9 13

1 3

1.244

1.3

4

9

1

15

10

16

D-IM3

5

65

1.3

66

4 14

1.3 40

8

7

5

37 1.4

7

[B(OH)3]

59 0.9 25

2 3

13

25 1.188

2

9

115.8

16

24

68 1.4

13

10 1.420

5

1.632

9 13 16

1.372

25 24

8

2.994

60

D

1.435

C-IM4 18

20

0.9

H2O

1.434

81.65 7 6 25

C-TS2

C-IM3

104.6

3

15

[B4O4(OH)5-]

20

16

85 1.4

1

23

1 11 0.962

13

[B5O5(OH)6-]

5 9

16

11

118. 8

1.3 47

3

2.755

21

0.959

15

1

13 16

11

2

5

12 2

5.4 12

3

25

15 9

23

11 3

16

1.368

2 5

8 1

4

C

10

7

11 2.8

11

12

12

2

11

23

08 1.4

22

77 1.3

18

82 1.3

3.163

20

3

1.21 18 1.2 25

9

5 68 0.9

12

4

1.691

18 4

4

24

1.49

18

12

1.378

23 0.96 1.38

8

24

18

20

D-TS2

D-IM4

Fig. 3. Hydrolysis pathway diagram of B5O5(OH)6-. The blue, red, white balls represent B, O, and H atom, respectively.

140.9 D-TS2

113.2

111.1

B-TS1

C-TS2

96.7 A-TS1

D-IM4 36.6

A-IM2 13.4 B-IM2 4.5

0.0 B5O6(OH)4+H2O

31.9 C-IM4

41.6 B4O4(OH)5+B(OH)3

B-IM2+H2O

B-IM1 -17.9

C-IM3 D-IM3

-20.2 A-IM1

Fig. 4. The calculated potential energy profile of the hydrolysis of B5O6(OH)4-

As seen in Fig. 3(C), in pathway C a water molecule reacts with B5O5(OH)6– at the branch position of B(7) and O(8) to form C–IM3. After absorbing 111 kJ/mol of energy, C–IM3 forms the transition state, C–TS2. The main change occurring during the transformation from C– IM3 to C–TS2 is the bond length of the water molecule and the distance between water and B(7)–O(8). One hydrogen atom dissociates from water and approaches the bridge oxygen atom O(8), while the OH of water approaches B(7). After the transition state, the energy gradually decreases until H(25) bonds with O(8) with a bond length of 0.962 Å, and O(23)H bonds to B(7) with a bond length B(7)–O(23) of 1.434 Å. The bond lengths of H(25)–O(8) and B(7)– O(23)H are similar to the B–O bond lengths of the BO3 and BO4 units. The B(7)–O(8) bond length increased to 1.656 Å, indicating that the B(7)–O(8) bond was broken. However, the LOL diagram of C–IM4 (Supporting Information, Fig. S2) also indicated a weak covalent interaction between B(7) and O(8), which means the B(7)–O(8) bond did not completely break 7

due to the strong covalent interaction between the boron and oxygen atoms. After absorbing ~10 kJ/mol of energy, the B(7)–O(8) bond was completely broken and formed B(OH)3 and a B4O4(OH)5– intermediate. The hydrolysis reaction can be expressed as: B5O5(OH)6– + H2O = B4O4(OH)5– + B(OH)3 In pathway D in Fig. 3, a water molecule reacts with the six–membered ring of B5O5(OH)6– to form a D–IM3 intermediate. During this process, another six–membered ring is broken to form the “net–chain” structure of D–IM4 (B5O4(OH)8–), which is composed of four BO3 units at the ends and one BO4 unit at the central position. Comparing the PES (Fig. 4) of these two pathways, pathway C requires 111 kJ/mol of energy to overcome its energy barrier, while pathway D requires 141 kJ/mol. Pathway C prefers the lower reaction energy and also produces B(OH)3, and is thus more likely to occur in the actual system. The "net– chain" structure of D–IM4 and B4O4(OH)5- have different structures and they will hydrolyze to different borate anions. To more thoroughly understand the hydrolysis of the pentaborate ion, the hydrolysis reactions of B4O4(OH)5– as a principal reaction and B5O4(OH)8– as a secondary reaction were further discussed in this study. 3. 2. Principal reaction 3.2.1. Hydrolysis of B4O4(OH)5– As seen in Fig. 5, B4O4(OH)5– consists of a six–membered ring and a chain–like branch structure attached to the bridge oxygen atom. These two positions can participate in the hydrolysis reaction of the six–membered ring near B(2)/B(9) positions and in the branch position near B(10). From the Mulliken charges in Table 1 and the ESP map in Fig. 5, the order of the magnitude of negative charges on oxygen atoms in the six–membered ring was O(11)
15

9

11

4

1 2

3

8 12

10 13

5

Fig. 5. Structure diagram and the electrostatic potential distribution diagram of B4O4(OH)5-. The blue, red, white balls represent B, O, and H atom, respectively. 8

In hydrolysis pathway E, a water molecule reacts with B4O4(OH)5– in the six–membered ring, which finally breaks the B(9)–O(4) bond in the six–membered ring as shown in Fig. 6. Therefore, the six–membered ring is broken and converts to a "network–chain" structure B4O3(OH)7– containing a BO4 unit in the center and three BO3 units at each end. In pathway F, a water molecule reacts with B4O4(OH)5– at the branch position, and this hydrolysis pathway finally breaks the B(10)–O(12) bond, as shown in Fig. 6. Therefore, hydrolysis at the branching position of B4O4(OH)5– produces two products, B3O3(OH)4– and B(OH)3, which have been found in pentaborate and other borate solutions [19,22,26]. The hydrolysis reaction can be expressed as:

98 1.3

11

12

1

3

10

13

04

8

1 3

12

7

E-TS1

9

19 85

.3

51

E-IM2

15

60 0.9

9

9 1.37

18 1.2

15

12 7 1.3 13 45 10 8 3

2 4

11

9

2 1.21 19 20

4

3

2

5 1.65

1 12 7 F-IM2

3

1

1.449

11 1810 7 4 4 1.5 1.4

[B3O3(OH)4-]

10 19

6

8 5 .36

1

4

1

1.3

1.368

11

13

3

2

37

F-TS1

15

9

15

1.4

F-IM1

15

12 10 8 1 7 1.496 13

15

15

9

4

1.431

4

61

1.380

B

19

0.9

3.309

H2 O

4 2.87

2 11

0

4 .97

1.489

15

1.680

+

104.67 60

15

1.4

4

1.335

7 1.31 1.401

6 1.325 7 1.38 [B4O4(OH)5-]

0.9

63

8

E-IM1

8

3

1.3

2

11

12

75 1.7

10 12

1.4 13

19

9

2.783

9

8

15

7

1

20

4

2.783

4

13

69 1.3

13

15

82

1.1

2

0 1.39

96

1.3

15

2

10 12

11

46

15

9

3

0.966

1.615

A

7

1

4 19

4 1.46

11 13

15

97 1.9

2

1.2

15

B3O3(OH)4– + B(OH)3

1.6

B4O4(OH)5– + H2O

66

2

[B(OH)3]

Fig. 6. Hydrolysis pathway diagram of middle product BC-IM4. The blue, red, white balls represent B, O, and H atom, respectively.

Based on the above results, two hydrolysis pathways are possible when B4O4(OH)5– reacts with water molecules. In one pathway, water reacts with the six–membered ring of B4O4(OH)5– to form a "net–chain" intermediate B4O3(OH)7– consisting of one BO4 unit and three BO3 units. In another pathway, hydrolysis occurs at the branch position to form B3O3(OH)4– and B(OH)3 products. From their PES diagrams in Fig. 7, the transition state formation requires 146 kJ/mol in the first pathway E and 119 kJ/mol in pathway F. Based on the energy and products, pathway E appears to be preferential, and is likely the pathway which occurs in an actual system. Therefore, B5O6(OH)4– and B4O4(OH)5– have similar hydrolysis processes, in which water molecules prefer to react at their branch position. Heller [50] reported many types of borate anions, from monoborates to hexaborates or borates with higher polymerization degrees in borate crystals, contain borate anions with branched structures which share an oxygen atom between their six–membered ring and BO3 or BO4 units. However, this study showed that hydrolysis readily occurs at the branch 9

position. This evidence suggests that borate anions containing branch units, such as sheets or chain–like borate anions, are not present in solution, especially in concentrated borate solutions [50]. Chemical equations (1–3) show the hydrolysis of pentaborate ions with the first three water molecules, and the overall chemical reaction is expressed as equation (4): B5O6(OH)4– + H2O B5O5(OH)6–+ H2O B4O4(OH)5– + H2O

B5O5(OH)6–

(1)

B4O4(OH)5–+B(OH)3

(2)

B3O3(OH)4– + B(OH)3

B5O6(OH)4–+3H2O

B3O3(OH)4–+2B(OH)3

(3) (4)

134.1 E-TS1

82.4 F-TS1

29.2 E-IM2 18.9 -0.26

0.0 B4O4(OH)5+H2O

B(OH)3 +B3O4(OH)4-

F-IM2

-11.6 E-IM1 -36.5 F-IM1

Fig. 7. Calculated potential energy profile of the hydrolysis of BC-IM4 B4O4(OH)5-

3.2.2. Hydrolysis of B3O3(OH)4– B3O3(OH)4– is a six–membered ring consisting of one BO4 unit and two BO3 units (Supporting Information, Fig. S3), and two positions in this structure can participate in hydrolysis. Table 1 shows the Mulliken charge values of B3O3(OH)4–, where the Mulliken charges on B(10) and B(9) are equal, and the negative Mulliken charge on O(6) is more negative than that on O(6) and O(4). Therefore, water molecules tend to react with B3O3(OH)4– near B(10) or B(9). Fig. 8 shows the hydrolysis diagram in which a water molecule reacts with B3O3(OH)4– near B(10). When [B3O3(OH)4–] undergoes hydrolysis at B(10), the intermediate G– IM1 forms and then absorbs 120.7 kJ/mol energy to reach the transition state G–TS1 (Fig. 9). One H of H2O approaches O(6) at a H…O(6)distance of 1.218 Å, and O(15)H bonds with B(10) with a bond length of 1.553 Å. The B(10)–O(6) bond length extends to 1.632 Å and eventually breaks the six–membered ring. When the energy decreases to –11 kJ/mol (Fig. 9), a "curve"– shaped intermediate product (G–IM2) forms in which the distance of O6…H16 and O(15)…B(10) decreased to 0.960 and 1.373 Å, which are similar to the bond length of O–H and B–O(BO3).

10

The B(10)...O(6) distance increases to 2.820 Å, which shows that the six–membered ring was completely broken. G–IM2 continues to react with a water molecule at B(9) and O(4) to form B(OH)3 and diborate anion B2O(OH)5–, as seen in Fig. 8. The diborate anion further hydrolyzes to produce the final products B(OH)3 and B(OH)4–, as shown in Fig. 8. Chemical equations (5–7) express the hydrolysis of B3O3(OH)4– with three water molecules, and the total chemical reaction is expressed as equation (8): B3O3(OH)4– + H2O

B3O2(OH)6–

(5)

B3O2(OH)6– + H2O

B(OH)3 + B2O(OH)5–

(6)

B2O(OH)5– + H2O

B(OH)3 + B(OH)4–

(7)

2 B(OH)3 + B(OH)4–

(8)

B3O3(OH)4–+ 3H2O

It can be seen that the first step of B3O3(OH)4– hydrolysis involves breaking the ring structure to form a "curve"–chain structure. In the second and third steps, two BO3 units detach from the "curve" structure to form B(OH)3 and B(OH)4– in a molar–ratio of 2:1. B3O2(OH)6– and B2O(OH)5– have similar structures and both contain BO4 and BO3 units which share an oxygen atom. These structures are similar to the branched portion in the six– membered ring of B5O6(OH)4– and B4O4(OH)5–. The BO3 unit easily decomposes to B(OH)3 as shown in B5O6(OH)4– and B4O4(OH)5–, which may be why B3O2(OH)6– and B2O(OH)5– are not observed in borate solutions. Pye summarized 30 kinds of diborate structures including “curve” and “ring” structures and advices that the “curve”-like diborate structure that obtained in this work is the stablest structure [39]. Applegarth et al. [17] found a very small shoulder peak at ~775 cm–1 using Raman spectroscopy and identified it as a characteristic peak of B2O(OH)5– using DFT calculations. These studies show that the “curve” like structure is more stable than that of the “ring” like structure, but the content of the “curve” like diborate is little in borate solutions. the reason of this may be the BO3 unit in B2O(OH)5– easily decomposes to B(OH)3 and B(OH)4– as discussed above.

11

5 9

2

1.405

7

G-IM1

H 2O

5

1.553 1.3 15 10 82

8 1

8

4

4

1.632

8

8 6

16

3

9

1.21

1 10 .373 1 7 1 1.34

104.6 0.9 60

6

3.465

4 3

1.214

9 16

[B3O3(OH)4-] +

5

0.961 15 17

3

2

1

2

9

10

0

0.9 60

5

1.385 50 1.3

8

2.366 1.387

6

35 10 1.3 1.38 7 7 1

1.382

3 2

4

2.82

6

15

7 1.373

G-IM2

G-TS1

6

1.375

46 1.3

1

1.3 84

9

2

7

41 2

6

15

4

8

10 1

20

19

3

1.3 55

6 9

1.371

7

4

5

15

G-IM4

18

1.

1.4 01

10 1

6

4

1.6 77

3

5

1.2 07

1.805

2 0.96

1.4 30

1.4 34

9

5

6 3

3

21 1.2 19

5

94 1.4

1

15

2

1.6 29

8

10

1.4 42

4

[B(OH)3]

18

2

4

3.665

2

7

0.975

1.368

1 65 1 .36 6 1.3 2

77 1.3

5

G-IM3

G-TS2

11

-

[B2O(OH)5 ]

9 1.37

15

73 1.235 1.6

1 3

1.506

3

6

1

1.626

[B(OH)4-]

11

1.433

6

5

2

11

7

118

11

7

0.962

H-TS1

[H-IM1]

H-IM2 2

5.4 12 1.368

1.3 81

2

1.483

14

4 5

.8

7 6 1.34

6

14

1.434

1

5

08 1.2

16 1.4

6 3

4

1.443

2

2.826

4

16

16

3.109

15

1.4 02

80 14 0.9

10 6.1

H2 O

65 1 1.3 1.3 66 115.8 4

[B(OH)3]

Fig. 8. Hydrolysis pathway diagram of

B3O3(OH)4-.

The blue, red, white balls represent B, O, and H atom,

respectively.

120.9

119.3

G-TS1

G-TS2 104.4 H-TS1

58.2 B(OH)3+ B2O5(OH)5-

43.1 B(OH)3 + B(OH)4-

34.3 G-IM4

+H2O 13.6 H-IM2

G-IM3 0.0

0.0 B3O3(OH)4+H2O

0.0 B2O5(OH)5+H2O

+H2O -22.6 G-IM1

-10.8 G-IM2

-25.1 H-IM1

Fig. 9. Calculated potential energy profile of the hydrolysis of B3O3(OH)4-

3.2. Secondary reaction 3.2.1. Hydrolysis of B5O4(OH)8– During the first two hydrolysis steps of B5O6(OH)4-, two products (B4O4(OH)5– and 12

B5O4(OH)8–) were produced as seen in Fig. 3, and the hydrolysis which formed B4O4(OH)5– is considered to be principal reaction. The hydrolysis of B5O4(OH)8– is signed as the secondary reaction. B5O4(OH)8– is composed of four BO3 units at its ends and one BO4 unit in the center which shares the bridge oxygen atoms between BO4 and BO3 (Fig. S4 (left)). The BO3 units are considered as the branched part of the structure, and hydrolysis will occur at these positions. The Mulliken charge order on three coordinated boron atoms was B(2)> B(11) > B(10) > B(6), and the Mulliken charge order on the bridge–oxygen atoms was O(3)< O(13) < O(12) < O(7) (Table 1). This observation indicates that a water molecule first reacts with B5O4(OH)8– at B(2) and O(3). As seen in Figs. 10 and 11, when a water molecule reacts with B5O4(OH)8– at B(2) and O(3), the B(2)O3 unit decomposed from B5O4(OH)8– to form B(OH)3. The hydrolysis equation can be expressed as follows: B5O4(OH)8– + H2O

B4O3(OH)7– + B(OH)3

(9)

It can be inferred that the hydrolysis of any borate anion containing a BO3 branch follows a similar hydrolysis pathway, i.e., the hydrogen atom of a water molecule bonds to the bridge oxygen atom, and the OH of water bonds to the B atom of a BO3 unit. Finally, the B(3)–O(bridge) bond is broken to form B(OH)3 and an intermediate which continues to undergo a similar hydrolysis reaction. Therefore, a similar hydrolysis process will occur on B4O3(OH)7– to form B(OH)3 and an intermediate B3O2(OH)6–, which further hydrolyzes to B(OH)3 and B2O(OH)5– until it forms the final products B(OH)3 and B(OH)4–. The pathways for these reactions are similar and are not described here, but hydrolysis reaction schemes and PSE are shown in Figs. S6–S9. Therefore, the secondary hydrolysis of B5O6(OH)4– can be described as follows. First, the double six–membered ring is broken to form a “network–chain” structure containing a BO4 unit in the center and four BO3 units at each end. Secondly, the hydrogen atom of water bonds to the bridge oxygen atom to form an OH bond, and the OH of water bonds to the boron atom of BO3 to form a B–OH bond. Then, the B–O bond between B(BO3) and the bridge oxygen atom breaks to form B(OH)3. The left part of the “network–chain” structure continually reacts with water via the same way. Finally, B5O6(OH)4– is hydrolyzed to form B(OH)3 and B(OH)4– in a molar–ratio of 4:1. The individual chemical equations for the hydrolysis of B5O6(OH)4– are expressed by equations (10–13). B5O4(OH)8–+ H2O

B4O3(OH)7– + B(OH)3

(10)

B4O3(OH)7– + H2O

B3O2(OH)6– + B(OH)3

(11)

B3O2(OH)6– + H2O

B2O(OH)5– + B(OH)3

(12)

B2O(OH)5– + H2O

B(OH)3 + B(OH)4–

13

(13)

14

7 3

1.38 8 1.396

5

25 1.3

4

1.

12 4

2

9

6

9

16

16

0.9 60

125

1.366

1.36 5

26

2

1.4

4

7 10

1 10 11

2

42 1.6

18

14

8 19

23

9 12

12

14

1.433

3 1

5

0.961

4

28

4

0.960

2

3

20 8

F'-TS1

B(OH)3

6

14

23

1.368

115.8

16

16 13 9

15 1

1.431

4

1

5 1.416

1.24 3 3

23

8.8 11

.4

6

27

12

F'-IM1

H2 O

261.605 2

18

20

7 1 8 12

15

104.67 0.9 60

1.192

18

13

B5O4(OH)8-

0.967 3.008

3

4

1.409

26 103.9

1.515

17

1

1.376

10

10

8

35 1

13

1.379

3.0

15

0.96 1

5

11

20

9 8

7 10

F'-IM2

B4O3(OH)7-

Fig. 10. Hydrolysis pathway diagram of middle product B5O4(OH)8-. The blue, red, white balls represent B, O, and H atom, respectively.

85.0 F'-TS1

20.4 B(OH)3+ B4O3(OH)7-

3.4 F'-IM2

0.0 B5O4(OH)8+H2O

-17.6 F'-IM1

Fig.11. Calculated potential energy profile of the hydrolysis of B5O4(OH)8-

Based on the above results, the hydrolysis of B5O6(OH)4– can occur via either the principal reaction or the secondary reaction. In the principal reaction, one of the six– membered rings is broken to form B5O5(OH)6–, which contains two BO3 branches which share a bridge oxygen atom with the ring. Then, hydrolysis occurs at the branch position to form B(OH)3 and B3O3(OH)4– in a molar–ratio of 2:1, and B3O3(OH)4– continues to hydrolyze. During the first step of hydrolysis, a six–membered ring is broken and forms an intermediate B3O2(OH)6– containing one BO4 unit at its center and two BO3 units at each of its ends which share a bridge oxygen atom. During the next two steps, hydrolysis occurs at the bridge oxygen atom between BO4 and BO3, and both of the BO3 units convert to B(OH)3, and BO4 is converted to B(OH)4–. In the secondary reaction, the first hydrolysis step of B5O5(OH)6– breaks the six– membered ring to form a “network–chain” structure of B5O4(OH)8– containing one BO4 unit at its center and four BO3 units at each end. Then, each BO3 decomposes to B(OH)3, and BO4 14

finally converts to B(OH)4–. Therefore, the main species are B3O3(OH)4–, B(OH)3, and B(OH)4– in the principal hydrolysis process and the main species B(OH)3 and B(OH)4– in the secondary hydrolysis process. B4O5(OH)42– and B3O3(OH)52– are not produced on above processes. If the hydrolysis/polymerization reaction is reversible, then two types of borate ions, B3O3(OH)4– and B5O6(OH)4–, are produced when a dilute pentaborate solution evaporates. Other polyborate anions, such as B3O3(OH)52– and B4O5(OH)42–, are also present in the solution[19,22,26] due to polymerization between B(OH)3 and B(OH)4–. Therefore, the role of each species during hydrolysis/polymerization has importance to determine the conversion relationship between the borate ions. In next section, the importance of each borate ion, the cations, and pH will be discussed. 3.3. The application of hydrolysis reaction mechanism Fig. 12 shows the distribution of borate ions over a wide range of potassium pentaborate solution concentrations in 1 mol/kg KCl solutions. The figure can be divided two regions ("water–poor" and "water–rich") to provide a detailed description of the conversion between the borate ions. When the concentration is higher than 0.1 mol/kg, a “water–poor” region is observed. When the concentration of the solution is lower in the “water–poor” region, the amount of B5O6(OH)4– decreases, while B(OH)3 increases. The amount of B3O3(OH)4– is nearly constant, and small amounts of B(OH)4– and B4O5(OH)42– appear. According to the hydrolysis mechanism of the pentaborate ion, the main hydrolysis reaction is the principal reaction which occurs in the “water–poor” region. A small amount of B(OH)4– is present in this region, which indicates that the secondary hydrolysis reaction also occurs during this process. Although B3O3(OH)4– can also hydrolyze to B(OH)4–, the amount of B3O3(OH)4– remained nearly constant in this region, which suggests that B(OH)4– is mainly produced from the secondary hydrolysis reaction. B4O5(OH)42– is not produced during the hydrolysis of B5O6(OH)4–, which indicates that B4O5(OH)42– is a polymerization product of [B(OH)4–] and [B(OH)3]. Therefore, both hydrolysis and polymerization occur in the “water– poor” region, and the chemical reaction equations in this region are as follows: B5O6(OH)4– +3H2O

2B(OH)3 + B3O3(OH)4–

B5O6(OH)4– + 6 H2O

4B(OH)3 + B(OH)4–

2B(OH)4– +2B(OH)3

B4O5(OH)42– +5H2O

15

0.6 0.5

Mole fraction

0.4 0.3 0.2 0.1 0.0 0.00

0.05

0.10

0.15

0.20

-1 Concentration /(mol  kg H O) 2

Fig. 12. Distribution map of chemical species of potassium pentaborate in 1mol/kg KCl solutions ●，B(OH)3；■，B(OH)4– ；▲，B3O3(OH)4–；▼，B3O3(OH)52–；◄，B4O5(OH)42–；►，B5O6(OH)4–

When the concentration of the borate solution is less than 0.1 mol/kg, the amounts of B5O6(OH)4– and B3O3(OH)4– rapidly decrease, and the amounts of B(OH)4– and B(OH)3 increase in the "water–rich" region. This observation indicates that in addition to the hydrolysis reaction of B5O6(OH)4–, B3O3(OH)4– also hydrolyzes to B(OH)4– and B(OH)3. Therefore, both the principal and secondary reactions occur in the "water–rich" region. Finally, B5O6(OH)4– hydrolyzes to form B(OH)4– and B(OH)3 in a molar ratio 1:4. However, Fig. 12 shows that the amount of B(OH)4– was ~35%, which is higher than the calculated theoretical value of 20%, and the amount of B(OH)3 was ~65%, which is lower than the calculated theoretical value of 80%. The reason for this phenomenon is that B(OH)3 reacts with OH– to form B(OH)4– because of the higher pH value (~8.0) in an alkaline pentaborate solution [19,22,26]. The amount of B4O5(OH)42– is lower in this region, and therefore, only hydrolysis occurs in the "water–rich" region, and the chemical reactions are as follows: B3O3(OH)4–+3H2O B5O6(OH)4–+6H2O B(OH)3 + OH–

B(OH)4–+2B(OH)3 B(OH)4–+4B(OH)3 B(OH)4–

Thus, borate ions play different roles as the concentration of the pentaborate solution decreases. B5O6(OH)4– always participates in hydrolysis reactions, B3O3(OH)4– is the product of the hydrolysis of B5O6(OH)4– in the “water–poor” zone, whereas it hydrolyzes to B(OH)4– and B(OH)3 in the “water–rich” zone. B(OH)4– and B(OH)3 play two roles in the “water–poor” zone. Specifically, they are the hydrolysis products of B5O6(OH)4– and the monomers during the polymerization of B4O5(OH)42–. Each species is a hydrolysis product of B5O6(OH)4– and B3O3(OH)4– in the “water–rich” zone. There is a small amount of B4O5(OH)42– in alkaline pentaborate solutions [19,22,26] and a small amount of B5O6(OH)4– in tetraborate solutions [24]. In contrast, the amount of other anions (including B3O3(OH)4–, B(OH)4–, and B(OH)3) are similar in each of these two alkaline solutions. Borate solutions with a higher pH favor 16

the production of B4O5(OH)42–, while a lower pH value is suitable for B5O6(OH)4– [19,22,24,26]. Similar conclusions have been drawn from the distribution of borate species in other salt solutions (Fig. S10). This study has shown that solution concentration and acidity are the key factors affecting the distribution of borate ions, while the counter–ion and temperature (< 100 oC [17]) have weaker effects on the type of borate ion present. Such results have also been observed in a tetraborate solution [24]. Moreover, previous studies have shown that B3O3(OH)52– content is very low [17–19,21–26], primarily because it is not produced during the hydrolysis of B5O6(OH)4–, B4O5(OH)42–, or B3O3(OH)4–. It may be difficult to produce B3O3(OH)52– in the polymerization process. Therefore, it is more likely that five types of borate species, rather than six, (including B(OH)3, B(OH)4–, B5O6(OH)4–, B4O5(OH)42–, and B3O3(OH)4–) are present in alkaline borate solutions. 4. Conclusions In this study, the hydrolysis mechanism of double six–membered ring B5O6(OH)4– was studied using DFT. During the first step of hydrolysis, one of the six–membered rings was broken to form an intermediate B5O5(OH)6– containing two BO3 units as branches which shared a bridge oxygen atom with the ring. Then, two possible hydrolysis pathways of B5O5(OH)6– were identified, namely the principal reaction and secondary reaction. In the principal reaction, hydrolysis occurs at the bridge position between the six–membered ring and BO3 branch units to form B(OH)3 and B3O3(OH)4– in a molar–ratio of 2:1. B3O3(OH)4– further hydrolyzes as the solution is diluted. The six–membered ring of B3O3(OH)4– is broken and forms an intermediate B3O2(OH)6– with one BO4 unit in the center and two BO3 units at both ends by sharing bridge oxygen atoms. Finally, B3O2(OH)6– is hydrolyzed to B(OH)3 and B(OH)4– in a molar ratio of 2:1. In the secondary reaction, hydrolysis of B5O5(OH)6– occurs at the bridge position in the ring and forms a “network–chain” structure B5O4(OH)8– with one BO4 unit in the center and four BO3 units at both ends. Then, hydrolysis occurs at the branch position, in which each BO3 unit decomposes to B(OH)3, and the BO4 unit changes to B(OH)4–. The distribution map of the alkali pentaborate solution shows that the principal reaction is the main hydrolysis reaction in the “water–poor” region, and the main species are B5O6(OH)4–, B3O3(OH)4–, and B(OH)3. Both the principal and secondary reactions occurred in the “water–rich” region, and the main species are B(OH)3 and B(OH)4–. B5O6(OH)4– always participates in the hydrolysis reaction in each region. B3O3(OH)4– was the hydrolysis product of B5O6(OH)4– in the “water–poor” zone, whereas it is the reactant which produces B(OH)4– and B(OH)3 in the “water–rich” zone. B(OH)4– and B(OH)3 were the hydrolysis products of B5O6(OH)4– and also the reactants of the polymerization of B4O5(OH)42– in the “water–poor” 17

zone. They are both hydrolysis products of B5O6(OH)4– and B3O3(OH)4– in the “water–rich” zone. Based on above results, a detailed hydrolysis process of B5O6(OH)4– are obtained and make us a new understanding of pentaborate solutions. Declaration of Competing Interest We confirm that there are NO conflicts of interest associated with this publication. Acknowledgments We thank the National Natural Science Foundation of China (No. U1607106; 21573268), the Natural Science Foundation of Qinghai (No. 2019–ZJ–7037) for financial support. We also acknowledge computing resources and time in the supercomputing center of National Super Computing Center in Shenzhen. References [1] Y.Z. Wei, R.W. Bell, Y. Yang, Aust. J. Agr. Res. 49 (1998) 867. [2] P. Becker, J. Adv. Mater. 13 (1998) 14. [3] D.M.Schubert, J. Struct. Bond. 105 (2003) 31. [4] N. Ingri, Acta Chem. Scand. 11 (1957) 1034. [5] J.L. Anderson, E.M. Eyring, M.P. Whittaker, J. Phys. Chem. 68 (1964) 1128. [6] R.E. Mesmer, C.F. Baes, F.H. Sweeton, J. Phys. Chem. 74 (1970) 1937; Inorg. Chem. 11 (1972) 537. [7] J.E. Spessard, J. Inorg. Nucl. Chem. 32 (1970) 2607. [8] R.K. Momii, N.H. Nachtrieb, Inorg. Chem. 6 (1967) 1189. [9] C.G. Salentine, Inorg. Chem. 22 (1983) 3924. [10] H.D. Smith, R.J. Wiersema, Inorg. Chem. 11 (1972) 1152. [11] J.D.S. Goulden, Spectrochim. Acta 15 (1959) 657. [12] D. Hecht, L. Tadesse, L. Walters, J. Am. Chem. Soc. 114 (1992) 4336. [13] J.J. Max, C. Chapados, J. Appl. Spectrosc. 52 (1998) 963. [14] J.O. Edwards, G.C. Morrison, V.F. Ross, J. Am. Chem. Soc. 77 (1955) 266. [15] L. Maya, Inorg. Chem. 15 (1976) 2179. [16] Z.H. Liu, B. Gao, M.C. Hu, Spectrochim Acta A 59 (2003) 2741. [17] L.M. S.G.A. Applegarth, C.C. Pye, J.S. Cox, P.R. Tremaine, Ind. Eng. Chem. Res. 56 (2017) 13983. [18] S. Sasidharanpillai, H. Arcis, L. Trevani, P.R. Tremaine, J. Phys. Chem. B 123 (2019) 5147. [19] Y.Q. Zhou, C.H. Fang, Y. Fang, Acta Phys. Chim. Sin. 26 (2010) 2323. [20] Y.Q. Zhou, S. Higa, C.H. Fang, Y. Fang, W.Q. Zhang, T. Yamaguchi, Phys. Chem. Chem. Phys. 19 (2017) 27878. [21] F.Y. Zhu, Y.Q. Zhou, C.H. Fang, Y. Fang, H.W. Ge, H.Y. Liu, Phys. Chem. Liq. 16 (2016) 49. [22] F.Y. Zhu, C.H. Fang, Y. Fang, Y.Q. Zhou, H.W. Ge, H.Y. Liu, J. Mol. Struct. 1083 (2015) 471. [23] F.Y. Zhu, C.H. Fang, Y. Fang, Y.Q. Zhou, H.W. Ge, H.Y. Liu, J. Mol. Struct. 1070 (2014) 80. [24] C.H. Fang, F.Y. Zhu, Y. Fang, Y.Q. Zhou, S. Tao, S. Xu, Phys. Chem. Liq. 51 (2013) 218. [25] W.Q. Zhang, C.H. Fang, Y. Fang, F.Y. Zhu, Y.Q. Zhou, H.Y. Liu, W. Li, J. Mol. Struct. 1160 (2018) 26. 18

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One of the six-membered rings is broken and forms an intermediate [B5O5(OH)6-]. In the principal reaction, [B5O5(OH)6-] hydrolyzes to [B(OH)3] and [B3O3(OH)4-]. In the secondary reaction, [B5O5(OH)6-] hydrolyzes to [B(OH)3] and [B(OH)4-]. Both the principal and secondary reactions are present in “water-rich” region. The principal reaction is the main hydrolysis reaction in “water-poor” region.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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