Identifying the types of water and quantifying their fractions in aqueous solutions can help us to understand their physiochemical properties and behaviors.^[1–9] To achieve this goal, the first challenge is to quantify hydration water. Accordingly, various technological methods with different spatial and temporal resolutions have been adopted to quantify the hydration number of solute, n_h. Regretfully, most of the reported values differ from each other. Recently, following our previous work in the past few years, the universal concentration dependence of the icing/vitrification behavior for aqueous solutions has been established,^[10–13] from which a convenient and reliable method of determining n_h is developed.

The value of n_h, quantified based on concentration-dependent crystallization and vitrification of water, reflects the degree of solutes affecting their adjacent water from the viewpoint of promoting solvent water vitrification in a dilute solution. These defined hydration water can easily vitrify at a moderate and even slow rate, e.g., as low as 10⁻² K/s.^[14] The critical cooling rate required for initiating vitrification of bulk water is about 10⁶ K/s.^[15] For the dilute solution, it can be simply regarded as a mixture of hydrated solute and bulk-like free water. However, with a decrease of water content, more hydration shells become closely compacted and even overlapped and, finally, free water disappears.^[5] The question here is whether or not there is an obvious critical concentration point, through which a mixture of hydrated solutes and free water for dilute solutions changes into that of hydrated solutes and confined water for medium-concentrated ones.

As recently reported, for a series of solutions of electrolytes and organic molecules, their glass-forming ability shows an abrupt change at a critical concentration point, defined as H₂O for brevity, where M is solute.^[10,13] For H₂O with , some water molecules can easily crystallize into ice upon cooling, even at a high rate. After that, the residual freeze-concentrated solution, which shows high glass-forming ability, can easily vitrify even at a slow cooling rate. In contrast, when water content decreases below that of H₂O, the solutions can easily vitrify totally. Most interestingly, as already confirmed, the value of is nearly solute-type-independent for electrolytes and molecules especially with higher molar weights, and .^[12]

Besides glass forming ability, many other properties of water and solute of organic molecule solutions, which are measured at room temperature, also manifest a deflection feature or abrupt change of their concentration dependence with the variation of water content.^[16–19] On the side of solvent water, these properties include spin-spin and spin-lattice relaxations,^[20] adiabatic compressibility coefficient,^[21] diffusion coefficient,^[22] viscosity,^[19] partial molar volume or vapor pressure,^[23] Raman shift, etc. On the side of organic molecules solute, the property mainly refers to the CH-stretching vibration.^[24] Due to the lack of a clear physical picture behind this behavior, the molar ratio of water to solute at such a deflection point for concentration dependence of physical properties has often been taken as the hydration number. Actually, in most cases, the concentration of this deflection point is consistent with that of H₂O.^[24]

Here, we focus our interest on concentration dependence of O–H stretching vibration of water in solutions of electrolytes at room temperature. We find that, like those scenarios observed in solutions of organic molecules, the O–H stretching vibration of water in solutions of electrolytes also displays obviously a deflection at a characteristic concentration, which, most importantly, is also very consistent with that of H₂O, and . Therefore, a universal characteristic water content of aqueous solutions highly correlated with the hydration numbers of solutes for properties measured at low and room temperatures is experimentally confirmed.

As an example, figure 1 shows the Raman spectra in a range from 2800 cm⁻¹ to 3800 cm⁻¹ for solutions of MgCl₂ of various concentrations measured at 295 K. We choose pure H₂O and mixture of H₂O with D₂O in a molar ratio of H₂O:D₂O=1:4, respectively, as a solvent.

Fig. 1.

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Fig. 1. (a) Raman spectra for OH-stretching vibration of H2O for MgCl2 solutions, MgCl2 nH2O, with n = 300, 200–80 in steps of 20, and 50–10 in steps of 2 (from bottom curve to top curve). (b) OH-stretching vibration of HDO in solution of MgCl2 dissolved in D2O mixed with dilute H2O with a molar ratio of 4:1. Molar ratios of water to solute n are 200 (bottom curve), 150, 60, 50, 40, 30, 26, 16, 14, 12 (top curve). (c) Peak position for OH-stretching vibration as a function of n plotted on the basis of data from panels (a) (solid circle) and (b) (solid diamond). The data of MgCl2 nH2O reported by Burikov et al.[25] are also shown for comparison (empty square). Moreover, the peak position of the component around 3400 cm−1 obtained by Gaussian fitting of the spectra in panel (a) is also presented (solid square). (d) Water content dependence of glass transition temperatures, Tg, of aqueous solution of MgCl2. In dilute solutions with , glass transition occurs after spontaneous icing in cooling process, thus it involves only the glass transition of freeze-concentrated solution, which manifests an almost constant Tg, defined as . The extension of –n can intersect the fitting curve of Tg–n for concentrated solutions at a feature point, i.e., MgCl2 nhH2O, where nh is the hydration number of solute. For more details, see Supplementary Information in Ref. [13].

In Figs. 1(a) and 1(b), the solution of D₂O for the electrolytes usually has an unaltered hydration number. In Fig. 1(b), the coupling of the OH-stretching vibration, both intramolecular and intermolecular, can be effectively suppressed, and thus improves the accuracy of the peak position at around 3400 cm⁻¹ from the Raman spectra. Figure 1(c) shows the plots of the locations of the peak maximum of Raman spectra plotted in Figs. 1(a) and 1(b), and those reported in Ref. [25] versus n for MgCl₂ nH₂O or MgCl₂ dissolved in D₂O with dilute H₂O with a molar ratio of 4:1. The variation of peak position for the component around 3400 cm⁻¹ obtained by Gaussian fitting of the spectra in Fig. 1(a), as conventionally done in the literature, is also presented for comparison. Clearly, in all the cases, the peak position of the OH-stretching vibration shows a deflection point, a change of tendency, in their water-content dependence. Noticeably, the deflection occurs at 20, corresponding to (n_h = 12^[13]).

The deflection behavior of the water content dependence of peak position of Raman spectra shown in Fig. 1(c) can be verified in aqueous solutions of various other electrolytes (Fig. 2), where the peak positions of Raman spectra for the OH-stretching vibration, measured at 295 K, are plotted as a function of n/n_h. As determined previously, n_h ranges from 6 for LiCl to 19 for AlCl₃.^[13] Over such a wide range of n_h, the water content dependence of the Raman shift measured on these aqueous solutions inclusively displays a deflection point at . All of these electrolyte solutions also show similar water content dependence of icing/vitrification of water to the behavior shown in Fig. 1(d). For more details, see Supplementary Information of Ref. [13].

Fig. 2.

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Fig. 2. Peak position of Raman spectra for the OH stretching vibration of water at about 3400 cm−1 as a function of the ratio of n/nh for aqueous solutions of various electrolytes H2O. In panel (a) M refers to CaCl2 (diamond), CaBr2 (hexagon), Ca(ClO4)2 (triangle), MgCl2 (circle), and AlCl3 (square), and in panel (b) M refers to MgBr2 (pentagon), Mg(ClO4)2 (triangle), LiCl[25] (circle), and MnCl2[25] (square).

The deflection occurring at , where , may be related to the variation of microstructure of water and solute in aqueous solution as the concentration changes. As mentioned earlier, the solvent water may be found to be in different status, namely free water, confined water (spatially confined among hydrated solutes), and hydration water, respectively, depending on the water content. To explain the abrupt change in glass forming ability of aqueous solutions at as shown in Fig. 1(d), we have recently suggested that aqueous solutions can be divided into three distinct concentration zones (Fig. 1(d)). Solutions within water-rich zone III, solvent water is comprised of hydration water and bulk-like free water. Free water can easily crystallize into ice, and, differently, hydration water can easily vitrify. The value of n_h is then quantified just based on this characteristic feature of hydration water. When water content decreases below , the aqueous solutions can easily vitrify, even at a slow cooling rate. It has been suggested that this abrupt change in glass forming ability of solution can be mainly attributed to the disappearance of free water. In other words, solutions change from a mixture of free water and hydrated solutes within zone III to a mixture of hydrated solutes and confined water in zone II. This proposition can be proved by the cold-crystallization behavior of water appearing upon thawing vitrified or deeply supercooled aqueous solutions at concentrations within zone II. Otherwise, if all water molecules in zone II are regarded as hydration water, then solutions within this zone show only devitrification behavior in heating process, such as that of the solutions within zone I, wherein solutes cannot be hydrated to the greatest extent.

The previously-mentioned division of concentration zone is further confirmed by an obvious change in concentration dependence of OH-stretching vibration of solvent water at H₂O as highlighted in this work. Actually, this non-monotonic dependence of OH-stretching vibration of water on concentration has already been tentatively discussed based on a proposed change in the configuration of ion-pairs with water content.^[25] With decreasing the water content, the ion-pairs in solution gradually come into contact from the initially isolating status through the solvent-sharing intermediate stage.^[26,27] For some solutes, such as LiCl presented in Fig. 2(b) (empty circles), the ions always tend to stay separated by hydration water due to a strong cation-water interaction and a relatively weak anion-water interaction.^[28] In this case, below a critical water content point, the hydration water can be believed to be structurally insensitive to a further increase of solute content. As a result, the peak position of the O–H stretching vibration remains nearly unchanged at low water content. However, in those aqueous solutions with stronger cation-anion interaction, even if solvent-separated or solvent-sharing ion-pairs are present in water-rich environment, the ion-pairs may come into contact with further reducing the water content. If the fraction of contacting ion-pairs increases with reducing water in the water-poor solutions, the water molecules will become more strongly hydrogen-bound to each other. Consequently, the Raman spectra of the solvent water will be red-shifted as the water content is reduced. This explanation in terms of ion-pair configuration above seems to be implacable to water in aqueous solution of CsCl, because the Cs⁺¹ and Cl⁻¹ ions will come into contact even in a water-rich solution,^[28] yet the solution still manifests this deflection feature of the water content dependence of the OH-stretching vibration.^[25] Therefore, the detailed mechanism obtained from the microstructures of the solution needs further investigation.

In this work, we have measured the Raman spectra of the O–H stretching vibration of water for aqueous solutions of a series of electrolytes in a wide range of water content. The results clearly exhibit a deflection point, which appears inclusively at the water content corresponding to , where n_h represents the hydration number of the given solute. The existence of the critical hydration number n_c, together with n_h which divides the aqueous solution into three distinct zones, is studied in the investigation of low temperature behaviors such as icing/vitrification. The critical hydration number n_c indicates a turning tendency for the variation of microstructures in the aqueous solution, and it is reasonable that it will exhibit some properties of the solutions at room temperature. This characteristic feature is universal for solutions of organic molecules and even of electrolytes, and it might help us to understand the bizarre variation tendency of properties of aqueous solutions, particularly those with water content in the neighborhood specified by the critical hydration number.