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Dudowicz J, Douglas JF, Freed KF. The meaning of the "universal" WLF parameters of glass-forming polymer liquids. J Chem Phys. 2015;142(1):014905doi: 10.1063/1.4905216.
Dudowicz, J., Douglas, J. F., & Freed, K. F. (2015). The meaning of the "universal" WLF parameters of glass-forming polymer liquids. The Journal of chemical physics, 142(1), 014905. https://doi.org/10.1063/1.4905216
Dudowicz, Jacek, et al. "The meaning of the "universal" WLF parameters of glass-forming polymer liquids." The Journal of chemical physics vol. 142,1 (2015): 014905. doi: https://doi.org/10.1063/1.4905216
Dudowicz J, Douglas JF, Freed KF. The meaning of the "universal" WLF parameters of glass-forming polymer liquids. J Chem Phys. 2015 Jan 07;142(1):014905. doi: 10.1063/1.4905216. PMID: 25573581.
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J Chem Phys. 2015 Jan 07;142(1):014905. doi: 10.1063/1.4905216.

The meaning of the "universal" WLF parameters of glass-forming polymer liquids.

The Journal of chemical physics

Jacek Dudowicz, Jack F Douglas, Karl F Freed

Affiliations

  1. The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
  2. Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.

PMID: 25573581 DOI: 10.1063/1.4905216

Abstract

Although the Williams-Landell-Ferry (WLF) equation for the segmental relaxation time τ(T) of glass-forming materials is one of the most commonly encountered relations in polymer physics, its molecular basis 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 τ(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((g)) and C2((g)) implies that τ(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 τ(T). The current paper addresses these apparent inconsistencies by first evaluating the macroscopic WLF parameters C1((g)) and C2((g)) from the generalized entropy theory of glass-formation and then by determining the dependence of C1((g)) and C2((g)) 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 < T < Tg + 100 K), where both the WLF and VFT equations apply.

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