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, Tg, and the melting point, Tm) 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 T0, maintaining A=-5 fixed (in Pa.s) to reduce the number of adjustable parameters. Regarding this restriction, the VFTH formula has shown to adjust very well to experimental data in wide temperature range. Previous assertions revealed that there is statistical correlation between B and T0. Principal Component Analysis (PCA) was used in the present study to verify the correlation between the B and T0 parameters [J. F. Mano, E. Pereira, J. Phys. Chem. A 108 (2004) 10824], as well as between Tg and Tm. 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, T0 and Tg as the main parameters for the fragility indexes m=d(log10eta)/d(Tg/T) at T=Tg and D = B/T0, where eta is the viscosity and T the absolute temperature.