The basics of WLF theory
WLF Isotherm Plots

One aspect of WLF theory is the ability to construct isotherms on mechanical property vs. testing time scale plots over large time scales.

Data taken at higher temperatures on a rapid time scale can be used to determine data at lower temperatures on a much slower time scale. This is an abstract concept, and is perhaps best understood by giving an example. Imagine that you have a polymer, and you are interested in tensile strength, measured on an Instron. You know that mechanical property results vary with the speed at which the Instron pulls the sample apart. You can pull a range of speeds, maybe from several centimeters in a second, to speeds that take minutes to travel a centimeter. This is a mechanical limitation. But you can repeat this test at several temperatures, and from these you can extrapolate Mechanical data at speeds either too fast for your Instron, or two slow for you to wait for.

A graph of actual data that was worked up in this manner is available.

Four grey isotherms of data are shown to the left. Some mechanical property is tested (y-axis) as a function of testing timescale (x-axis.)
For Instron tests, testing timescale would be how fast the sample was pulled.
Different temperatures are used, and the results for each temperature constitutes an isotherm.
As you can see, there are four isotherms in the graph below.

Color is added to the isotherms to show where the slopes of the lines are similar (i.e., where the isotherms can be joined to form a continuous function, as shown in the polymer texts.) Notice that the yellow part on one isotherm corresponds to the yellow part on another isotherm.
It was necessary to put more than one color on an isotherm to drive home the idea that the information towards the end of one isotherm relates to the information at the start of the next.
When adding the color, the choice of where to stop one color and start another was arbitrary.

The colorized isotherms are shown again, only this time all the isotherms are attached to the isotherm on top to form a continuous "long function." This theoretical extrapolation would be reproduced if the tests were carried out at the temperature of this top isotherm over the entire time scale. Remember that the x axis is the time scale.

If you think about it, it makes sense that you can connect isotherms to any other isotherms to form as many "long functions" as there are isotherms in the original data. This is shown below. Note that there are four "long functions" and that we started with four isotherms. The grey shows you the data actually collected, and the colorized data is the information gained from extrapolation.

Last Update- July 4, 1995- wld

The basics of WLF theory WLF Isotherm Plots

The basics of WLF theory
WLF Isotherm Plots