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

: Bohn, Manfred

Fulltext ()

Propellants, explosives, pyrotechnics 44 (2019), No.6, pp.696-705
ISSN: 0340-7462
ISSN: 0721-3115
ISSN: 1521-4087
Journal Article, Electronic Publication
Fraunhofer ICT ()
WLF equation; Arrhenius equation; modified Arrhenius equation; Doolittle equation; Vogel-Fulcher equation

The description of the change in characteristic temperatures of thermomechanical and viscoelastic proper-ties of polymers and elastomers with deformation frequency or of temperature dependence of polymer proper-ties 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 be-tween 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 keyrole, 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.