An extended topological model for binary phosphate glasses

Abstract

We present a topological model for binary phosphate glasses that builds on the previously introduced concepts of the modifying ion sub-network and the strength of modifier constraints. The validity of the model is confirmed by the correct prediction of Tg(x) for covalent polyphosphoric acids where the model reduces to classical constraint counting. The constraints on the modifying cations are linear constraints to first neighbor non-bridging oxygens, and all angular constraints are broken as expected for ionic bonding. For small modifying cations, such as Li(+), the linear constraints are almost fully intact, but for larger ions, a significant fraction is broken. By accounting for the fraction of intact modifying ion related constraints, qγ, the Tg(x) of alkali phosphate glasses is predicted. By examining alkali, alkaline earth, and rare earth metaphosphate glasses, we find that the effective number of intact constraints per modifying cation is linearly related to the charge-to-distance ratio of the modifying cation to oxygen.

Response to “Comment on ‘A model for phosphate glass topology considering the modifying ion sub-network”’ [J. Chem. Phys. 142, 107103 (2015)]

“…Sidebottom believes that his constraint onset temperature (T γ = 590 K 2 ) of modifier-related γ constraints is too high relative to the T g (x) of xNa 2 O (1 − x)P 2 O 5 . Our recent work 15 concurs with this assessment, and for sodium phosphates, the γ constraints are only partially intact at T g . However, some γ constraints could explain the high T g of sodium phosphate glasses.…”

Modifier Interaction and Mixed-Alkali Effect in Bond Constraint Theory Applied to Ternary Alkali Metaphosphate Glasses

“…In this work, we will be using the former interpretation for two main reasons: first, it provides internal consistency on how the modifier constraints are treated, being considered either completely broken or completely intact, the same as all other constraints present in the system. Second, and more importantly, the distribution of modifier sites according to the calculations from Hermansen et al (2014b) does not seem to correspond to experimental data. According to Hermansen et al (2014b), the number of modifier constraints is given by 2 × X R (x) for x ≤ x cr and CN R × X R (x − x crit ) + 2 × X R (x crit ) for x > x crit , where X R (x) is the modifier's molar fraction, x is the compositional variable as in xR 2 O × (1 − x)P 2 O 5 and x crit is Hoppe's critical composition (x crit = ν/CN R , with the modifier valency ν) (Hoppe, 1996), above which the number of doublebonded oxygens is not enough to fully coordinate the modifier ions, which in consequence begin to share non-bridging oxygens and effectively repolymerize the phosphate network.…”

“…Second, and more importantly, the distribution of modifier sites according to the calculations from Hermansen et al (2014b) does not seem to correspond to experimental data. According to Hermansen et al (2014b), the number of modifier constraints is given by 2 × X R (x) for x ≤ x cr and CN R × X R (x − x crit ) + 2 × X R (x crit ) for x > x crit , where X R (x) is the modifier's molar fraction, x is the compositional variable as in xR 2 O × (1 − x)P 2 O 5 and x crit is Hoppe's critical composition (x crit = ν/CN R , with the modifier valency ν) (Hoppe, 1996), above which the number of doublebonded oxygens is not enough to fully coordinate the modifier ions, which in consequence begin to share non-bridging oxygens and effectively repolymerize the phosphate network. One can see that according to these equations, even at the metaphosphate composition (x = 0.5), there would still be a finite number of modifiers that should be surrounded by double-bonded oxygens since 2 × R(x crit ) > 0, but from 31 P NMR measurements, it is known that at the metaphosphate composition there are no (or almost no) Q 3 groups and, therefore, double-bonded oxygens (Brow, 2000) and also NMR from the modifiers does not show evidence for more than one site (Schneider et al, 2013).…”

“…This adaptation was achieved by the introduction of the characteristic "constraint strengths" to the model, for which there are now two ways of implementation: in our previous work , we argue that the "constraint strength" defined as the ratio between the number of constraints each modifier R adds to the system (K R ) and its coordination number (CN R ) represents the number of constraints each modifier/non-bridging oxygen bond adds to the system, with the caveat that the numbers are relative to the absolute strength of all other constraints which are assumed to be equal to unity. Alternatively, Hermansen et al (2014b) argue that the "constraint strength" (q γ in this notation) also represents the fraction of the modifier constraints that are still intact at the temperature in question. Both approaches result in equivalent glass transition temperature predictions for the studied binary phosphate glasses and both "constraint strength" values are linearly dependent on the Coulombic forces between the modifiers and non-bridging oxygens (Hermansen et al, 2014b;.…”

“…Alternatively, Hermansen et al (2014b) argue that the "constraint strength" (q γ in this notation) also represents the fraction of the modifier constraints that are still intact at the temperature in question. Both approaches result in equivalent glass transition temperature predictions for the studied binary phosphate glasses and both "constraint strength" values are linearly dependent on the Coulombic forces between the modifiers and non-bridging oxygens (Hermansen et al, 2014b;. In this work, we will be using the former interpretation for two main reasons: first, it provides internal consistency on how the modifier constraints are treated, being considered either completely broken or completely intact, the same as all other constraints present in the system.…”