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The WLF equation is a consequence of time–temperature superposition (TTSP), which mathematically is an application of Boltzmann's superposition principle. It is TTSP, not WLF, that allows the assembly of a compliance master curve that spans more time, or frequency, than afforded by the time available for experimentation or the frequency range ...
The empirical relationship of Williams-Landel-Ferry, [10] combined with the principle of time-temperature superposition, can account for variations in the intrinsic viscosity η 0 of amorphous polymers as a function of temperature, for temperatures near the glass transition temperature T g. The WLF model also expresses the change with the ...
Robert F. Landel (October 10, 1925 – September 10, 2024) was an American physical chemist at the Jet Propulsion Laboratory noted for his contribution to development of the Williams–Landel–Ferry equation, [1] [2] and for a particular form of hyperelastic energy function, the Valanis-Landel form.
The kinetic theory of gases allows accurate calculation of the temperature-variation of gaseous viscosity. The theoretical basis of the kinetic theory is given by the Boltzmann equation and Chapman–Enskog theory, which allow accurate statistical modeling of molecular trajectories.
Ferry was born in Dawson City, Yukon Territory, Canada, [5] and attended a one-room school in Murray, Idaho. [2] At age 19, Ferry received his bachelor of arts degree at Stanford University in 1932. [5] Three years later, he received his Ph.D at Stanford [5] and became a research assistant at Stanford's Hopkins Marine Station. [3] [4]
This hardening follows the Williams-Landel-Ferry equation, not the Arrhenius equation. Organic polymers are thus called fragile glass formers. Silicon glass (e.g., window glass), is in contrast labelled as a strong glass former. Its viscosity changes only very slowly in the vicinity of the glass-transition point T g and follows the Arrhenius ...
This can be particularly useful when working with materials which relax on a long time scale under a certain temperature. The practical application of this idea arises in the Williams–Landel–Ferry equation. Time-temperature superposition avoids the inefficiency of measuring a polymer's behavior over long periods of time at a specified ...
The Vogel–Fulcher–Tammann equation, also known as Vogel–Fulcher–Tammann–Hesse equation or Vogel–Fulcher equation (abbreviated: VFT equation), is used to describe the viscosity of liquids as a function of temperature, and especially its strongly temperature dependent variation in the supercooled regime, upon approaching the glass transition.