Long-term deep-supercooling of large-volume water and red cell suspensions via surface sealing with immiscible liquids

Supercooling of aqueous solutions is a fundamentally and practically important physical phenomenon with numerous applications in biopreservation and beyond. Under normal conditions, heterogeneous nucleation mechanisms critically prohibit the simultaneous long-term (> 1 week), large volume (> 1 ml), and low temperatures (< −10 °C) supercooling of aqueous solutions. Here, we report on the use of surface sealing of water by an oil phase to significantly diminish the primary heterogeneous nucleation at the water/air interface. We achieve deep supercooling (down to −20 °C) of large volumes of water (up to 100 ml) for long periods (up to 100 days) simultaneously via this approach. Since oils are mixtures of various hydrocarbons we also report on the use of pure alkanes and primary alcohols of various lengths to achieve the same. Furthermore, we demonstrate the utility of deep supercooling via preliminary studies on extended (100 days) preservation of human red blood cells.


Supplementary Note 1 Derivation of Young's equation at triple interface
When an ice embryo forms at the air/water interface, water wets ice at a contact angle of iwa as shown in Supplementary Figure 1a. The vector components of interface tensions wi (between water and ice), wa (between water and air), and ia (between ice and air) are depicted in the inset. To achieve force balance at coordinate, following equation has to be satisfied, ia = wi + wa cos iwa Or wi = ia − wa cos iwa Of note, these equations also can be interpreted as the requirement for minimum free energy in the triple phase system 3 . The contact angle iwa generally is not zero (12 ° as measured in 4 ). However, when the surface is sealed by immiscible oils, the water contact angle on ice ( iwo ) approaches toward zero to minimize the overall free energy of interfaces 5, 6 .

Stochastic process of ice nucleation and freezing
The formation of a critical ice embryo, i.e. a successful nucleation, in metastable supercooled water is generally regarded as a stochastic process that does not depend on the number of previous nucleation trials or correlate to other nucleation events during the same period 7,8 . In addition, heterogenous nucleation is the major type of crystallization in this study since homogeneous nucleation in water occurs at much lower temperatures (around -40 °C). As a result, the heterogeneous ice nucleation on water surfaces/interfaces would follow Poisson statistics In (1 − f ( )) = − ( ) • • where f ( ) is the freezing frequency after supercooling of a period , ( ) is the nucleation rate at temperature , and is the area of heterogeneous nucleation sites. Therefore, for water samples of the same volume and shape under a constant temperature, the non-frozen (supercooled) fraction is expected to decline exponentially with time.
However, in our experiments we found that f ( ) of DSC water with oil sealing does not change significantly after Day 3 as shown in Fig. 1 Using similar heuristics, our experimental results also suggest that the freezing we observed is not due to homogeneous ice nucleation either, where the formation of critical ice embryo is caused by spontaneous aggregation of water molecules via random translational, rotational, and vibrational movements that would conform stochastic process 9 . The exact kinetics and statistics of this heterogeneous ice nucleation in DSC water sealed by oil phase is still unknown and detailed future investigations are certainly warranted.

Freezing point depression due to oil-water mixing
When a water sample is sealed by an oil phase (i.e mixed oils, and pure alkanes and alcohols) for DSC, the "immiscible" oil might slightly dissolve in supercooled water to decrease the equilibrium melting temperature below 0 °C, the equilibrium melting point of pure water under atmospheric conditions. We, therefore, quantified the potential depression of freezing point due to this effect and assessed whether it's comparable to the high degree of supercooling we observed in our experiments. According to the Bladgen's Law, the extent of freezing point depression ∆ F can be calculated by where is the Van't Hoff factor ( = 1 for nonelectrolytes or oil phase in this study), is the molality of oil phase in water, and F is the cryoscopic constant ( F = 1.85 K kg mol^-1 for water). Therefore, ∆ F can be determined by the solubility of sealing oils in water at DSC temperatures. Solubility of oils in metastable water at DSC temperatures are not readily available; as such we have assessed ∆ F using the available solubility data of oils in water under room temperature. This approach, likely, leads to an overestimation since solubility of oils in water typically increases with temperature 10 .
For oil mixtures (MO, OO, PO, NO, and PDMS) and linear alkanes (C5 ~ C11) utilized in this study, the maximum solubility is 0.04 g L^-1 (or 0.55 mM) (C5 in water), and the corresponding estimate for ∆ F is less than 1.03 × 10 -3 °C, which is negligible compared to the degree of supercooling ∆ (10 to 20 °C) achieved using these oil phases as sealing agents.
For alcohols used in this study, the maximum solubility is 73 g L^-1 (or 0.98 M) (C4OH in water at room temperature) and the corresponding estimate for ∆ is less than 1.82 °C. This likely overestimated freezing point depression accounts for about 9.1% of ∆ (20 °C) enabled by alcohol sealing. Moreover, the DSC water and sealing alcohols are likely not mixed altogether. The stable contact interface with strong hydrogen bonding on the head and a long hydrophobic tail of alcohols, low molecular mobility, and viscous water at -20 °C would significantly impede the diffusion of alcohol molecules into water. We, therefore, conclude that the depression of freezing temperature due to oil-water mixing does not play a significant role in achieving the observed high degree of supercooling in our experiments.