It has been well-corroborated both experimentally and theoretically that the top most water layer of the air-water interface is organized with a majority of O-H dangling bonds pointing toward the vapor phase.36, 37, 38 Just beneath the topmost layer and parallel to the instantaneous fluctuating surface there is a two-dimensional hydrogen bond network39, 40 that supports the "free O-H" configuration. These structural and dynamical features of the air-water interface, which has a thickness of ~ 2 solvation layers deep40, will yield electric field signatures that are expected to be distinct from the bulk-like interior of the droplet. Indeed the free O-H of the water molecules at the surface generates asymmetric stretching frequencies that are highly sensitive to their hydrogen-bonding structural and electronic environment and/or presence of excess ionic charge. As such, they are also direct reporters of surface electric fields as shown by Cooper et al. using Infrared Photodissociation (IRPD) spectroscopy in which the measured Stark shifts are linearly proportional to the local electric field at the surface,41 depend on cluster size, and the absence or presence of ions and their identity.42
Figure 1A displays the experimental IRPD measurement which shows that the neutral water and anionic water clusters exhibit a red-shift of the free O-H band with increasing cluster size42, 43, 44, whereas for positively charged cations there is a blue-shift of the free O–H band when progressing to larger clusters, accompanied by a transition in slope that correlates with the ion's charge (n = 100 and 30 for Ca2+ and Na+, respectively). This trend is not reproduced using simple fixed charge models that instead exhibits a linear function of the Stark shift with 1/r2 (Figure S1), and is an important indicator that the surface features of microdroplets arise from many-body effects such as charge transfer35, 45 and intramolecular and intermolecular polarization.46, 47, 48. In this work we have utilized a reactive force field model of water, ReaxFF/C-GeM49, 50, that explicitly models coarse-grained electrons45, and yet can handle the relatively large sub-micron droplets simulated over tens of nanoseconds that we have examined here that is not accessible to ab initio molecular dynamics. Figure 1B verifies that the Stark shift trends are very well captured by the ReaxFF/C-GeM model, which is relevant for not only the validation of the simulation model, but plays an important interpretative role in analyzing the electric field for large water droplets in terms of electron density, protonation states, and ion effects at the air-water interface.
Now we turn to the profile of the electric field normal and parallel to the droplet surface and evaluated from contributions from the interior water and due to that from waters at the surface for much larger droplets of 80–160 Å (R40-R80) in diameter (Fig. 2). The electric field property has been difficult to determine experimentally owing to challenges of sensitivity and spatial resolution, and the choice of appropriate optical probes for reporting absolute electric field strength. For the larger droplet sizes we simulate, we determine an average electric field normal to the surface of − 8.5 MV/cm, in excellent agreement with the SREF experiments (Table S1). The negative sign of the electric field of the pure water droplet arises from an overall positive surface potential, i.e. an integration of the distance weighted charge density as shown in Fig. 2(A). Although a recent study has determined a small negative surface potential35, the signs may differ for low electric field strengths depending on how the charge density is averaged and the definition of the surface thickness at the air-water interface. What we believe is mutually supportive of the work of Poli et al is the idea that it is how the electron density is organized at the interface, a critical factor for pH in their study35 and electric field strengths for surface reactivity which is the topic here.
Although the averaged electric field at the surface is consistent with the SREF measurements, a radial profile of the charge density details its organization at the interface. Starting from the inner droplet the charge density first increases to L2 and then decreases in the L1 region before increasing rapidly at the outermost L0 interfacial region (Fig. 2A). These integrated nuclear and electronic charge density features track the radial dependence of the surface normal electric field that reaches values of close to − 25 MV/cm at L0 as shown in Fig. 2B. This is because the electronic shells are displaced such that the atomic cores are less shielded at the outermost L0 surface, and resulting in an increase in the electronic density in the L1 region.
Whether the surface electric fields are evaluated from the inner droplet (r < L2) or at the surface (r > L2), the electric field distributions obey Gaussian fluctuation statistics as seen in Fig. 2C and 2D. Finally, there is a notable increase in the electric field as the nanodroplet sizes increase (Fig. 2B), increasing by ~ 3 MV/cm when doubling the droplet diameter when using the instantaneous surface method of Willard and Chandler51 (Table S1), suggesting that the surface fluctuations further magnify the size dependence of the electric field effect. If we were to extrapolate the electric field trends to a micron-sized droplet we might see the outer surface field strengths that would increase significantly, and potentially even shift water’s autodissociation constant to larger values.
In regards an additional surface active charged species, we consider an excess of cationic species in the form of 24 H3O+, or an excess using 24 OH−. The ion distribution profiles are provided in Figure S2, and show that H3O+ ions have a greater propensity for the surface while the OH− ions distribute throughout the surface and inner droplet region. With an excess of 24 H3O+ for a R40 droplet that is ~ 88% of the Rayleigh limit, the positive charge density increases significantly given the greater propensity for hydronium at the surface (Fig. 3A), such that the electric field is about 3–10 times larger than that emanating from the inner droplet region (Fig. 3B). By contrast, in the presence of the OH− ions which are better mixed throughout the droplet, there is a diminished positive surface potential (Fig. 3A) that yields an integrated electric field that is notably smaller than the pure water droplet (Fig. 3B). Similar trends are observed for excess Na+ and Cl−, or corresponding salt mixtures (Table S1 and Figures S3 and S4). The electric fields at the surface also exhibit Gaussian fluctuation statistics, such that the response of the surface water fields increases (decreases) linearly with the cation (anion) solute charge (Figs. 3C,D).
Overall this is consistent with the larger Stark shifts seen with small nanodroplets in the presence of cations, whereby electron density displaces toward the hydronium charge and deshielding the hydrogen of the free O-H at the surface to create an even larger positive surface potential compared to pure water. By contrast the anions push greater electron density onto the exposed O-H bond at the surface such that the magnitude of the Stark shift is found to be smaller due to a reduction of the positive surface potential. Thus the variations of the electric fields at the surface arise from not just structural variations tracked by the permanent water dipole direction, but due to polarization effects whereby the coarse-grained electrons organize differently in the L0 vs L1 region.
To further analyze the effect of the electric field that can potentially catalyze chemical reactions and break chemical bonds in a microdroplet, we project the electric fields onto the O-H bond vector of water molecules in the inner droplet and onto the free O-H bond at the surface (Fig. 4). The electric field projections exhibit a non-Gaussian distribution, a consequence of the non-linear coupling of the intramolecular polarization of the solute with the intermolecular solvent modes as anticipated by Matyushov and co-workers.46 For a pure water droplet, or in the presence of charge, the surface free O-H bonds are more destabilized due to a higher averaged electric field of − 163 MV/cm compared to the interior bonds which experience smaller field strengths of − 131 MV/cm.
The significance of an approximately − 30 MV/cm increase in field strengths at the air-water surface would correspond to lowering an energy barrier by about 2.9 kcal/mol, which in the exponential would increase the rate of reaction by over two orders of magnitude for a rate limiting bond breaking step. The primary effect due to the presence of excess H3O+ ions or OH− ions is to yield electric field projections with much larger field strengths in the much wider wings of the Lorentzian as seen in Fig. 4. This potentially increases the odds for chemical bond weakening relative to pure water, which may be relevant in the electrospray process that generates a large number of droplets of various charge states. The electric field projections in all other variations with excess ions/charges are qualitatively consistent with that found for hydronium and hydroxide and can be found in the SI.