PREDICTION OF THE CRYSTALLIZATION ONSET TEMPERATURES OF MOLECULAR LIQUIDS

Abstract

The processes of nucleation and crystallization while cooling are crucial to industry and require specialized models for characterization for process optimization, predictive ca-pabilities and final products quality. Triacylglycerols (TAG) are essential in biology and nutrition, as well as in pharmaceutical and cosmetic industries. Liquid TAG mole-cules require deep undercooling to crystallize, and it is very difficult for them to form glasses. Their kinetics of crystallization are slow enough to be studied in reasonable timeframes, i.e. seconds to minutes. Upon crystallization TAG molecules self-arrange in lamellar-shaped nanocrystals, which can exist in several polymorphic forms, classi-fied by their unit cells. These polymorphs are monotropic with a distinct thermodynam-ic stability hierarchy. However, predicting the type of polymorph and the temperature at which it will be formed is a know-how that is still missing from the current state of the art. A very fundamental tool to describe the process that happens before nuclei are ob-served (pre-nucleation) is the Fisher-Turnbull equation, which is based on the theory of homogeneous nucleation. It links the rate of forming embryos of growing sizes, up to the critical size (made up of a certain number of molecules) with the free energy needed to make a stable nucleus and the temperature at which crystallization begins (crystalli-zation onset). In this study, to allow for time-temperature profiles, we used the differen-tial version of the Fisher and Turnbull model to calculate the nucleation rates of the TAG tridodecanoyl-glycerol (LLL), when it is cooled at different rates. The parabolic partial differential equation was solved algebraically and programmed to be solved nu-merically with MATLAB, making this model accessible to many researchers. The crys-tallization temperatures were calculated as the point where temperatures deviated from the heat flow baseline obtained from differential scanning calorimetry (DSC) thermo-grams. The detection of these onset temperatures was carried out using a custom MATLAB code. The polymorphic forms were identified using time-resolved small and wide-angle X-ray diffraction (SAXD and WAXD) data obtained from experiments at a synchrotron. This is necessary to link thermal properties, such as undercooling (Tm-Tonset), enthalpy, entropy, and Gibbs free energy of crystallization to the identified pol-ymorphs. For our model, we introduced three critical factors: a nanoplatelet embryo ge-ometry, an interfacial energy dependent on temperature, and an activation energy barri-er which varies based on temperature and the number of embryo molecules. Additional-ly, we expanded this model to describe the secondary heterogeneous nucleation of the α polymorph on the surface of the β’. Based on the model, it was found that critical em-bryo size of the β’ polymorph was i¬* = 44 molecules when cooled at 15.0 K/min, and the minimum interfacial energy, δ, is 11 to 14 ×10-24 kJ/nm2 for ΔT= 13 to 20 K. With this information, we can accurately predict the types of polymorphs that will form and at what specific temperature they crystallize.