Non‐Arrhenius and non‐WLF kinetics in food systems

Abstract

AbstractThe classic Arrhenius and WLF equations are commonly used to describe rate–temperature relations in food and biological systems. However, they are not unique models and, because of their mathematical structure, give equal weight to rate deviations at the low‐ and high‐temperature regions. This makes them particularly useful for systems where what happens at low temperatures is of interest, as in spoilage of foods during storage, or where the effect is indeed exponential over a large temperature range, as in the case of viscosity. There are systems, however, whose activity is only noticeable above a certain temperature level. A notable example is microbial inactivation, for which these two classical models must be inadequate simply because cells and spores are not destroyed at ambient temperature. For such systems a model that identifies the temperature level at which the rate becomes significant is required. Such an alternative model is Y = ln{1 + exp[c(T − T c)]} m, where Y is the rate parameter in question (eg a reaction rate constant), Tc is the marker of the temperature range where the changes accelerate, and c and m are constants. (When m = 1, Y at T ≫ Tc is linear. When m ≠ 1, m is a measure of the curvature of Y at T ≫ Tc.) This model has at least a comparable fit to published rate–temperature relationships of browning and microbial inactivation as well as viscosity–temperature data previously described by the Arrhenius or WLF equation. This alternative log logistic model is not based on the assumption that there is a universal analogy between totally unrelated systems and simple chemical reactions, which is explicitly assumed when the Arrhenius equation is used, and it has no special reference temperature, as in the WLF equation, whose physical significance is not always clear. It is solely based on the actual behaviour of the examined system and not on any preconceived kinetics.© 2002 Society of Chemical Industry