# Parameterizing Temperature-Viscosity Relations

Parameterizing Temperature-Viscosity Relations

The adjustable parameters of six temperature-viscosity models are estimated from two or three experimental temperature-viscosity data points.

The models are the traditional Arrhenius model (one parameter); a modified Arrhenius model (two parameters); the Williams–Landel–Ferry (WLF) and Vogel–Tammann–Hesse (VTF) equations (two and three parameters, respectively); and two ad hoc hybrid models, a reciprocal power law (2) and an exponential power law (two parameters each).

The first estimate is obtained by using the chosen model's parameter sliders to match a reconstructed temperature-viscosity curve with the two or three experimental points. You can examine the parameter slider positions once a visual match is reached. Except for the Arrhenius model, where the activation energy can be calculated analytically from two points, the estimated values so obtained are used as initial guesses for the numerical solution of three simultaneous nonlinear equations to extract the best model parameter estimates, using statistical criteria. Although it has been shown that the modified Arrhenius, WLF and VTF equations are three different mathematical expressions of the very same model, they are all shown.

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