Interfacial Free Energy as the Key to the Pressure-Induced Deceleration of Ice Nucleation

The avoidance of water freezing is the holy grail in the cryopreservation of biological samples, food, and organs. Fast cooling rates are used to beat ice nucleation and avoid cell damage. This strategy can be enhanced by applying high pressures to decrease the nucleation rate, but the physics behind this procedure has not been fully understood yet. We perform computer experiments to investigate ice nucleation at high pressures consisting in embedding ice seeds in supercooled water. We find that the slowing down of the nucleation rate is mainly due to an increase of the ice $I$-water interfacial free energy with pressure. Our work also clarifies the molecular mechanism of ice nucleation for a wide pressure range. This study is not only relevant to cryopreservation, but also to water amorphization and climate change modeling.

Figure 1

Plotted for 1 (black) and 2000 bar (red) as a function of the supercooling: (a) number of particles in the ice Ih critical cluster; (b) decimal logarithm of the ice nucleation rate; (c) absolute value of the chemical potential difference between ice Ih and the liquid from thermodynamic integration [17]; (d) water-ice Ih interfacial free energy. In (a), (b), and (d) solid circles correspond to data obtained from inserted clusters and solid lines to fits [CNT-like in (a) and (b) as explained in Ref. [17], and linear in (d)]. Diamonds in (d) correspond to the direct calculation of $\gamma$ at coexistence (flat interface) from the MI method [6] (error is the size of the symbol). Dashed lines in (b) and (d) correspond to the boundaries of our statistical error (see SM [9]). The black solid square in (b) corresponds to the forward flux sampling calculation performed at 1 bar for TIP4P/Ice in Ref. [18]. Empty diamonds in (b) correspond to experimental measurements of $J$ at 1 bar [19].

Figure 2

(a) The experimental HNL (dotted blue) has a larger negative slope than the melting line (solid blue). The TIP4P/Ice model, in red, captures this effect almost quantitatively. (b) Snapshot of a typical critical cluster embedded in the supercooled fluid at the experimental HNL at 1 bar. Particles with an icelike environment are shown in red and those with a liquidlike environment in blue. The size of liquidlike particles has been scaled down to make the ice cluster visible.

Figure 3

(a) Difference in $\ln J$ and $-\mathrm{\Delta }{G}_c/(k_{B}T)$ between 2000 and 1 bar as a function of the supercooling. (b) Black curve: factor by which $\mathrm{\Delta }{G}_c/(k_{B}T)$ increases in raising the pressure from 1 to 2000 bar as a function of the supercooling. Colored curves: different factors that contribute to such an increase, as indicated in the figure. The product of the colored curves gives the black curve.