Floppy Mode Degeneracy and Decoupling of Constraint Predictions in Super-Cooled Borate and Silicate Liquids

Abstract

The theory of temperature-dependent topological constraints has been used to successfully explain the compositional dependence of glass properties for oxide and non-oxide compositions. It relates the number of topological degrees of freedom with the glass transition temperature through the configurational entropy of the system. Based on this, we estimated the number of degrees of freedom directly from viscosity measurements of binary alkali borate and silicate glasses. Both approaches exhibit a strong decoupling, which we suggest can be traced to the presence of medium-and long-range constraints that are not taken into account by bond constraint counting. The observed variation of the energy barrier for structural rearrangement and floppy mode degeneracy also corroborate our interpretation. We provide evidence that the degeneracy of floppy modes changes with chemical composition and that the parameter K (x ) of the MYEGA viscosity equation could be used to assess changes in the medium-range order.

Activation volume of selected liquid crystals in the density scaling regime

“…Thus, the floppy mode considered as a broken antiparallel doublet involves two unconstrained states (molecules) characterized by the same energy of the breakage of the antiparallel doublet. This simple picture shows that the degeneracy of the floppy mode can be quantified by Ω = 1/2 in terms of the unconstrained state, and then lnΩ is negative, similarly as that evaluated in some cases of recently reported predictions based on the MYEGA model for supercooled borate and silicate liquids 66 . Thus, in case of examined LC systems, the preexponential factor dependent on lnΩ is also negative in Eqs (S21) and (S22) presented in Section S4 in Supplementary Information .…”

“…(S21) earlier postulated 23 for GF liquids in the way outlined in Section S4 in Supplementary Information . In the MYEGA model, the number of floppy modes has been considered as the number of broken constraints 65 66 . If we assume that the intact constraints result in forming the antiparallel doublets, the breakage of such a constraint leading to two unconstrained states (molecules) requires providing a sufficient energy to break the interaction between the molecules forming the antiparallel doublet.…”

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

“…On the other hand, the BCT does not provide the tools to allow for the calculation of the values of constraint strength and γ, so, while they tie in reasonably well with some material properties, in order to use the correct values, one must always resort to use experimental data. Another open question is whether the trend observed in Figure 2 is valid for all modifier pairs and all other glass-forming oxides (such as silicates, borates, and germanates), or if the values of γ depend on the network, the modifiers are embedded within, much like the values of the constraint strength (Rodrigues and Wondraczek, 2015); or if they also depend on the pair of modifiers in question, meaning that the data points for mixed Na-R metaphosphate glasses would be shifted from the Li-R and so on.…”

“…While useful applications of the BCT need detailed structural information, the strength of this approach lies in its simplicity, as only the knowledge of the components' first shell coordination number and a reasonable guess about the relative strength of the constraints considered are required for relatively accurate property prediction. However, the BCT is not without problems, which start already with its basic assumptions (Rodrigues and Wondraczek, 2015) as how to incorporate structural influences beyond the short range (Rodrigues and Wondraczek, 2013). In glass science, one such example is the so-called "mixed-alkali effect" (MAE), where the mixture of two alkali species results in a non-linear variation of several properties, such as ionic conductivity, glass transition temperature, internal friction, and volumetric relaxation (Bunde et al, 2004;Changstrom and Sidebottom, 2008).…”