Quantitative StructureâProperty Relationship (QSPR) Analysis of ZrO2

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A Quantitative Structure-Property Relationship (QSPR) Analysis of ZrO2-Containing Soda-Lime Borosilicate Glasses Xiaonan Lu, Lu Deng, Stéphane Gin, and Jincheng Du J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11108 • Publication Date (Web): 14 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019

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The Journal of Physical Chemistry

A Quantitative Structure-Property Relationship (QSPR) Analysis of ZrO2Containing Soda-Lime Borosilicate Glasses Xiaonan Lu1, Lu Deng1, Stéphane Gin2 and Jincheng Du1* 1Department

of Materials Science and Engineering, University of North Texas, Denton, TX 76203, USA

2CEA,

DEN, DE2D, SEVT, F-30207 Bagnols sur Cèze, France *Corresponding Author: [email protected]

Abstract: QSPR analysis is a promising approach to correlate structural features with properties of glass materials that lack long range order and usually have complex structures. By using carefully chosen descriptors based on structural models generated from molecular dynamic simulations, correlation with properties and insights on glass behaviors can be obtained. Zirconia can significantly alter glass properties including chemical durability, even with a small amount, hence plays an important role in vitrification of nuclear waste where long-term chemical durability is desired. In this study, borosilicate glasses with composition of xZrO2-(61-x)SiO2-17B2O3-18Na2O-4CaO with x=0, 1, 2, 4, 6 and 8 were simulated using classical molecular dynamics (MD) simulations with recently developed composition-dependent potentials. Short-range (e.g., bond distance and coordination numbers) and medium-range structural features (e.g., Qn distribution, network connectivity and ring-size distribution) altered by ZrO2 were obtained and analyzed. By using a descriptor that combines short-range structural characters, from MD simulations, and single bond strength, the Fnet descriptor was found to provide excellent linear correlations with density and initial dissolution rate of these glasses. The results show that by combining MD simulations and QSPR analysis, composition effect on properties can be elucidated of complex multicomponent glasses thus suggesting this is a promising approach in future glass research and new composition design. 1. Introduction Quantitative structure-property relationships (QSPR) analysis is an approach to find correlations between materials properties and predefined structural descriptors, through 1 ACS Paragon Plus Environment

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regression or machine learning approaches.1–6 QSPR is a faster and more economical approach than traditional materials research, which often adopts a “trial-and-error” approach, hence highly valuable in material discovery or new material design. Through discovering optimum statistical correlations between the structural descriptor and targeted properties in a small set of material compositions or processing conditions, QSPR can be used to predict properties of materials that are not yet measured or synthetized.7 The QSPR approach has been successfully utilized to study various properties of polymers (e.g., refractive indices,8–11 glass transition temperature12–14 and viscosity15,16). This approach has also been tested on inorganic glass materials to rationalize their structure-property relationships.7,17–20 The structural descriptor can be obtained from known structural information based material chemistry, experimental characterization, or computer simulations. The latter approach is especially valuable for materials with complex atomic structures, such as inorganic glasses that are amorphous in nature and lack long range order. For example, Linati et al.2 on multicomponent bioactive glasses, structural descriptors were derived from MD simulations to rationalize experimental data such as density, glass transition temperature and chemical durability in water. Later on, a theoretical structural descriptor contained not only structural information but also energetic properties was developed by Lusvardi et al.3 for fluorinecontaining glasses. This descriptor works well for a wide range of glass compositions and for different properties such as glass transition temperature and chemical durability.3 Chemical durability is an important property of glasses and high chemical durability is the virtual of glass materials in many commercial and technological applications. This is especially so in designing glass compositions to immobilize radioactive nuclear wastes, where release of radioactive elements to the environment due to corrosion is a primary concern. Predicting the dissolution rate of glasses is otherwise a very complicated task, as glass dissolution not only depends on the bulk glass composition and structure, but also the external parameters such as solution pH,21–23 temperature24 and solution chemistry.25 Long-term chemical durability of glasses, for example those for nuclear waste disposal, is usually divided into three stages: 26 stage I dissolution is ion exchange between the glass and solution followed by hydrolysis of glass network by water in the solution, where the dissolution rate is usually called forward rate; stage II dissolution is when the dissolution 2 ACS Paragon Plus Environment

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rate slows down and reaches a much slower dissolution rate that is usually called residual rate. The mechanism of the slowing down and residual rate dissolution is not completely understood, but it is believed that this is related to the formation of silica-rich gel layer formed on the top of the glass surface that serves as a “passivation layer” that prevents or significantly slows down further corrosion of the glass underneath.27,28 For some glasses, stage III behavior also exists when the resumption of fast dissolution rate happens. This is commonly attributed to the formation of zeolite or clay minerals in the solution.22 There are efforts to correlate silicate glass and crystal dissolution rate with the topological constraints using the topological constraint theory, where it was found that the activation energy of dissolution is linearly correlated to the number of constraints per atom (nc).5 This correlation was explained by using nc as indicator of the steric effect of how easy the reorganization of the network to accommodate intermediates defects during dissolution.5 More recently, machine learning was used to study the composition, pH and temperature effect on dissolution of a series of sodium aluminosilciate glasses;29 however, no structural information was incorporated in the fitting process. The purpose of this work is to use MD simulations to generate detailed and realistic structural information of a series of zirconia containing borosilicate glasses, and then to use QSPR analysis to find the relationships between glass structural features informed descriptors and a number of physical properties of these glasses. Molecular dynamic (MD) simulations is one of the most effective methods to understand the atomic-level structure of glasses and other amorphous materials. MD has been used to study the structures and properties of glass materials such as silicate,30–32 aluminosilicate33 and aluminophosphate glasses.34 In this study, the glasses with compositions of (61−x)SiO2·xZrO2·17B2O3·18Na2O·4CaO, where x ranges between 0 to 8 mol%, have been selected and studied using MD simulation with recent development of boron related potentials.35 This potential sets have been successfully utilized to study multicomponent nuclear waste glasses36,37 and boron-containing bioactive glasses.38–40 ZrO2 is an important component in glass technology, especially in vitrification of liquid nuclear wastes, where ZrO2 comes from fission products and cladding materials.41,42 Experimentally, ZrO2-containing silicate/borosilicate glasses have been extensively studied regarding their structural information,43–51 physical properties42,52,53 and 3 ACS Paragon Plus Environment


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dissolution behavior.42,52–60 On the other hand, computer simulations such as molecular dynamic (MD) simulation and Monte Carlo simulation have also be utilized to study the effect of ZrO2 on the structural and dissolution properties of silicate/borosilicate glasses. 37,41,46,56,61–63

There exist a number of experimental studies in literature on the structure and dissolution behaviors of the ZrO2-containing soda-lime borosilicate glass series mentioned in the previous paragraph,48,50,55–57,59,60 owing to their great interests for the disposal and immobilization of nuclear wastes. In these studies, Zr ions exist mainly as six-folded octahedra55 with a Zr-O distance of 2.09 Å,48 and charge compensated preferentially by Na ions in the glass system.57 In terms of dissolution behavior altered by ZrO2 in the glass system, initial dissolution rate drops significantly with increasing ZrO2 concentration; whereas, inhibiting effect from ZrO2 on the dynamics of reorganization of the alteration layer ultimately results in a greater degree of corrosion in the long term.56,57,59 Recent study observed a presence of two layers in the gels of the ZrO2containing soda-lime borosilicate glass series altered at pH 1 and pH 7, where significant fraction of 7- and 8-coordinated Zr appear in bulk gel.60 This study highly suggests that glass dissolution is driving by in situ condensation and dissolution-precipitation, where the pH has a greater influence on the structure of gels as compared to Zr content.60 This paper is arranged as follows: methodology of experiments, MD simulation and QSPR analysis, structural information obtained from MD, correlations between a structural descriptor and experimental properties through a QSPR analysis, followed by discussions and conclusions. 2. Methodology 2.1.

Experimental details

Compositions (mol%) of the glasses studied are listed in Table 1. Glass preparation details can be found in a study by Bergeron et al.57 Glass density was measured by a hydrostatic weighing method with an experimental error of 0.005 g·cm-3. Two sets of initial dissolution rate measurements from literature were takin into consideration. First, initial dissolution rates of studied glasses were obtained by 4 ACS Paragon Plus Environment

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Cailleteau et al.,56 where r0 were measured with a glass surface area to solution volume ratio (SA/V) of 10 m-1 at 90 ºC in a buffered solution (pH = 6.9) without agitation. The initial dissolution rate was obtained by linear regression of the normalized silicon mass loss versus time in the short-term experiment (typically 8 h). Second, initial dissolution rate measurements were performed by Bergeron et al.57 at 90°C and in deionized water, using single-pass follow through (SPFT) experiments. This experimental setup insures that the solution remained sufficiently diluted to maintain the dissolution rate at its maximum value. The pH90°C of the outlet solution was 8.0  0.2 for all the tested glasses. The value of the initial dissolution rate was obtained from the Si concentration in the 𝑄

leachate during the first three hours of alteration according to the equation 𝑟0 =

𝐶𝑆𝑖 × 𝑆𝐴 𝑓𝑆𝑖

,

where 𝐶𝑆𝑖 is the silicon concentration in the alteration solution (mg·L-1), 𝑓𝑆𝑖 is the weight fraction of Si in the glass, and Q/SA is the flow rate per unit glass surface area.57 2.2.

MD simulation details

Molecular dynamics simulations were performed with DL_POLY 2.20 program developed at Daresbury Laboratory in the UK.64 Three random configurations with ~12,000 atoms for each composition were generated and simulated through a meltquench process. Numbers of atoms in each simulation cell are listed in Table 1. Table 1. Experimental density and composition of glasses studied, and numbers of atoms in each MD simulation cell. Glass

Density

Composition (mol%)

Numbers of atoms

(g·cm-3)

Na2O

CaO

B2O3

ZrO2

SiO2

Na

Ca

B

Zr

0Zr

2.531

18

4

17

-

61

1312

146

1236

-

2218 5856

1Zr

2.575

18

4

17

1

60

1312

146

1236

36

2182 5856

2Zr

2.594

18

4

18

2

59

1290

144

1290

72

2114 5806

4Zr

2.633

18

4

18

4

57

1290

144

1290

144

2024 5824

6Zr

2.692

18

4

17

6

55

1312

146

1236

218

2000 5856

8Zr

2.724

19

4

18

8

51

1374

144

1302

290

1844 5750

Si

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O


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The initial atom positions were generated randomly with experimental density (shown in Table 1) in a cubic simulation box. After initial relaxation at 300 K under zero pressure, the glasses were melted at 6000 K and the temperature was gradually cooled down to 300 K with a nominal cooling rate of ~1.4 K/ps. At each temperature, the system was run under canonical ensemble (constant number, volume and temperature (NVT)) for 200 picosecond (ps), which was followed by equilibration under microcanonical ensemble (constant number, volume and energy (NVE)) for another 200 ps. Finally, the glasses were equilibrated under NVT and NVE ensembles at 300K and trajectory was recorded every 50 steps of the last 40,000 steps under NVE ensemble for final structural analysis. The reason to choose constant volume cooling is due to the potential used was developed under constant volume cooling procedure to reproduce the boron coordination number.35 Relaxation under isothermal isobaric ensemble (NPT) with zero external pressure at 300K was applied to some compositions and led to a small change of glass density but very similar structures. The cutoff distance used for the short-range interactions was 8 Å, and 10 Å for the real-space part of the electrostatic interactions, which were calculated using the Ewald sum method with a relative precision of 1 × 10−6. Integration of motion equations was carried out using the Verlet Leapfrog algorithm with a time step of 1 femtosecond (fs). The interatomic interactions are described by the Born model of solids using partial charge pairwise potentials. The detailed description of the interaction can be found in our previous study38 and the atomic charges and Buckingham potential parameters used are listed in Table 2. Table 2. Atomic charges and Buckingham potential parameters. Pair

A (eV)

ρ (Å)

C (eV·Å6)

Si2.4-O-1.2

13702.905

0.193817

54.681

Na0.6-O-1.2

4383.756

0.243838

30.700

Ca1.2-O-1.2

7747.183

0.252623

93.109

B1.8-O-1.2

14550.972* 0.171281

28.500

Zr2.4-O-1.2

17943.394

127.650

0.226627


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O-1.2-O-1.2

2029.220

0.343645

192.580

*A value is for 0Zr. A value for 1Zr, 2Zr, 4Zr, 6Zr and 8Zr is 14606.77, 14652.59, 14802.00, 15001.73 and 14965.37, respectively. 2.3.

QSPR analysis details

A theoretical structural descriptor (Fnet) was derived according to a study by Lusvard et al. 3, and Fnet has a formula of 1 𝐹𝑛𝑒𝑡 = 𝑁

𝑐𝑎𝑡𝑖𝑜𝑛𝑠

∑𝑛

𝑋

∙ 𝐶𝑁𝑋𝑂 ∙ 𝑆𝐵𝑆𝑋𝑂 ∙ 𝑚𝑋

𝑋

where N is the total number of atoms, 𝑛𝑋 is the number of atoms of the X species (X = [4]

B,

[3]

B, Si, Zr, Na, Ca), 𝐶𝑁𝑋𝑂 is the average coordination number of X-O pairs. 𝑆𝐵𝑆𝑋𝑂

is the single bond strength (kcal·mol-1) obtained by Sun.65 Earlier QSPR studies of glasses used dissociation energy of gas phase dimers as the single bond energy, 7,17–20 while we decide to use the Sun’s single bond strength as it provides bonding energy information for most common oxides used in glass compositions and bonding energies for different cation coordination.65 𝑚𝑋 factor is used to evaluate the contribution of each cation to the overall network strength.3 For network former (NF), 𝑚𝑋 is the maximum ability (or highest probability) of one type of NF connecting with the rest of NFs. For modifier, 𝑚𝑋 can be interpreted as the maximum ability of one type of modifier charge compensating the NFs. Single bond strength and multiplicative factor (𝑚𝑋) for each cation-oxygen pair used for the calculation is shown in Table 3. Table 3. Single bond strength and multiplicative factor (𝑚𝑋) for each cation-oxygen pair. Pair [4]

Single bond strength (kcal·mol-1) 65

𝑚𝑋 (multiplicative factor)

B-O

89

4

B-O

119

3

Si-O

106

4

Zr-O

81

6

[3]



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Na-O

20

1

Ca-O

32

2

3. Results 3.1.

Structural information obtained from MD


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Total correlation functions (T(r)) of cation-oxygen pairs in simulated 4Zr glass are shown in Figure 1. Bond distance (first maximum peak position of T(r)) of Si-O, Na-O, Ca-O and Zr-O is 1.61, 2.44, 2.40 and 2.11 Å, respectively. T(r) of B-O pair has a peak and a shoulder, corresponding to [3]B-O at 1.45 Å and [4]B-O at 1.54 Å. These values are consistent with experimental observations. A detailed summary of bond distances for nuclear waste glasses with similar compositions (Na-Ca-B-Al-Zr-Si glass system) and comparisons with experimental values can be found in a previous study.37 No significant difference was observed on bond distance of cation-oxygen pairs between compositions. Snapshots of simulated 4Zr glass exhibiting Zr and B polyhedra distributions in the glass structure is shown in Figure 2.

Figure 1. Partial total correlation functions (T(r)) of cation-oxygen pairs in simulated 4Zr glass. The inserted figure shows PDF of B-O, [3]B-O and [4]B-O pairs.



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Figure 2. Snapshots of simulated 4Zr glass showing [ZrO6] distribution (a), and [BO3] and [BO4] distribution (b) in glass structure. Yellow and red balls represent Si and O ions, while blue and red crosses represent Na and Ca ions, respectively. Blue octahedra, yellow triangles and yellow tetrahedra represent [ZrO6], [BO3] and [BO4] units, respectively.


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Accumulated coordination numbers (CN) of cation-oxygen pairs in simulated 4Zr glass are shown in Figure 3. The coordination number of Si and Zr show a clear plateau region indicating their coordination number of 4 and 6, respectively. The average CN of B is ~3.7, contributed by [3]B and [4]B. The average CNs of Na and Ca are ~8 and ~7, respectively. Detailed CN of each cation for all glass compositions obtained from MD simulations are shown in Table 4. These coordination numbers were obtained from integration of the partial correlation function to the cutoff distance of each pair. The cutoff distance was determined by locating the first minium of the partial correlation function. The coordination number obtained are in very good agreement with experimental values of 4 for Si, around 6 for Zr, and around 6 for Ca as found in borosilicate glasses66. The coordination number of Na is slightly higher than what was found in silicate glasses (around 6)30 but consistent with studies of other borosilicate glasses36.

Figure 3. Coordination numbers (CNs) of cation-oxygen pairs in simulated 4Zr glass. The inserted figure shows CN of B-O, [3]B-O and [4]B-O pairs.



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Coordination numbers (CNs) of cation-oxygen pairs, percentage of 4-coordinated boron (N4, %) from MD simulation, Yun, Dell and Bray (YDB) model67,68 and nuclear magnetic resonance (NMR) data50 are shown in Table 4. No significant variations were observed on CNs of network-formers between compositions, while CNs of Na-O and CaO slightly increases from 7.75 to 7.86 and 6.76 to 6.99 for 0Zr to 8Zr, respectively. N4 obtained from MD for 0Zr, 1Zr, 2Zr and 4Zr has an average number of ~73, 75, 72, 72%, respectively, which has less than 8% of difference as compared to NMR data.50 However, for 6Zr and 8Zr, there is a disagreement (~18% of difference) on N4 value obtained from MD and NMR. This difference suggests a probable weakness of the potential parameters for boron, where the potential sets35 was developed based on the N4 values calculated from YDB model.67,68 Future studies on the structural role of oxide (e.g., ZrO2) according to its concentration would greatly benefit the improvement of potential parameter development. In our QSPR analysis, N4 values obtained from MD were used for Fnet calculation. Additionally, N4 values obtained from NMR were tested in the Fnet calculation for comparison, where it shows the same trend but with a slightly smaller value of Fnet when the N4 is much smaller than the MD value (e.g., 6Zr and 8Zr glass). Table 4. Coordination numbers (CNs) of cation-oxygen pairs, percentage of 4coordinated boron (N4, %) from MD simulation, YDB model and NMR for simulated 0Zr, 1Zr, 2Zr, 4Zr, 6Zr and 8Zr glasses. Cation coordination numbers

B N4

Glass

NMR5

B-O

Si-O

Zr-O

Na-O

Ca-O

MD

YDB67,68

Cutoff (Å)

1.85

5.25

2.51

3.16

3.14

-

-

-

0Zr

3.72 ± 0.01

4.00

-

7.75 ± 0.01

6.76 ± 0.03

73.5 ± 0.8

72.4

73

1Zr

3.74 ± 0.01

4.00

5.94 ± 0.03

7.85 ± 0.05

6.92 ± 0.08

75.4 ± 0.8

72.1

71

2Zr

3.70 ± 0.02

4.00

5.93 ± 0.03

7.89 ± 0.06

6.89 ± 0.04

72.3 ± 2.0

70.5

68

4Zr

3.69 ± 0.01

4.00

5.90 ± 0.05

7.89 ± 0.02

6.98 ± 0.03

71.8 ± 1.0

69.8

64


0

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6Zr

3.71 ± 0.00

4.00

5.91 ± 0.04

7.85 ± 0.01

6.95 ± 0.04

72.7 ± 0.2

70.2

56

8Zr

3.70 ± 0.01

4.00

5.91 ± 0.01

7.86 ± 0.04

6.99 ± 0.03

71.2 ± 1.1

67.7

53

From our previous MD simulation studies of ZrO2 concentration effect on structural and properties of silicate glasses63 with a composition of (75-x)SiO2-15Na2O-10CaOxZrO2, x=0, 1, 3, 5, 7 and borosilicate glasses37 with a composition of (61.9-x)SiO212.6Na2O-5.7CaO-16.0B2O3-3.8Al2O3-xZrO2, x=0, 1.7, 3, 4, it was found that local environments (e.g., bond distance, bond angle and coordination numbers) of cationoxygen pairs are not sensitive with ZrO2/SiO2 substitution, which is also observed for the series studied in this paper. The substitution results in higher network connectivity, fewer non bridging oxygen species and smaller sized-rings;37,63 therefore, the following contents will focus on these medium-range structural analyses. Network connectivity of Si, B, Zr and overall NC calculated from Qn (meaning n bridging oxygen per network former cation) 69 distribution for simulated 0Zr, 1Zr, 2Zr, 4Z, 6Zr and 8Zr glasses is listed in Table 5 and the calculations of NC can be found in a previous paper.37 NC of Si slightly increases from 3.73 to 3.80 for 0Zr to 8Zr, while NC of Zr slightly decreases from 5.46 to 5.32. There is no significant change for NC of B between compositions. Due to the high content of Si, the overall NC increases by ~4.6% from 0Zr to 8Zr. ZrO2/SiO2 substitution results in a smaller percentage of non-bridging oxygen (NBO), higher percentage of bridging oxygen (BO) and tri-bridging oxygen (TBO) cluster. The percentage of NBO decreases by ~3.3% from 0Zr to 8Zr. Primitive ring size distributions as a function of ZrO2 concentration are shown in Figure 4 (b) and average ring size (Si, B and Zr are considered as network formers) for all compositions is between 7 to 8 (listed in Table 5), indicating a well-connected random network for all compositions. The average ring-size decreases from 7.78 to 7.12 for 0Zr to 8Zr, which is in agreement with our pervious observation.37 As shown in Figure 4 (b), the intensity of peaks around 6membered rings increases with increasing ZrO2 concentration, suggesting a strengthened network after adding ZrO2. Figure 4 (a) shows the ring size distribution of 4Zr glass calculated for different network formers, where omitting Zr out of the calculation decreases the peak intensity around 7 and produces a tail for large rings (12-18 membered rings). When only Si is considered as network former in the calculation, the glass 13 ACS Paragon Plus Environment


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network is much more fragmented with a wide distribution of rings as shown in Figure 4 (d). This indicates that Si, B and Zr are well incorporated and connected in the glass network. Table 5. Network connectivity (NC) of Si, B, Zr, overall NC, percentages of non-bridging oxygen (NBO), bridging oxygen (BO) and tri-bridging oxygen (TBO) cluster and average ring size in simulated 0Zr, 1Zr, 2Zr, 4Zr, 6Zr and 8Zr glasses. Standard deviation was obtained from three parallel tests and numbers without errors have a standard deviation less than 0.005. Network connectivity

Oxygen species

Ave. ring-size

Si

B

Zr

Overall

NBO

BO

TBO

0Zr

3.73

3.64±0.01

-

3.70±0.01

10.04±0.11

89.73±0.10

0.24±0.04

7.78±0.09

1Zr

3.72

3.68±0.01

5.46±0.09

3.74

9.17±0.10

90.39±0.14

0.45±0.11

7.63±0.02

2Zr

3.77±0.01

3.65±0.03

5.47±0.05

3.76±0.01

8.20±0.37

91.16±0.42

0.63±0.04

7.58±0.06

4Zr

3.79

3.65±0.01

5.39±0.04

3.80±0.01

7.43±0.10

91.43±0.30

1.14±0.08

7.39±0.04

6Zr

3.79

3.66±0.01

5.33±0.02

3.84±0.01

7.21±0.19

91.38±0.31

1.41±0.13

7.20±0.06

8Zr

3.80±0.01

3.64±0.02

5.32±0.01

3.87

6.73±0.14

91.42±0.40

1.85±0.27

7.12±0.06


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Figure 4. Ring size distribution of 4Zr glass calculated for different network formers (a), Si-B-Zr considered as formers (b), Si-B considered as formers (c) and only Si considered as formers (d) calculated as a function of ZrO2. In order to further analyze the polyhedral linkages and Zr distribution, the theoretical linkage probability (XA-O-A or XA-O-B, where A and B are NFs) by assuming a random distribution of NFs was calculated by the following equations according to a study by Ren et al.:70 𝑁𝐴 (𝑁𝐴 ― 1)

𝑋𝐴 ― 𝑂 ― 𝐴 = 𝑁𝑁𝐹 (𝑁𝑁𝐹 ― 1)

(1)

or 2 × 𝑁 𝐴 × 𝑁𝐵

𝑋𝐴 ― 𝑂 ― 𝐵 = 𝑁𝑁𝐹 (𝑁𝑁𝐹 ― 1)

(2) 15

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where NA/B and NNF are the number of atom A or B and total number of network formers, respectively. Table 6 shows the ratio of the percentage of a former-former linkage obtained from MD to its theoretical value. If the ratio is higher than 1, it suggests that the two network formers have a high probability to connect, and vice versa. As shown in Table 6, Zr has a high probability to connect with other network formers, indicating that [ZrO6] units are well incorporated in the glass network. Additionally, [ZrO6] units have a higher preference to link with Si as compared to B. The linkage probability ratios of SiSi, B-Si and Zr-Si slightly decrease with increasing ZrO2 concentration. The large standard deviations of the ratios obtained for Zr-Zr linkages are caused by the small amount of Zr in the compositions. Table 6. Linkage probability ratios calculated from the percentage of a former-former linkage obtained from MD to its theoretical value. Ratio

0Zr

1Zr

2Zr

4Zr

6Zr

8Zr

Si-Si

0.98±0.00 0.96±0.01 0.96±0.01 0.93±0.01 0.89±0.01 0.86±0.01

B-B

0.85±0.02 0.87±0.04 0.86±0.00 0.82±0.02 0.84±0.03 0.82±0.03

B-Si

1.06±0.01 1.04±0.02 1.02±0.01 1.00±0.01 0.97±0.01 0.94±0.01

B-Zr

-

1.19±0.09 1.44±0.09 1.41±0.08 1.40±0.03 1.37±0.08

Si-Zr

-

1.86±0.04 1.73±0.08 1.69±0.03 1.67±0.03 1.68±0.02

Zr-Zr

-

1.95±0.84 1.55±1.09 1.90±0.70 1.83±0.15 1.85±0.31

3.2.

Correlation between structural descriptor and experimental properties from QSPR analysis

Experimental density (g·cm-3), initial dissolution rate (r0, g·m-2·d-1) measured by two different setups and structural descriptor (Fnet, kcal·mol-1) calculated for the glasses studied are shown in Table 7.


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Table 7. Experimental density (g·cm-3), initial dissolution rates (r0, g·m-2·d-1) measured by Cailleteau et al.56 and Bergeron et al.57, and structural descriptor (Fnet, kcal·mol-1) calculated for the glasses studied. Glass Density

(g·cm-3)

r0 (g·m-2·d-1) by

r0 (g·m-2·d-1) by

Fnet

Cailleteau et al.56

Bergeron et al.57

(kcal·mol-1)

0Zr

2.531

37

51

472.1 ± 0.1

1Zr

2.575

15

34

476.7 ± 0.2

2Zr

2.594

5.1

-

480.1 ± 0.2

4Zr

2.633

1.30

14

484.2 ± 0.3

6Zr

2.692

0.19

-

493.3 ± 0.3

8Zr

2.724

0.091

4

495.9 ± 0.0



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Correlation between Fnet descriptor and density is shown in Figure 5. Experimental density is in an excellent linear relationship (R2>0.99) with Fnet. Correlations between Fnet descriptor and experimental initial dissolution rates obtained by two different experimental setups56,57 are shown in Figure 6. After taking the logarithm of the experimental initial dissolution rates, Ln(r0) is in an excellent linear relationship (R2>0.99) with Fnet as well. In the study by Cailleteau et al.,56 dissolution rates were measured at 90 ºC in a buffered solution (pH = 6.9) without agitation. In comparison, dissolution rate measurements performed by Bergeron et al.57 were in deionized water at 90°C using a flow through system. This experimental setup insures that the solution remained sufficiently diluted to maintain the dissolution rate at its maximum value. As shown in Figure 6, dissolution rates measured by the flow through system are much higher as compared to the rates obtained in a static environment without agitation. The latter setup is more appropriate for obtaining initial dissolution rate to the best knowledge of the authors.

Figure 5. Correlation between the Fnet descriptor and experimental density.


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Figure 6. Correlation between the Fnet descriptor and experimental initial dissolution rate (r0) obtained by Cailleteau et al.56 (a) and Bergeron et al.57 (b).

4. Discussion Local environments (e.g., bond distance, bond angle and coordination numbers) of cation-oxygen pairs are found to be not sensitive with ZrO2/SiO2 substitution, which is consistent with our previous studies of ZrO2 concentration effect on structural and properties of silicate glasses63 with a composition of (75-x)SiO2-15Na2O-10CaO-xZrO2, x=0, 1, 3, 5, 7 and borosilicate glasses37 with a composition of of (61.9-x)SiO212.6Na2O-5.7CaO-16.0B2O3-3.8Al2O3-xZrO2, x=0, 1.7, 3, 4 using MD simulations. In all the three series, Zr ions are in slightly distorted [ZrO6] octahedral environments and have a higher preference of Ca ions as charge compensators in comparison with Na ions.37,63 ZrO2/SiO2 substitution results in higher network connectivity, fewer non-bridging oxygen species and smaller sized rings. The results of this study support the usage of Fnet as a characteristic descriptor in describing the properties of glass materials. Both density and initial dissolution rate were found to provide excellent correlation with Fnet calculated from structural features obtained from MD simulations. The result of this work, together with the success of 19 ACS Paragon Plus Environment


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several earlier applications, suggests that QSPR is a promising approach for obtaining the structure-property correlation and predictive modeling of glass material properties. The reason why Fnet is such a successful descriptor can be explained by the following reasons: Firstly, the Fnet not only takes into account of structural information but also energetic properties 3. In the Fnet, CN gives the first coordination shell environment for each cation and m factor evaluates the contribution of each cation to the overall network strength. Earlier studies used dissociation energies of gas phase dimers17–20 while we chose to single bond strength by Sun65, which is well known in glass science as it was widely used as a criteria to classify oxides into glass formers, intermediates and modifiers. In addition to providing single bond strength for most of common oxides found in oxide glasses, it provides the bond strengths for cation-oxygen pairs for different charge state and coordination number of each cation, e.g. different bonding strength for 3- and 4-fold coordinated boron. 65,71 Secondly, the structural information from MD simulations provides\ detailed coordination environment for each cation-oxygen pair and N4 values of boron for each composition. Thirdly, the Fnet descriptor not only includes the contribution of network formers to the overall structure but also modifiers, in comparison with the usage of network connectivity (NC) for prediction of glass dissolution and bioactivity.38,72–74 Extending the current QSPR framework to other properties and glass systems will rely on understanding and improving the structure descriptor, which is the core of QSPR analysis. With the excellent linear regression of experimental glass density and initial dissolution rate, Fnet seemed to be a great starting point for QSPR analysis of other properties. It is conceivable for more complex properties such as fracture toughness, long-term residual dissolution rate, and bioactivity, modification of the descriptor might be needed. From the current framework, in addition to the single bond strength mentioned earlier, modification of other factors can be explored. For example, the multiplicative factor, m, is used for evaluation the contribution of each cation to the overall network strength. For high NF-containing glasses such as the glass system studied, assuming factor m of each NF as their highest probability of connecting with the rest of NF might be appropriate due to their high network connectivity. However, for high modifier-containing glasses, it might be better to use the network connectivity as 20 ACS Paragon Plus Environment

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factor m instead of using a universal value. Further validation of this assumption is required for wider composition ranges. As for the factor m of modifiers, assuming m is the maximum ability of one type of modifier to charge compensate NFs seems to work with high NF-containing glasses as well. Whereas, it can be problematic for high modifier-containing glasses. Excess modifiers will create more non-bridging oxygen species instead of acting as charge compensators, resulting in a weakened glass network. Recent studies in cluding this work show the versatility of Fnet to correlate with several different glass properties. In a study by Lusvardi et al.,3 a good linear correlation (R2=0.912) was observed between Fnet and Tg for soda-lime silicate and phosphor-silicate glasses. Density, glass transition temperature and initial dissolution rate are three very different properties for glass materials, which governed by different mechanisms. Density characterizes the compactness and polymerization of glass network structure. Glass transition temperature represents the temperature required for overcome flow activation energy.3 Glass dissolution mechanism is the most complicated property among these three, where extrinsic factors (e.g., pH,21–23 temperature,24 solution chemistry,25 etc.) other than glass structures can greatly change the mechanism interpreted. Excellent correlation of the initial dissolution rates with Fnet indicates that the structural descriptor based on the bulk glass structure and bonding energies can accounts for the glass chemical durability in terms of the initial dissolution stage. Other aspects of glass dissolution such as the residual dissolution rate can be more complicated and affected by many other factors (e.g., passivating effect from alteration layers and precipitation of secondary phases26,75–77). In order to correlate glass composition and structure with the residual dissolution rate, the effect of formation of the passivating gel layer will need to be taken into consideration. A more sophisticated descriptor to incorporate latent features of gel formation capability will be needed. Fnet that accounts for the average bulk behavior and gives good correlation of the forward dissolution rate but might not be suitable for finding correlations of long-term residual rate of glass dissolution. Additionally, further modifications of the descriptor for specific glass properties and dissolution rates tested under different environments are thus needed. For instance, developing various structural descriptors for initial dissolution rates measured under basic, neutral and acid environments in combining with density function 21 ACS Paragon Plus Environment


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theory (DFT) calculations of various energy barriers78,79 of breaking cation-oxygencation linkages under different environments. Moreover, other structural features such as ring-size distribution, bottle-neck and interstitial site distribution can also affect dissolution of glasses to a certain extent. Overall, the descriptor of Fnet provides accurate account of bulk properties and initial dissolution rate of the borosilicate glasses. Based on this and earlier studies of QSPR analysis of glass property-structure correlation, further development can be made to correlate with more complex behaviors for example mechanical properties and residual rate of long term glass corrosion. Combining MD simulations and QSPR analysis is thus a promising glass genome80 approach for glass composition design and optimization. 5. Conclusions In this study, glasses with composition of xZrO2-(61-x)SiO2-17B2O3-18Na2O-4CaO with x=0, 1, 2, 4, 6 and 8 were simulated using MD simulations with recently developed composition-dependent potential sets. Bond distance of Zr-O is ~2.11 Å, and slightly distorted [ZrO6] octahedra appear in all the glass compositions. Local environments of cations, such as bond distance and coordination numbers are not sensitive with SiO2/ZrO2 substitution, which is also observed for a soda-lime silicate and boroalumino silicate glasses previously. Medium-range structural information altered by ZrO2 substitution was systematically investigated. ZrO2/SiO2 substitution results in higher network connectivity, fewer non-bridging oxygen species and smaller sized rings. Importantly, a theoretical structural descriptor (Fnet) containing both structural and energetic information was derived. Fnet was correlated with experimental properties (e.g., density and initial dissolution rate) through the quantitative structure-property relationship analysis. Excellent linear correlations (R2>0.99) were found between Fnet with density and initial dissolution rate. Even though that this structural descriptor should be modified and tested with more compositions and different glass properties, the QSPR analysis is a promising approach to connecting structural features obtained from computer simulations with experimentally measured glass properties, for the benefit of designing new generation materials.


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Acknowledgments We gratefully acknowledge financial support by the Center for Performance and Design of Nuclear Waste Forms and Containers, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0016584. Computational resources were provided by UNT's High Performance Computing Services, a division of the University Information Technology with additional support from UNT Office of Research and Economic Development.

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Quantitative StructureâProperty Relationship (QSPR) Analysis of ZrO2

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Quantitative StructureâProperty Relationship (QSPR) Analysis of ZrO2