Cooperativity in Ion Hydration

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Science  21 May 2010:
Vol. 328, Issue 5981, pp. 1006-1009
DOI: 10.1126/science.1183512


Despite prolonged scientific efforts to unravel the effects of ions on the structure and dynamics of water, many open questions remain, in particular concerning the spatial extent of this effect (i.e., the number of water molecules affected) and the origin of ion-specific effects. A combined terahertz and femtosecond infrared spectroscopic study of water dynamics around different ions (specifically magnesium, lithium, sodium, and cesium cations, as well as sulfate, chloride, iodide, and perchlorate anions) reveals that the effect of ions and counterions on water can be strongly interdependent and nonadditive, and in certain cases extends well beyond the first solvation shell of water molecules directly surrounding the ion.

The properties of solutions of ions in water are of relevance for a wide range of systems, including biological environments (1) and atmospheric aerosols (2). Even for simple binary solutions, the effect of ions on the structure and dynamics of water has been the subject of ongoing debate (35). Key questions concerning ion effects on water pertain to the number of water molecules affected and how the degrees of freedom of these water molecules are influenced.

During the past decade, a variety of measurement techniques have provided evidence that ions primarily have an effect on the structure and dynamics of the first solvation shell of water molecules directly surrounding the ion. This evidence consists of structural measurements of ion hydration using neutron and x-ray diffraction (6, 7), x-ray absorption spectroscopy (8), and infrared and Raman spectroscopy (9). Information on the effects of ions on water dynamics has been mainly obtained from femtosecond time-resolved infrared (fs-IR) vibrational spectroscopy (1012) and optical Kerr-effect spectroscopy (13). These reports support the notion that the effect of ions on water is largely limited to the first solvation shell. A different dynamical technique, dielectric relaxation (DR) spectroscopy, also showed that for many different cations and anions, the effect is limited to the first solvation shell (1417). However, for certain ion combinations, an effect beyond the first solvation shell was observed (1820). It is currently unclear what factors determine the degree of hydration and what constitutes the molecular-level structure and dynamics; a unifying molecular picture of ion hydration is lacking.

Here, we studied the effect of ions on water by means of fs-IR spectroscopy and terahertz DR spectroscopy. It turns out that these techniques are uniquely complementary, in that they are sensitive to water reorientation dynamics along different molecular axes of water. Moreover, the ability to independently resolve water reorientation along different directions helps to uncover previously unappreciated cooperativity between hydrated cations and anions. We studied dissolved salts containing various combinations of ions that have different charge densities and water affinities. For specific combinations of cations and anions, we observed dynamic hydration effects that extend well beyond the first structural solvation shell.

We first present the results of DR spectroscopy of five different dissolved salts (21). These measurements were performed by characterizing in time the propagation of a terahertz (THz) pulse with a duration of ~1 ps through the salt solution. In the inset of Fig. 1A, we show THz pulses as transmitted through solutions of Cs2SO4 (0.5 mol/kg), MgSO4 (0.5 mol/kg), and a reference solution of CsCl (16). Generally, THz pulses are delayed as a result of refraction and experience a decrease in amplitude as a result of absorption. In water, a marked frequency dependence of refraction and absorption arises when the dipoles of water molecules fail to keep up reorienting with an externally applied oscillating electric field. This is the DR process, which leads to a large absorption peak at 20 GHz and a smaller one around 0.6 THz, for pure water molecules at room temperature. These peaks are attributed to the collective reorientation of water molecules (Debye relaxation time τD ≈ 8 ps) and the reorientation of undercoordinated water molecules (relaxation time τ2 ≈ 250 fs), respectively (22, 23). In Fig. 1A, we show the imaginary part of the extracted dielectric function ε, which is associated with the absorption of electromagnetic radiation by water molecules. As a result of the interaction with solvated ions, the reorientation of water molecules around ions slows down, shifting the absorption peak to lower frequencies and thereby reducing the absorption of radiation at THz frequencies (depolarization).

Fig. 1

Results of DR spectroscopy. (A) The imaginary part of the dielectric function ε for solutions of CsCl, Cs2SO4, and MgSO4 (all 0.5 mol/kg) and the corresponding transmitted THz pulses (inset). (B) Depolarization [corrected for kinetic depolarization due to conductivity (21)] and fraction of slow water as a function of concentration for the investigated salt solutions. The fraction of slow water is equal to the depolarization divided by the difference between the dielectric response of pure water at zero and infinite frequency, which equals 74 at 298 K. The lines are linear fits to the depolarization values (or slow fractions) and serve to distinguish the studied salts. Error bars represent the 95% confidence interval and are derived through error propagation of the experimental uncertainty in the dielectric function. *Data from (16).

It is typically found that the dynamics of water molecules in salt solutions are nonuniform and show two or more time scales. Previous dielectric relaxation studies found that a certain fraction of water molecules displays very slow reorientation dynamics, whereas for the remaining water molecules the orientational dynamics are similar to those of bulk liquid water (1420). Also, computer simulations found that a fraction of water remains unaffected by the presence of the ions (24, 25). In analyzing the THz DR data, we follow the literature by identifying two sub-ensembles of water molecules in ionic solution: those whose dynamics are predominantly unaffected by the presence of ions, and those whose dynamics are slowed down. Both sub-ensembles are characterized by a distribution of reorientation time scales.

In Fig. 1B, we show the concentration-dependent depolarization and corresponding slow water fraction. The hydration number Np is defined as the number of moles of slow water dipoles (p) per mole of dissolved salt and is directly proportional to the slopes of the lines in Fig. 1B (1420). The hydration number Np is a dynamical property and is therefore distinct from the structural concept of solvation shells. Solvation shells are often defined in terms of the distance distribution of the water molecules from the center of the ion, but as such do not present information on the dynamics of the water molecules. It is typically found that ions with a larger charge density (small, multivalent ions) affect the dynamics of a larger number of water molecules (i.e., have a higher hydration number) than ions with a lower charge density (large, monovalent ions) (6, 7, 1416, 1820). This is caused by the larger local electric field around small, multivalent ions, which affects the orientation of a larger number of surrounding water molecules.

Our results for MgCl2, LiCl, and CsCl are in good agreement with this general rule. For Mg(ClO4)2 we find Np = 6; because ClO4 is a very weakly hydrated anion, the observed slowly reorienting water molecules are likely located in the first geometrically surrounding solvation shell of the Mg2+ ion. In contrast, for Cs2SO4, Np is only 1. Apparently, the water molecules in the solvation shell of Cs+ show reorientational dynamics similar to those of bulk liquid water (16), probably because the positive charge of the Cs+ ion is distributed over a large volume: The slowly reorienting water can be attributed to a water molecule located within the solvation shell of strongly hydrated SO42–, presumably forming hydrogen bonds with both OH groups to two oxygen atoms of the SO42– ion. The low value of Np found for Cs2SO4 indicates that the effect of anions on water reorientation is either negligible or not measurable by DR measurements. Similarly, a previous GHz DR measurement of the anions Br, I, NO3, ClO4, and SCN found that the impact of these anions on water dynamics is remarkably small and remarkably similar, despite the different water affinities of these ions (17).

We used fs-IR measurements (21) to complement our DR measurements. The fs-IR technique allows direct study of the reorientational dynamics of individual water molecules with high temporal resolution (~150 fs). In these experiments, we excite the OD-stretch vibration of a subset of HDO molecules in H2O (4% D2O in H2O). Molecules with their OD group preferentially aligned along the polarization axis of the excitation (pump) pulse are most efficiently tagged. By using a second laser (probe) pulse to interrogate the number of tagged molecules parallel and perpendicular to the excitation axis, the rotation of tagged molecules can be followed in time. The anisotropy R(t) [corrected for heating due to the excitation according to (26)] as a function of pump-probe delay time t reflects the orientational dynamics of the probed water molecules. For bulk water, the decay time constant of R(t) is directly related to the Debye relaxation time τD, as measured by DR spectroscopy (27). Figure 2, A to C, shows the anisotropy decay for the dissolved salts Mg(ClO4)2, Cs2SO4, and MgSO4, each for concentrations ranging from 0 to 2 mol/kg. A remarkable conclusion can be drawn from these three measurements: MgSO4 shows a very large slow reorientation component, whereas Mg2+ and SO42– individually, in combination with other ions (ClO4 and Cs+, respectively), do not. This shows that the effect of ions on water dynamics can be nonadditive (as discussed below).

Before discussing the non-additivity, we focus our attention on the observation that there is an apparent discrepancy between the DR measurements and the fs-IR measurements. For hydrated cations, DR and fs-IR spectroscopies give different results: Mg2+ and Li+ show large immobilized fractions when measured with DR, but the fs-IR measurements of Mg(ClO4)2 and LiI show complete reorientation, with a negligible slow fraction (Fig. 2D). These fractions have been obtained using a bimodal model, analogous to the DR measurements: The slow time constant and the associated fraction of hydration water are obtained from a double-exponential fit to the anisotropy decay, in which the fast time constant equals the reorientation time constant of 2.6 ps for bulk water. This fast time constant is determined in an independent measurement performed in the absence of salt. The slow component represents a weighted average of water molecules that have in common that they reorient much more slowly than the water molecules in bulk liquid water. Note that the exchange of water molecules between the dynamic hydration shells and the bulk typically takes place on a time scale of tens to hundreds of picoseconds (28). This exchange time scale is much longer than the reorientation time of ~2.6 ps of bulk liquid water. Hence, the reorientation of the water molecules outside the dynamic hydration shells is well separated from the reorientation dynamics of the water molecules in the dynamic hydration shells. In analogy to the DR measurements, the slow water fraction as measured with fs-IR spectroscopy can be translated into a hydration number Nμ. This corresponds to the number of moles of slowly reorienting OH groups (with transition dipole moment μ) per mole of dissolved salt (keeping in mind that there are two OH groups per water molecule).

Fig. 2

Results of fs-IR spectroscopy. (A to C) The normalized decay of the anisotropy R(t) for Mg(ClO4)2 (A), Cs2SO4 (B), and MgSO4 (C) at concentrations of 0, 1, 1.5, and 2 mol/kg. We fit the anisotropy decay of all different salt solutions using double exponentials with floating amplitudes and fixed time scales: a time scale of 2.6 ps, as in bulk water (26), and a slow water time scale of 10 ps. (D) The fraction of slow water relative to bulk-like water. The lines are linear fits and serve as guides to the eye to distinguish the studied salts. The error bars are based on at least four measurement runs and represent the 95% confidence interval.

The differences between the results of DR and fs-IR spectroscopies, in terms of their apparent sensitivity toward the dynamics of water hydrating cations and anions, can be understood by noting the different vectors that the two measurement techniques probe: the permanent dipole moment of water molecules p in the case of DR spectroscopy, and the OD-stretch transition dipole moment μ in the case of fs-IR spectroscopy (Fig. 3). The local electric field around the ions causes the dipole vector p of water molecules in the solvation shell of a cation to point radially away from the cation, whereas for an anion, one of the OH groups of a hydrogen-bonded water molecule linearly points toward the anion (9, 29). From Fig. 3, it is clear that there is rotational motion of water molecules in the cationic solvation shell, which does not lead to reorientation of the vector p, but does result in randomization of the transition dipole vector μ. For the case of anions, the reverse effect occurs: For water molecules in the anionic solvation shell, the motion of p is unrestricted within a cone with fixed axis μ, where μ is the OD bond that is hydrogen-bonded to the anion. Reorientation in a cone with a semi-cone angle between μ and p of α ≈ 52° (half the HOD-bond angle) leads to a complete randomization of the vector whose motion is unrestricted within the cone (21). This explains the insensitivity of DR spectroscopy toward anionic hydration and of fs-IR spectroscopy toward cationic hydration. For both cations and anions, these observations lead to a molecular picture of semi-rigid hydration (i.e., water molecules in ionic solvation shells that reorient in a propeller-like manner), giving rise to partial reorientation along a distinct axis. The molecular picture of semi-rigid hydration explains the ion effect on water molecules directly surrounding the ion. This picture holds for salts for which one of the counterions is weakly hydrated. However, when both ions are strongly hydrated, the effect on water dynamics can be much stronger and nonadditive. The THz DR data show that Mg(ClO4)2 has a hydration number Np = 6 and that Cs2SO4 has a hydration number Np = 1; these values are associated with water molecules directly adjacent to the Mg2+ ion and a water molecule hydrating the SO42– ion, respectively. For MgSO4, Np = 18, which is much larger than the sum of the hydration numbers of Mg(ClO4)2 and Cs2SO4 (Fig. 1). This means that the dynamics of a large number of water molecules are affected because of a cooperative effect of the cation and the anion. The size of most ions allows them to be structurally surrounded by four to six water molecules. Hence, a value of Np > 6 and Nμ > 12 implies that the effect of the ion on the orientational dynamics of water extends well beyond the first structurally surrounding shell of water molecules.

Fig. 3

Semi-rigid hydration and cooperativity. (A and B) A water molecule in the solvation shell of a cation (A) and an anion (B). Dielectric relaxation measurements probe the reorientation of the permanent dipole vector p. Femtosecond infrared spectroscopy is sensitive to the reorientation of the OD-stretch transition dipole moment μ. The dotted arrows indicate reorientation in a cone, in the case of semi-rigid hydration. (C) Proposed geometry, in which the water dynamics are locked in two directions because of the cooperative interaction with the cation and the anion.

The same cooperativity is observed in the fs-IR measurements (Fig. 2), where MgSO4 has a much larger fraction of slowly reorienting water molecules (corresponding to a hydration number Nμ = 32) than Mg(ClO4)2 and Cs2SO4 (with hydration numbers Nμ of 4 and 9, respectively). For MgSO4, there are about twice as many slowly rotating OH groups (Nμ) as slowly rotating dipoles (Np), which indicates that the same collection of slow water molecules is observed by fs-IR and THz DR spectroscopies. Even the combination of the moderately strongly hydrated cation Na+ with the strong anion SO42– is observed to affect the dynamics of a large number of water molecules (Nμ = 24; Fig. 2D). Thus, the effects of ions and counterions can be strongly interdependent and nonadditive. The key parameter determining how strongly ions affect water dynamics is thus the combination of the solvated cation and anion.

It is clear that the effect of MgSO4 and Na2SO4 on water extends well beyond the first solvation shell of the ions and that the ions show strong cooperativity in affecting the dynamics of water molecules. Note that this effect is not related to ion pairing. Previous GHz DR studies by Buchner et al. showed the presence of a certain amount of ion pairs for solutions of MgSO4 and Na2SO4 (18, 20). Ion pairs lead to additional resonances at very low frequencies (<5 GHz), located well outside our THz DR measurement window (0.4 to 1.2 THz). For our fs-IR measurements we can also neglect the direct contribution of ion pairs to the anisotropy data, because this technique excites and probes specifically the hydroxyl vibrations of water molecules. Hence, the slowing of the anisotropy decay for MgSO4 and Na2SO4 corresponds to the slow reorientation of water molecules, not the slow reorientation of ion pairs. A remaining question is whether the observed slow water molecules could be water that hydrates ion pairs. This is in fact very unlikely because the amount of ion pairing is generally small—less than 10% for MgSO4, even at high salt concentrations (18)—whereas the observed cooperative effect leads to a slowing down of a large fraction of the water (up to 70% of all water molecules in the solution; see Fig. 2D). Hence, the slow water fraction is associated with hydration of nonpaired Mg2+ and SO42–.

The cooperativity in ion hydration can be explained by the fact that the cation and anion lock different degrees of freedom of the water molecules—that is, the direction of the bisectrix (p) and the direction of OH (μ), respectively. The nearby presence of both ions can thus lead to a locking in both directions of the hydrogen-bond structure of several intervening water layers, giving rise to the observation by DR and fs-IR of slowed water molecules well beyond the first solvation shell. This cooperativity is schematically illustrated in Fig. 3C. We expect the solvation structures to be quite directional between the ions; if an ion forms ~4 of these structures with surrounding counterions, the value of Np = 18 implies that each of these structures consists, on average, of four or five water molecules. This interpretation also means that for solutions such as MgSO4 and Na2SO4, the slowly reorienting water molecules are not arranged in a spherically symmetric way around the ions.

The reorientation of water molecules in the rigid, locked hydrogen-bond structure occurring for MgSO4 can be expected to show a temperature dependence different from that of pure liquid water. We measured the temperature dependence of the anisotropy decay for a MgSO4 solution (1.5 mol/kg) over an interval of about 50°C (Fig. 4A). We also compared the temperature dependence to that of a Cs2SO4 solution (4 mol/kg) (Fig. 4B) with the same hydration level (Fig. 2D) but no cooperativity. At room temperature, the anisotropy for MgSO4 decays more slowly than for Cs2SO4, but with increasing temperature the situation reverses. To quantify the results, we fit the anisotropy data at different temperatures with a single averaged time scale for all water molecules in the system. This means that a change in this time scale represents both the change in time scales and change in the relative fractions of bulk-like and slow water molecules. Figure 4C shows a much stronger temperature dependence of this average time scale for a solution of MgSO4 (1.5 mol/kg) than for a solution of Cs2SO4 (4 mol/kg).

Fig. 4

Temperature dependence of the reorientation. (A and B) Temperature-dependent anisotropy decay data for MgSO4 (A) and Cs2SO4 (B) with fits as explained in the text. (C) Average reorientation times of solutions of MgSO4 (1.5 mol/kg), Cs2SO4 (4 mol/kg), and neat HDO:H2O [from (27)] as a function of temperature.

The difference in temperature dependence of the reorientation of MgSO4 and Cs2SO4 solutions indicates that the reorientation within the hydration structures involves a different mechanism. For pure water, molecular dynamics simulations indicated that the reorientation of water follows a concerted mechanism and that the rate-limiting step for reorientation of a water molecule is the motion of a second water molecule in and out of the solvation shell of the first (30, 31). For the Cs2SO4 solution, the hydration number Nμ has a value of 9, which is likely associated with the OH groups of water molecules that are hydrogen-bonded to the SO42– ion. In view of the small value of Nμ, these water molecules are surrounded by water molecules that show bulk-like dynamics. Hence, although the reorientation of the water molecules hydrating the SO42– is slow, the temperature dependence of this reorientation is similar to that of pure liquid water, because the reorientation is governed by hydrogen-bond interactions to water molecules that show bulk-like behavior. Correspondingly, the temperature dependence of the reorientation time of Cs2SO4 is similar to that of bulk water. In contrast, for MgSO4 the solvation structures are large, as expressed by the large values of the hydration numbers Np = 18 and Nμ = 32. Hence, the reorientation of a water molecule in the solvation structure relies on the motions of water molecules that are contained in the same solvation structure. These motions are substantially slowed down, and reorientation thus involves a collective reorganization of the extended solvation structure, which explains the difference in temperature dependence with a solution of Cs2SO4 and pure liquid water.

Our results show that the hydration structure of a strongly hydrated ion depends critically on the nature of its counterion. If the counterion is weakly hydrated, the strongly hydrated ion is surrounded by a semi-rigid solvation shell, where reorientation is restricted only in a certain direction but is still allowed in other directions. However, if strongly hydrated cations and anions are combined, the dynamics of water molecules well beyond the first solvation layer are affected. In this case, the hydrogen-bond network is locked in multiple directions. These findings show that the effect of ions on water dynamics can be strongly interdependent and nonadditive.

Supporting Online Material

Materials and Methods

Figs. S1 to S3


References and Notes

  1. See supporting material on Science Online.
  2. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). We thank H. Schoenmaker for technical support, R. L. A. Timmer and E. H. G. Backus for useful discussions, and D. Frenkel and E. W. Meijer for helpful comments on the manuscript.
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