Snapshot 1:
versus
where
and
Snapshot 2:
versus
where
and
Snapshot 3:
versus
where
and
and
The original WLF model can be written as
, where
is the shift factor,
is a reference temperature in °K, and
and
are experimentally determined constants (
is dimensionless and
is in °K). When the arbitrary reference temperature is shifted to the glass transition temperature
, the equation becomes
, where
and
, with
[1].
The WLF model's authors suggested that in the absence of experimental data one could use
and
as first approximations. These values were derived by averaging the experimental values of several rubbery polymers and are widely known as the WLF model's universal constants.
In this Demonstration, experimentally determined constants
and
, the reference temperature
, and the polymers or food's glass transition temperature
are entered with sliders. The program then calculates the corresponding
and
and displays, on the same graph, the resulting
versus
relationship superimposed on that produced with the universal constants. The two curves, together with the calculated values of
and
, are presented in the forms of
versus
(top) and
versus
(bottom) whose ranges can also be selected with sliders. Notice that even for the same polymer, the observed glass transition temperature
can vary dramatically depending on the method of its determination, the test's conditions, and the heating or cooling rate [2, 3].
Note that not all combinations of slider-entered values describe a realistic
versus
relationship. When this occurs, all panel output is replaced by the message "unrealistic entries".
[1] M. Peleg, "On the Use of the WLF Model in Polymers and Foods,"
Critical Reviews in Food Science and Nutrition,
32(1), 1992 pp. 59–66. doi:
10.1080/10408399209527580.
[2] R. J. Seyler, ed.,
Assignment of the Glass Transition, Philadelphia: American Society of Testing Materials, 1994.
[3] E. Donth,
The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials, Berlin
: Springer–Verlag, 2001.
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