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Medium-Range Structural Organization of Phosphorus-Bearing Borosilicate Glasses Revealed by Advanced Solid-State NMR Experiments and MD Simulations: Consequences of B/Si Substitutions Yang Yu, Baltzar Stevensson, and Mattias Edén* Physical Chemistry Division, Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden S Supporting Information *

ABSTRACT: The short and intermediate range structures of a large series of bioactive borophosphosilicate (BPS) glasses were probed by solid-state nuclear magnetic resonance (NMR) spectroscopy and atomistic molecular dynamics (MD) simulations. Two BPS glass series were designed by gradually substituting SiO2 by B2O3 in the respective phosphosilicate base compositions 24.1Na2O−23.3CaO− 48.6SiO 2 −4.0P 2 O 5 (“S49”) and 24.6Na 2 O−26.7CaO− 46.1SiO2−2.6P2O5 (“S46”), the latter constituting the “45S5 Bioglass” utilized for bone grafting applications. The BPS glass networks are built by interconnected SiO4, BO4, and BO3 moieties, whereas P exists mainly as orthophosphate anions, except for a minor network-associated portion involving P− O−Si and P−O−B[4] motifs, whose populations were estimated by heteronuclear 31P{11B} NMR experimentation. The high Na+/Ca2+ contents give fragmented glass networks with large amounts of nonbridging oxygen (NBO) anions. The MDgenerated glass models reveal an increasing propensity for NBO accommodation among the network units according to BO4 < SiO4 < BO3 ≪ PO4. The BO4/BO3 intermixing was examined by double-quantum−single-quantum correlation 11B NMR experiments, which evidenced the presence of all three BO3−BO3, BO3−BO4, and BO4−BO4 connectivities, with B[3]−O−B[4] bridges dominating. Notwithstanding that B[4]−O−B[4] linkages are disfavored, both NMR spectroscopy and MD simulations established their presence in these modifier-rich BPS glasses, along with non-negligible B[4]−NBO contacts, at odds with the conventional structural view of borosilicate glasses. We discuss the relative propensities for intermixing of the Si/B/P network formers. Despite the absence of pronounced preferences for Si−O−Si bond formation, the glass models manifest subtle subnanometer-sized structural inhomogeneities, where SiO4 tetrahedra tend to self-associate into small chain/ring motifs embedded in BO3/BO4-dominated domains.

1. INTRODUCTION Multicomponent borosilicate glasses feature a plethora of important applications, ranging from glassware both for the kitchen and laboratory (e.g., Pyrex) to optics, ion-conductor materials, and radioactive waste encapsulation.1,2 Most applications demand highly polymerized glasses combining a high hardness and durability with low thermal expansion; this is also mirrored in the main research efforts for establishing composition−structure−property correlations of borosilicate glasses, which have generally emphasized silica-rich compositions with low amounts of network modifiers (for instance Na+, K+, and Ca2+) to maintain dense glass networks that provide strong and chemically inert materials. However, the past decade has witnessed borosilicate glass formulations for biomedical use,3−6 such as for bone grafting and tissue engineering. Here, the targeted properties are rather biocompatibility and the development of a strong interface with © 2017 American Chemical Society

the surrounding bone tissue (”bioactivity”), which generally require glasses that readily degrade when subjected to body fluids.7,8 Such amorphous borosilicates also incorporate low amounts of P to improve the bioactivity, thereby involving three coexisting potential glass-network formers (B, Si, and P), whose preferential intermixing may significantly influence the physical/chemical glass properties, sometimes nonlinearly by the “mixed network former effect”.9−11 Hence, besides the fundamental scientific value of a better understanding of the borophosphosilicate (BPS) glass-network organization, there is an application-driven impetus for investigating composition− structure relationships of BPS networks for facilitating the future design of biomedical glasses, notably for tuning their Received: July 6, 2017 Revised: August 31, 2017 Published: September 6, 2017 9737

DOI: 10.1021/acs.jpcb.7b06654 J. Phys. Chem. B 2017, 121, 9737−9752

Article

The Journal of Physical Chemistry B

prevalence of P−O−Si linkages, at least for Si-rich BPS glasses. Here we provide a detailed analysis by MD simulations along with heteronuclear 31P{11B} solid-state NMR experimentation. We also report a pilot study of the borate/silicate/phosphate intermixing in modifier-rich BPS glasses. Such aspects have been studied extensively for B and Si in alkali/alkaline-earth bearing M(2)O−B2O3−SiO2 glasses devoid of P.30−40 Since the detailed structural model of Na2O−B2O3−SiO2 glasses proposed by Yun-Dell-Bray-Xiao (YDBX),28,29 numerous experimental structural studies are presented for borosilicate glasses, encompassing reports on the {BO3, BO4} speciation,28−32,35−37 37 the NBO partitioning among SiO4 and BO3 groups,31,33−37 as well as the intermixing of borate and silicate network building blocks.30−40 Overall, these results suggested a preference for Si−NBO over B−NBO contacts and a growing propensity for SiO4 to interlink with other network-formers according to B[3](ring) < B[3](nonring) < B[4] ≈Si,35−37 where “ring” and “nonring” refers to BO3 moieties of boroxol rings (B3O6) and linear B[3]−O−B[3]/B[4]/Si bonding constellations, respectively.35−37 Analogously with the excess negative charge of an [AlO4]− tetrahedron,58,66,67 the [BO4]− counterpart is usually assumed not to accommodate NBO species,28,29,38,58,66 while direct B[4]−O−B[4] linkages are absent,27−29,35−38,58 along the wellknown “Loewenstein Al avoidance rule”.68 Yet, the validity of the B[4]−O−B[4] avoidance has been questioned,30,39,40 and more recent work on borate/borosilicate glasses highlight the potentially stabilizing effects from divalent cations on B[4]−O− B[4] motifs.41,42,69 Moreover, atomistic MD simulations reveal non-negligible NBO-bearing BO4 populations in borosilicate glasses.46,47 Considering that most studies concerned relatively modifier-poor borosilicate compositions involving monovalent alkali metal ions (M+), it remains unclear how well the “conventional” structural role of B[4] applies to the Ca2+-bearing and modif ier-rich BPS glasses targeted herein. As indeed demonstrated in the context of rare-earth (RE) based aluminosilicate glasses,67,70−72 trivalent RE3+ cations introduce both Al[4]−NBO contacts and abundant Al[4]−O−Al[4] linkages in the glass network, structural features that are negligible in M+/M2+-based aluminosilicate analogs of comparable compositions. Here we demonstrate both experimentally and by MD simulations that the B[4]−B[4] avoidance is far from strict in modifier-rich Na−Ca−B−Si−P−O glasses, while the glass models also reveal non-negligible B[4]−NBO contacts. Our MD calculations utilized novel B−O and P−O pairpotential parameters accounting for polarization effects, where we demonstrate an improved modeling of the {QnP} speciation of phosphosilicate glasses relative to previous reports.18−21,25 Notwithstanding usage of a fixed (glass-composition independent) B−O parameter set, it reproduced well 11B NMR-derived {B[3], B[4]} fractional populations over large compositional regions, as shown herein for BPS glasses and to be demonstrated elsewhere for Na-based amorphous borates and borosilicates (Stevensson, Yu, and Edén, manuscript in preparation).

degradation in aqueous media, where B incorporation is reported to enhance the glass dissolution.3−6 This article concerns modifier-rich BPS glasses of the Na2O− CaO−B2O3−SiO2−P2O5 system, where SiO2 was progressively substituted by B2O3 at a f ixed total Na2O and CaO content in two Na−Ca−Si−P−O base compositions comprising 46 mol % SiO2 (“S46”) and 49 mol % SiO2 (“S49”).12 The S46 glass members constitute B-bearing analogs 3,4 of the “45S5 Bioglass”7,8 that is exploited for bone grafting in periodontal and orthopedic surgery. In contrast with the well-studied and simpler phosphosilicate13−26 and borosilicate27−50 systems, structural characterizations of BPS glasses are very sparse and mainly concerned formulations with low modifier contents relative to Si and/or relatively P-rich compositions.11,51−54 The present structural report expands on our recent pilot study of these BPS glasses, which involved a short-range probing by 11B, 29 Si, and 31P magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy,12 along with some conjectures for the medium-range (≲1 nm) glass-network organization. The latter will partially be revised herein, where we examine the medium-range glass structure directly by atomistic molecular dynamics (MD) simulations and advanced MAS NMR experimentation, encompassing double-quantum−single-quantum (2Q−1Q) correlation 11B NMR55−57 to assess the interconnectivities among borate groups, while the B/P intermixing was explored by experiments exploiting heteronuclear 11B−31P dipolar interactions.58−61 Phosphorus normally assumes a network-forming role in phosphate glasses and when coexisting with other network formers, such as B, Al, or Si.9−11,13,14,51−53,58,62,63 Yet, for the current Na+/Ca2+-rich BPS glasses, we demonstrated that P contributes marginally to the glass network and is mainly 12 as for analogous present as orthophosphate (PO3− 4 ) anions, (B-free) Na2O−CaO−SiO2−P2O5 glasses with low P2O5 content (≲6 mol %).15−26 This property is important for biomedical applications, as it ensures readily leached PO3− 4 anions when the BPS glass is exposed to body fluids.19,25,64 Hence, the networks of modifier-rich Na2O−CaO−B2O3−SiO2− P2O5 glasses are largely borosilicate in nature, built by planar BO3 triangles interconnected with tetrahedral [BO4]− and SiO4 groups. Henceforth, QnP denotes a PO4 tetrahedron with n bridging oxygen (BO) atoms and 4 − n nonbridging oxygen (NBO) anions. One portion of the total Na+/Ca2+ ensemble constitutes network modif iers that depolymerize the glass network and charge-balance NBO species,58 with the remaining Na+ and Ca2+ cations balancing the negatively charged [BO4]− and QnP tetrahedra.12 While orthophosphate anions (Q0P) account for >85% of the total phosphate speciation in the present Na−Ca−B−Si−P−O glasses,12 there is a non-negligible fraction of Q1P phosphate groups, whose population grows slightly for increasing B content of the glass.12 Besides retarding the phosphate release in aqueous media by the presence of a covalent O bridge at the tetrahedron (PO3−O−X), identifying the preferential bonding partner X becomes important. For phosphosilicate glass analogs, the Q1P moieties involve P−O−Si bonds, while P− O−P fragments are normally negligible in phosphosilicate glasses with low P content.22−25,65 However, given the wellknown strong propensity for the P5+ cation to form P−O−Al/B bonds with trivalent Al3+/B3+ cations in alumino/borophosphate phases,9,11,53,58,62,66 the anticipated bonding partner of P in BPS glasses is B rather than Si. Yet, preliminary solidstate NMR results (commented on in ref 12) suggested a

2. BOROPHOSPHOSILICATE GLASS SERIES Table 1 collects the Na2O−CaO−B2O3−SiO2−P2O5 glass compositions of the present study, each denoted SNp(q), with N representing the sum of SiO2 and B2O3 contents in mol %, and p and q constituting the mol % of P2O5 and B2O3, respectively. This glass series originates from two phosphosilicate base compositions, S462.6(0) and S494.0(0), in each of 9738


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The Journal of Physical Chemistry B Table 1. Borophosphosilicate Glass Compositions, and B/P Speciationsa oxide equivalents label

f (%)b

S462.6(0) S462.6 (5) S462.6(9) S462.6(14) S462.6(18) S462.6(28) S462.6(37) S462.6(46)

0 10 20 30 40 60 80 100

0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246

S494.0(0) S494.0(2) S494.0(5) S494.0(7) S494.0(10) S494.0(15) S494.0(19) S494.0(24) S494.0(39)

0 5 10 15 20 30 40 50 80

0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241

x(Na2O) x(CaO)

molar ratios

x(B2O3)

x(P2O5)

0.267 0.267 0.267 0.267 0.267 0.267 0.267 0.267

0.461 0.415 0.369 0.322 0.277 0.184 0.092 0.000

0.000 0.046 0.092 0.138 0.184 0.277 0.369 0.461

0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026

1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84

0.233 0.233 0.233 0.233 0.233 0.233 0.233 0.233 0.233

0.486 0.462 0.437 0.413 0.389 0.340 0.292 0.243 0.097

0.000 0.024 0.049 0.073 0.097 0.146 0.194 0.243 0.389

0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040

2.08 2.08 2.08 2.08 2.08 2.08 2.08 2.08 2.08

B populations

R′d

Ke

x0P

x1P

x[3] B

x[4] B

ρ (gcm−3)f

0.00 0.22 0.50 0.86 1.33 3.00 8.00 −

− 9.46 4.73 3.15 2.37 1.58 1.18 0.95

− 9.00 4.00 2.33 1.50 0.67 0.25 0.00

0.959 0.952 0.952 0.952 0.949 0.941 0.935 0.916

0.041 0.048 0.048 0.048 0.051 0.059 0.065 0.084

− 0.831 0.740 0.705 0.684 0.665 0.660 0.666

− 0.169 0.260 0.295 0.316 0.335 0.340 0.334

2.704 2.685 2.669 2.652 2.633 2.600 2.556 2.515

0.00 0.11 0.22 0.35 0.50 0.86 1.33 2.00 8.00

− 14.7 7.37 4.91 3.69 2.46 1.85 1.48 0.93

− 19.0 9.00 5.67 4.00 2.33 1.50 1.00 0.25

0.900 0.897 0.897 0.893 0.890 0.887 0.871 0.864 0.832

0.100 0.103 0.103 0.107 0.110 0.113 0.129 0.136 0.168

− 0.635 0.612 0.589 0.576 0.568 0.567 0.567 0.581

− 0.365 0.388 0.411 0.424 0.432 0.433 0.433 0.419

2.650 2.649 2.649 2.649 2.648 2.645 2.630 2.616 2.570

xNa/xCac xB/xSic

x(SiO2)

P populations

a

Each glass is labeled SNp(q), where N = 100[x(SiO2) + x(B2O3)] is the sum of mol % of SiO2 and B2O3, whereas p and q are the mol % of P2O5 and B2O3, respectively. xE denotes the atomic fraction of element E, whereas x(···) is the molar fraction of the as-indicated oxide. All glass-composition [4] data and NMR-derived fractional populations of {Q0P, Q1P} and {BO3,BO4} groups, denoted {x0P, x1P} and {x[3] B , xB }, respectively, are reproduced from 12 Yu and Edén except for the S462.6(46) and S494.0(39) specimens. The uncertainty of each fractional population is ±0.01. bf = 100x(B2O3)/ [x(SiO2) + x(B2O3)] is the percentage of B2O3-for-SiO2 substitution. cRatios of the atomic fractions of Na and Ca (xNa/xCa), and B and Si (xB/xSi), respectively. dRatio R′ = x(4 2O)/x(B2O3) = x4 /x B, with x4 calculated from eq 1. eK = x(SiO2)/x(B2O3). fDensity measured by the Archimedes method in distilled water (ρ[H2O] = 0.997 g cm−3) with an uncertainty of ±0.007 g cm−3.

of the R′4 2 O−B2O3−KSiO2 composition (Table 1) constitutes the direct analog of R = x(Na2O)/x(B2O3) utilized in the YDBX model applied to borosilicate glass compositions parametrized as RNa2O−B2O3−KSiO2 glasses.28,29 Equations 1 and 2 allow for comparing results from the current fivecomponent BPS glasses with those of limiting borosilicate analogs in the literature. Note that the {x0P, x1P} values are not a priori known and must be determined experimentally. However, for BPS glasses featuring high (low) modifier (phosphate) content, no significant errors are introduced in eq 1 by assuming that P is exclusively present as orthophosphate ions (i.e., x0P = 1; see Table 1). Once the NBO consumption by the phosphate species is accounted for, the polymerization degree of the remaining borosilicate glass network will henceforth be specified by its network connectivity,58,64,66,73 which represents the average number of BO atoms per network-forming (Si or B centered) polyhedron. To assess the BO/NBO partitioning among the various {SiO4, BO3, BO4} groups (see section 4.2), we consider the network connectivity NFBO of the (fictive) subnetwork formed by each F[Z]={Si[4], B[4], B[3]} species, which constitutes the average number of BO atoms per F[Z] site.64,66 Likewise, NFNBO represents the average number of NBO ions coordinated by F. Note that NFBO + NFNBO = Z.

which SiO2 was progressively replaced by B 2 O 3 ; the nomenclature “S46” and “S49” refers collectively to all BPS members of the respective series. Besides the Si contents, the members of the S46 and S49 glass series mainly differ in their respective P2O5 contents of 2.6 mol % and 4.0 mol %;12 see Table 1. Noteworthy, the S462.6(0) member is the “45S5 Bioglass” composition of Hench,7,8 while all S46 glasses represent the B-substituted 45S5 analogs introduced for biomedical applications by Rahaman, Day, and co-workers.3,4 Note that the S46 glass series encompasses all BPS compositions between the limiting phosphosilicate 24.6Na2O−26.7CaO−46.1SiO2−2.6P2O5 and borophosphate 24.6Na2O−26.7CaO−46.1B2O3−2.6P2O5 glasses, while the Pricher S49 series only allowed preparation of homogeneous glasses with an upper limit of 80% B 2 O 3 −for−SiO 2 substitution. The symbol “x” is herein reserved for f ractions; see Table 1. As explained in ref 12, a SNp(q) glass of the Na2O−CaO− B2O3−SiO2−P2O5 system with K = x(SiO2)/x(B2O3) may be mapped onto a borosilicate 4 2 O−B2O3−SiO2 counterpart. Here the fictive monovalent 4+ ion accounts for the net amount of positive charges available for either depolymerizing the borosilicate network or charge-balancing the [BO 4]− tetrahedra. Its molar fraction is given by x4 = x Na + 2xCa − x P(3x P0 + 2x P1)

(1) +

3. MATERIALS AND METHODS 3.1. Glass Preparation and Characterization. Except for the B-richest S462.6(46) and S494.0(39) glasses that were prepared specifically for this study, all specimens of Table 1 are those reported in ref 12, where detailed glass preparation and characterization procedures were described; here we only recapitulate the most important information.

2+

Equation 1 accounts for the amount of Na /Ca cations consumed for compensating the negatively charged {Q0P, Q1P} phosphate groups of the BPS glass (with fractional populations {x0P, x1P}), while the parameter R′ = x(4 2O)/x(B2O3) = x4 /x B

(2) 9739


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kHz during dipolar recoupling and 44.4 kHz for the 90° pulses interconverting antiphase magnetization and MQC. All 11B CTselective 90°/180° pulses operated at νCT B ≈ 10.8 kHz. For each real/imaginary data-set of a States-TPPI acquisition,77 typically 12(t1) × 800(t2) time-points were recorded with dwell times {Δt1 = τr, Δt2 = 5.2 μs}, 1024−5632 coadded transients per t1value, and 2 s relaxation delays. Each 2D grid was zero-filled to 64 × 4096 time-points and apodized by 50−300 Hz full-width at half-maximum (fwhm) Gaussian broadening along both spectral dimensions. 31 11 P{ B} rotational-echo adiabatic-passage double resonance (REAPDOR)59,78 experiments were recorded at B0 = 9.4 T and 10.00 kHz MAS. REAPDOR involves two separate NMR experiments for a given dipolar recoupling interval τrec: one is referred to as the “reference” spectrum [Sref(τrec)] and constitutes a rotor-synchronized train of 180° rf pulses (νP = 61 kHz) applied to the observed nucleus (31P). The 180° pulses were cycled according to the XY4 or XY8 schemes.79 The other NMR data-set [S(τrec)] recouples the MAS-averaged 31P−11B dipolar interactions by additionally applying an adiabaticpassage pulse of duration 33.3 μs (νB = 82 kHz) to 11B at the midpoint of the recoupling interval (τrec/2);59 this results in an NMR signal-intensity reduction (“dephasing”) from the 31P sites in close spatial proximity to 11B, with the dephasing f raction59,78 [Sref(τrec) − S(τrec)]/Sref(τrec) reflecting the degree of 31P−11B contact. During the 1.40 s signal acquisition interval, a CPMG train80,81 of 537 rotor-synchronized Meiboom-Gill loops was applied, using 180° rf pulses of duration 9.0 μs. Between 128−640 transients were accumulated with 30 s relaxation delays. The resulting “spikelet” NMR spectrum was transformed into the standard representation using the procedure of ref 82. 3.3. Molecular Dynamics Simulations. Classical atomistic MD simulations were performed with the DLPOLY4.08 program83,84 for ensembles of ≈6500 atoms in a cubic box with periodic boundary conditions to match the glass composition and the experimental glass density (Table 1). Each melt-quench protocol involved a nominal cooling rate of 10 K/ps and started from a random atom configuration that was pre-equilibrated for 100 ps at 3500 K, followed by a stepwise temperature reduction of 100 K every 10 ps to 300 K and another equilibration for 200 ps, from which the last 150 ps were averaged to yield the structural data. The equations of motion were integrated in steps of 0.2 fs using the velocity Verlet integrator, and the temperature was controlled by a gentle stochastic thermostat with a 1.0 ps time constant and a Langevin friction constant of 1.0 ps−1. This procedure was completed 2−3 times with different initial atom configurations for each glass composition, from which the average value and uncertainty of each reported structural parameter were derived. NVT ensembles were employed throughout, except for the Si-richest S462.6(5) and S462.6(9) models, where {BO3, BO4} populations closer to the experimental data were obtained by first equilibrating an NPT ensemble at 3500 K, followed by a gradual volume contraction during the melt-cooling, before finalizing the NVT calculation as described above. We comment that using NPT simulations lead to underestimated densities (by 3−8%) at 300 K, and borate speciations in worse agreement with experiments. The computations involved a polarizable shell-model potential, where each cation carries its full formal charge, whereas the O2− species are represented by core (OC) and shell (OS) portions with charges zC = +0.8482e and zS = −2.8482e, respectively.18,19 Coulombic interactions were calculated by a

6.0 g batches of the BPS glasses were prepared by a standard melt-quench method, using precursors of SiO2 (99.99%), Na2CO3 (99.99%), and CaCO3 (99.9%) from ChemPur, NaH2PO4 (99.99%, Merck), and H3BO3 (99.9%, Sigma). Each precursor mixture was transferred to a Pt crucible and heated in an electric furnace at 950 °C for 120 min to allow for complete CO2 removal, whereupon the temperature was raised to 1200−1250 °C (S46 series) and 1300−1400 °C (S49 series), held for 20 min (S46 specimens) or 30 min (S49), before quenching the melt by immersing the bottom of the crucible in water. The evaporation losses during synthesis remained ≲1.5 wt % throughout [except for 3.7 wt % for S462.6(100)], while the integrated intensities in 11B and 31P MAS NMR spectra gave further support for overall intact batched glass compositions.12 Several glasses were examined by scanning electron microcopy (JEOL JSM-7000F microscope) in backscatter electron mode at a 15 kV acceleration voltage, throughout confirming each specimen to be an homogeneous amorphous single phase down to ≈1 μm. 3.2. Solid-State NMR Experiments. The NMR experimentation was performed at magnetic fields (B0) of either 9.4 T or 14.1 T, using Bruker Avance-III spectrometers and standard Bruker triple-resonance MAS probeheads. Glass powders were filled in 4 mm zirconia rotors, except for the 2Q−1Q 11B NMR experimentation (3.2 mm rotors). 31P (spin1/2) and 11B (spin-3/2) shifts are quoted relative to 85% H3PO4(aq) and neat BF3·OEt2, respectively, the latter also used for determining 11B nutation frequencies (νB) of all strong radio frequency (rf) pulses. 2Q−1Q correlation 11B NMR experiments55−57 were performed at B0 = 14.1 T (−192.5 MHz 11B Larmor frequency) and the MAS rate νr = 20.00 kHz, using the rf pulse scheme depicted in Figure 2d of Edén.57 Two-spin 2Q coherence (2QC) excitation was accomplished by one completed [SR212] dipolar recoupling sequence (90°-pulse-sandwiched SR212 ≡ R212R22−1).56 The recoupling operated at the 11B centraltransition (CT) nutation frequency of νCT B = νr/2 = 10.0 kHz with equal 2QC excitation and reconversion intervals of τexc = 4τr = 200 μs, where τr = ν−1 r is the rotor period. All other CTselective pulses employed νCT B ≈ 12.7 kHz, which provided 90°/180° pulse durations of 19.5/39.5 μs. A Hahn-echo spanning two rotor periods applied before the t1-evolution stage ensured rotor-synchronized 2QC excitation and reconversion stages,56 as well as rejection of all single-spin 2QC associated with the satellite transitions.55 For each real/imaginary part of a hypercomplex States 2D NMR acquisition,74 40(t1) × 350(t2) time-points were collected with dwell times {Δt1 = τr, Δt2 = 25.2 μs} and 1.5 s relaxation delays. Between 256−2688 signal transients were accumulated per t1-value depending on the B content of the glass. Complementary 2Q filtration (2QF) NMR experiments55,57 with variable 2QC excitation periods were recorded on vitreous B2O3 and the BPS glasses (see the Supporting Information). Adequate 2QF performance of the SR212 sequence was verified by also implementing the SR214 recoupling scheme.75 11 31 B{ P} dipolar-mediated heteronuclear multiple quantum coherence (D-HMQC60,61) 2D NMR spectra were acquired at B0 = 14.1 T and νr = 14.00 kHz using the protocol shown in Figure 1a of ref 61. 11B−31P multiple quantum coherences (MQC) were generated by two completed SR412 ≡ {R412 76 2 −2 2 −2 R4−2 (τexc = 1 }0{R41R41 }120{R41R41 }240 pulse sequences 12τr = 857 μs), where {···}ϕ indicates an overall phase-shift by ϕ (in degrees). The 31P nutation frequency (νP) was 28.0 9740


Article

The Journal of Physical Chemistry B Table 2. MD-Derived Structural Parameters B populationsb a

P populationsc

x(Q1P−F)e

BO/NBOd

x[3] B

x[4] B

x0P

x1P

x2P

xNBO

NSiBO

NSiNBO

NB3 NBO

NB4 NBO

NPNBO

Si

[3]

label

f (%)

S462.6(0) S462.6(5) S462.6(9) S462.6(18) S462.6(37) S462.6(46)

0 10 20 40 80 100

− 0.804 0.795 0.676 0.647 0.636

− 0.196 0.205 0.324 0.353 0.364

0.928 0.893 0.834 0.713 0.482 0.346

0.072 0.107 0.162 0.267 0.366 0.447

0.000 0.000 0.003 0.020 0.131 0.164

0.69 0.66 0.63 0.55 0.42 0.37

2.11 2.32 2.52 2.93 3.62 −

1.89 1.68 1.48 1.07 0.38 −

− 1.88 1.74 1.54 1.06 0.84

− 1.19 1.06 0.73 0.42 0.28

3.93 3.89 3.83 3.69 3.32 3.11

1.00 0.72 0.64 0.22 0.04 0.00

0.00 0.00 0.00 0.07 0.07 0.09

S494.0(0) S494.0(5) S494.0(10) S494.0(15) S494.0(24) S494.0(39) σf

0 10 20 30 50 80

− − 0.597 0.403 0.584 0.416 0.569 0.431 0.580 0.420 0.581 0.419 0.003−0.012

0.837 0.786 0.672 0.579 0.482 0.281 0.026

0.159 0.189 0.284 0.348 0.402 0.461 0.023

0.004 0.025 0.042 0.067 0.108 0.221 0.011

0.62 0.58 0.54 0.50 0.44 0.35 0.001

2.52 2.71 2.91 3.10 3.41 3.73 0.01

1.49 1.28 1.09 0.90 0.60 0.28 0.01

− 1.65 1.55 1.40 1.16 0.80 0.03

− 0.80 0.73 0.67 0.42 0.25 0.03

3.83 3.76 3.63 3.50 3.36 3.00 0.04

0.97 0.62 0.41 0.28 0.18 0.05 0.04

0.00 0.01 0.03 0.02 0.06 0.09 0.02

B

x(Q2P−F)e Si

B[4]

0.00 0.28 0.34 0.64 0.62 0.64

0.00 0.00 0.00 0.01 0.03 0.00

0.00 0.00 0.02 0.06 0.22 0.26

0.00 0.25 0.43 0.54 0.55 0.54 0.04

0.03 0.05 0.04 0.04 0.02 0.00 0.02

0.00 0.07 0.09 0.11 0.17 0.31 0.02

B

[4]

a c [4] n n [3] [4] Percentage of B2O3-for-SiO2 substitution. bFractional populations {x[3] B , xB } of {B , B } coordinations. Fractional populations {xP} of {QP} groups, obeying the normalization ∑nxnP = 1; any apparent deviation thereof stems from the presence of minute Q3P populations in the B-richest glasses. dFractional population of NBO ions (xNBO) in the glass (where xBO + xNBO = 1), average number of BO atoms per SiO4 tetrahedron (NSiBO), e B4 P n and average number of NBO species at the SiO4 (NSiNBO), BO3 (NB3 NBO), BO4 (NNBO), and PO4 (NNBO) groups. Fractional population x(QP−F) of 1 2 2 [3] P−O−F bonds associated with QP or QP groups. Note that x(QP−B ) = 0, and that P−O−P contacts are absent throughout: x(Q1P−P) = x(Q2P−P) = 0. fTypical data uncertainties.

smoothed particle-mesh Ewald summation84 with a 1.2 nm realspace cutoff and an accuracy of 10−6. A modified Buckingham potential accounted for all short-range OS−OS and cation−OS pair interactions, where the interaction energy of two species α and β separated at a distance r is given by ⎧ ⎫ ⎪ r ⎪ ⎬ Uαβ(r ) = Aαβ exp⎨ − ⎪ ⎪ ⎩ ραβ ⎭ ⎡ ⎧ ⎛ ⎞6 ⎫⎤ ⎪ r ⎟ ⎪⎥ −6 ⎢ ⎜ − Cαβr ⎢1 − exp⎨−⎜ ⎟ ⎬⎥ ⎪ ⎝ 4.3ραβ ⎠ ⎪⎥ ⎢⎣ ⎩ ⎭⎦

and good transferability among different glass compositions and systems (Stevensson, Yu, and Edén, manuscript in preparation). 4.1.1. Borate Speciations. Figure 1a plots the BO4 fractional populations (x[4] B ) observed across the S46 and S49 glass series against the molar fraction of B2O3, where results from 11B MAS NMR are contrasted with the predictions from MD simulations. The relative BO3 population (x[3] B ) dominates throughout all BPS glasses, but x[4] grows concomitantly with B the B content toward the asymptotic NMR-derived fractions ≈0.33 and ≈0.43 for the S46 and S49 series, respectively. Note [4] [4] the normalization x[3] B + xB = 1 and that xB is identical to the “N4” parameter often employed in the literature. The MDgenerated glass models match the experimentally determined B speciations very well, with the respective x[4] B values typically agreeing within 95%, and the largest discrepancy (14%) observed for the S462.6(9) glass; see Figure 1a. The good agreement is gratifying, particularly when considering our use of f ixed B−O potential parameters, in contrast with most recently proposed force fields for the modeling of borosilicate glasses, which invoked adjustable parameters depending on the glass composition45,46,86 (except for the very recent work of Pacaud et al.87 that employed one unique parameter-set that also accounted for polarization effects). Figure 1a also displays the predictions from the generalized YDBX theory (section 2), which accords reasonably well with the experimental/simulated B speciations, albeit the BO4 populations are consistently underestimated. Except for the Si-richest glasses featuring K > 8 (Table 1) that are not encompassed by the YDBX theory,28,29 all BPS glasses herein conform to “region IV” of the model by Dell and coworkers:28,29 (K/8 + 1)/2 ≤ R′ < K + 2 (see eq 2). For such compositions, a lower x[4] B value is predicted than the theoretical maximum of x[4] (max) = (K/8 + 1)/2, because the modifier B content is sufficiently large to charge-balance all [BO4]− tetrahedra, as well as converting some of them into NBObearing BO3 moieties.29 In contrast, in RNa2O−B2O3−KSiO2 glasses with low Na2O contents, B[3] → B[4] conversions occur up to R ⩽ Rmax = (K/8 + 1)/2 (regions I and II), meaning that all Na+ cations are predicted to associate with [BO4]−.29

(3)

All {Uαβ(r)} energies were evaluated out to r = 0.8 nm. We employed the parameters of refs 18 and 85, except for those of P−O and B−O, which were developed by us and utilized herein for the first time. The new B−O interatomic potential conforms to eq 3 with Cαβ ≡ 0 but additionally incorporating a repulsive term Dαβr−12. The various parameter sets {Aαβ, ραβ, Cαβ, Dαβ} are listed in Table S1. Moreover, the O−Si−O and O−P−O intratetrahedral angles were constrained with three-body truncated harmonic potentials.84

4. RESULTS 4.1. Basic Glass Building Blocks. To prepare for the discussion on the intermediate-range structural features, as well as validating the MD-generated glass models directly against experimental constraints, we first examine the {BO3, BO4} and {QnP} speciations, as well as the NBO-partitioning among these glass building blocks and the SiO4 tetrahedra (section 4.2). Table 2 collects various MD-derived structural parameters, while E−O pair-distribution functions and O−E−O bond-angle distributions are plotted for E = {Na, Ca, Si, P, B[4], B[3]} in Figure S6. The short-range structural features of BPS glasses will be treated more thoroughly in an upcoming publication discussing and evaluating the B−O and P−O pair-potential parameters in the contexts of borate, borosilicate, and phosphosilicate glasses, demonstrating their wide applicability 9741


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amounts of more polymerized {Q1P, Q2P, Q3P} groups; see Figure 1(b, c). The problem of underestimated orthophosphate contents by MD simulations is evident from numerous studies of Na2O−CaO−SiO2−P2O5 glasses.18−21,24,25 The underestimation of xP0 accentuates for growing glass network polymerization [i.e., when the silicate network connectivity (NSiBO) is increased].25 The MD simulations with our new P−O potential parameters cannot accurately handle the substantial repolymerization of the BPS glass-networks that accompanies the SiO2 → B2O3 substitution at constant Na+/Ca2+ content (section 4.2). Yet, compared with previous reports on B-free phosphosilicate glasses,18−21,23−25 the present potential enhances the agreement between the experimental/simulated {xPn } fractions across the entire range 2.0 ≤ NSiBO ≤ 2.6 (which is relevant for modeling of bioactive glasses64), as well as for variable xNa/xCa molar ratios of the Na−Ca−Si−P−O glass. The currently modeled x1P fractions of S462.6(0) [NSiBO = 2.11] and S494.0(0) [NSiBO = 2.54] reproduce the experimental values within 97% and 93%, respectively (Tables 1 and 2); markedly lower respective agreements of 89% and 82% were observed by employing the P−O potential parameter-set of ref 19 under otherwise identical simulation conditions. The advantages of the new potential parameters accentuate further for increasing silicate network connectivity, as will be discussed in detail elsewhere. 4.2. NBO Bonding Preferences Among Si/B/P. The parent S462.6(0) and S494.0(0) phosphosilicate glasses exhibit Si Si silicate network connectivities NBO =2.11 and NBO =2.54, respectively, implying a more polymerized S49 glass network than its S46 counterpart. These nominal NSiBO-values calculated from the glass compositions with the split-network procedure64,66 are in excellent agreement with the results from 29Si NMR of 2.14 (ref 25) and 2.58 (ref 12), respectively, as well as with the MD-derived values of NSiBO = 2.11 for S462.6(0) and NSiBO=2.52 for S494.0(0); see Table 2. When each S46/S49 glass series is formed by progressively substituting one Si atom by two B atoms (SiO2 → B2O3), the NBO population diminishes gradually and the glass network repolymerizes (see Table 2). This trend was also observed in a very recent MD simulation study of one BPS glass series.86 All our glass compositions conform to “region IV”, for which the YDBX model postulates that solely SiO4 and BO3 groups accommodate NBO ions, which distribute proportionally between the SiO4 and BO3 species according to their relative abundances.28,29 This feature predicted for borosilicate glasses is now examined in the context of BPS glasses. Figure 2(a, b) plots the average number of NBO ions accommodated by the network-formers F = {Si, B[3], B[4]}. Both S46/S49 glass families manifest the same trend of decreasing F−NBO contacts when the B content of the glass is increased at the expense of Si. The af f inity of each Si, B[3], B[4], and P[4] species to coordinate NBO ions diminishes along the series P[4] ≫ B[3] > Si > B[4], where particularly two aspects are noteworthy: (i) the B[3]−NBO preference is larger than that of Si−NBO throughout, which strongly restricts the intermixing of B[3] with other network-forming species, particularly the B[3]−O−B[3] linkages (see section 4.3). (ii) As expected, the B[4] species is least prone to coordinate NBO ions, but a nonnegligible (average) number of 0.3−1.2 NBOs resides at the BO4 tetrahedra, depending on the B content of the glass network and thereby its net polymerization degree; see Figure 2(a, b) and Table 2. Both features (i) and (ii) are remarkable but are attributed to the relatively large NBO reservoirs in the

Figure 1. Fractional populations of (a) BO4 species, and (b) orthophosphate (Q0P) and (c) {Q1P, Q2P} groups, plotted against the molar fraction of B2O3 of the S46 and S49 glasses. Solid and open symbols display results from MD simulations and 11B/31P NMR, respectively. The dashed lines in (a) show predictions from the YunDell-Bray-Xiao (YDBX) model28,29 generalized for BPS glasses (see section 2). Most of the experimental data were taken from ref 12. Here and in other figures, error bars are displayed only when they are well outside of the symbol sizes.

4.1.2. Phosphate Speciations. All P and Si atoms are tetrahedrally coordinated (P[4]; Si[4]) in the present BPS glasses.12 These features are fully reproduced by the MD simulations. Figure 1(b, c) plots the fractional populations {xnP} of the {QnP} species in the glass structures against x(B2O3), as obtained by 31P MAS NMR and MD simulations. As discussed previously,12 the experimental data reveal solely {Q0P, Q1P} groups, with the minor Q1P population growing for an increase in either (i) the B content of the BPS glass or (ii) the net glassnetwork polymerization degree [our glass design makes (i) and (ii) coupled; see section 4.2]. Feature (ii) was first demonstrated in the context of B-free phosphosilicate glasses.19,23,25 It is manifested in a twice as large NMR-derived fractional population of xP1 = 0.10 for the S49 4.0 (0) phosphosilicate base glass relative to x1P = 0.04 observed for the more fragmented S462.6(0) counterpart, while property (i) translates into B-richest end-members exhibiting x1P values of 0.08 [S464.0(46)] and 0.17 [S494.0(39)]. Both trends (i) and (ii) are reproduced qualitatively by the MD-generated glass models, but the reduction in the orthophosphate population is markedly stronger for increasing B incorporation, such that x0P becomes a minor species in the Brichest members of each S46/S49 family, along with significant 9742


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Figure 2. (a, b) MD-derived average number of NBO ions per network-forming species F (NFNBO) plotted against x(B2O3) for the (a) S46 and (b) S49 glasses with F[Z]={Si[4], B[4], B[3]}. The results for P are not displayed: 3.0≤ NPNBO ≤ 3.9. (c, d) The fraction out of the total NBO ensemble accommodated by the {SiO4, BO3, BO4, PO4} moieties across the (c) S46 and (d) S49 glass families. Dashed curves represent a statistical NBO partitioning among the various network-building species according to their relative abundances in the structure (i.e., bonding preferences are absent). Each dotted vertical line at x(B2O3) ≈ 0.14 marks the B2O3 content where equal NBO populations are accommodated by the individual silicate (SiO4) and borate (BO3/BO4) ensembles.

present BPS glasses and to the presence of divalent Ca2+ cations that more efficiently stabilize otherwise energetically disfavored negatively charged moieties. Several experimental studies reveal that the B[3]−NBO contacts emphasize for growing charge/ field-strength of the M+/M2+ cations.41,42,69 Indeed, our MDgenerated glass models reveal a weak but significant preference for the NBO-bearing BO4 tetrahedra to coordinate Ca2+ cations relative to Na+, while the propensity for Ca2+ accommodation around the BO3 triangles grows with their number of NBO ions (data not shown). Figure 2(c, d) plots the fractions of the total NBO reservoir associated with each {SiO4, BO3, BO4, PO4} ensemble for increasing B2O3 content of the glass, along with the results for a nonpreferential NBO partitioning that directly reflects the relative abundances of each network-forming species. Despite the low P2O5 contents in these glasses, the very strong P−NBO affinity yields relatively large (and constant) portions of ≈20% and ≈30% of the total NBO population accommodated by the phosphate groups in the S46 and S49 glass structures, respectively, regardless of their Si/B contents [Figure 2(c, d)]. Yet, most NBO ions are associated with the SiO4 and BO3 ensembles, where the latter NBO reservoir increases concomitantly with the amount of B (relative to the number of Si− NBO contacts, not in terms of net NBO content). The regions to the left and right of each vertical threshold line in Figure 2(c, d) comprise glass compositions with a majority of their NBO populations residing in the SiO4 and BO3/BO4 subnetworks, respectively. Notably, the MD-derived results in Figure 2(a, b) and Table 2 reveal a higher (lower) number of NBO ions at the BO3 (SiO4) groups than those previously conjectured by us from 29 Si and 31P NMR data.12 However, those estimates were approximate and were not based on a direct experimental probing of the Si/B−NBO populations. Further work is

required to unambiguously (dis)prove our MD-derived inference of a higher affinity of B[3]−NBO associations relative to Si−NBO, as well as the presence of B[4]−NBO motifs. Unfortunately, this is a very challenging experimental task for these BPS glasses. 17O triple-quantum MAS NMR is one option, but existing data thereof from M(2)O−B2O3−SiO2 glasses34−37,43 suggest that the present mixed-modifier Na2O− CaO−B2O3−SiO2−P2O5 glasses may give insufficient NMR spectral resolution to unambiguously resolve, and let alone quantify, the resonances of the various NBO−Si/B[3]/B[4] contacts. This is currently under investigation. 4.3. Connectivities Among Borate Groups. There are three possible BOp−BOq interconnectivities in a BPS glass: BO3−BO3, BO3−BO4, and BO4−BO4. In the prevailing structural understanding of borosilicate glasses,27−29,35−38,58 inferred mainly from modifier-poor compositions, BO3−BO3 pairs build boroxol rings and connect such rings with other “superstructural borate” units, while BO3−BO4 constellations often signify superstructural units, and BO4−BO4 pairs are disfavored/absent. However, the partitioning of the B[3]−O−B[3]/B[4] bridges among boroxol rings and other superstructural units in borosilicate glasses is largely unknown because the 11B NMRderived grouping of B[3] into ring/nonring species is ambiguous, while similar problems apply to Raman spectra interpretations. Strictly, previous 11B[3] NMR assignments to “ring” and “nonring” moieties35−37,49,88−90 originate from results on B2O3, where they unambiguously imply boroxol rings and linear B[3]−O−B[3] (“nonring”) constellations, respectively.88 However, such assignments in more complex modif ied borate89 and (notably) borosilicate35−37,49 glass systems are far from unique and other options are conceivable, such as the grouping of B[3] in any ring constellation into “B[3](ring)”.90,91 We will henceforth employ the nomenclature 9743


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Figure 3. 2Q−1Q correlation 11B NMR spectra from the (a) S462.6(5), (b) S494.0(24), and (c) S462.6(46) glasses, recorded by using the [SR212] dipolar recoupling sequence,56 with τexc = 200 μs for 2QC excitation at B0 = 14.1 T and νr = 20.00 kHz. Projections along the 2Q and 1Q dimensions of the 2D NMR spectra are displayed at the right and at the top, respectively. Each pairwise B[3]−B[3], B[3]−B[4], and B[4]−B[4] correlation is indicated in (b). Note that the “autocorrelation” signals associated with the B[3]−B[3] and B[4]−B[4] pairs extend along the diagonal of slope 2, marked by a dotted line.

“boroxol” and “nonboroxol” B[3] sites, however, with the former taken to encompass both boroxols (B3O6/2) and NBO-bearing BO3 groups in three-member rings, such as the cyclic metaborate anion [B3O3/2(O−)3/1] whose 11B resonances are not readily resolved from those of the boroxol rings.90 In contrast, the nonboroxol sites involve any B[3]−O−B[3]/B[4]/Si bond constellation,35−37,49 encompassing both chains and ring configurations, such as B[3]−O−B[4] and B[3]−O−Si linkages in any superstructural unit. 4.3.1. 11B−11B Double-Quantum NMR. To examine the nature of the borate intermixing and the extent of “B[4]−B[4] avoidance” in the relatively fragmented networks of modifierrich BPS glasses, we performed 11B−11B dipolar recoupling experiments57,58 to generate 2QC by the through-spacemediated 11B−11B dipolar interaction, which depends on the inverse cube of the interatomic B−B distance.57,58 The 2QC buildup rate depends mainly on the shortest 11B−11B distances in the structure. Insight about pairwise B[p]−O−B[q] bonding preferences in the glass network is gained by selecting a sufficiently short 2QC excitation interval that NMR signals are detected solely from directly interlinked 11BOp−11BOq polyhedra;57,58 see the Supporting Information. Figure 3 displays a selection of 2Q−1Q correlation NMR spectra acquired with a short 2QC excitation interval (τexc = 200 μs) from BPS glasses with increasing B contents. A 11 [p] 11 [q] B − B linkage is revealed along the vertical “2Q dimension” of the 2D NMR spectrum by a resonance at the [p] [q] 2Q shift-coordinate δpq 2Q = δB + δB , given by the sum of the [q] respective correlated δ[p] and δ B B shifts that appear along the horizontal “1Q dimension”; its projection is similar to the directly excited 11B MAS NMR spectrum presented previously12 and comprises two signals from 11BO3 and 11BO4 groups resonating at δ[3] ≈ 14 ppm and δ[4] ≈ 1 ppm, B B respectively. The symmetric 11BO4 environment produces a narrow NMR peak, whereas the 11BO3 counterpart is markedly more broadened by second-order quadrupolar interactions.58,67 The quadrupolar broadening manifests as broad ridges of all

correlation signals involving 11BO3 groups. Regardless of the precise BPS glass composition, all 2Q−1Q correlation NMR spectra of Figure 3 evidence the presence of all three BO3−BO3, BO3−BO4, and BO4−BO4 pairs in the structure, as revealed by their respective 2Q signals that appear around δ33 2Q ≈ 2 ppm, 44 δ34 2Q ≈ 15 ppm, and δ2Q ≈ 28 ppm. These correlation peaks are contrasted further in Figure 4 that displays the projection along the 2Q dimension of each 2Q−1Q NMR spectrum from five BPS glasses with variable B contents.

Figure 4. Projections along the 2Q dimension of 2Q−1Q correlation 11 B NMR spectra recorded from the as-indicated BPS glasses, with the observed B[3]−B[3], B[3]−B[4], and B[4]−B[4] connectivities indicated. All spectra are normalized to a unity integrated NMR intensity, and other conditions are as in Figure 3.

4.3.2. BOp−BOq Bonding Preferences: NMR versus MD Simulations. Owing to the hurdles of generating 2QC among half-integer spins,57 such as 11B (spin-3/2), the integrated 2D peak volume of each 2Q−1Q NMR correlation signalor the corresponding peak area in the spectra of Figure 4only approximately reflects the abundance of the BOp−BOq motif in 9744


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The Journal of Physical Chemistry B Table 3. Relative Abundances of BOp−BOq Connectivitiesa B populationsb label

f (%)

x[3] B

S462.6(5) S462.6(37) S462.6(46) S494.0(7) S494.0(24)

10 80 100 15 50

0.83(0.80) 0.66(0.68) 0.67(0.64) 0.59(−) 0.57(0.58)

MD(random)c

NMR x[4] B

x33 B

x34 B

x44 B

x33 B

x34 B

x44 B

0.17(0.20) 0.34(0.32) 0.33(0.36) 0.41(−) 0.43(0.42)

0.63 0.36 0.36 0.35 0.29

0.33 0.54 0.53 0.54 0.58

0.04 0.11 0.10 0.11 0.13

0.18(0.39) 0.21(0.25) 0.20(0.25) − 0.15(0.17)

0.73(0.47) 0.63(0.50) 0.63(0.50) − 0.64(0.49)

0.09(0.14) 0.16(0.25) 0.17(0.25) − 0.21(0.34)

11 Fractional populations of pairwise BOp−BOq connectivities (xpq B NMR or by MD simulations. B ), as obtained either by 2Q−1Q correlation Experimental fractions, with MD-derived values in parentheses. cValues within parentheses represent results from a statistical BOp−BOq [4] intermixing, assuming a binomial distribution and using the MD-derived {x[3] B , xB } fractions and average numbers of BO atoms at the BO3/BO4 44 B3 [3] B3 [4] B4 2 34 groups in each glass structure from Table 2: {x33 = p , x = 2p(1 − p), x = (1 − p)2}, with p = x[3] B B B B NBO/(xB NBO + xB NBO). a b

the glass network, as discussed in the Supporting Information. [p] [q] linkages Using the notation xpq B for the fraction of B −O−B out of all available B−O−B bridges, Table 3 lists the fractional 34 44 populations {x33 B , xB , xB } obtained either experimentally by NMR or predicted by MD simulations. While the experimental/modeled data deviate markedly, each one reveals very similar results within each BPS glass ensemble, approximately 34 44 amounting to {x33 B , xB , xB } triplets of {0.35, 0.55, 0.10} and {0.20, 0.63, 0.17} obtained by NMR and MD simulations, respectively. The near invariance of the relative B[3]/B[4]−B[3]/B[4] contacts in glass structures within each S46/S49 family (conveyed in Table 3) is readily rationalized from the essentially constant BO3/BO4 abundances among the glass structures, regardless of their precise xB/xSi ratios [except for the S462.6(5) glass of lowest B content, discussed below]. Yet, 34 44 each {x33 B , xB , xB } triplet also depends on the number of BO atoms present at the BO3 and BO4 species: despite the higher abundance of BO3 groups throughout all glasses, their markedly lower number of 1−2 accessible BO atoms (compared with 3− 4 at the BO4 tetrahedra) strongly limits the B[3]−O−B[3] contacts relative to those of B[3]−O−B[4], whose statistical probability becomes emphasized, as reflected both in the NMR/MD-derived results in Table 3. Moreover, the enhanced BO 3 −BO 3 contacts anticipated from the higher BO 3 populations of the S46 glasses (relative to their S49 counterparts) are largely counterbalanced by a greater number of NBO species at the BO3 groups in these modifier-richer 34 44 glasses, thereby yielding similar {x33 B , xB , xB } data sets for all S46/S49 glasses. This feature is most transparent for the larger ensemble of MD-derived {xpq B } populations plotted in Figure 5. The predictions from a statistical {BO3, BO4} intermixing are also displayed, revealing significantly higher (lower) B[4]−B[4] (B[3]−B[4]) contacts than the MD glass model, but overall much closer simulated/statistical B[3]−B[3] populations. The S462.6(5) structure involves markedly emphasized (NMR-derived) BO3−BO3 associations relative to any other glass, which is naturally attributed to its larger BO3 population; see Figure 4 and Table 3. While the experimentally estimated B[3]−B[3] contacts are emphasized relative to the glass models throughout all structures, the S462.6(5) glass manifests the strongest deviations (Table 3). The higher experimental x33 B population in this specimen originates either from formation of boroxol rings or B[3]−B[3] contacts involving at least one nonboroxol BO3 group. Extensive boroxol-ring formation is not reproduced in the simulated glasses: only