Viscosity of strong and fragile glass-forming liquids investigated by means of principal component analysis

Abstract

The Vogel-Fulcher-Tammann-Hesse (VFTH) equation has been the most widespread tool for describing the temperature dependence with viscosity for strong, moderate and fragile glass-forming liquids. In this work, the VFTH equation was applied over a wide temperature range (between the glass transition temperature, T g , and the melting point, T m ) for 38 oxide glasses, considering simple, binary and ternary compositions of silicate and borate systems. The Levenberg-Marquart non-linear fitting procedure was used to assess VFTH viscosity parameters B and T 0 , maintaining A ¼ À5 fixed (in Pa Á s) to reduce the number of adjustable parameters. Regarding this restriction, the VFTH formula has shown to adjust very well to experimental data in a wide temperature range. Previous assertions revealed that there is statistical correlation between B and T 0 . Principal component analysis (PCA) was used in the present study to verify the correlation between the B and T 0 parameters [J. F. Mano, E. Pereira, J. Phys. Chem. A 108 ( 2004) 10824], as well as between T g and T m . In brief, PCA is a mathematical method aimed at reorganizing information from data sets. The results have shown that it is possible to map either borate (and almost fragile) or silicate (usually strong up to near fragile) systems. As a statistical tool, PCA justifies the use of B, T 0 and T g as the main parameters for the fragility indexes m ¼ dðlog 10 ZÞ dðT g =TÞ T¼Tg and D ¼ B/T 0 , where Z is the viscosity and T the absolute temperature.

Connecting Glass-Forming Fragility to Network Topology

“…The values of f 4 , f 3 , and f 2 , for example, are set by values taken directly from data tables in the NMR study (Maekawa et al, 1991). For the SiO 2 glass, the minute fraction of rings (f R = 0) is ignored while the values of f F = 20%, f ST = 30%, and f ES = FIGURE 10 | The fragility indices of SiO 2 and selected sodium and potassium silicate glasses (Poole, 1949;Nascimento and Aparicio, 2007;Nemilov, 2007) plotted as a function of the connectivity coarse-grained to include IRO structures as described in the text. Also shown are the data from Figure 4 for both the chalcogenides (plotted as a function of the average bond per atom) and the alkali phosphates (plotted as a function of the average BO per phosphate).…”

Low-Temperature Excess Specific Heat in Oxide Glasses: Comprehensive Study of Thermometrically Observed Boson Peak

“…Glass properties (e.g., glass-transition temperature, fragility, and elasticity) may also depend on the ionic radius of AAEM species. 31,32) Since the BP feature also correlates with these physical properties, the dependence found in this study of the BP on composition provides information that elucidates the nature of the BP.…”

Bond Strength—Coordination Number Fluctuation Model of Viscosity: An Alternative Model for the Vogel-Fulcher-Tammann Equation and an Application to Bulk Metallic Glass Forming Liquids

“…In order to check the exact fitting between the VFT equation and the BSCNF model, in this analysis, we used the collection of fitting parameters by the VFT equation given in reference [4], where the values of B VFT , T 0 , T g , and the fragility index m for various oxide glass forming materials are provided. The numerical values of both, ln( η T g / η 0 ) calculated by Equation 6, and the best fitting parameters ( B * , C * ) determined by the BSCNF model, are also indicated in Table 1.…”

“…The Vogel-Fulcher-Tammann (VFT) equation [1,2,3] is one of the most commonly used expressions for the analysis of the temperature dependence of viscosity [4,5,6,7,8,9], relaxation time [5,8,10,11], diffusion coefficient [5,6,7,9], and electrical conductivity [5,6,7], etc . The application of the VFT equation covers a wide field of research [12].…”

“…Such systems are called fragile system. To describe the behavior observed in fragile systems, the VFT equation has often been employed [4,6,7]. Although the physical background of the VFT equation has been fully discussed from the theoretical point of view [10,22], there might be some discrepancies between the experimental data and its interpretation when the actual data and the VFT equation are compared.…”