RESULTS AND DISCUSSION
Freeze–Thaw Temperature Profiles
A freezing process begins by cooling the liquid down to its transition temperature (approximately 0 °C in this study). The
system then releases its latent heat of solidification at nearly constant temperature, creating a temperature "plateau" whose
duration indicates the rate of ice crystal growth. This phase is the most crucial part of a freezing process because the rate
of crystal growth will determine the importance of the cryoconcentration effect, and therefore, the product stability. In
this study, we defined the freezing time as the plateau duration.
Figure 2 shows a temperature profile of the DoE "best case" point with a freezing plateau of 2 h. By lowering further the
temperature after the 2 h plateau, the products' temperature profiles drop down very quickly with the same slope as the HTF
temperature profile, indicating the end of freezing. The temperature set point with a "stair shape," and especially the short
pulse of low temperature at –45 °C at the beginning of the freezing process (i.e., between 2 and 3 h), was implemented to
limit the undercooling effect typical of low salt solutions. This pulse was necessary to give enough energy to start the nucleation,
thereby avoiding a delay in the freezing process.
Undercooling lowers the liquid temperature below a solution's freezing temperature while maintaining its liquid form. A liquid
below its standard freezing point will crystallize in the presence of a nucleus around which a crystal structure can form.
However, lacking any such nucleus, the liquid phase can be maintained all the way down to the temperature at which homogeneous
crystal nucleation occurs. The homogeneous nucleation can occur above the glass transition where the system is an amorphous
(non-crystalline) solid and will occur very quickly (Figure 3).4 Undercooling occurs randomly and cannot be completely eliminated. It can indirectly affect protein quality and can clearly
generate differences in batch-to-batch or sample-to-sample preparation, creating unwanted heterogeneities in the process.
Therefore, a limitation or a partial control of the undercooling effect can reduce the risks of eventual sample damaging.
Figure 3. Description of the undercooling phenomenon
With the Celsius S3 system, the thawing phase cannot be defined by a clear plateau. In fact, if during the freezing process
the heat exchange has an outside–inside direction resulting in a precise LPTF, thawing occurs in the opposite direction, resulting
in a growing liquid zone without a well-defined point (i.e., there is no "last point to thaw"). Therefore, the thawing time
is defined as the time to melt the whole product.
Figure 4. Description of the freeze–thaw process occurring in the bag. (LPTF: last point to freeze)
For this study, the end of thawing was determined by a small drop on the thawing profile (Figure 5). At the end of the thawing
phase, the remaining ice starts detaching from the wall's container and moves to the surface of the liquid toward the temperature
probe (located in the center of the container at the LPTF), resulting in a small drop in the temperature. In other words,
the thawing time was defined as the time period covering the beginning of thawing, i.e., when the HTF set point is switched
to the target thawing temperature, up to the small drop of temperature previously described. Finally, for each thawing time
required by the DoE, a specific thawing temperature set point was defined.
Figure 5. Temperature profile of the thawing phase for the best case point (2 h freezing and 2 h thawing) generated with the
S3 system. Solid line: interferon; dashed line: set point; dotted line; heat transfer fluid temperature.