the handbook of food engineering practice crc press chapter 10 ...

A number of recent publications debate the relative validity of the Arrhenius and
WLF equations in the rubbery state namely in the range 10 to 100° C above Tg. This
dilemma may very well be an oversimplification. (Karel,1993). As mentioned above,
processes affecting food quality that depend on viscosity changes (e.g. crystallization,
textural changes) fit the WLF model. However chemical reactions may be either kinetically
limited, when kαD or dependent on both when k and αD of the same
order of magnitude. In the latter case the effective reaction rate constant can be expressed
k
as . k in most cases exhibits an Arrhenius type temperature dependence and D
1+k/αD
has been shown in many studies to either follow the Arrhenius equation with a change in
slope at T g or to follow the WLF equation in the rubbery state and especially in the range
10 to 100° C above T g . The value of the ratio k/αD defines the relative influence of k and
D and determines whether the deteriorative reaction can be successfully modeled by a
single Arrhenius equation for the whole temperature range of interest or a break in slope
occurs at T g with a practically constant slope above T g or with a changing slope in which
case the WLF equation will be used for the range 10 to 100° C above T g . In complex
systems where multiple phases and reaction steps can occur, successful fit to either model
has to be considered as an empirical formula for practical use and not an equation
explaining the mechanism or phenomenon.
When several reactions with different E A 's are important to food quality, it is
possible that each of them will predominantly define quality for a different temperature
range. Thus, for example, if quality is measured by an overall flavor score, the quality
change rate vs. 1/T will have a different slope in each of these regions. This is shown
schematically in Figure 5. A typical example of such a behavior is quality loss of
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