Data classification with the Vogel–Fulcher–Tammann–Hesse viscosity equation using correspondence analysis

Abstract

The well-known Vogel–Fulcher–Tammann–Hesse equation (VFTH, log 10 η= A+ B/( T− T 0), η in Pa s and T in K) has been extensively used in the description & characterization of cooperative molecular motion by means of the temperature dependence with viscosity, η, e.g., using Angell's classification. Experimental evidence has been pointed out for the statistical correlation between its three adjustable parameters A, B and T 0, which may bring questions on the reliability of fitted VFTH parameters. In this work VFTH equation was applied over a wide temperature range (between glass transition temperature, T g and the melting point, T m) for 38 oxide glasses, considering simple, binary and ternary compositions of silicates and borates systems. These systems include strong, moderate and fragile glass-forming liquids. For this task was used the Levenberg–Marquart non-linear fitting procedure to find viscosity parameters B and T 0, maintaining A=−5 fixed, intending to reduce the number of adjustable parameters. Despite this restriction, the VFTH equation has shown to adjust very well to experimental data in wide temperature range. Simple criteria were developed in the past to characterize glass-forming liquids, one of them (due to Angell) is the strong–fragile classification. In this work we apply correspondence analysis (CA) to verify the correlation between B and T 0 parameters as well as between T g and T m. CA is a descriptive and exploratory technique designed to analyze simple multi-way tables containing some measure of correspondence between rows and columns. From these results is possible to map either borate (and almost fragile) or silicate (usually strong up to near fragile) systems. As a statistical tool, CA corroborates correlation mainly between B and T 0 and justifies the use of B, T 0 and T g as the main parameters for the fragility indexes m= BT g/( T g− T 0) 2 and D= B/ T 0.