The Connection Between the Parameters of WLF Equation and of Arrhenius Equation

Abstract

AbstractThe description of the change in characteristic temperatures of thermomechanical and viscoelastic properties of polymers and elastomers with deformation frequency or of temperature dependence of polymer properties is widely achieved by two equations: (1) the Williams‐Landel‐Ferry (WLF) equation and (2) the Arrhenius equation. Mostly the WLF equation is used. Often the distinction between the two descriptions is based on the argument: if volume processes play the key role, then WLF equation is the right one, if thermally activated processes play the key role, then Arrhenius equation is the right one. Both equations are based on the activation of processes, and always the temperature is the variable, which activate the processes. Both descriptions are methods to parameterize the temperature dependence of properties or the change of characteristic temperatures, as glass‐rubber transition temperature, with deformation rate. Also, the so‐called ‘volume processes’ are controlled by temperature, but the thermal activation can be small in energy to initiate the change in spatial position from one site to another for a molecule. This means both descriptions should be congruent. In this article, the congruence is shown and the relation between WLF parameters and Arrhenius parameters will be established. For this, a slight modification of the usual Arrhenius equation is necessary. Also, other descriptions are discussed in short: Doolittle equation and Vogel‐Fulcher equation, they were or are used to describe the change of viscosity with temperature in melts or solutions.