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The connection between WLF equation and Arrhenius equation

: Bohn, Manfred A.

University of Pardubice:
21th Seminar on New Trends in Research of Energetic Materials, NTREM 2018. Proceedings. Pt.1 : April 18-20, 2018, Pardubice, Czech Republic
Pardubice: University of Pardubice, 2018
ISBN: 978-80-7560-136-0
Seminar on New Trends in Research of Energetic Materials (NTREM) <21, 2018, Pardubice>
Fraunhofer ICT ()

The description of the change of thermomechanical and viscoelastic properties of polymers and elastomers with deformation frequency 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 to initiate for a molecule the change in spatial position from one site to another. 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, Andrade equation and Vogel-Fulcher equation, all were or are used to describe the change of viscosity in melts or solutions with temperature.