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

Other forms of the k(T) function have been proposed (Kwolek and Bookwalter,
1971) like linear, power and hyperbolic equations, but over a wide range of temperatures,
the Arrhenius equation gave as good or better correlation.
Eyring's equation was utilized in the pharmaceutical industry (Kirkwood,1977):
ln k = ln(k B /h) + S/R - H/RT + ln T (34)
where H is the heat of activation, h is the Planck constant, k B the Boltzmann constant and
S is the entropy. Eyring's equation was applied to calculate the enthalpy/entropy
compensation in food reactions (Labuza, 1980a)
Theoretical equations based on the
collision theory and the activated complex theory that introduce an additional temperature
term to the Arrhenius relation were also discussed by Labuza (1980a). An example of
such an equation is:
k = k' T n exp (- E A
RT ) (35)
where k' the preexponential factor and n a constant with value between 0 and 1.
It was concluded that the contribution of these terms is negligible at the temperatures
relevant to food processing and storage.
Nevertheless, there are factors relevant to food and food quality loss reactions
that can cause significant deviations from an Arrhenius behavior with temperature. (Labuza
and Riboh, 1982). Phase changes are often involved. Fats may change to the liquid state
contributing to the mobilization of organic reactants or vice-versa (Templeman et al., 1977).
In frozen foods the effect of phase change of the water of the food is very pronounced in
the immediate subfreezing temperature range. Generally, as freezing proceeds and the
temperature is lowered, the reaction rate in nonenzymatic frozen systems follows a
common pattern: (a) just below the initial freezing point the rate increases (in an almost
discontinuous fashion) to values well above those obtained in the supercooled state at the
same temperature; (b) passes through a maximum; and (c) finally declines at lower
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