Oxygen sites coordinating three network-forming cations in aluminosilicate (AS) glasses—i.e., O^[3] coordination species referred to as “oxygen triclusters”—was proposed 60 years ago and has since then been heavily debated because irrefutable experimental proof for their existence is still lacking. We introduce a protocol for predicting the O^[3] population from the average coordination number of Al () and the fraction of non-bridging O (NBO) species, which are available from routine ²⁷Al and ¹⁷O NMR experiments, respectively. Although O^[3] species were proposed for balancing the negatively charged [AlO_4/2]^- groups that typically dominate the Al speciation in AS glasses, recent computational modeling reveals a stronger propensity for the higher-coordination Al^[5] (AlO₅) and Al^[6] (AlO₆) species to coordinate O triclusters for charge-compensation. We discuss the structural roles of the O^[3] and Al^[5]/Al^[6] entities, all of which remain unclear despite extensive previous research. For a large set of AS glasses involving various  M⁺, M²⁺, and M³⁺ cations, the fractional O^[3] population () increases concurrently with the net number of Al^[5] and Al^[6] sites in the glass, but decreases for increasing M^z+ cation potential. Both O^[3] and Al^[5]/Al^[6] species have been suggested to enhance the glass hardness and crack resistance. For AS glasses involving various trivalent rare-earth cations, the microhardness correlated better with the average coordination number of Al () than with , as did the crack resistance of a limited set of Ca AS glasses. Nevertheless, contributions from O^[3] sites cannot be excluded for the latter glasses and further studies are needed for firm conclusions.

By using density functional theory (DFT) calculations, we refined the H atom positions in the structures of β-caffeine (C), α-oxalic acid (OA; (COOH)₂), α-(COOH)₂·2H₂O, β-malonic acid (MA), β-glutaric acid (GA), and I-maleic acid (ME), along with their corresponding cocrystals of 2 : 1 (2C–OA, 2C–MA) or 1 : 1 (C–GA, C–ME) stoichiometry. The corresponding ¹³C/¹H chemical shifts obtained by gauge including projector augmented wave (GIPAW) calculations agreed overall very well with results from magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy experiments. Chemical-shift/structure trends of the precursors and cocrystals were examined, where good linear correlations resulted for all COO¹H sites against the H⋯O and/or H⋯N H-bond distance, whereas a general correlation was neither found for the aliphatic/caffeine-stemming ¹H sites nor any ¹³C chemical shift against either the intermolecular hydrogen- or tetrel-bond distance, except for the ¹³COOH sites of the 2C–OA, 2C–MA, and C–GA cocrystals, which are involved in a strong COOH⋯N bond with caffeine that is responsible for the main supramolecular stabilization of the cocrystal. We provide the first complete ¹³C NMR spectral assignment of the structurally disordered anhydrous β-caffeine polymorph. The results are discussed in relation to previous literature on the disordered α-caffeine polymorph and the ordered hydrated counterpart, along with recommendations for NMR experimentation that will secure sufficient ¹³C signal-resolution for reliable resonance/site assignments.

We discuss the prospects for accurate ¹¹B magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectral deconvolutions for reaching beyond the readily extracted borate speciations offered by the integrated resonances of the coexisting B^[3] and B^[4] species of the respective BO₃ and BO₄ network groups in borosilicate (BS) glasses. We critically review hitherto proposed ¹¹B^[3] and ¹¹B^[4] NMR-peak assignments relating to their neighboring Si, B^[3] and B^[4] species, as quantified by MAS NMR spectral deconvolution. Guidance to these resonance assignments was offered from double-quantum–single-quantum (2Q–1Q) ¹¹B MAS NMR experiments that inform about the B^[p]–O–B^[q] network linkages. The NMR spectral deconvolutions from two BS glass series with low nonbridging oxygen (NBO) contents and fixed molar ratios n_Si/n_B = {1.0, 2.0} but variable network-modifying cations of alkali metals and Mg²⁺ revealed a dominance of B^[4]–O–Si linkages, yet with a significant dependence on the BO₃ population of the glass, which was rationalized by the different propensities for B^[4]–O–{Si, B^[3], B^[4]} linkage formation. For BS glasses with comparable B and Si contents, we recommend three-peak deconvolutions of the ¹¹B^[4] spectral region, whose ¹¹B^[4](mSi) sites differ in their (average) numbers of m B^[4]–O–Si and 4 – m B^[4]–O–B^[p] bonds, where B^[p] may assume B^[3] or B^[4]. We also discuss the structural origin of the two rather arbitrarily classified “ring” and “non-ring” B^[3] entities, where 2Q–1Q ¹¹B NMR suggests the former to primarily constitute BO₃ groups that coexist with BO₄ moieties in (superstructural) ring units largely devoid of bonds to Si, whereas the “non-ring” B^[3] sites involve linkages to all of B^[3], B^[4], and Si, with B^[3]–O–Si linkages prevailing. The limitations of ¹¹B NMR spectral deconvolutions are discussed, including the remaining challenges in analyzing NBO-rich BS glasses.

Magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations were employed to investigate Na2O-B2O3-SiO2 and MgO-Na2O-B2O3-SiO2 glass structures up to ≈0.3 nm. This encompassed the {Na[p]}, {Mg[p]}, and {B[3], B[4]} speciations and the {Si, B[p], M[p]}-BO and {Si, B[p], M[p]}-NBO interatomic distances to the bridging oxygen (BO) and nonbridging oxygen (NBO) species, where the superscript indicates the coordination number. The MD simulations revealed the dominance of Mg[5] coordinations, as mirrored in average Mg2+ coordination numbers in the 5.2-5.5 range, which are slightly lower than those of the larger Na+ cation but with a narrower coordination distribution stemming from the higher cation field strength (CFS) of the smaller divalent Mg2+ ion. We particularly aimed to elucidate such Na+/Mg2+ CFS effects, which primarily govern the short-range structure but also the borosilicate (BS) glass network order, where both MD simulations and heteronuclear double-resonance 11B/29Si NMR experiments revealed a reduction of B[4]-O-Si linkages relative to B[3]-O-Si upon Mg2+-for-Na+ substitution. These effects were quantified and discussed in relation to previous literature on BS glasses, encompassing the implications for simplified structural models and descriptions thereof.

We examine the borate group intermixing in a series of 25 borosilicate (BS) glasses from the [0.5M₍₂₎O–0.5Na₂O]–B₂O₃–SiO₂ systems with M = {Li, K, Rb, Mg, Ca} along with ternary K₂O–B₂O₃–SiO₂ and Na₂O–B₂O₃–SiO₂ glasses by double-quantum–single-quantum (2Q–1Q) ¹¹B 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 “BO₄–BO₄ 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 BO₄ 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 ¹¹B 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 BO₃–BO₃ and BO₃–BO₄ 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.

In molecular dynamics simulations utilizing enhanced-sampling techniques, reweighting is a central component for recovering the targeted ensemble averages of the unbiased system by calculating and applying a bias-correction function c(t). We present enhanced reweighting protocols for variationally enhanced sampling (VES) simulations by exploiting a recent reweighting method, originally introduced in the metadynamics framework [Giberti et al. J. Chem. Theory Comput., 2020, 16, 100-107], which was modified and extended to multiple-walker simulations: these may be implemented either as independent walkers (associated with one unique correction function per walker) or cooperative ones that all share one correction function, which is the hitherto only explored option. When each case is combined with the two possibilities of determining c(t) by time integration up to either t or over the entire simulation period , altogether four reweighting options result. Their relative merits were assessed by well-tempered VES simulations of two model problems: locating the free-energy difference between two metastable molecular conformations of the N-acetyl-l-alanine methylamide dipeptide, and the recovery of an a priori known distribution when one water molecule in the liquid phase is perturbed by a periodic free-energy function. The most rapid convergence occurred for large cooperative walkers, regardless of the upper integration limit, but integrating up to t proved advantageous for small walker ensembles. That novel reweighting method compared favorably to the standard VES reweighting, as well as to current state-of-the-art reweighting options introduced for metadynamics simulations that estimate c(t) by integration over the collective variables. For further gains in computational speed and accuracy, we also introduce analytical solutions for c(t), as well as offering further insight into its features by approximative analytical expressions in the high-temperature regime.

The impact of the cation field strength (CFS) of the glass network-modifier cations on the structure and properties of borosilicate glasses (BS) were examined for a large ensemble of mixed-cation (R/2)M₍₂₎O–(R/2)Na₂O–B₂O₃–KSiO₂ glasses with M⁺ ={Li⁺, Na⁺, K⁺, Rb⁺} and M²⁺ ={Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺} from four series of {K, R} combinations of K = n(SiO₂)/n(B₂O₃) = {2.0, 4.0} and R =[n(M₍₂₎O) ​+ ​n(Na₂O)]/n(B₂O₃) = {0.75, 2.1}. Combined with results from La³⁺ bearing glasses enabled the probing of physical-property variations across a wide CFS range, encompassing the glass transition temperature (T_g), density, molar volume and compactness, as well as the hardness (H) and Young's modulus (E). We discuss the inferred composition–structure/CFS–property relationships. Each of T_g, H, and E revealed a non-linear dependence against the CFS and a strong Tg/H correlation, where each property is maximized for the largest alkaline-earth metal cations, i.e., Sr²⁺ and Ba²⁺, along with the high-CFS La³⁺ species. The ¹¹B MAS NMR-derived fractional BO₄ populations decreased linearly with the average M^z+/Na⁺ CFS within both K–0.75 glass branches, whereas the NBO-rich K–2.1 glasses manifested more complex trends. Comparisons with results from RM₂O–B₂O₃–KSiO₂ glasses suggested no significant “mixed alkali effect”.

For a series of conventional soda-lime-silicate glasses with increasing Al₂O₃ content, we investigated the thermal, mechanical, and structural properties before and after K⁺-for-Na₊ ion-exchange strengthening by exposure to molten KNO₃. The Al-for-Si replacement resulted in increased glass network polymerization and lowered compactness. The glass transition temperature (T_g), hardness (H) and reduced elastic modulus (E_r), of the pristine glasses enhanced monotonically for increasing Al₂O₃ content. H and E_r increased linearly up to a glass composition with roughly equal stoichiometric amounts of Na₂O and Al₂O₃ where a nonlinear dependence on Al₂O₃ was observed, whereas H and E_r of the chemically strengthened (CS) glasses revealed a strictly linear dependence. T_g, on the other hand, showed linear increase with Al-for-Si for pristine glasses while for the CS glasses a linear to nonlinear trend was observed. Solid-state ²⁷Al nuclear magnetic resonance (NMR) revealed the sole presence of AlO₄ groups in both the pristine and CS glasses. ²³Na NMR and wet-chemical analysis manifested that all Al-bearing glasses had a lower and near-constant K⁺-for-Na⁺ ion exchange ratio than the soda-lime-silicate glass. Differential thermal analysis of CS glasses revealed a “blurred” glass transition temperature (T_g) and an exothermic step below T_g; the latter stems from the relaxation of residual compressive stresses. The nanoindentation-derived hardness at low loads and <5 mol% Al₂O₃ showed evidence of stress relaxation for prolonged ion exchange treatment. The crack resistance is maximized for molar ratios n(M₍₂₎O)/n(Al₂O₃)≈1≈1 for the CS glasses, which is attributed to an increased elastic energy recovery that is linked to the glass compactness

Interactions between biomolecules and structurally disordered calcium phosphate (CaP) surfaces are crucial for the regulation of bone mineralization by noncollagenous proteins, the organization of complexes of casein and amorphous calcium phosphate (ACP) in milk, as well as for structure–function relationships of hybrid organic/inorganic interfaces in biomaterials. By a combination of advanced solid-state NMR experiments and metadynamics simulations, we examine the detailed binding of O-phospho-l-serine (Pser) and l-serine (Ser) with ACP in bone-adhesive CaP cements, whose capacity of gluing fractured bone together stems from the close integration of the organic molecules with ACP over a subnanometer scale. The proximity of each carboxy, aliphatic, and amino group of Pser/Ser to the Ca²⁺ and phosphate species of ACP observed from the metadynamics-derived models agreed well with results from heteronuclear solid-state NMR experiments that are sensitive to the ¹³C–³¹P and ¹⁵N–³¹P distances. The inorganic/organic contacts in Pser-doped cements are also contrasted with experimental and modeled data on the Pser binding at nanocrystalline HA particles grown from a Pser-bearing aqueous solution. The molecular adsorption is driven mainly by electrostatic interactions between the negatively charged carboxy/phosphate groups and Ca²⁺ cations of ACP, along with H bonds to either protonated or nonprotonated inorganic phosphate groups. The Pser and Ser molecules anchor at their phosphate/amino and carboxy/amino moieties, respectively, leading to an extended molecular conformation across the surface, as opposed to an “upright standing” molecule that would result from the binding of one sole functional group.

Conventional structural models of aluminosilicate (AS) glasses assume that there are no direct bonds between four-coordinated Al (Al^[4]) species and non-bridging oxygen (NBO) anions, along with the (near) absence of Al^[4]–O–Al^[4] linkages (the “Loewenstein Al avoidance rule”). Yet, accumulating evidence from advanced solid-state NMR experiments on AS glasses that incorporate (moderately) high field-strength cations, notably so those of rare-earth metals (RE³⁺), reveal significant Al^[4]–NBO and Al^[4]–O–Al^[4] populations. Here we review such NMR experimentation that enable a direct probing of these “exotic” structural motifs. We also re-analyze and discuss previously presented experimental and modeling results of a large set of RE₂O₃–Al₂O₃–SiO₂ glasses with RE={La, Y, Lu, Sc}, where the structure/composition-related parameters that dictate the degrees of Al^[4]–NBO and Al^[4]–O–Al^[4] bonding in AS glasses are identified, leading to new quantitative composition–structure relationships. Moreover, for a given AS composition, criteria are presented for whenever Al^[4]–O–Al^[4] linkages must exit in its glass structure.