Methods for food shelf life determination and prediction - Oxidation in Foods and Beverages and Antioxidant Applications - page 214

Fig. 9.8 Modified Arrhenius plots of apparent oxidation rate of biscuits (Calligaris et
al., 2007a with permission).

By applying a similar approach, modified Arrhenius equations can be
identified for foods containing water undergoing crystallization below 0 ëC. For
instance, in tomato derivatives undergoing carotenoid oxidation, the concentra-
tion of reactants in the unfrozen aqueous solution was assessed by calorimetric
analysis (Manzocco et al., 2006). However, in this case, to obtain an effective
predictive model, beside the C-factor relevant to the water phase, an additional
factor has to be considered in the modified Arrhenius equation. Since oxygen
concentration in the aqueous solution is well-known to increase as temperature
decreases affecting the reaction rate, k has been defined as follows:
k C O 9:9

where O is the oxygen solubility factor defined as the ratio between oxygen
solubility at temperature T and oxygen solubility at 0 ëC. Figure 9.9 shows the
goodness of the fitting of the new dependent variable kC ÿ1 O ÿ1 versus tem-
perature. A similar approach was found to work well even for tomato derivatives
having different water activity.

9.5.4 Other accelerating factors
The Arrhenius model performs well only if temperature really affects the reaction
rate in reasonable times, which is not always the case. For instance, in the case of