Atomistic origin of the passivation effect in hydrated silicate glasses

ABSTRACT When exposed to water, silicate glasses and minerals can form a hydrated gel surface layer concurrent with a decrease in their dissolution kinetics—a phenomenon known as the

“passivation effect.” However, the atomic-scale origin of such passivation remains debated. Here, based on reactive molecular dynamics simulations, we investigate the hydration of a series

of modified borosilicate glasses with varying compositions. We show that, upon the aging of the gel, the passivation effect manifests itself as a drop in hydrogen mobility. Nevertheless,

only select glass compositions are found to exhibit some passivation. Based on these results, we demonstrate that the passivation effect cannot be solely explained by the repolymerization of

the hydrated gel upon aging. Rather, we establish that the propensity for passivation is intrinsically governed by the reorganization of the medium-range order structure of the gel upon

aging and, specifically, the formation of small silicate rings that hinder water mobility. SIMILAR CONTENT BEING VIEWED BY OTHERS BOROSILICATE GLASS ALTERATION IN VAPOR PHASE AND AQUEOUS

MEDIUM Article Open access 04 November 2022 MECHANISMS AND ENERGETICS OF CALCIUM ALUMINOSILICATE GLASS DISSOLUTION THROUGH AB INITIO MOLECULAR DYNAMICS-METADYNAMICS SIMULATIONS Article Open

access 15 March 2024 STRUCTURE AND PROPERTIES OF DENSIFIED SILICA GLASS: CHARACTERIZING THE ORDER WITHIN DISORDER Article Open access 23 December 2020 INTRODUCTION When exposed to water,

silicate glasses and minerals tend to dissolve via several mechanisms, including hydration, hydrolysis, and ion-exchange.1,2,3 In most cases, the leaching of the mobile cations initially

present in the silicate phase (e.g., B and alkali), their replacement by hydrated species, and the restructuring of the leached material results in the formation of a disordered, porous, and

hydrated “gel” layer on the surface of the dissolving phase.3,4 The formation of this alteration layer is usually associated with a drop in the corrosion rate—a behavior known as the

_passivation effect_.4,5 This slowdown in the corrosion kinetics of silicate phases upon their passivation has important consequences in earth science and technological applications

involving outdoor silicate phases.6,7 In particular, such passivation is expected to largely control the long-term durability of glasses used as a matrix to immobilize nuclear waste.8,9

Despite the importance of silicate corrosion, the origin of the passivation effect has thus far remained debated.3 The passivation effect is typically understood as (i) a consequence of

solution saturation (i.e., a decrease in chemical potential difference between solid and solution),10 (ii) the precipitation of amorphous silica following the congruent dissolution of the

glass,11,12,13,14,15,16 or (iii) the reorganization of the hydrated gel layer upon aging.2,17,18,19 In the latter case, the passivation effect has been suggested to arise from a decrease in

water mobility in the gel or pristine glass.4,5,20,21 Nevertheless, the atomic-scale mechanism that governs the passivation effect remains largely unknown. Although the reorganization of the

gel likely cannot explain alone all the features of the passivation effect,20 we investigate herein this hypothesis by means of reactive molecular dynamics simulations. Starting from a

series of sodium borosilicate glasses with varying compositions, several hydrated gels are prepared by mimicking the leaching of B and Na mobile cations and their replacement by hydrated

species. We show that the passivation effect manifests itself as a drop in hydrogen mobility upon the aging of the gel. We find that Na-rich glasses feature such passivation effect, whereas

B-rich glasses do not. In turn, all hydrated gels are found to exhibit some degree of repolymerization upon aging—which highlights that the passivation effect cannot be solely explained by

the repolymerization of the gel. Rather, we demonstrate here that the passivation effect is controlled by the reorganization of the medium-range order structure of the gel upon aging and,

specifically, the formation of small silicate rings. RESULTS PARENT GLASSES AND PREPARATION OF THE HYDRATED GEL To investigate the effect of the composition of the parent glass on the

propensity of the resulting hydrated gel to exhibit some passivation, we first simulate using molecular dynamics a series of modified borosilicate glasses

(Na2O)0.3–_x_(CaO)0.1(B2O3)_x_(SiO2)0.6, where _x_ = 0.00, 0.05, 0.10, 0.15, 0.20, and 0.30 (see Methods section). These compositions are intended to offer a simplified model for complex

multi-component nuclear waste glasses and to study the effect of the Na-to-B ratio (i.e., the two types of mobile/soluble cations considered in this series of glasses).8 Fig. 1a shows a

snapshot of the atomic configuration of a simulated glass comprising 10% B2O3. As expected, we observe a coexistence of three- and four-fold coordinated boron atoms (noted B[3] and B[4]

hereafter, respectively), wherein B[4] units are charge-balanced by Na or Ca cations (see the inset of Fig. 1a).22 In agreement with previous observations,22,23 the fraction of B[4] is found

to decrease with increasing _x_ (see Fig. 1b), i.e., increasing B2O3 molar fraction and decreasing Na2O molar fraction. This arises from the fact that, as the B2O3 molar fraction increases,

the (Na + Ca)/B ratio decreases, thereby representing a relative decrease in the amount of available charge-compensating ions.22 These glasses are then used as “parents” to form some

hydrated silicate gels. To this end, we mimic the hydration process by manually replacing the leached species (i.e., Na and B) by H atoms, while the other elements (Si, Ca, and O) are

retained in the hydrated glass (see Fig. 1c and Methods section).4,24 No distinction is made between network-modifying and charge-compensating Na cations during the leaching phase. Note that

Ca cations are not replaced here as this element has been found to be largely retained in the altered gel.24 Note that this method does not explicitly simulate the solution or the degree of

saturation thereof. Although it would be desirable to explicitly simulate the entire ion exchange process rather than manually replace the leached cations, the timescale of this reaction

far exceeds that allowed by MD simulations. As such, our simulations cannot offer any information on the kinetics of the ion exchange process. Nevertheless, the methodology used herein was

previously used to simulate ion exchange in silicate glasses (in the context of ion exchange strengthening), wherein the structure and properties of the simulated ion-exchanged glasses were

found to be in good agreement with experimental data.25,26,27 REPOLYMERIZATION OF THE HYDRATED GELS Following the hydration of the glasses, we now study the reorganization of the resulting

gels upon accelerated aging (see Methods section). We initially focus on the degree of polymerization of the gel, as captured by the fraction of bridging oxygen atoms (BO, i.e., O atoms that

are connected to two Si or B atoms—note that no B atoms are retained in the gel). First, we note that the degree of polymerization of the hydrated gel decreases with increasing B2O3 molar

fraction in the parent glass (see Fig. 2a,b). This arises from the fact that, initially, (i) the leaching of each Na cation results in the transformation of a NBO into a silanol group

(Si–OH)—so that the connectivity remains unchanged, whereas (ii) the leaching of each B cation involves the transformation of 3 or 4 BOs into silanol groups—which significantly decreases the

local connectivity. Second, we observe that, upon aging, the degree of polymerization of the gels tends to increase via recondensation (see Fig. 2a).28 Such recondensation occurs via the

transformation of two silanol groups into a water molecule. Eventually, the degree of polymerization of the gel appears to plateau after 1 ns of accelerated aging (see Fig. 2a). Importantly,

we observe that all the gels exhibit a comparable extent of repolymerization upon aging (see Fig. 2b), regardless of the composition of the parent glass. Interestingly, after aging, select

gels become even more polymerized than their parent glasses—a behavior that is observed here in Na-rich glasses (i.e., B2O3 molar fraction < 5%). Such recondensation of the gel echoes

previous experimental observations.5,17,24 Further, we observe that the reorganization of the gel upon aging also manifests itself in its overall density. We first note that the density of

the parent borosilicate glass increases with increasing B2O3 molar fraction, in agreement with experimental observations (see Fig. 2c).22,23 The leaching of Na and B cations then result in a

drop in the density of the hydrated gel, as observed experimentally.24 This can be explained by the fact that B and Na atoms are much heavier than H atoms. Interestingly, we observe that

select gels (i.e., for B2O3 molar fraction < 20%) tend to slightly densify upon aging, whereas others (gels formed from B-rich glasses) do not (see Fig. 2c). This highlights the fact

that, although all the gels tend to repolymerize over time, the details of the reorganization mechanism appear to be composition-specific. WATER MOBILITY AND PASSIVATION EFFECT We now

investigate whether the aged hydrated gels exhibit any signs of a passivation effect. To this end, we study the mobility of hydrogen atoms, which, ultimately, controls the ability of water

to diffuse through the gel.29,30 Specifically, we characterize the effect of the aging of the gel on water mobility by computing the diffusion coefficient of hydrogen before and after aging

(see Methods section and Supplementary Material).31,32 Note that, here, thanks to the reactive nature of the present MD simulations, H atoms can freely dissociate into silanol groups and

reform water molecules as they diffuse. To avoid any effect of the time-dependent gel reorganization on diffusion, the diffusion simulations are restricted to fairly low temperature, that

is, wherein the kinetics of the gel reorganization far exceeds the simulation timescale. Figure 3a shows an example mean-square displacement (MSD) of hydrogen in a hydrated gel (formed from

a parent glass comprising 10% B2O3), before and after aging. We observe that the MSD exhibit two stages of diffusion, namely, an initial ballistic regime up to about 2 ps, which is followed

by the diffusive regime at long time.33 These regimes manifest themselves by a slope of 2 and 1 in the log–log plot of the MSD vs. time (see Fig. 3a).31,34 Importantly, we observe that the

aging of the hydrated gel results in a decrease in the MSD of hydrogen (see Fig. 3a). This strongly supports the idea that the passivation effect manifests itself by a decrease in hydrogen

mobility in the hydrated gel upon its aging. To further describe the role of the composition of the parent glass in controlling the propensity of the resulting gel to exhibit a passivation

effect, we compute the diffusion coefficient of hydrogen atoms in the hydrated gels at 300 K (_D_H) and the associated activation energy (_E_A) by relying on an Arrhenius description of the

temperature-dependence of diffusion (see Methods section). Figure 3b shows the diffusion coefficient of hydrogen in the hydrated gels, before and after aging. We observe that, before aging,

the mobility of H atoms only weakly depends on the composition of the parent glass. In turn, the aging of the gel significantly affects hydrogen mobility. After aging, the diffusion

coefficient of hydrogen strongly depends on the composition of the parent glass. Specifically, _D_H is found to increase exponentially with increasing B2O3 molar fraction in the parent glass

(see Fig. 3b). Importantly, we observe that the aging of the gel results in a drop in _D_H in gels resulting from Na-rich glasses (by up to almost two orders of magnitude), whereas _D_H

increases upon aging in gels resulting from B-rich glasses. Similarly, as shown in Fig. 3c, we observe that aging results in an increase in the activation energy of diffusion _E_A in gels

created from Na-rich glasses, whereas _E_A decreases upon aging in gels resulting from B-rich glasses. Here, an increase in _E_A indicates that, on average, hydrogen atoms need to overcome

larger energy barriers to jump from one pocket to another.34 Altogether, these results indicate that only the gels resulting from Na-rich glasses feature a passivation effect (i.e., a

decrease in hydrogen mobility upon aging), whereas those resulting from B-rich glasses do not. These results are unexpected as dissolution rate and diffusion activation energy have

previously been suggested to be controlled by the connectivity of the atomic network.35 As such, the fact only select glasses exhibit a decrease in H mobility contrasts with the fact that

all gels tend to repolymerize upon aging (see Fig. 2b). This suggests that the passivation effect cannot be solely explained by the recondensation of the gel upon aging. ATOMISTIC ORIGIN OF

THE PASSIVATION EFFECT The lack of correlation between the degree of repolymerization of a gel upon aging (see Fig. 2b) and its propensity to exhibit a passivation effect (see Fig. 3b)

suggests that the drop in hydrogen mobility is not controlled by the short-range connectivity of the gel. Rather, we now focus on the evolution of the medium-range order of the hydrated gels

upon aging. In disordered silicate phases, the medium-range order is mostly determined by the ring size distribution—wherein (boro)silicate rings are defined as the shortest closed-path

within the Si–O/B–O network.36 Fig. 4a shows an example of ring size distribution in a hydrated gel (derived from the parent glass with 10% B2O3), before and after aging (see Methods section

and Supplementary Material). Overall, we observe that the ring size distributions exhibit a shape that is similar to those observed in silicate glasses—with an average ring size of 6–7 (see

Fig. 4b), wherein the ring size is here defined in terms of the number of Si and B atoms belonging to the ring).23,37,38 As shown in Fig. 4b, we observe that the averaging ring size is

maximum in the hydrated gels derived from parent glasses comprising around 15% B2O3. This maximum arises from a balance between the two effects of B atoms, namely, they tend to increase the

degree of polymerization in the parent glass (by consuming some network-modifying Na cations and forming BO4 units), whereas, in contrast, their leaching eventually results in a decrease in

the degree of polymerization of the gel (with respect to that of the parent pristine glass). Importantly, we note that, upon the aging of the gel, the average ring size tends to decrease in

gels resulting from Na-rich glasses (i.e., those that exhibit a passivation effect), whereas it increases in those resulting from B-rich glasses (i.e., those that do not exhibit a

passivation effect). Overall, the comparison of Figs. 3b,c and 4b strongly suggests that the propensity for a hydrated gel to exhibit a passivation effect is controlled by the decrease in

its average ring size upon aging. In details, we observe that the ring size distribution exhibits some coarsening (see Fig. 4a), wherein the fractions of small (i.e., 3-membered and

4-membered rings) and some of the large rings (6-membered and larger rings) increase at the expense of intermediate rings (i.e., the fraction of 5-membered rings decreases). Specifically,

the decrease in the average ring size is mostly driven by the formation of a significant fraction of small silicate rings (i.e., 3-membered and 4-membered rings). We also note that, as

expected, a decrease in the average ring size results in an increase in density (see Fig. 2c), which is in line with previous results.23 Overall, our results suggest that the formation of

small silicate rings in the hydrated gels upon aging is the structural origin of the passivation effect. This can be understood from that the fact that such small rings exhibit a lower

diameter than their larger counterparts. As such, since hydrated species need to travel through these rings to jump from one pocket to another in the gel, a decrease in ring diameter tends

to hinder water mobility. To confirm this, we compute the structure factors of the hydrated gels before and after aging—i.e., another signature of their medium-range order (see Methods

section).39 Specifically, the position of the first sharp diffraction peak (FSDP) of the Si–Si partial structure factor has been shown to be inversely correlated with the diameter of the

silicate rings.40 As shown in Fig. 4c, we note that the FSDP of the Si–Si partial structure factor is located around 1.8 Å–1, which corresponds to a typical repetition distance of 3.5 Å in

real space—i.e., the typical diameter of a five-membered silicate ring (see Methods section). Importantly, we observe that, upon the aging of the gel, the position of the FSDP increases in

gels resulting from Na-rich glasses (i.e., those that exhibit a passivation effect). This confirms that the average diameter of the silicate rings decreases upon the aging of the hydrated

gel—which is key in controlling the propensity for passivation of the gel formed from the hydration of alkali-rich (or B-poor) parent glasses. DISCUSSION Finally, we further discuss the

relationship between parent glass composition, ring size distribution evolution upon the aging of the gel, and passivation effect. First, we note that the parent glasses virtually do not

exhibit any small (boro)silicate rings.23 Note that, although the addition of B atoms in the pristine glass tends to increase its initial connectivity (i.e., by consuming some NBOs, see Fig.

2b), this does not result in the formation of small rings.23 Starting from this observation, Fig. 5 summarizes the distinct effects of Na and B leaching on the ring size distribution in the

hydrated gel and, eventually, on the propensity for passivation. Starting from a B-rich parent glass, the leaching of B cations significantly depolymerizes the glass network and results in

the formation of large rings. This arises from the fact that the leaching of B cations converts some BOs (i.e., O atoms connected to two Si or B atoms) into NBOs (i.e., Si–O–H groups). As

the gel ages, some recondensation can occur via the transformation of two silanol groups into a water molecule. However, as shown in Fig. 5a, such recondensation will at best restore some of

the rings that preexisted in the parent glass. As such, no small silicate rings silicate rings will be formed. In contrast, starting from a Na-rich parent glass, the leaching of Na cations

initially does not change the degree of polymerization of the silicate network—since this process simply converts Si–O–Na into Si–O–H bonds. Further, as the gel ages, the mutual

recondensation of silanol groups will result in the formation of new rings (see Fig. 5b), that is, rings that did not initially exist in the parent glass. These new rings will necessarily be

small (i.e., smaller than the rings initially present in the parent glass) as they form through the subdivision of existing rings. In turn, when traveling through such small rings, hydrated

species need to impose an elastic strain on the ring to accommodate their size,35,41 which results in an increase in the activation energy of diffusion (see Fig. 3c) and block some of the

diffusion pathways for H atoms. Overall, our results suggest that the loss of water mobility resulting from the formation of small silicate rings upon alkali leaching explains the

passivation effect in hydrated silicate glasses. Note that, in addition of the structural evolution of the hydrated gel, the reorganization of the silicate rings in precipitated amorphous

silica (if any) may also contribute to the passivation effect.42 METHODS PREPARATION OF THE PARENT BOROSILICATE GLASSES A series of parent borosilicate glasses

(Na2O)0.3–_x_(CaO)0.1(B2O3)_x_(SiO2)0.6 with _x_ = 0%, 5%, 10%, 15%, 20%, and 30% comprising around 3000 atoms are simulated by classical molecular dynamics (see Supplementary Material for

more details about the simulated glasses). To this end, we adopt the Wang–Bauchy (WB) potential, which has been shown to offer an excellent description of the structure and properties of

borosilicate glasses.23 In particular, the WB forcefield allows us to properly predict the average coordination of B atoms over a large range of compositions.23 The WB potential relies on a

two-body Buckingham formulation with fixed parameters and partial charges: $$U_{ij}\left( {r_{ij}} \right) = \frac{{q_iq_j}}{{r_{ij}}} + A_{ij}\;{\mathrm{exp}}\left( { -

\frac{{r_{ij}}}{{\rho _{ij}}}} \right) - \frac{{C_{ij}}}{{r_{ij}^6}}$$ (1) where _r__ij_ is the distance between a pair of atoms _i_ and _j_, _q__i_ is the partial charge of atom _i_, and

_A__ij_, _ρ__ij_, and _C__ij_ are the energy parameters for the pair of atoms (_i_, _j_). Long-range Coulombic interactions are computed with the PPPM algorithm with an accuracy of 10–5.43

The cutoff for the short-range and Coulombic interactions are set at 11 Å. More details about the parameterization of the WB potential can be found in ref. 23 and in Supplementary Material.

All the simulations presented herein are carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code.44 The motion of atoms is described using the

velocity-Verlet integration algorithm with a time step of 1 fs. The parent borosilicate glass models are prepared with the melt-quenching procedure,45 as described in the following. First,

an initial configuration is built by randomly placing the atoms into a cubic box while ensuring any unrealistic overlap by using the PACKMOL package.46 Then, the system is melted at 4000 K

in the canonical (_NVT_) ensemble for 200 ps and at zero pressure in the isothermal–isobaric (_NPT_) ensemble for 100 ps—to ensure the loss of the memory of the initial configuration.

Subsequently, the system is linearly cooled down to 300 K at zero pressure with a cooling rate of 1 K/ps in the _NPT_ ensemble. Note that, in select cases (e.g., B2O3 molar fraction < 

10%), the initial configuration tends to “explode” at high temperature in the _NPT_ ensemble. In such case, the system is initially cooled from 4000 to 2000 K in the _NVT_ ensemble,

equilibrated at 2000 K in the _NPT_ ensemble under zero pressure, and finally cooled down to 300 K in the _NPT_ ensemble with a cooling rate of 1 K/ps. Select structural features of the

simulated glasses (partial pair distribution functions (PDF) and bond angle distributions) are presented in Supplementary Material. PREPARATION OF THE HYDRATED GELS To describe the hydration

of the parent borosilicate glasses, we adopt the reactive forcefield ReaxFF47 parametrized by Manzano et al.48 ReaxFF is a bond-order-based potential that allows for both the breakage and

formation of chemical bond through the calculation of interatomic bond orders—a feature that is required to properly describe the formation hydration of the silicate network and subsequent

recondensation.49 Additionally, in contrast to conventional classical force fields with fixed atomic charges like the WB potential, ReaxFF dynamically assigns the charges of the atoms based

on the charge equilibration method (QEq)—which is key to model chemical reactions.50 Based on these features, ReaxFF has been shown to properly describe the reactivity of silicate phases

while remaining far more computationally efficient than ab initio methods.29,49,51 The energy formulation used by ReaxFF consists in several energy terms as follows: $$E_{{\mathrm{total}}} =

E_{{\mathrm{bond}}} + E_{{\mathrm{VDW}}} + E_{{\mathrm{Coul}}} + E_{{\mathrm{under}}} + E_{{\mathrm{over}}} + E_{{\mathrm{lp}}} + E_{{\mathrm{val}}} + E_{{\mathrm{tors}}} +

E_{{\mathrm{conj}}} + E_{{\mathrm{pen}}}$$ (2) where these terms describe, following the order above, the bond energy, Van der Waals energy, Coulombic potential energy, under-coordination

energy, over-coordination energy, lone electron pairs energy, valence angle energy, torsion energy, conjugation energy, and penalty energy. The detailed description of these terms can be

found in ref. 47. The ReaxFF parametrization used in this study can be found in Supplementary Material. The hydrated gels are prepared by subjecting the parent borosilicate glasses to

leaching, wherein mobile species (B and Na) are replaced by H atoms, whereas the other atoms (Si, Ca, and O) are retained in place. Specifically, each Na is manually replaced by 1H, whereas

B is replaced by 3H atoms—to retain charge neutrality. No undissociated water molecules are initially inserted as the gel initially remains densely packed. Following leaching, the obtained

hydrated gel is subjected to an energy minimization and equilibrated at 300 K for 100 ps in the _NVT_ ensemble and, finally, at zero pressure for 250 ps in the _NPT_ ensemble (using the

ReaxFF potential). All the reactive molecular dynamics simulations are carried out using the USER-REAXC package in LAMMPS.52 ACCELERATED AGING OF THE HYDRATED GELS The recondensation of

silanol groups into water molecules upon the aging of the hydrated gels involves the breaking Si–O–H and formation of Si–O–Si bonds, a process that is associated to high-energy barriers.28

As such, the limited timescale of molecular dynamics simulations (i.e., a few ns) would not allow for such energy barriers to be overcome. To this end, we here accelerate the aging of the

gels by increasing the temperature—a strategy that is commonly used to enhance the sampling kinetics in atomistic simulations.28,53 We here adopt a temperature of 2000 K, which was

previously found to be high enough to accelerate the polymerization kinetics of silicate gels while remaining low enough not to affect the nature of the condensation mechanism.28 The leached

hydrated gels are then subjected to accelerated aging by being relaxed at 2000 K in the _NVT_ ensemble for 1 ns—which is found to be long enough to achieve a plateau in the degree of

polymerization (see Fig. 2a). Following aging, the gels are cooled down to 300 K with a cooling rate of 10 K/ps in the _NVT_ ensemble and subsequently relaxed under zero pressure in the

_NPT_ ensemble for 100 ps before any further analysis. WATER MOBILITY The mobility of the H atoms in the hydrated gels—before and after aging—is studied by computing the mean square

displacement (MSD) of each H atom as: $${\mathrm{MSD}}_i\left( t \right) = {\mathrm{\Delta }}r_i^2\left( t \right) = \left| {r_i\left( {t + \tau } \right) - r_i(\tau )} \right|^2$$ (3) where

_r__i_(_t_) is the position of the _i_th atom at time _t_ and the brackets represent the averaging over multiple time origins (_τ_). The self-diffusion coefficient _D_s is related to the

slope of the MSD vs. time in the diffusion regime and can be computed from the Einstein relationship in 3D: $$D_{\mathrm {s}} = \frac{1}{6}\begin{array}{*{20}{c}} {} \\ {{\mathrm{lim}}} \\

{t \to \infty}\\{}\end{array}\frac{{{\mathrm{MSD}}(t)}}{t}$$ (4) Note that, to calculate the diffusion coefficient, we ensure that a diffusion regime is achieved (i.e., which manifests

itself as a slope of 1 in the log–log plot of MSD vs. time). All MSD calculations are here conducted in the _NVT_ ensemble to avoid any spurious effect due to volume changes. Starting from

hydrated gels configurations obtained before and after aging, respectively, the MSD is computed at 500, 600, and 700 K during 600 ps of dynamics. These temperatures are chosen so as be high

enough so that the diffusion regime can be achieved, but low enough to prevent any repolymerization of the gel during the timescale of the MSD simulations. The temperature dependence of the

computed diffusion coefficients is then fitted by an Arrhenius fit: $$D_{\mathrm {s}} = D_0\exp \left( {\frac{{ - E_{\mathrm {A}}}}{{RT}}} \right)$$ (5) to estimate the activation energy of

diffusion (_E_A) and, by extrapolation, the diffusion coefficient of the water molecules in the hydrated gels at 300 K. COORDINATION ANALYSIS The O atoms are distinguished into BO (i.e.,

connected to two network formers Si or B) and NBO (i.e., connected to only one network former) based on their local topology. To this end, we first compute the partial PDF for each system

and chose the position of the minimum after the first peak of the PDF as the cutoff distinguishing the first from the second coordination shell. The topology of each O atom is then

determined by enumerating the number of Si and B atoms present in its first coordination shell. The overall degree of polymerization of the phase is here defined by the number of BO atoms

per network-forming species (Si and B). RING SIZE DISTRIBUTION The ring size distribution of each system is computed by using the RINGS package,54 wherein a (boro)silicate ring is defined as

the shortest closed paths within the borosilicate skeleton network—that is, excluding network-modifying species and terminating O atoms.55 The ring size is here defined in terms of the

number of Si and B atoms they comprise. A maximum ring size of 15 is here adopted, which is found to be high enough for the ring size distribution to converge. STRUCTURE FACTOR AND

FIRST-SHARP DIFFRACTION PEAK We compute the Faber–Ziman Si–Si partial structure factors _S_FZSiSi(_Q_) through the Fourier transform of the Si–Si partial PDF _g_SiSi(_r_):56

$$S_{{\mathrm{SiSi}}}^{{\mathrm{FZ}}}\left( Q \right) = 1 + 4\pi \rho \mathop {\int }\limits_0^\infty {\mathrm {d}}r\,r^2\frac{{{\mathrm{sin}}\,Qr}}{{Qr}}\left( {g_{{\mathrm{SiSi}}}\left( r

\right) - 1} \right)$$ (6) where _Q_ is the reciprocal vector and _ρ_ is the atomic density. The first-sharp diffraction peak (FSDP) of the Si–Si partial structure factor is then by fitted

by a Lorentzian function—since it has been shown that Lorentzian functions better fit the FSDP of the structure factor of glassy silica than Gaussian functions.57 This fit allows us to

extract the position (_Q_FSDP) of the FSDP—which is found to be in the range of 1.7–1.85 Å−1, in agreement with previous experiment and simulation results.58,59 The Si–Si typical repetition

distance in real space is then computed as _d_ = 2_π_/_Q_FSDP.60 DATA AVAILABILITY All data that support the findings of this study are available from the corresponding author upon

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Google Scholar  Download references ACKNOWLEDGEMENTS This research was performed using funding received from the DOE Office of Nuclear Energy’s Nuclear Energy University Programs. The

authors also acknowledge some financial support provided by the National Science Foundation (Grant No. 1562066) and China Scholarship Council (Grant No. 201706120252). AUTHOR INFORMATION

AUTHORS AND AFFILIATIONS * Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology), Ministry of Education, 150090, Harbin, China Tao Du * School of Civil

Engineering, Harbin Institute of Technology, 150090, Harbin, China Tao Du & Hui Li * Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and

Environmental Engineering, University of California, Los Angeles, CA, 90095, USA Tao Du, Qi Zhou, Zhe Wang & Mathieu Bauchy * Laboratory for the Chemistry of Construction Materials

(LC2), Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, 90095, USA Gaurav Sant * California Nanosystems Institute (CNSI), University of

California, Los Angeles, CA, 90095, USA Gaurav Sant * Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA, 99352, USA Joseph V. Ryan Authors * Tao Du View

author publications You can also search for this author inPubMed Google Scholar * Hui Li View author publications You can also search for this author inPubMed Google Scholar * Qi Zhou View

author publications You can also search for this author inPubMed Google Scholar * Zhe Wang View author publications You can also search for this author inPubMed Google Scholar * Gaurav Sant

View author publications You can also search for this author inPubMed Google Scholar * Joseph V. Ryan View author publications You can also search for this author inPubMed Google Scholar *

Mathieu Bauchy View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS M.B. designed the research, T.D. performed the atomistic simulations, T.D.,

Q.Z., and Z.W. analyzed the simulation results, T.D., H.L, G.S., J.V.R., and M.B. wrote the manuscript. CORRESPONDING AUTHORS Correspondence to Hui Li or Mathieu Bauchy. ETHICS DECLARATIONS

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