A probabilistic approach to model the nonisothermal nucleation of triacylglycerol melts

Crystallization studies are usually performed under isothermal conditions. Kinetic parameters characterizing the isothermal nucleation and growth processes can be obtained using classical nucleation and growth models. However, crystallization regimes found in nature, as well as those used in food and pharmaceutical processing, are rarely isothermal. Focusing on the nucleation stage, the approach followed in this work was to define a new parameter to characterize the driving force of nucleation, the supercooling-time exposure (beta), which not only depends on the difference between the melting temperature (T-m) and the onset temperature of nucleation (T-c) Delta T-c but also on the induction time of nucleation, t(c) and therefore the cooling rate (phi), namely, beta = (1/2)Delta T-ctc = Delta T-c(2)/2 phi. An exponential probability density function of the values of beta was utilized to model changes in nucleation rate as a function of beta the form J/J(max) = ke(-k root beta). From this parametrization procedure, the energy of activation for the nucleation process in palm oil, milkfat, and other palm oil based fats could be estimated.