TMAP DMTA TTS WLF

WLF and TTS

Williams-Landel-Ferry (WLF) is a model for implementation of Time-Temperature Superposition (TTS) principle.

Time-Temperature Suprposition priciple can apply to Thermp-Rheologically Simple (TRS) materials. TTS suggests that in log-log scale of viscoelstic prperties against frequency (or rate)

WLF has the following form:

$\log (a_{T}) = - \frac{C_{1} (T_{-} T_{r})}{C_{2} + (T_{-} T_{r})}$

In the above equation, C₁ and C₂ are empirical paramters (to be determined from testing) and T_r is the reference temperature.

On suggestion is that when T_r=T_g, where T_g is the glass transition temperature of the material, C₁=17.4 and C₂=51.6 .

Van Krevelen recommendation is that T_r=T_g+43, C₁=8.9 and C₂=101.6 .

From the data : T_r=25°C, C₁=40 and C₂=130 K could be suggested.

Below an interactive tool is presented for estimation of parameters of the WLF equation.

Try controls like sliders or use the input boxes to change parmaters.

To view original i.e. unshifted test data, simply set C₁=0 using the controls.

Interactive WLF Fitting for Frequency Sweep Data From DMA Testing of Elium 150-50

T_r

°C

C₁

C₂