is the decadic logarithm of the WLF shift factor,[2] T is the temperature, Tr is a reference temperature chosen to construct the compliance master curve and C1, C2 are empirical constants adjusted to fit the values of the superposition parameter aT.
The equation can be used to fit (regress) discrete values of the shift factor aT vs. temperature.
Here, values of shift factor aT are obtained by horizontal shift log(aT) of creep compliance data plotted vs. time or frequency in double logarithmic scale so that a data set obtained experimentally at temperature T superposes with the data set at temperature Tr.
[3] When the constants are obtained with data at temperatures below Tg, negative values of C1, C2 are obtained, which are not applicable above Tg and do not represent Arrhenius behavior.
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 of the instrumentation, such as dynamic mechanical analyzer (DMA).
While the time span of a TTSP master curve is broad, according to Struik,[4] it is valid only if the data sets did not suffer from ageing effects during the test time.
Even then, the master curve represents a hypothetical material that does not age.
[4] needs to be used to obtain useful prediction for long term time.
[5] Having data above Tg, it is possible to predict the behavior (compliance, storage modulus, etc.)
of viscoelastic materials for temperatures T>Tg, and/or for times/frequencies longer/slower than the time available for experimentation.
With the master curve and associated WLF equation it is possible to predict the mechanical properties of the polymer out of time scale of the machine (typically
The Williams-Landel-Ferry model, or WLF for short, is usually used for polymer melts or other fluids that have a glass transition temperature.
, we get and Van Krevelen recommends to choose and Using such universal parameters allows one to guess the temperature dependence of a polymer by knowing the viscosity at a single temperature.