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The meaning of the “universal” WLF parameters of glass-forming polymer liquids



Jack F. Douglas, Jacek Dudowicz, Karl Freed


Although the Williams-Landell-Ferry (WLF) equation for the segmental relaxation time tau of glass forming materials is one of most commonly encountered relations in polymer physics, the molecular basis for this equation is not well understood. The WLF equation is often claimed to be equivalent to the Vogel-Fulcher-Tammann (VFT) equation, even though the WLF expression for the segmental relaxation time tau (T) contains no explicit dependence on the fragility parameter D of the VFT equation, while the VFT equation lacks any explicit reference to the glass transition temperature Tg, the traditionally chosen reference temperature in the WLF equation. The observed approximate universality of the WLF parameters C1 and C2 implies that tau(T) depends only on T − Tg, a conclusion that seems difficult to reconcile with the VFT equation where the fragility parameter D largely governs the magnitude of tau(T). The current paper addresses these apparent inconsistencies first by evaluating the macroscopic WLF parameters C1 and C2 from the generalized entropy theory (GET) of glass-formation and then by determining the dependence of C1 and C2 on the microscopic molecular parameters (including the strength of the cohesive molecular interactions and the degree of chain stiffness) and on the molar mass of the polymer. Attention in these calculations is restricted to the temperature range (Tg
Journal of Chemical Physics


Douglas, J. , Dudowicz, J. and Freed, K. (2015), The meaning of the “universal” WLF parameters of glass-forming polymer liquids, Journal of Chemical Physics (Accessed May 27, 2024)


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Created January 7, 2015, Updated June 2, 2021