Atomistic simulation of ion solvation in water explains surface preference of halides

Results and Discussion

Fig. 1 B and C presents potentials of mean force ΔG(r) for the ion solvation into the water droplet, where r denotes the distance of the ion from the center of mass of the water droplet, as illustrated in Fig. 1A. The gray dashed lines in the figures indicate the Gibbs dividing surface of a water droplet with no ion. The surface of the droplets are not at all smooth, especially not when an ion is being dragged out from the droplet (as can be seen in Fig. 2), and the Gibbs dividing surface should therefore be seen as an approximation only. The PMFs were defined to be zero in the droplet interior, and the flat regions at r > 2.5 nm correspond to the fully desolvated ions and thus indicate the complete desolvation free energy. The insets of Fig. 1 B and C show a close-up of the PMF, revealing local minima near the droplet surface in the PMFs for Cl^-, Br^-, and I^- (Fig. 1B). The surface preference as measured from the depth of the minimum increases with the size of ion but only for the halide anions.

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Fig. 2.

Characteristic trajectory snapshots of K⁺ and Br^- ions in a water droplet. Region I: ion at the center of mass of the water droplet. Region II: ion 0.9 nm from center of mass of the water droplet. This region is the energetically most favorable for the halide anions. Region III: ion 1.4 nm from the center of mass of the droplet. Here all ions experience a force pulling them back into the water. Compare the three regions to Fig. 3. Movies S1 and S2 show the ions being pulled out of the droplets.

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Fig. 3.

Decomposition of the potentials of mean force into enthalpic components (A and B) and entropic components (C and D), as well as decomposition of the enthalpic component into (E and F) water–water and (G and H) ion–water interactions. The entropy and enthalpy are plotted as the energy difference with respect to the droplet interior. (A) The surface preference of Cl^-, Br^-, and I^- is induced by a substantial minimum in the enthalpic component ΔH(r) near the droplet surface (r ≈ 1 nm), which is only partially compensated by a lower entropy (C). In contrast, for F^- on the droplet surface, the substantial loss of entropy (C, black curve) is only partly compensated by a slightly decreased enthalpy (A, black curve), indicating that an entropic driving force explains the bulk preference of F^-. (B) Alkali cations are in the droplet bulk due to the favorable enthalpy. Partly desolvated halide anions on the droplet surface allow for more favorable water–water interactions (E). Alkali cations are driven into the bulk by more favorable ion–water interactions (H).

The PMFs can be used to compute concentration enhancement in the outermost water layer (0.75 nm ≤ r ≤ 1.1 nm). For Cl^- the surface concentration will be 1.6 times higher than in the bulk, for Br^- and I^- the factors are 7 and 13, respectively (see Methods in SI Appendix). Thus, I^- is enhanced twice as strong on the surface than Br^-, in qualitative agreement with experimental findings (9). Comparing the individual concentration enhancement factors to experiments requires incorporation of the probe depth of the specific experiment (10). Assuming an exponentially decaying probe signal with decay length between 0.5 and 1 nm, the PMFs would imply that experiments measure concentration enhancements by factors of approximately 1, 4, and 6, for Cl^-, Br^-, and I^-, respectively (Methods in SI Appendix). Hence, the slight concentration enhancement of Cl^- may not be visible in such experiments. The value for Br^- would translate into a surface affinity of approximately 3 kJ/mol, in excellent agreement with recent spectroscopic experiments (19). In contrast to the large halide ions, the PMFs for F^- as well as for the alkali cations Fig. 1C Inset) monotonically increase with r, demonstrating the bulk preference of these ions, in accord with previous observations (12, 22–24). Now that we have established quantitative correspondence of our calculations with available data, we can tackle the question of why the ions behave like they do.

Fig. 3 A and B shows the enthalpic component ΔH(r), and in Fig. 3 C and D the entropic component TΔS(r) of the free energy of solvation. Note that these components sum up to the PMF via ΔG(r) = ΔH(r) - TΔS(r). Remarkably, the enthalpies for all halide anions display a minimum at the droplet surface (referred to as region II in Fig. 2). For Cl^-, Br^-, and I^-, this enthalpic minimum is only partially compensated for by a reduced entropy on the surface as compared to the bulk (Fig. 3C). Hence, the surface preference of the large halide anions is based on an enthalpic effect. For F^-, the smallest halide anion, the entropic component overcompensates the slight enthalpic minimum at the surface, summing up to a monotonically increasing PMF. Hence F^- ions are driven from the surface into the droplet by an effective entropic force. The alkali cations show monotonically increasing PMFs as well (Fig. 1C), which is entirely due to the enthalpic term ΔH(r) (Fig. 3B). Entropic effects do not seem to play a role in the bulk preference of alkali cations, because the entropic profiles (Fig. 3D) are nearly flat inside the droplet.

By decomposing the enthalpic component ΔH(r) into water–water and water–ion interactions, represented by the time averaged interaction potentials (Fig. 3 E–H), we can pin down the factors that govern surface/bulk preference of ions. The potential energies are plotted relative to the center of the droplet (i.e., V(r = 0) ≡ 0 in all cases). In this manner, the water–water and the ion–water interactions sum up to the enthalpic plots in Fig. 3 A and B. For the halide anions, the water–water interaction is more favorable (more negative) by several tens of kJ/mol if the ion is partially desolvated, as compared to a fully solvated ion (Fig. 3E). As expected, some ion–water interaction is lost upon partial desolvation (Fig. 3G), but the gain in water–water interaction outweighs the loss in ion–water interaction, yielding the minima in the ΔH(r) curves around r = 1 nm in Fig. 3A. Only for larger r > 1.5 nm—that is, when the ions start to become fully desolvated—does the loss in ion–water interaction outweigh the gain in water–water interaction, leading to the unfavorable sharp increase in ΔH(r). Compared to the halide anions, the solvation energetics of the alkali cations are qualitatively different. Here, the water–water interaction is almost unaffected by a partial desolvation of the ions (Fig. 3F). Instead, the monotonic loss of ion–water interaction (Fig. 3H) accounts for the monotonically increasing ΔH(r) curves and, hence, also for the bulk preference of the alkali cations.

Is there a structural explanation for the shape of the enthalpic and entropic curves in Fig. 3? Experiments suggest that water–ion interactions are highly localized in space. Femtosecond pump–probe spectroscopy demonstrated that sulfate and perchlorate ions do not influence the rotational dynamics of water molecules outside the first solvation shells of the ions (25), indicating that the insertion of these ions does not affect the hydrogen bond network on a larger scale. Similar findings were reported for the solvation of alkali cations based on O-H vibrational spectroscopy (26). It has, however, also been reported that at higher concentrations some ions can have strong nonadditive effects on water dynamics (27), obscuring the simpler picture of Omta et al. (25). In an attempt to find structural explanations for the energetic curves (Fig. 3), we have computed radial distribution functions (RDFs) for water molecules around the ions and around other water molecules (Figs. S1 and S2 in SI Appendix). We found that the changes in the ion–water RDF as the ions move from bulk to surface is identical for all ions—the changes merely reflect the gradual desolvation of the ions. The water–water RDFs are virtually independent of the ion position in all cases. The water–ion structure can be examined by correlating the features of the PMFs (Fig. 1 B and C) with order parameters representing the hydration structure around the ions. To this end, we have calculated two-dimensional energy landscapes with distance r on one axis and either the ionic coordination number or the orientation of water in the first solvation shell with respect to the ion on the other axis (Figs. S3 and S4 in SI Appendix). Neither of these analyses yields a simple mechanistic explanation for the bulk/surface preference. This indicates that the structural rearrangements underlying changes in enthalpy are very subtle.

Specific ion properties such as the polarizability and the size of the ions have been proposed to explain the bulk versus surface preference (for reviews see refs. 10 and 11). In particular, it has been suggested that the surface potential at the water–air interface induces a dipole in polarizable anions, whereas the ion is not polarized in the bulk. Consequently, the induced dipole of the ion would be attracted by the air–water interface, compensating for the loss of solvation as the ions move to the surface. Our results do not support this view, because the ion–water interaction becomes less favorable as the halide anions move to the surface (Fig. 3G). Remarkably, the loss in ion–water interaction is most prominent for the highly polarizable I^-, demonstrating that the water molecules do not attract the ion to the surface. To shed more light on the putative effect of ion polarization, Fig. 4 A and B presents the average ion dipole as a function of position. The polarization of the halide ions increases only slightly as the ions move to the surface (Fig. 4A), but this slight increase is in fact strongest for F^-, which does not display any surface preference. In addition, Fig. 4 C and D shows the average dipole of water molecules as a function of ion position. Interestingly, as halide anions move to the surface, the water dipoles increase simultaneously with more favorable water–water interaction (Fig. 3E), which explains how the water–water interaction energy can become stronger without changing the water–water structure. However, F^- shows a water dipole curve similar to the large halide anions, despite its qualitatively different bulk preference. Thus, we must conclude that neither the ion- nor the water-polarization can provide a complete explanation for the bulk/surface preference. To assess if polarizability in combination with the size of the ion could explain the bulk/surface preference, we have computed PMFs for hypothetical cations with size and polarizability taken from the halide ions but with an inverted (positive) charge (Fig. S5 in SI Appendix). In contrast to the large halide ions, none of these hypothetical ions show any surface preference. This demonstrates that the specific polarizability/size combination of halide ions is not sufficient to determine the bulk/surface preference either, because the sign of the charge plays an important role as well. This notion rules out the possibility to fully explain the surface preference based on continuum models that do not explicitly include the asymmetry of the water molecules.

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Fig. 4.

Ion dipole as a function of ion position for (A) halide anions and (B) alkali cations (with respect to the center of charge). Average dipole of water molecules as a function of ion position for (C) halide anions and (D) alkali cations. Errors in the figures are less than 1%.

Our simulations demonstrate that the source of the bulk/surface preference is different for different ions and that simple models and approximations may have to be abandoned in favor of the quantitative energetic description of solvation presented here. The simulations suggest that no single mechanistic explanation exists that elucidates the bulk/surface preference of all the alkali and halide ions. In fact, structural changes must be interpreted with care. For instance, the two-dimensional energy landscape for I^- as a function of r and water orientation (Fig. S4 in SI Appendix) indicates higher configurational freedom of water when I^- is located at the surface. This could lead to the false conclusion that the surface preference of I^- is due to higher water entropy. However, our energetic analysis clearly demonstrates that, on the contrary, I^- on the surface is entropically unfavorable (Fig. 3C, blue curve).

The energetics of partial ion desolvation, which govern the bulk versus surface preference of ions, are significantly more complex than what was appreciated previously. Recall that the large free-energy differences for moving ions from vacuum to bulk are dominated by the favorable ion-water interaction. In contrast, the bulk versus surface preferences are based on a fine balance between entropic and enthalpic driving forces, where the latter are in turn based on competing ion–water and water–water interactions. The surface preference for the highly polarizable halide anions Cl^-, Br^-, and I^- was found to be enthalpically driven, because partly desolvated halide anions allow for more favorable water–water interactions compared to fully solvated halide anions. The F^- bulk preference is due to an entropic effect, whereas the alkali cations are driven into the bulk by the highly favorable ion–water interactions. It would be very interesting if the experiments of Onorato et al. (19) on Br^- were repeated at different temperatures (and, obviously, with Cl^- and I^-) in order to be able to decompose the surface affinity into entropic and enthalpic components, as this would yield a route to verify the results in Fig. 3 in this work.

The fundamental properties of aerosols remain among the largest uncertainties in climate science (6). By now, it must be excruciatingly clear that the properties of aerosols are determined by a complex interplay of enthalpy and entropy: Approximations and simplified models can give results that are both quantitatively and qualitatively incorrect (28). The fact that the effects of salts can be nonadditive complicates matters further (27). We have shown here that atomistic simulations that include polarization explicitly can unravel the intricate energetics of ion solvation and, with this, enhance understanding of aerosols.