On modeling changes in food and biosolids at and around their glass transition temperature range

Temperature-induced mechanical and other changes in biosolids are regulated by three types of kinetics, depending on whether the material is in the glassy state, undergoing a transition, or fully plasticized. The transition itself can take place over a considerable temperature range, which in many food and biological systems happens to be the most pertinent to their functionality and stability. At the transition onset, the plot of stiffness vs. temperature has a downward concavity. It is reversed only at an advanced stage of plasticization after much of the stiffness has already been lost. Consequently, the WLF, Arrhenius, or any other model that implies a continuous upward concavity cannot account for changes in the transition region, and it is unsafe to use them to predict properties through extrapolation. The mechanical changes in the transition region can be described by a model with the mathematical structure of Fermi's function. Its applicability has been demonstrated with published data on a variety of foods and biosolids. Because the plot of stiffness vs. moisture, or water activity, has the same general shape as that of the stiffness vs. temperature plot, it too can be described by a model with the same mathematical format. Because moisture lowers the transition center temperature in a manner that can be described by a simple algebraic expression, the combined effects of temperature and moisture can be incorporated into a single general model. The latter can be used to create three-dimensional displays of the stiffness-temperature-moisture characteristic relationships of biosolids at and around their transition. At temperatures well above that of the transition, though, where a plot of log stiffness vs. temperature has a clear upper concavity, this model is no longer applicable, and the changes are better described by the WLF or an alternative model.