Time-temperature equivalence (or superposition) can be applied, for example, in the measurements of linear properties and . Usually, devices allow a measurement within a given interval of angular frequencies. However, when performing measurements at different temperatures, it is possible to expand the interval of angular frequencies. If the relationship between linear properties and temperature is unknown, it is reasonable to assume that the dependence is the same for and . Hence the ratio , when plotted against the angular frequency, will typically have the same shape for different temperatures, though the curves will shift along the horizontal axis. That is, an experiment performed at a lower temperature corresponds to an experiment at a higher temperature within a higher interval of angular frequencies. You can then combine the data by shifting the curves and thereby expand the interval of angular frequencies, possibly beyond the technological limits of the measurement device. Simultaneously, the identification of the corresponding shift factor will characterize the dependence with respect to temperature for subsequent analysis; this is relevant, for example, for the complex viscosity. It is therefore possible to acquire information on the temperature dependence of the properties, as well as to expand the knowledge of linear properties.

To illustrate how time-temperature equivalence can be used, consider the following figure, which shows the measurement of linear properties (thick lines) and (thin lines) for angular frequencies ranging from 10^–2 to 10². The data is measured at four temperatures, represented here in black, blue, magenta, and red.

Figure 9.1: G' and G" vs. Angular Frequency [rad/s]

The next figure shows the properties , for each temperature ranging from black to red. The blue temperature is the reference temperature that will be used to build the master curves.

Figure 9.2: G"/G' vs. Angular Frequency [rad/s]

The curves from the previous figure can be combined into a single curve, as shown in the following figure. The black curve is shifted to the right, while the magenta and red curves are shifted to the left; the shift factors are kept for further evaluation of the temperature dependence of the properties. Combining these four curves into the dashed line enables you to expand the interval of angular frequencies.

Figure 9.3: Combining G"/G' Curves

The shift factors obtained in the previous step can be applied to the linear properties and , in order to obtain the master curves in the figure that follows.

Figure 9.4: Master Curves for G' and G" vs. Angular Frequency [rad/s]

The applicability of the time-temperature equivalence depends on the material considered, and is affected by the actual temperature dependence of the properties. Experience and specialized literature can provide further information.