The decisive role of free water in determining homogenous ice nucleation behavior of aqueous solutions

It is a challenging issue to quantitatively characterize how the solute and pressure affect the homogeneous ice nucleation in a supercooled solution. By measuring the glass transition behavior of solutions, a universal feature of water-content dependence of glass transition temperature is recognized, which can be used to quantify hydration water in solutions. The amount of free water can then be determined for water-rich solutions, whose mass fraction, Xf, is found to serve as a universal relevant parameter for characterizing the homogeneous ice nucleation temperature, the meting temperature of primary ice, and even the water activity of solutions of electrolytes and smaller organic molecules. Moreover, the effects of hydrated solute and pressure on ice nucleation is comparable, and the pressure, when properly scaled, can be incorporated into the universal parameter Xf. These results help establish the decisive role of free water in determining ice nucleation and other relevant properties of aqueous solutions.


Results
Quantification of hydration water. We find that the water content dependence of T g for aqueous solutions displays a quite universal feature, which in turn can provide a simple and reliable method for quantifying hydration number of solutes. Figure 1a,b show the DSC thermograms for the aqueous H 2 SO 4 + HNO 3 solutions with a mass fraction of water of X aqu = 0.39 and 0.85, respectively. The mass fraction of HNO 3 is fixed at X HNo3 = 0.07. The concentrated H 2 SO 4 + HNO 3 solutions such as the one with X aqu = 0.39 can totally vitrify. This behavior was observed in solutions with increasing water content up to a critical value of X aqu c = 0.69 (Fig. 1c). For c (zone III), primary ice precipitates first and then the residual freeze-concentrated solution vitrifies, obviously, at an almost constant temperature, termed ′ T g . T m and T f refer to the melting and freezing points of primary ice precipitated within zone III. As shown in (b) and (c), during cooling solution with X aqu = 0.85 from temperature point A, precipitation of primary ice begins at temperature point B and terminates at temperature point C. Below C, water content in freeze-concentrated solutions keeps nearly constant, which is equal to ′ X aqu .
Scientific RepoRts | 6:26831 | DOI: 10.1038/srep26831 water-rich solutions with X aqu > X aqu c , as illustrated by the sample with X aqu = 0.85 in Fig. 1b, crystallization of primary ice occurs firstly, followed by the vitrification of freeze-concentrated solutions.
Those water molecules in vitrified freeze-concentrated solutions are defined as hydration water herein. The corresponding n h can be deduced from the concentration of the freeze-concentrated solution. Traditionally, this concentration is determined by the point of intersection of T g curve of concentrated solutions and the extrapolated T m curve of ice in water-rich solutions. This method is valid mainly for solutions of larger organic molecules which have narrow temperature and/or concentration gaps between T g and non-extrapolated T m curves 20,26 . However, the error from extrapolating T m curve cannot be neglected for solutions of electrolytes and small organic molecules, which have lager temperature and concentration gaps between T g and non-extrapolated T m curves. Moreover, it may be unreasonable to extrapolating T m curve down to T g curve. As can be seen from Fig. 1b,c, when cooled H 2 SO 4 + HNO 3 solution of X aqu = 0.85 from temperature A, crystallization of primary ice begins at temperature B and finishes at C. Therefore, the concentration of freeze-concentrated solutions keeps constant when further decreasing temperature below C. This problem has already been noticed 28 , however, cannot be resolved mainly due to the difficulty in determining C point.
A comparison between T g of freeze-concentrated solutions and those at which concentrated solutions totally vitrify can accurately determine the concentration of freeze-concentrated solutions. As shown in Fig. 1c, freeze-concentrated solutions vitrify at a nearly constant temperature, denoted as ′ T g . Therefore, the concentration of the freeze-concentrated phases corresponds to that of the solution that totally vitrifies at T g = ′ T g determined on the monotonous part of the T g versus X aqu curve. The determined concentration is denoted as ′ X aqu , at which solution can also be written as M·n h H 2 O, here M stands for the solute. With the known ′ X aqu and X aqu c , the solutions for a given solute can be categorized into three distinct zones with regard to different vitrification and crystallization behaviors of water (Fig. 1c). For solutions in zone I there is less water to complete the hydration; while solutions in zone III are water-rich, wherein ice precipitation occurs spontaneously in the cooling process. For solutions falling in zone II with > > ′ X X X aqu c aqu a qu , water can totally vitrify when cooled at moderate rates, however, crystallization of water can still be observed on the reheating process or after performing long-time holding treatment at temperatures above T g 29 . These recrystallized water molecules are normally named the freezable bound water.
The water-content dependence of T g depicted in Fig. 1c was also measured in solutions of electrolytes such as LiCl, CaCl 2 , Ca(NO 3 ) 2 , MnCl 2 , Mn(NO 3 ) 2 , MgCl 2 , Mg(NO 3 ) 2 , Mg(CH 3 COO) 2 , ZnCl 2 , FeCl 3 , Fe(NO 3 ) 3 , CrCl 3 , Cr(NO 3 ) 3 , AlCl 3 , HNO 3 -H 2 SO 4 , and of simple organic molecules such as glycerol, ethylene glycol (EG), polyethylene glycol (PEG) 300, dimethyl sulfoxide (DMSO), and 1,2,4-butanetriol; and some mixtures such as those of MgCl 2 + ZnCl 2 , ZnCl 2 + glycerol (see Supplementary Figs. 1-10). Experimental results show that the feature of X aqu -dependent T g illustrated in Fig. 1c is quite universal at least to the systems investigated and cited in this work. The obtained ′ X aqu and n h for the measured solutes are listed in Supplementary Table I. Mass fraction of free water as pertinent parameter. For dilute solutions in zones II & III with a X aqu > ′ X aqu , which containing more water than hydration, the mass fraction of free water, X f , can be calculated without any assumption. Briefly, where M s is the molar weight of the solute. For any aqueous solutions specified by a > ′ X X aqu a qu , X f can be directly calculated from Remarkably, the original scattering T H and T m data when plotted against X aqu ( 25,26,28,34,[39][40][41][42] or read from the position of the endothermal peaks on DSC curves measured in the current work. We measured T m data for solutions of Mg(CH 3 COO) 2 , EG, 1,2,4-butanetriol, glycerol + ZnCl 2 (1:1), MgCl 2 + ZnCl 2 (1:1), MgCl 2 + ZnCl 2 (1:3), and HNO 3 + H 2 SO 4 . Additionally, the observed roughly universal X f -dependence of T H and T m is also valid for electrolytic solutions wherein the freeze-concentrated phase preferably crystallizes instead of undergoing vitrification, such as aqueous solutions of H 2 O 2 , (NH 4 ) 2 SO 4 , H 2 SO 4 , and HNO 3 (see Supplementary Table 1 and the note therein). In this case, free water was still defined as the part of water that crystallizes into primary ice. Figure 2b indicates that T H depends solely on X f and is insensitive to the specific solute-water interaction. This insensitiveness can be attributed to the screening effect of hydration water to the solutes. In other words, the influence of solutes on ice nucleation can be evaluated via the hydration capability of the solute, i.e., n h , which increases roughly linearly with the Gibbs energies of hydration of cations and molecules (see Supplementary  Fig. 11), and increases from 6 for LiCl to about 19 for AlCl 3 (Supplementary Table I). As we know, the number of water in the first and second hydration shells of ions is about 6 and 9~20 (depending on the type of cations), respectively 17,18 . Therefore, regarding influence upon ice nucleation occurring in dilute solutions, the solute− water interaction cannot extend beyond the first hydration shell for monovalent electrolytes and simple organic molecules, and cannot extend beyond the second hydration shell for multivalent electrolytes. Strictly speaking, n h can be regarded as a reflection of the ability of solutes to increase the fraction of high-density local heterogeneities in supercooled water. H.E. Stanley et al. made a similar suggestion for the effect of pressure on water structure 43 . Moreover, the gap between T H and T m curves plotted in Fig. 2b becomes widen with decreasing X f (or with increasing the mass fraction of hydrated solute (1 − X f )). This behavior is also analogous to the effect of pressure 44 . Therefore, the following text discusses the equivalent relationship between pressure and (1 − X f ) from the point of view of depressing T H .
The equivalency relation between solute concentration, c, and external pressure, P, with regard to their effect upon reducing T H has drawn much attention, and such an equivalency relation was first observed in alkali halide solutions 45 . However, no valuable information has ever extracted because the variation of T H with c is apparently very sensitive to the solute type. Koop Figure 3a comparatively plots the X f -dependence of T H for solutions and P-dependence of T H for pure water 45 . Obviously, in depressing T H , P can be linearly scaled against the mass fraction of hydrated solute in the following way: P X f f where P is in MPa, and the coefficient α P→Xf = 3.32× 10 −3 MPa −1 . This linear scaling relation in Eq. (3) holds for pressure range 0.1 < P < 200 MPa, corresponding to 180 K < T H < 236 K. This is to say that T H values are approximately the same for pure water under P and solutions with a mass fraction of free water The dominating mechanism for solutes to suppress ice nucleation is to combine with hydration water so as to reduce the amount of free water. We applied this picture to understand the effect of pressure. For a solution of X f , when further subject to an external pressure of P, an effective mass fraction of free water, X f eff , can be introduced in analog to the definition for X f ,   where X f and − α ⋅ → P (1 ) P X f represent the contributions from solutes and pressure, respectively. Eq.(6) implies that in reducing the amount of free water in a solution, the pressure and the solute work in close collaboration. The hydrated solutes exert influence on the local hydrogen bonding network in water, while, pressure promotes the high-density non-tetrahedral local structure in free water, both lead to the suppression of ice nucleation probability. Figure 3b shows the X f eff dependence of T H for solutions of 1.0 mol. kg −1 LiCl 45 and 5.56 mol. kg −1 glycerol 46 under pressures up to 200 MPa (for NaCl, see Supplementary Fig. 12). As expected, all the T H data points fall exclusively onto the same curve referring to that in Fig. 2b. The regular dependence of T H obtained under various concentrations or pressures on the parameter X f eff also suggests that the pressure in the given range has almost no bearing on the hydration water of LiCl and glycerol.

Discussion
Interestingly, the T H data referred to Fig. 2a also merge into a very compact distribution when plotted as a function of a w 9 , which is a good thermodynamic parameter for comprehensively describing the effect of solutes on ice nucleation. a w and the related osmotic pressure have been widely used to characterize the formability of nanosized water domains in supercooled solutions 4,10 , or the change in entropy and the activation energy required for water molecules to cross the nucleus/liquid interface 9,12 . The application of a w undoubtedly provides a simplified treatment of the complex interactions among the different components in a solution. However, this simplified treatment also hinders understanding the detailed role of solute in determining ice nucleation, in part because of a lack of general relations between a w and other features of the solution concerning the solute-water interaction 15 . Figure 4 plots a w measured at 298 K for various aqueous solutions against X f . For comparison, Fig. 4 also plots X f dependence of a w at T m for solutions calculated according to the following equation: exc m m w m where ∆G exc is the excess Gibbs free energy of supercooled water, which is defined as the excess heat capacity of supercooled bulk water with respect to bulk ice 47 , and R is the gas constant. The data points are no more randomly scattered as plotted versus molar fraction of water or even versus molar fraction of free water ( Supplementary Figs  13 and 14), rather they fall onto two seemingly distinct branches (Fig. 4). The lower branch includes electrolytic solutions and the solutions of small organic molecules such as 1,2,4-butanetrio, glycerol, and DMSO, all measured at 298 K 13,47-59 . Consequently, the relationship between a w (T m ) ~ X f can be deduced by relationship between a w (T m ) and T m established according to Eq. (7) and that between T m and X f plotted in Fig. 2b. Noticeably, the deduced a w (T m ) as a function of X f (blue line) fits well a w data measured at 298 K for the electrolytic solutions and those of small organic molecules. The a w data measured at 298 K differ from those measured at the corresponding T m only negligibly, thus we suggest that n h is insensitive to temperature.
The quite universal dependences of T H and a w (T m ) on X f , at least for electrolytic solutions, explains the successful application of a w in describing the effect of solutes on ice nucleation, as a w indirectly reflects the availability of free water in supercooled solutions.
The above-mentioned fitted T H versus X f and T m versus X f relations are not valid for solutions of large organic molecules illustrated in Fig. 4, including solutions of xylose, sorbitol, glucose, maltose, sucrose, and trehalose. Obviously these a w data fall apart from those for electrolytes and small organic molecules, and yet, interestingly, they also roughly merge into one single curve. This difference in a w versus X f between electrolytic solutions and those of large organic molecule may lie in the structural heterogeneity in the latter ones. Of the similarX f levels, the region of free water may be larger due to the aggregation of (unevenly) hydrated large organic molecules, thus manifesting a higher value for a w and T H . PEG 300 is an exception, that its data at T m and at 298 K fall on two branches respectively, i.e., its hydration water number is sensitive to temperature 60 .
The X f ~ a w relation displaying two distinct branches reminds us that, for the same nominal X f , it refers to a larger a w thus a higher T H for solutions of large organic molecules (data not shown). As T H depends on the local amount of free water in solution, this clearly results from the structural inhomogeneity in those solutions arising from aggregation of the large organic molecules. Thus one must be cautious in understanding T H , T m and other water-related properties for such solutions, since the locally available amount of free water is not necessarily consistent with the nominal concentration of the solution. This case can partially explain the invalidity of colligative property for describing the effect of solutes on T H and a w even when hydration is also taken into consideration.
The universal dependence of T H on X f , or T H (c, P) on X f eff , and even the deviation of a w (T m ) ~ X f for electrolytic solutions and solutions of larger organic molecules, lead to recognition of the pivotal role of free water, or the hydration water, in determining the ice nucleation behavior. The solute ions or molecules differ, with regard to suppressing the ice nucleation temperature, in their hydration capability. Ice nucleation in different solutions can thus be understood on the same footing with the concept of hydrated solute or mass fraction of free water. We suggest that hydration of solutes reflect their abilities to increase the fraction of high-density heterogeneities in supercooled water. Different solutions at the same mass fraction of free water have the same temperature dependence of probability of forming critical-sized low-density domain in supercooled free water. However, it still is difficult to estimate the size of the free water domains in solutions from the nominal water content of the solution, as the free water regions are interconnected, and at least in solutions of large organic molecules the distribution of free water may show a severe inhomogeneity. Moreover, a fact remains quite puzzling that why it is mass fraction of free water that universally describe the ice nucleation in solutions.
In summary, by measuring the water-content dependence of glass transition temperature for many different aqueous solutions we recognized that the nearly constant glass transition temperature for the freeze-concentrated phases from the super-cooled water-rich solutions provides a method to quantify the number of hydration water for a given solute. A relevant parameter, the mass fraction of free water, can be well defined and determined. A universal dependence on this parameter was established for the homogeneous ice nucleation temperature, T H , the melting temperature of primary ice, T m , and even a w (T m ). This observation is also valid for water-rich solutions in which the freeze-concentrated phase preferably crystallizes instead of undergoing vitrification. When properly scaled, for suppressing ice nucleation, the effect of pressure can be incorporated into an effective mass fraction of free water. The one-to-one correspondence between water activity and mass fraction of free water (for electrolytic solutions to the least) explains the validity of water activity in describing the homogeneous ice nucleation behavior in supercooled solutions. It reveals the fact that water activity is essentially a measure of free water.

Methods
Samples. High-purity water was prepared by using a Millipore Milli-Q system. Thermal measurement. Differential scanning calorimetric measurement on droplets (∼ 5.0 μ L) of aqueous solutions was performed on a calorimeter (PE DSC8000) operating at a cooling/heating rate of 20 K min. − 1 unless otherwise specified. When cooled down to 110 K, the sample was held at this temperature for 1 min. before the heating procedure began. All of the DSC curves were normalized against sample weight.