Analysis on the crystallization degree inside the cryoprotectant microdroplets during freezing process on the liquid nitrogen surface

Abstract

Based on the non-isothermal crystallization kinetic model, the temperature distribution and the degree of crystallization inside cryoprotectant (CPA) microdroplets are theoretically investigated when they are frozen on the liquid nitrogen surface. The results show that the ice crystallization degree in surface region is the largest one during the phase transition temperature zone, while the middle region is intermediate, and the center region is the lowest. Also, the higher the concentration of CPA, the more uneven both the temperature and the crystallization inside the droplets. The maximum temperature difference between the surface and the center region of 50% glycerol with a volume of 4 μL is about 8 K, but the crystallization degree of the former is about 41 times larger than that of the latter. For water case, the temperature difference is only 1.1 K, and the degree of ice crystallization on the surface is roughly 6 times higher than that in the center. The volume of microdroplets seems to have few effects on the final crystallization degree for lower concentration solutions, but prolongs the freezing phase transition duration (i.e. 14.48 s for 2 μL and 19.82 s for 8 μL for 20% glycerol case). For the higher concentration solutions, the freezing phase change temperature zone is not obvious, but the final crystallization degree will increase significantly as the volume of microdroplets rising (i.e. 0.29×10−6 for 2 μL, 0.80×10−6 for 8 μL for 50% glycerol case). As CPA agent concentration increases, the phase transition temperature obviously decreases (i.e. 273.15 K for water, 250 K for 20% glycerol, 225 K for 50% glycerol, 158 K for Vs55) and the final crystallization degree also has the same trends (i.e. 1 for both water and 20% glycerol, 5.61×10−7 for 50% glycerol, and 5.7×10−16 for Vs55).