Kinetics of water freezing in mesopores determined by differential scanning calorimetry

The manuscript considers the kinetics of water freezing in mesopores of gamma aluminum oxide with the average pore diameter equal to 7.8 nm, investigated using differential scanning calorimetry. Four cooling rates: 1.0, 3.0, 5.0 and 10.0 °C/min are tested. The series of experiments are performed in order to determine the reaction kinetics, which appears to be independent of the cooling rate. The isoconversional method is used to determine the activation energy. The pre-exponential factor and reaction model are estimated using the methodology proposed by Málek. The Å esták-Berggren model gives the most reliable approximation of the conversion function. Additionally we apply the procedure proposed lastly by Arshad and Maaroufi to confirm the proper selection of the kinetic model. We also find the relation between parameters of empirical Å esták-Berggren model and phenomenological Johnsom-Mehl-Avrami model. Moreover, we perform very slow cooling and heating test assuming that the temperature rate is equal to 0.1 °C/min. For such a slow test we could assume that ice grows much faster than temperature changes, therefore the equilibrium between ice and water exists at any temperature. Based on the results obtained for the slowest test and applying Gibbs-Thompson equation we estimate the pore distribution.