Methods for food shelf life determination and prediction - Oxidation in Foods and Beverages and Antioxidant Applications - page 212

In order to find out a feasible predictive model, Calligaris et al. (2004)
proposed a modified Arrhenius equation that can be used to predict the
temperature dependence of the oxidation rate in partially crystallised matrices:
k k 0 k e ÿE a =RT 9:8

where k is a corrective factor included into the Arrhenius equation to take into
account the influence of variables, other than temperature, which significantly
affect the reaction rate in the partially crystallized matrix. Since at a given
temperature the rate at which any reaction develops can be considered as the
result of the ratio between driving forces and resistances, k can be defined by
the identification of the proper forces and resistances involved in the Arrhenius
deviation.
Starting from the simplest case, involving only lipid phase transition, the
changes in the relative reactant concentration has been indicated as the main
driving force affecting the oxidation rate (Calligaris et al., 2004). In fact, the
progressive separation of fat crystals gradually leads to an increase in the
reactant concentration (i.e., unsaturated TAGs, O 2 , antioxidants and pro-
oxidants) in the liquid phase surrounding fat crystals causing an unexpected
acceleration of the oxidation rate. In such context it should be remembered that
the phase transition behaviour of triacylglycerols is peculiar due to their
compositional complexity. As temperature decreases, a number of crystallisation
events could take place: the higher saturated fractions firstly crystallize followed
by the more unsaturated ones. In addition, the geometry of the crystals could
greatly differ depending on heating/cooling profile and storage conditions
according to lipid polymorphic properties (Sato, 1999).
In order to quantify the effect of the changes in the reactant concentration as a
consequence of crystallization and build up a predictive model, a concentration
factor (C), defined as the ratio between the liquid fraction (LF) originally present
in the sample and the liquid fraction at selected temperatures, has been
proposed. C value indicates how many times compounds involved in the oxida-
tive process concentrate in the liquid phase as a consequence of crystallization.
A C value equal to 1 indicates that, at the given temperature, crystallization did
not occur and sample concentration remained unchanged. By contrast, C values
higher than 1 indicate that lipid/water partially crystallized at the given tem-
perature leading to a C-times increase in the concentration of the liquid phase.
The liquid fraction (LF) of the oil/fat at selected temperatures could be easily
determined by the partial integration of the melting curve obtained via
differential scanning calorimetry. In such way the enthalpy of the mass melted at
the selected temperature can be computed and compared with the total peak
enthalpy (Fig. 9.7). Table 9.8 shows, as example, the liquid fraction and the
relevant C factor of the fat extracted from biscuits at different temperatures.
After the computation of the C factor at different temperatures, such value
can be integrated in the modified Arrhenius equation (9.8). Figure 9.8
graphically shows the temperature dependence of the new dependent variable