Cool-down time of a polypropylene vial quenched in liquid nitrogen

Snap-freezing of a tissue is usually realized by enclosing it in a polypropylene cryo-vial and subsequently immersing the vial in liquid nitrogen. The cooling rate of the vial is very critical to the frozen-tissue quality. However, quantitative information on the heat transfer process at the vial-liquid interface is still a mystery limiting the cool-down prediction of the vial and the tissue. In this paper, an analytical model is developed to predict the temperature variation inside the polypropylene vial-wall and the tissue. This model also include temperature-dependent thermal properties of the polypropylene material. The cooling time of an empty polypropylene tube of wall thickness 1.5 mm, replicating a typical commercial polypropylene vial is predicted with a maximum error of less than 10%. We also verified the model using temperature-time measurements performed with several other polypropylene tubes of different wall thickness. An interesting finding from this work is that the difference in the cool-down time of a tissue in a tube and an empty tube is proportional to the product of the tissue heat capacity and the tube-wall thermal resistance. This enables researchers to estimate the cooling trajectory of the tissue during the cooling process allowing the development of improved snap-freezing protocols.