Role of proton ordering in adsorption preference of polar molecule on ice surface

Abstract

Adsorption of polar monomers on ice surface, relevant to the physical/chemical reaction in ice clouds as well as growth of ice, remains an open issue partially due to the unusual surface characteristics with protons at the top layer of ice. Using first-principle calculations, we explore the adsorption properties of ice surface in terms of a surface proton order parameter, which characterizes the inhomogeneity of the dangling atoms on ice surface. We show that, due to an effective electric field created by dangling OH bonds and lone pairs of water molecules not only directly neighboring but also further away from the adsorbed polar molecule on the ice surface, the adsorption energy of polar monomer on ice surface exhibits large variance and a strong correlation with the proton order parameter of ice surface. Our results about the positive correlation between the inhomogeneity of ice surface and adsorption energies suggest that the physical/chemical reactions as well as the growth of ice may prefer to occur firstly on surfaces with larger proton order parameter.

Ice, one of the most abundant materials on earth, plays an important role in interstellar phenomena, life in the cryosphere and global climate (1–3). Adsorption on ice surface, especially hexagonal ice, is related to the fundamental question of how ice particles grow into hexagonal ice crystal or snow flakes, and what kind of roles it plays for the reactive and catalytic properties of atmospheric ice associated with environment-related issues (1–4). For instance, the ice surface acts as a catalyst in heterogeneous physical/chemical reactions leading to the destruction of ozone (5). It has long been recognized that the adsorption properties depend on the structure of the ice surface (6–9). However, it is still striking to see that many properties of ice surfaces vary greatly even on a prefect ice surface where the oxygen atoms are ordered in a hexagonal lattice (10–13). Yet, due to the complexity of the surface structure at the atomic level, our understandings of the activity and adsorption property on the ice surface are still far from consistent and complete.

At interfaces, the Bernal–Fowler–Pauling ice rule (14, 15) cannot be obeyed; that is, nearest neighboring water molecules cannot satisfy all hydrogen bonds, thus forming dangling protons and lone pairs. Recent works (16–18) have shown that the inhomogeneity of dangling atoms, which can be characterized by a proton order parameter (17), is important for the energies of water ice surfaces (17, 18). This order parameter, C_OH, characterizing the arrangement of dangling OH bonds on the ice surface (17), is defined as

[1]

where N_OH is the total number of dangling OH bonds on the surface and c_i is the number of the nearest neighboring dangling OH bonds around the ith OH bond. For the ice slab without dipole moment perpendicular to the surface, the order parameter ranges from 2 to 6 (17). We note that the most ordered dangling OH distribution on ice surface corresponds to C_OH = 2 (Fig. S1A), while C_OH ∼ 3 corresponds to the ice surface with the most disordered dangling OH (Fig. S1B), and when the order parameter becomes larger than 3.0, the ice surface becomes more inhomogeneous (see Fig. S1C and ref. 17).

The adsorption of water monomer on ice surface is associated with the growing of ice, an opposite process associated with premelting, where the ice surface forms a quasi-liquid layer below the melting point (1, 19–21). However, how the surface structure in terms of proton order parameter in general affects the adsorption of water monomers as well as the relation between adsorption and proton order parameter has never been explicitly explored. Here, by employing density functional theory (DFT) calculations, we address the fundamental question of the adsorption of water monomer on ice surface, which strongly connects to the initial growth of ice and other gas reactivity on ice surface in the clouds. We show that for ice basal surface (0001) (SI Text), the adsorption of monomers and initial growth of ice is more likely to happen on surfaces with larger proton order parameter due to a positive correlation with the effective electric field created by dangling OH bonds and the polarized dipole moment of adsorbed monomers, indicating that the initial growth of ice may start to nucleate at ice surface with inhomogeneous proton region. Our studies here about the relation between adsorption properties and surface proton order may shed light on a better understanding of cloud microphysics and nanoscale atmospheric chemistry in the upper atmosphere.

Methods

Our system consists of a unit cell with 4-bilayer ice with 48 water molecules in each bilayer (Fig. 1A, SI Text) generated according to Hayward and Reimers’ method (22) and a 15 Å vacuum gap for the simulation of the surface. The density fluctuation theory (DFT) calculations using Vienna ab initio simulation package (VASP, see 23) are employed in our study for the adsorption behavior of polar monomer on ice surface. PBE exchange-correlation functional (24) is used with projector augmented wave method [PAW (25)] at a 550 eV plane-wave cutoff and only the gamma point is taken into account in DFT calculations. We also tested the non-local exchange-correlation functional with van der Waals interaction (see SI Text, Table S1). The entire system is relaxed until the maximum force on any atom is below 0.01 eV/Å. Molecular dipole moment is calculated using CP2K/Quickstep program suite with maximally localized Wannier function centers (26, 27). The wave functions are expanded by Gaussian orbitals, DZVP-MOLOPT (28) and the electronic density is represented by the plane waves with a cutoff of 360 Ry.

Fig. 1.

A side view of a slab of ice Ih and top views of different adsorption sites. (A) A slab consists of four bilayers of proton disordered ice Ih with proton order parameter C_OH = 2.67. (B) A1-type (Left) and A2-type (Right) adsorption site, without or with a water molecule directly underneath the adsorbed water molecule, respectively. We note that oxygen on ice surface is colored in red, hydrogen is colored in white, and oxygen of the adsorbed water molecule is colored in green.

We also perform molecular dynamics (MD) simulations in NVT-ensemble using LAMMPS (29) for the dynamic study of adsorption of water monomer on ice surface. For this study, our system is a 2 × 2 × 2 replicate of the former cell in DFT calculations, consisting of 8-bilayer ice (35.3616 Å × 45.9362 Å × 210 Å) with the bottom bilayer fixed. Three dimensions periodic boundary conditions are applied with an approximately 180 Å vacuum gap in z-direction. We choose TIP4P/Ice potential and use SHAKE algorithm to keep water molecule rigid (30–32). The cutoff distance is 9 Å for interactions between two water molecules and 13 Å for Coulomb interaction. The typical duration of the equilibration run is about 2 ns.

Results

Previous studies (33, 34) have shown that the adsorption energy of ice surface depends on the number of hydrogen bonds and their orientations of the three nearest neighboring water molecules with respect to the adsorbed water monomer. For instance, at sites (A-type site as shown in Fig. 1) with one dangling proton and with or without water molecule directly underneath the adsorbed water monomer, the adsorption energy of water monomer can be significantly larger than the cohesive energy with empirical TIP4P potential (33). However, it is surprising to see that in some cases, the binding energy is lower than the cohesive energy when using first principle calculations even for similar adsorption sites (34), different from the results by molecular dynamics simulations (33). One immediate question is what may cause such kind of inconsistencies.

To tackle this question, we take into account the proton order of the ice surface, which was not considered in previous studies (33, 34). We investigate adsorptions on ice surfaces varying from perfect proton ordering surface with an order parameter C_OH = 2 [e.g., the striped phase for ice basal surface (35)] to more inhomogeneous ones with C_OH > 2 possibly occurring at relatively high temperature with certain degree of proton disorder due to excitations. The adsorption energy for different A-type sites as a function of surface order parameter is shown in Fig. 2. When the order parameter is larger than about 2.5, the adsorption energy for water monomer can be larger than the cohesive energy of bulk ice 0.662 eV (Fig. 2). The largest adsorption energy for ice surface with order parameter C_OH = 4.67 is 0.960 eV, about one and a half times as large as that for ice surface with C_OH = 2.0. However, when ice surface with C_OH = 2 is considered, the largest adsorption energy (0.619 eV for A1-type and 0.583 eV for A2-type), slightly larger than but pretty close to that obtained from DFT calculation (0.575 eV and 0.552 eV, respectively, see ref. 34), is about 80% of the bulk cohesive energy.

Fig. 2.

Demonstration that the proton ordering C_OH affects the adsorption energy of ice surface. Approximately, the larger the order parameter (the more inhomogenous the ice surface) is, the higher the adsorption energy. There exists a large variation in the adsorption energy for a fixed order parameter, among which the largest adsorption energy is lower than the bulk cohesive energy (dashed line) for C_OH < 2.5 but higher than the bulk cohesive energy for C_OH > 2.5.

Thus, the inconsistency in the adsorption energy with respect to bulk cohesive energy between DFT calculation and TIP4P calculation (33, 34) lies in the fact that they checked different surface even though both calculations considered the same type of adsorption site, A-type site. Our calculations indicate that previous study by DFT mainly focuses on the highly ordered ice surface with C_OH = 2.0, while the latter one for TIP4P corresponds to a disordered one with C_OH ∼ 3.0, respectively. Our calculations based on the more inhomogeneous surfaces with higher order parameters (C_OH > 2.5) shows that the largest adsorption energy for ice surface can be much larger than the bulk cohesive energy. Thus, proton order parameter of ice surface is a more general parameter than previous classifications [A/B type classification* (33)] in characterizing adsorption energy of water monomers.

Another interesting question is the large variance in adsorption energy (Fig. 2). For example, the largest and lowest adsorption energy for C_OH = 4.17 is different by ∼0.3 eV, almost half of the adsorption energy (∼0.6 eV) for C_OH = 2 (Fig. 2). According to a previous study by Watkins, et al. (10), when a molecule is removed from ice surface, which is related to the premelting of ice, the vacancy formation energy varies greatly, partially due to the local electric field created by the dangling protons. How about adsorption energy in the opposite physical/chemical process—the adsorption process which is related to the initial growth of ice? In the following, we answer this question by directly calculating the local electric field caused by the dangling charges, protons and dangling lone pairs, to see how it contributes to the adsorption energy.

According to previous study by Pan, et al. (17), the dangling proton has an effective charge on ice surface, q = 0.21 e. We define the effective electric field as the projection of local electric field along the dipole direction of the adsorbed water molecule,

[2]

where ε₀ is vacuum permittivity, r is the distance from the oxygen atom of the adsorbed water molecule to the dangling proton or oxygen atom on ice surface, and θ is the angle between the direction of r and the direction of the dipole of adsorbed molecule. With d_H as the distance from oxygen atom of the adsorbed water molecule, Θ(r_i) = 1 within d_H, while Θ(r_i) = 0 outside d_H. The effective electric field as function of d_H is presented in Fig. 3. It is obvious that the effective electric field becomes more or less a constant when d_H > 10 Å. Thus the contribution to the effective electric field is not only from the nearest neighboring dangling protons or oxygen atoms (d_H < 3 Å), but also from further neighboring ones. Please note that in the type A/B classification, only the nearest neighboring dangling atoms are considered^* (33).

Fig. 3.

Demonstration of the effective electric field created by dangling protons and dangling lone pairs on ice surface. Magnitude of effective electric field becomes more or less constant when d_H > 10 Å. For different adsorption sites such as A1-type sites (A1a: filled circle, A2b: filled square), the effective electric fields are different. Thus, for ice surfaces with large variation of absorption sites, there exists large variation of effective electric field.

As shown in Fig. 4, the magnitude of the largest effective electric field increases with increasing ice surface order parameter. For the stripped ice surface, C_OH = 2.0, the magnitude of the effective electric field E (∼0.511q/4πε₀ for A1-type and ∼0.497q/4πε₀ for A2-type) is the smallest along the dipole direction of adsorbed water monomer among all A-type sites. This is due to a cancellation effect from the interlaced displacement of the dangling protons and oxygen atoms on the ice surface (Fig. S2A). For the ice surface with larger C_OH, the dangling OH bonds stay together and the ice surface becomes more inhomogeneous. Hence, the overall electric field due to the effective charges of the dangling atoms is stronger (Fig. S2 B and C).

Fig. 4.

The largest effective electric field of each surface increases with increasing order parameter C_OH. The triangles indicate the effective electric field for striped ice, which is the smallest among all ice surface models.

The adsorption energy U of ice surface depends on the dipole moment P of the adsorbed water monomer and the effective electric field E, U = E^∗P. We note that P varies under different polarization conditions (36), e.g., P ∼ 1.855D in gas phase (37) and in the range of 2 to 4D with an average value of 3.1D in liquid phase under ambient condition (38). Because the local arrangement of water molecule on ice surface with dangling protons is quite different from either gas or liquid, the dipole moment of the adsorbed water molecule may change as well. Here, we give the calculated dipole moment of the adsorbed water molecule with A-type structures on ice surfaces. The dipole moment for the adsorbed water molecule is about 2.7D for C_OH = 2.0 and 3.1D for C_OH = 4.67, following a positive correlation with C_OH (Fig. 5). This shows that the effective electric field created by dangling atoms on ice surface affects the polarization of adsorbed water molecule, thus influencing the adsorption properties of ice surface.

Fig. 5.

Positive correlation between the dipole moment for adsorbed water molecule and surface order parameter C_OH. The largest dipole moment of the adsorbed water molecule follows a linear trend as the inhomogeneity of the ice surface.

The adsorbed energy, influenced by the effective electric field, is also a function of the relative orientation of the dipole moment and local electric field. As shown in Fig. 6 for one type of adsorption site, the A-type site, the adsorption is enhanced when the local electric field caused by dangling atoms lineup with the dipole moment and is reduced vice versa. Due to large variations in local arrangements, there exist large variations in effective electric field, polarized dipole moment as well as a large variation in their relative orientations, which are the sources of the large variation in adsorbed energy (∼0.3 eV). For instance, the adsorption energy is different for different A1-type site, about 0.921 eV (Fig. 6A) and 0.614 eV (Fig. 6B), due to a variation in effective electric field contributed by dangling protons from the second (or third, fourth, and so on) nearest neighbors.

Fig. 6.

Relative orientation of the dipole moment of the adsorbed water molecule and the local electric field at different A1-type adsorption sites on the same surface with C_OH = 4.17. (A) Stronger enhancement of adsorption due to a lineup of local electric field with the dipole moment, and (B) a weaker enhancement of adsorption of water molecule (the yellow molecule). The thin black arrow indicates the direction of the dipole of adsorbed water molecule, while the thick blue arrow shows the local electric field caused by dangling atoms nearby the adsorbed water molecule. The scale bars are 10 Å.

It is interesting to ask whether our findings of adsorption property of H₂O on ice surface with respect to order parameter C_OH is still valid for other polar molecule. We take hydrogen sulphide (H₂S) as an example, a gas that is regarded as a main reason for changes in ocean circulation when released to surface water at the Precambrian/Cambrian boundary (39). H₂S shares similar shape as H₂O but different in dipole moment [∼0.97D (40)]. As shown in Fig. 7, similarly to that of H₂O, the adsorption energy of H₂S is positively related to order parameter. However, the adsorption energy of H₂S on ice surface is lower than the corresponding adsorption energy of H₂O, confirming a linear dependence of dipole moment on adsorption energy of polar molecule (Fig. S3). The reason behind the weaker adsorption of H₂S on ice surface is possibly due to the fact that S atom has smaller electronegativity than O atom, therefore, compared to water monomer, H₂S has a smaller dipole moment, which forms a weaker H-bond, and thus becomes less active with ice surface, resulting in lower adsorption energy (41). Our findings suggest that the proton ordering on the surface is very important for growth on the ice surface. When a water molecule or similar polar molecule deposits on the surface, it prefers the surface patch with large order parameter because of larger adsorption energy.

Fig. 7.

Adsorption energies for H₂O and H₂S are positively correlated with surface order parameter C_OH. Similar to the adsorption of H₂O, the adsorption energy of H₂S increases with order parameter. However, for ice surface with same order parameter, the adsorption energy of H₂S is smaller than that of H₂O due to a smaller dipole moment compared with that of H₂O.

To further verify the point of the adsorption to large local electric field, we have performed additional molecular dynamics simulations for ice surface (3.75 nm*4.59 nm) with different local adsorption site using TIP4P/ice (30, 31) interaction model. We choose this potential because it can correctly reproduce the melting point of ice at ambient condition. Studies (21) have shown that different proton order of ice Ih surface has an effect on premelting behavior, but does not affect the melting temperature estimated based on the liquid-solid coexistence method (42, 43). The simulation details are described in the method section. We find that the admolecule moves on the ice surface until it is adsorbed to a site with large local electric field created by dangling atoms on ice surface (Fig. S4). This is consistent with our conclusion that the initial growth of ice prefers to occur on the ice surface with higher inhomogeneity. Thus, the ice surface patches with large order parameter are probably the initial favorable basis for adsorption/reaction on the ice surface in the upper atmosphere which is an interesting point that needs additional effort to confirm in future experiments.

To summarize, we have studied the adsorption of water monomers on ice surface in terms of proton order parameter. Our studies show that the adsorption of water monomer on ice surface depends largely on the dangling protons and lone pairs, which create an effective electric field ultimately affecting the adsorption energy. The contribution of dangling atoms to the effective electric field varies greatly for surfaces with different order parameters, which explains some existing inconsistencies. The variance in local arrangement and orientation of dangling atoms leads to a variation of effective electric field, which further affects the dipole moment of the adsorbed water molecule, resulting in broad variance of adsorption energy of water monomer on ice surface. Furthermore, the positive correlation of adsorption energy of water monomer with surface proton ordering suggests that the adsorption may prefer to occur first at surface with large order parameter, which may shed light on our understanding of the initial growth of ice as well as other physical/chemical reactivity in high altitude clouds.