BO₃/BO₄ Intermixing in Borosilicate Glass Networks Probed by Double-Quantum ¹¹B NMR: What Factors Govern BO₄–BO₄ Formation?

Abstract

We examine the borate group intermixing in a series of 25 borosilicate (BS) glasses from the [0.5M (2) O−0.5Na 2 O]−B 2 O 3 −SiO 2 systems with M = {Li, K, Rb, Mg, Ca} along with ternary K 2 O−B 2 O 3 −SiO 2 and Na 2 O− B 2 O 3 −SiO 2 glasses by double-quantum−single-quantum (2Q−1Q) 11 B correlation nuclear magnetic resonance (NMR) experiments. The alterations of the fractional populations of B [3] −O−B [3] , B [3] −O−B [4] , and B [4] −O−B [4] linkages in the glass networks were monitored for variable n Si /n B molar ratios, nonbridging O contents of the glass, and the (average) cation field strength (CFS) of the M z+ /Na + network modifiers. A significant B [4] −O−B [4] bonding is observed in all glasses, thereby conclusively demonstrating that the normally assumed "BO 4 −BO 4 avoidance" is far from strict in BS glasses, regardless of the M z+ field strength. We show that the degree of B [4] −O−B [4] bonding depends foremost on its underlying BO 4 population and to a lesser degree on the NBO content of the glass; we also provide a straightforward prediction of the B [4] −O−B [4] population in an arbitrary BS glass from parameters readily obtained by routine 11 B NMR. The propensity for forming B [4] −O−B [4] linkages increases concurrently with either the CFS or the amount of glass network modifiers, roughly scaling as the square root of the "effective CFS" that encompasses both parameters. Although BO 3 −BO 3 and BO 3 −BO 4 pairs remain favored throughout all examined BS glass networks, the borate group intermixing randomizes significantly for increasing effective CFS, out of which the amount and charge of the glass-network modifier cations dominate over their size. Our results are discussed in relation to the two prevailing but formally mutually exclusive "random network" and "superstructural unit" models of borate and BS glasses.

Sub-Nanometer-Range Structural Effects From Mg2+ Incorporation in Na-Based Borosilicate Glasses Revealed by Heteronuclear NMR and MD Simulations

“…Here, P ( F –O– F ′) = 1 denotes a strictly nonpreferential F / F ′ intermixing, whereas P ( F –O– F ′) > 1 and P ( F –O– F ′) < 1 imply a preference and reluctance for F –O– F ′ linkage formation, respectively. Although the bonding preferences depend slightly on the glass composition, the trends of Table conform well to those discussed previously for Na/Ca-bearing boro(phospho)silicate glasses, ,,, revealing the strongest preference (reluctance) for BO 3 –BO 4 (BO 4 –BO 4 ) pairs. While B [3] –O–B [3] linkages are also disfavored, all remaining Si–O–{Si, B [3] , B [4] } linkages form nearly statistically, i.e., each fractional population is given roughly by the product of the respective { x Si , x normalB x normalB false[ 3 false] , x normalB x normalB false[ 4 false] } molar fractions in the glass structure.…”

“…The MD derived M 2 rel (B) data, and notably the experimental counterparts, are markedly larger than M 2 rel (stat) for all glasses but MgNa4.0–0.75, in particular for the NBO-rich R = 2.1 members (Table ). Two structural factors account for these observations: The NBO partitioning among Si, B [3] , and B [4] species in BS glasses was discussed previously, ,, suggesting a substantially stronger propensity for B [3] –NBO bonding relative to B [4] –NBO. Except for very NBO-rich glasses, the latter is even considered “forbidden” by most scientists in the field ,,− but remains frequently observed to minor extents in numerous MD-derived glass models. ,,,,, Consequently, a progressively growing NBO accommodation at the BO 3 groups for increasing x NBO reduces the possibility of any B [3] –O– F linkage type, thereby boosting the M 2 rel (B) values of all NBO-rich glasses (Table ), while the relative dipolar second moment (eq ) is independent of the degree of Si–NBO bonding. The second effect underlying the increased NMR/MD-derived M 2 rel (B) values in any BS glass is less influential but stems from a slightly higher preference for B [4] –O–Si bridges than B [3] –O–Si linkages.…”

“…The underestimated (overestimated) modeled BO 4 (BO 3 ) populations are reasons for concern regarding reliable predictions of some medium-range (0.3–1 nm) glass-structure features. Gratifying, however, is the typically (very) good agreement observed consistently relative to experimental data on several interatomic-distance-related structural parameters, such as the relative B [3] /B [4] ···Na + and P–O–B [ p ] contacts in boro(phospho)silicate glasses, , as well as their B [ p ] –O–B [ q ] linkage statistics, ,, which constitute the most sensitive medium-range structural parameters on the precise { x normalB false[ 3 false] , x normalB false[ 4 false] } fractions; notwithstanding that the NMR/MD-derived B [ p ] –O–B [ q ] populations do differ, all experimental findings were reproduced qualitatively/semiquantitatively by the glass models. ,, Moreover, the relative B [3] /B [4] –O–Si contacts predicted by the glass models in section agree very well with our experiments, encompassing the Na4.0–0.75 glass. Indeed, out of the plethora of B–O force fields proposed to date (e.g., refs − ), solely the herein utilized option , has been assessed extensively against experimental interatomic-distance-related parameters directly reflecting the medium-range glass organization.…”

“… a Fractional x ( M –O [1] ) and x ( M –O [2] ) populations out of the entire O speciation for M = {Na, Ca, Mg}, along with the corresponding preferences for M –O [ p ] bonding defined by P ( M –O [ p ] )= x ( M –O [ p ] )/ x normalO false[ p false] , where x normalO false[ 1 false] ≡ x NBO and x normalO false[ 2 false] ≡ x BO = ( 1 − x NBO ) . The data from the CaNa K – R glasses were obtained from MD-generated models presented in ref b The data uncertainties are ±1σ with σ given for each entity. …”

“…Our study involved the eight BS glass compositions listed in Table , encompassing four ternary R Na 2 O–B 2 O 3 – K SiO 2 glasses and four quaternary R [0.5MgO–0.5Na 2 O]–B 2 O 3 – K SiO 2 analogs. They constitute a subset of a large BS glass ensemble examined previously. ,, We adopt the glass nomenclature of ref , where each Na- and Mg/Na-based glass is denoted by Na K – R and MgNa K – R , respectively, with the { K , R } parameters defined by , K = n ( SiO 2 ) / n ( B 2 O 3 ) R = [ n false( MgO false) + n false( Na 2 normalO false) ] / n ( B 2 O 3 ) Each nominal glass composition in Table is expressed in terms of its oxide equivalents and the atomic fraction of each element E in the (Mg)–Na–B–Si–O glass, x E = n E / ( n Mg + n Na + n B + n Si + n O ) where n E is the corresponding stoichiometric amount.…”