Critical Droplet Theory Explains the Glass Formability of Aqueous Solutions

When pure water is cooled at $\sim {10}^6\mathrm{K}/\mathrm{s}$, it forms an amorphous solid (glass) instead of the more familiar crystalline phase. The presence of solutes can reduce this required (or “critical”) cooling rate by orders of magnitude. Here, we present critical cooling rates for a variety of solutes as a function of concentration and a theoretical framework for understanding these rates. For all solutes tested, the critical cooling rate is an exponential function of concentration. The exponential’s characteristic concentration for each solute correlates with the solute’s Stokes radius. A modification of critical droplet theory relates the characteristic concentration to the solute radius and the critical nucleation radius of ice in pure water. This simple theory of ice nucleation and glass formability in aqueous solutions has consequences for general glass-forming systems, and in cryobiology, cloud physics, and climate modeling.

Figure 1

Critical cooling rate (CCR)—the minimum cooling rate to obtain a vitrified sample—of aqueous solutions as a function of solute concentration, for each of the eight solutes studied. Solid lines represent exponential fits of the form $CCR=CC{R}_0{e}^{-\beta c}$, where $c$ is the solute concentration. The fits extrapolate to similar values of $\sim 3\times {10}^5\mathrm{K}/\mathrm{s}$ at $c=0$ (corresponding to pure water).

Figure 2

Schematic illustration of the exclusion volume involved in cubic ice ($I_c$) nucleation. If the region inside radius $R_{I_c}$ is to be completely free of solutes, the center of mass of all solute atoms must be excluded from a region of radius $R_e=R_{I_c}+R_s$. Differences in effective solute radii $R_s$ are responsible for the differences in slope in Fig. 1.

Figure 3

The exclusion radius $R_e$ determined for each solute versus the solute’s Stokes radius. The solid line is the model prediction: $R_e=R_{I_c}^{*}+R_{\mathrm{Stokes}}$ with a critical radius for pure water $R_{I_c}^{*}=7.5\AA$ [13]. The open symbols are calculated as $R_e=R_{I_c}^{*}+R_{\mathrm{Stokes}}+R_H$, where $R_H$ is the hydration shell thickness measured by THz spectroscopy in Ref. 23.