Isochoric conditions enhance stability of metastable supercooled water

Effective preservation of complex organ and tissue systems is essential to a wide range of medical and research efforts of the 21st century,¹ including expanding access to lifesaving organ transplantations, enabling the storage and transportation of engineered tissues for drug-testing, etc. While classical approaches to preservation have often included high doses of cryoprotectant chemicals and ultralow cryogenic temperatures, a new generation of protocols is leveraging thermodynamic supercooling to dramatically enhance the duration and quality of biopreservation while operating in the high-subzero centigrade regime (between −20 °C and −3 °C) and minimizing cryoprotectant concentrations.^2–5 

Although this approach has produced strong early biological results in the laboratory, the reduction of these protocols to practice in a clinical or industry setting faces a fundamental limitation: thermodynamic stability.⁶ Supercooling is a metastable thermodynamic state, in which a substance remains liquid at temperatures lower than its freezing point due to a lack of sufficient kinetic stimuli. Upon even slight agitations, a supercooled system can rapidly and destructively freeze, returning to thermodynamic equilibrium and destroying any preserved biologics. Thus, in order to develop supercooling preservation protocols that are practicable outside a highly controlled laboratory environment, transportable, and clinically convenient, new methods should be sought to enhance the stability of supercooled systems.

In this work, we introduce isochoric (constant-volume) supercooling, a simple thermodynamic alteration to standard supercooling techniques that significantly enhances the stability of supercooled water in the face of a range of mechanical and thermal disturbances. We furthermore develop several hypotheses concerning the fundamental mechanisms contributing to this enhancement, unifying factors that stem from thermodynamics, fluid dynamics, and kinetics. While a complete theoretical explanation is outside the scope of this experimental validation, the results herein may be put to immediate practical use in high-stability supercooling of sensitive biological matter.

Nucleation of a stable ice phase from supercooled (metastable) water occurs when a perturbation within the system proves sufficiently large to drive the free energy of a cluster of liquid molecules over the nucleation barrier.⁷ Such perturbations can stem from the constant microscopic fluctuations undergone by any system with a finite temperature, or from macroscopic mechanical or thermal agitation.⁸ Thus, for a supercooling-based preservation technique to become practical or clinically relevant, it must maintain stability not only when experiencing microscopic fluctuations, but also when experiencing the macroscopic agitations that characterize practical use and mobility, including motion, macroscopic vibration, impact with rigid surfaces, temperature swings, etc.

Most supercooling preservation protocols operate under isothermal (constant temperature) and isobaric (constant pressure) conditions. According to statistical thermodynamics, systems in contact with a temperature reservoir (such as a cooling bath) and a pressure reservoir (the atmosphere) are free to fluctuate in energy and volume⁹ (or density if the mass is constant), the extensive conjugates of temperature and pressure [Fig. 1(a), left]. Thus, systems under isobaric conditions are constantly undergoing microscopic density fluctuations due to the random motion of particles, which can lead to the formation of ice clusters that meet and exceed the critical size required for nucleation. Furthermore, when exposed to macroscopic perturbations, isobaric systems in contact with the atmosphere are susceptible to bulk fluid motion and bulk mixing with air, which can also lead to nucleation through cavitation or the introduction of new nucleation sites.^4,8,10

Isochoric (constant-volume) systems however, by their very definition, do not microscopically fluctuate in density⁹ [Fig. 1(b), left], and restrict bulk motion of the contained liquid. Furthermore, we have shown in our previous studies^11,12 that both the process of ice nucleation and growth and the fundamental water–ice phase equilibria are different under isochoric conditions: as seen by comparing the T–P and T–V phase diagrams for pure water [Figs. 1(a) and 1(b), right], nucleation at constant pressure yields complete freezing, while nucleation at constant volume yields only partial freezing, resulting in a two-phase water–ice equilibrium. This ultimate two-phase equilibrium has myriad useful consequences, and prior studies have theoretically predicted that among these consequences may be heightened nucleation barriers and reduced thermodynamic driving forces for nucleation.^11,13 Additionally, isochoric conditions inherently eliminate the air–water interface, which has been suggested to facilitate heterogeneous nucleation.⁴ Based on the sum of these thermodynamic considerations, we hypothesized that isochoric conditions should yield enhanced supercooling stability.

In order to test this hypothesis, we supercooled de-ionized water in identical rigid glass chambers [Figs. 2(b) and 2(c)] under three sets of conditions:

1. Standard isobaric conditions, in which the chambers were filled to approximately 95% volume and capped, leaving a bulk layer of air approximately 2 cm in height to function as an effective atmospheric pressure reservoir.

2. Oil-sealed isobaric conditions, in which chambers were filled as in (1) but sealed with an approximately 2 mm tall layer of mineral oil before capping, maintaining isobaric conditions while completely eliminating the air–water interface.⁴ 

3. Isochoric conditions, in which chambers were assembled using a simple cap modification that enabled filling and sealing of the jars without the introduction of any air (see the details in Methods), leaving a totally constrained liquid volume incapable of any manner of visible flow when turned upside down.

All systems were initially supercooled to −3 ± 0.01 C in a constant-temperature circulating bath and then exposed to various macroscopic perturbations [shown schematically in Fig. 2(a)], including drop-impact from a height of 1 ft onto a hard acrylic surface, 2.2 g vibrational loading on a rotary shaking table, ultrasonication in a cooled bath at 55 kHz, and continuous thermal cycling between 0 and −6 C for 24 h (experimental details are available in Methods). For mechanical and acoustic perturbation testing, nucleation was evaluated visually [as in Fig. 2(b)]. When nucleation was observed in isochoric systems, care was taken to warm the nucleating chamber immediately, as prolonged ice growth under isochoric conditions will produce pressures capable of shattering the glass chambers.¹² For thermal perturbation testing (occurring over 24 h), breakage of the chamber was also used as an indicator of nucleation.

The nucleation frequency was recorded as the number of chambers per group that experienced ice formation. All tests were conducted in n = 6 trials of N = 12 chambers and repeated in two sizes (approximately 65 ml and 130 ml) of borosilicate glass media bottles with rigid threaded polypropylene caps. In order to ensure the relevance of these tests to preservation protocols of interest, which invariably involve the introduction of other potential nucleation sites into the system, a PDMS-on-glass chip was also added to each container [visible in Figs. 2(b) and 2(c)], representative of the lab-on-a-chip systems used to house engineered tissue constructs.¹⁴ 

The nucleation frequency as a function of disturbance type is plotted for all three chamber configurations in Fig. 3(a), and comparisons between chamber configurations for each disturbance type are presented individually in Figs. 3(b)–3(e) for statistical evaluation. As demonstrated in Fig. 3(a), isochoric conditions afford greatly enhanced supercooling stability across all perturbation types, at both volume scales. Notably, isochoric supercooling at a 65 ml volume remained stable in 90% of trials when exposed to ultrasonication, which is perhaps the most universal and sure-fire trigger of ice nucleation,^15–17 and remained stable in all trials when exposed to vibrational loading comparable to that encountered during a commercial flight. Standard isobaric conditions yielded the least stability by comparison, while oil-sealing provided statistically significant stability enhancements during exposure to macroscopic vibrational loading and acute impact, but did not significantly affect resistance to ultrasonic or thermal perturbation.

Previous work has suggested that the removal of the air–water interface is responsible for the vibrational stability enhancement experienced during oil-sealed supercooling.⁴ The results presented in Figs. 3(b) and 3(d) therefore confirm that the stabilizing effect realized under isochoric conditions must transcend the simple removal of air as a nucleation site, given the relative superiority of stability between isochoric and oil-sealed chambers. Furthermore, the fact that oil-sealing affects stability in the face of bulk vibrational loading and acute impact, both of which can result in bulk motion of the supercooled water under isobaric conditions, suggests that the effect of oil-sealing itself may be more complex than previously considered, resulting to some degree due to immobilization of the water phase. In order to clarify this prospect, we further examined the behavior of the free water surface during vibration under isobaric conditions with and without oil sealing.

The results of this examination are featured in Fig. 4, and clearly represent a previously unaccounted for phenomenon. In Fig. 4(a), when the unconstrained water surface interfaces directly with air, unstable turbulent behavior is observed at the surface, due in principal to the Faraday instability.¹⁸ However, when an oil layer is added atop the water, as in Fig. 4(b), this extreme instability is observed only to occur at the oil–air interface, while the water–oil interface remains stable. This phenomenon is caused principally by the high kinematic viscosity of the oil relative to the air, and is observable for vibrations that occur at frequencies beneath a characteristic cutoff.^18–20 Surface instabilities of this nature in multi-layer fluid systems are a contemporary area of research.^18,19,21

Mechanical stimuli have long been known to induce ice nucleation,²² and the last century of research into the topic has clarified that cavitation is the most prominent responsible mechanism.^10,17,23,24 While cavitation is frequently associated with ultrasonication, it can also be caused by all manner of shockwaves²⁵ and by vibrational surface effects such as the Faraday instability²⁰ displayed in Fig. 4.

The results obtained in this study demonstrate that isochoric supercooling is significantly more stable than its isobaric counterparts when exposed to mechanical stimuli of any kind, and it is thus suggested that one fundamental mechanism driving this isochoric stability may be a reduced likelihood of cavitation. By totally constraining the liquid volume, isochoric conditions eliminate opportunities for cavitation from effects that require bulk fluid–fluid interfaces (such as the Faraday instability or analogous effects), and eliminate opportunities for cavitation from bulk motion of the stored water. They furthermore present two thermodynamic obstacles to cavitation from shockwaves or ultrasonication: first, because there is no bulk air anywhere in the system, cavitation must occur in dissolved air that is first forced out of solution with the supercooled water; second, the formation of a low-density air bubble in a constrained volume of water will create a positive pressure due to Le Chatelier's principle, increasing its energetic barrier to formation. While theoretical analysis of this latter effect is outside the scope of this work, it is directly analogous in concept to the increased energy barriers produced by the formation of ice in a constrained volume.¹¹ 

This cavitation-centered explanation is also consistent with the observed behaviors of the oil-sealed chambers, which showed some enhancement of vibrational stability as compared to their un-sealed counterparts. In effect, oil-sealing reduces the likelihood of cavitation at the free water surface by removing direct contact with air and stabilizing the interface [Fig. 4(b)], but does not otherwise energetically deter cavitation throughout the liquid volume.

In total, the superior supercooling stability experienced in isochoric systems is likely a composite effect, reflective of the complex thermodynamic and kinetic factors driving ice nucleation in systems of bulk volume. Thermodynamic factors such as the reduction or elimination of microscopic density fluctuations and the increase in the ice nucleation barrier under isochoric conditions likely contribute;^11,13 the elimination of the air–water interface as a nucleation site likely contributes;⁴ and an increased resistance to cavitation may play a central role. While these effects must be independently clarified in future theoretical and experimental work and may reveal routes to further stability enhancement, the experimental reality of enhanced supercooling under isochoric conditions may be employed immediately for low-risk preservation and transportation of sensitive biological matter.

Finally, it should be noted that the sealed chambers employed in this work are of course only capable of producing approximately isochoric conditions; both the glass chambers themselves and the rigid polypropylene caps have a finite stiffness, and thus minor changes in volume due to deformation or thermal expansion effects may occur during cooling. We therefore anticipate that additional enhancements in supercooling stability may be elicited in chambers of increasing rigidity, and future theoretical and experimental work should examine the chamber rigidity range over which isochoric supercooling effects may be observed.

See the supplementary material for a detailed account of the methods and materials employed in the described experiments.

This work was supported by the USDA National Institute of Food and Agriculture, AFRI Project Proposal No. 2017-05031, Award No. 2018-67017-27826 “Preservation of food by isochoric (constant volume) freezing.”