Letter pubs.acs.org/JPCL
Characterizing Charge Transfer at Water Ice Interfaces Alexis J. Lee and Steven W. Rick* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148, United States ABSTRACT: Simulations are carried out for the ice/vapor and ice/liquid interfaces using models for water which include intermolecular charge transfer, as well as polarizability. The models transfer a small amount of charge for each hydrogen bond formed, as indicated from electronic structure calculations, from the molecule that accepts the hydrogen bond to the molecule that donates the hydrogen bond. Depending on distance from the interface, molecules can, on average, have more of one type (donor or acceptor) than the other. The asymmetric local environment leads to net charge transfer at the interface, with layers of molecules with small net charges. Molecules at the ice side of the interface tend to be positively charged, while molecules at the vapor or liquid side tend to be negatively charged. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis fluctuating charge TIP4P-FQ model,41 resulting in the TIP4P-FQ+DCT model. For this study, the TIP4P-FQ model, both with and without charge transfer, was implemented to simulate the ice/water and ice/vapor interfaces. The simulations were set up for the primary prism interface. For the ice/vapor simulations, 1536 water molecules were used, in a simulation box of about 29 Å × 34 Å × 120 Å, with exact box lengths in x and y, adjusted to give a pressure of 1 atm in that direction. These simulations were done at constant temperature (273 K), volume, and particle number. The ice/ liquid simulations used 1440 water molecules in a simulation box of about 23 Å × 23 Å × 85 Å. Those simulations were done at constant temperature, pressure, and particle number. The temperature was taken to be the melting temperature for each model: 303 K for TIP4P-FQ42 and 302 K for TIP4P-FQ +DCT.40 Temperature was controlled by a Nosé−Hoover thermostat.43 Atomic charges were treated as dynamical variables, assigned fictitious masses, and propagated with extended Lagrangian formalism.41 Ewald summations were used to calculate the electrostatic interactions.43 Both interfaces used 4 ns of simulation time. Calculations were carried out using our own programs. The Ice/Vapor Interface. The properties of the ice/vapor interface are shown in Figure 1. All properties are shown as a function of the coordinate perpendicular to the interface (the z coordinate) for the oxygen atom on each molecule. The density (Figure 1A) shows a change from the bulk values in the peaks around −5 Å and shows one melted, or disordered, layer between 0 and 5 Å, giving the interface a width of about 10 Å. Simulations with other (nonpolarizable) models have found similar density profiles,44−46 with a thickness that depends on temperature.44,46 The value z is set equal zero at the point between the disordered and ordered layers. The results for the
T
he electrostatic properties of ice surfaces are important for a variety of processes, including the formation of thunderstorms,1,2 the adhesion of ice to other materials,3 and the adsorption of particles to ice surfaces in the atmosphere.4 These properties can be characterized by the surface potential,5−9 the zeta potential,10 the surface charge,11 and the Workman−Reynolds freezing potential.12,13 The charged nature of ice surfaces is also suggested by experiments that show that water freezes at very different temperatures and nucleates at a different interface (the ice/vapor or the ice/ water) next to a positively or negatively charged surface.14 The surface charge has been attributed to lattice defects,15,16 salt ions,12,13 hydronium or hydroxide ions,9 and the ordering of dipole moments at the surface,11,17,14 all of which can be kinetically trapped, by a growing interface, or thermodynamically stable. Another source of surface charge is proposed in recent computer simulations of liquid water interfaces.18−20 In these studies, charge transfer interactions lead to charged molecules at the surface. This charge transfer results from asymmetries in the environments of water molecules at the interface. In this paper, we use a recently developed charge transfer model to examine the properties of the ice/vapor and ice/liquid interfaces.21 Simulation Methods. Electronic structure calculations22−32 and experimental data33−39 reveal that charge transfer contributes significantly to the interactions between water and other hydrogen-bonded molecules. These studies indicate that small amounts of charge are transferred from one water molecule to another, which contributes to both short-ranged near-neighbor interactions and long-ranged electrostatic interactions. Recently, a charge transfer model has been developed for liquid water21 and has been used to study bulk ice.40 This model transfers charge between two molecules forming a hydrogen bond. Each hydrogen bond transfers a charge of −0.02 e from the hydrogen bond acceptor to the hydrogen bond donor, as is indicated by electronic structure calculations.25,26,28,29 Details of the models are given elsewhere.21 Charge transfer was added to the polarizable © 2012 American Chemical Society
Received: September 13, 2012 Accepted: October 16, 2012 Published: October 16, 2012 3199
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used.57 Molecules at the edge of the interface show a tendency to accept more hydrogen bonds than they donate, indicating that the molecules have dangling hydrogens. Dangling hydrogens have been previously observed in both experiment and simulation.58,59 Note that the hydrogen bond difference is very small, with a maximum value near 0.1, corresponding to one molecule out of 10 having a hydrogen bond imbalance. At the very edge of the interface, where the density is almost zero, near z = 5 Å, molecules donate more hydrogen bonds than they accept. Molecules on the other edge of the disordered density peak, just above z = 0 Å, also have Nacc < Ndon. Molecules in the adjacent, more ice-like layer, below z = 0 Å, accept more than they donate. Both models give similar results, except for the one feature at −5 Å, which corresponds to a low density region and sparse molecular population. Hydrogen bond asymmetry leads to a net amount of charge transfer for molecules at the interface (Figure 1). Charge transfer between molecules causes three layers of molecules with net charges. At the edge of the interface, there is net positive charge, corresponding to the small number of molecules at the surface with Nacc > Ndon. For the rest of the disordered peak, around z = 1 Å, there is a net negative charge. Molecules in the first structured layer, below z = 0 Å, tend to be positively charged. The maximum charge density of 0.04 e/nm3 corresponds to a concentration of a 0.07 M solution or 1 charge for every 832 water molecules. The integrated charge, starting from the vapor phase is shown with the dotted line in Figure 1. This shows that there is a negative charge on the surface, with the compensating layer of positive charge on the ice side of the ice/vapor interface. The integrated charge shows a maximum negative valye of −0.004 e/nm2 right at the position between the disordered and ordered layers (z = 0 Å). A similar charge profile (small positive peak at the surface, followed by a larger negative peak, then the compensating positive peak) is seen in simulations of the liquid water/vapor and liquid water/oil interfaces.18−20 Those interfaces, using the same or similar models to TIP4P-FQ+DCT, find a charge transfer amount that is smaller by about a factor of 2, perhaps because the liquid surface is rougher, with some of the charge transfer effects being reduced due to capillary waves.19,20 Figure 1D is the molecular charge from charge transfer only. The atomic charges lead to a charge density profile as well (Figure 2 A). There are clearly visible positive layers from hydrogen atoms and negative layers from oxygen atoms. This layering is evident even in the disordered layer above z = 0 Å. The results are very similar for the TIP4P-FQ model. The Galvani potential difference between the solid and vapor phases, commonly called the surface potential, is the difference between the electrostatic potential in the interior of both phases.60,61 It can be calculated from the atomic charge density, ρq(z), by
Figure 1. Properties of the ice/vapor interface as a function of the z coordinate perpendicular to the interface: (A) density for the TIP4PFQ+DCT model; (B) molecular dipole moment for TIP4P-FQ+DCT (solid line) and TIP4P-FQ (dashed line); (C) the number of hydrogen bonds accepted minus the number donated; (D) the molecular charge density (solid line and left axis label) and integrated charge density (dotted line and right axis label).
TIP4P-FQ model (not shown) are essentially identical. The dipole moment of a molecule in the ice phase is about 3 D for both the TIP4P-FQ and TIP4P-FQ+DCT models.40,47 The charge transfer model is a little less polarizable, so it gives a slightly smaller dipole moment. Both models are parametrized to have the correct dipole for an isolated water molecule, 1.85 D. The molecules at the ice/vapor interface have a reduced dipole (Figure 1 B). A value of about 3 D is predicted based on the experimental dielectric constant.48,49 Models that have this value are the only models that have been shown to give a dielectric constant close to the experimental value.50−53 Electronic structure calculations on ice also give a value close to 3 D.54−56 The molecular geometry of the interface creates hydrogen bond asymmetry (Figure 1 C). This plot shows the difference in the number of hydrogen bonds a molecule accepts (Nacc) and the number it donates (Ndon). A hydrogen bond definition that requires an oxygen−oxygen distance less than 3.5 Å and an oxygen−hydrogen-oxygen bond angle greater than 150° is
δϕ(z) = ϕ(z) − ϕ(z 0) = −
∫z
z
Ez(z′) dz′ 0
(1)
where the electric field in the direction perpendicular to the interface, Ez(z), is given by Ez(z) =
1 ε0
∫z
z
ρq (z′) dz′ 0
(2)
and ε0 is the vacuum dielectric permittivity.60 The resulting surface potential is shown in Figure 2B. The surface potential is not translationally invarient, but averaging over the region in 3200
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Figure 2. Charge density (A) and surface potential (B) for the ice/ vapor interface using the TIP4P-FQ+DCT model.
the center of the ice phase (from about −31.4 Å to −11.9 Å) gives a value equal to −0.42 ± 0.01 V. For the liquid/vapor interface, the same model gives a value of −0.53 V.20 The contribution from charge transfer to the surface potential can be calculated by using the charge transfer electron density from Figure 1D in eqs 1 and 2, resulting in a value of +0.015 ± 0.003 V. The charge transfer profile with the negative charges on the vapor side of the interface makes the potential more positive inside the ice phase. Electron holography experiments have measured the surface potential for vitrified ice, finding a value of 3.5 ± 1.2 V.7 This value is of larger magnitude and opposite sign compared to our surface potential results. For the liquid/vapor interface, simulations using force fields all find a negative surface potential, with many values around −0.5 V,61 whereas ab initio calculations give values of 3.1 V62 and 3.6 V,63 close to the experimental result. The difference has been attributed to the contribution to the surface potential from regions inside the volume of the molecules.62,63 This effect stems from integrating through the electron density of the molecule and does not reflect any special thermodynamic property of the interface or bulk water. (Solid neon, for example, also has a surface potential of 3.6 V according to ab initio calculations.63) A number of recent papers have discussed the importance of the difference between the ab initio and classically calculated surface potentials on the properties of liquid water.62−66 The Ice/Liquid Interface. The interface of ice and liquid is broader than that of the ice and vapor (Figure 3A), with density peaks that are different from bulk ice beginning at −9 Å to about 5 Å along the z coordinate. This interface may be thicker than the ice/vapor interface because it is at a higher temperature, 302 K, the melting temperature of the model, as opposed to 273 K. Similar widths for the prism ice/water interface of about 10 Å have been reported from other simulations.42,67−69 Zero for the z coordinate was chosen to be consistent with the choice for the ice/vapor interface. The density profile for the TIP4P-FQ model is, again, very similar to
Figure 3. Properties of the ice/liquid interface as a function of the z coordinate perpendicular to the interface: (A) density for the TIP4PFQ+DCT model; (B) molecular dipole moment for TIP4P-FQ+DCT (solid line) and TIP4P-FQ (dashed line); (C) the number of hydrogen bonds accepted minus the number donated; (D) the molecular charge density (solid line and left axis label) and integrated charge density (dotted line and right axis label).
that if the TIP4P-FQ+DCT model, and is not shown. Over the interfacial region, the dipole moment decreases from the ice value, about 3 D to the liquid value, approximately 2.6 D. Water molecules at the ice/liquid interface show layers of hydrogen bond asymmetry (Figure 3 C). Molecules on the liquid side of the density peak tend to accept more hydrogen bonds than they donate; molecules toward the ice side donate more than they accept. This hydrogen bond imbalance creates layers of net charge (Figure 3D). The amount of charge transfer is similar to the ice/vapor interface, but occurs over more layers. Charge transfer leads to positively charged molecules on the ice side of the interface and negatively charged molecules on the liquid side. Water molecules at the ice interface with both the liquid phase and the vapor phase have an asymmetric arrangement of neighbors. The asymmetry results in charge transfer between molecules leading to layers of molecules with small net charges near the interface. Similar results have been described by simulation of liquid water with vapor19,20 and oil,18 although 3201
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(14) Ehre, D.; Lavert, E.; Lubomirsky, I. Water Freezes Differently on Positively and Negatively Charged Surfaces of Pyroelectric Materials. Science 2010, 327, 672−675. (15) Nelson, J.; Baker, M. Charging of Ice−Vapor Interfaces: Applications to Thunderstorms. Atmos. Chem. Phys. 2003, 3, 1237− 1252. (16) Nelson, J.; Baker, M. Charging of Ice−Vapor Interfaces. Atmos. Chem. Phys. Discuss. 2003, 3, 41−73. (17) Iedema, M. J.; Dresser, M. J.; Doering, D. L.; Rowland, J. B.; Hess, W. P.; Tsekouras, A. A.; Cowin, J. P. Ferroelectricity in Water Ice. J. Phys. Chem. B 1998, 102, 9203−9214. (18) Vácha, R.; Rick, S. W.; Jungwirth, P.; de Beer, A. G. F.; de Aguiar, H. B.; Samson, J.; Roke, S. The Orientation and Charge of Water at the Hydrophobic Oil Droplet−Water Interface. J. Am. Chem. Soc. 2011, 133, 10204−10210. (19) Vácha, R.; Marsalek, O.; Willard, A. P.; Bonthuis, D. J.; Netz, R. R.; Jungwirth, P. Charge Transfer Between Water Moleculeas as the Possible Origin of the Observed Charging at the Surface of Pure Water. J. Phys. Chem. Lett. 2012, 3, 107−111. (20) Wick, C. D.; Lee, A. J.; Rick, S. W. How Intermolecular Charge Transfer Influences the Air−Water Interface. J. Chem. Phys. 2012, in press. (21) Lee, A. J.; Rick, S. W. The Effects of Charge Transfer on the Properties of Liquid Water. J. Chem. Phys. 2011, 134, 184507. (22) Kitaura, K.; Morokuma, K. A New Energy Decomposition Scheme for Molecular Interactions within the Hartree−Fock Approximation. Int. J. Quantum Chem. 1976, 10, 325−340. (23) Reed, A. E.; Wienhold, F. Natural Bond Orbital Analysis of Near-Hartree−Fock Water Dimer. J. Chem. Phys. 1982, 78, 4066− 4073. (24) Stevens, W. J.; Fink, W. H. Frozen Fragment Reduced Variational Space Analysis of Hydrogen Bonding Interactions. Applications to the Water Dimer. Chem. Phys. Lett. 1987, 139, 15−22. (25) van der Vaart, A.; Merz, K. M., Jr. Charge Transfer in Biologically Important Molecules: Comparison of High-Level ab initio and Semiempirical Methods. Int. J. Quantum Chem. 2000, 77, 27−43. (26) Gálvez, O.; Gómez, P. C.; Pacios, L. F. Variation with the Intermolecular Distance of Properties Dependent on the Electron Density in Hydrogen Bond Dimers. J. Chem. Phys. 2001, 115, 11166− 1184. (27) Chen, W.; Gordon, M. S. Energy Decomposition Analysis for Many-Body Interaction and Applications to Water Complexes. J. Phys. Chem. 1996, 100, 14316−14328. (28) Korchowiec, J.; Uchimaru, T. New Energy Partitioning Scheme Based on the Self-Consistent Charge and Configuration Method for Subsystems: Application to Water Dimer System. J. Chem. Phys. 2000, 112, 1623−1633. (29) Glendening, E. D. Natural Energy Decomposition Analysis: Extension to Density Functional Methods and Analysis of Cooperative Effects in Water Clusters. J. Phys. Chem. A 2005, 109, 11936−11940. (30) Piquemal, J.; Marquez, A.; Parisel, O.; Giessner-Prettre, C. A CSOV Study of the Difference Between HF and DFT Intermolecular Interaction Energy Values: The Importance of the Charge Transfer Contribution. J. Comput. Chem. 2005, 26, 1052−1062. (31) Khaliullin, R. Z.; Bell, A. T.; Head-Gordon, M. Electron Donation in the Water−Water Hydrogen Bond. Chem.Eur. J. 2009, 15, 851−855. (32) Stone, A. J.; Misquitta, A. J. Charge-Transfer in SymmetryAdapted Perturbation Theory. Chem. Phys. Lett. 2009, 473, 201−205. (33) Thompson, W. H.; Hynes, J. T. Frequency Shifts in the Hydrogen-Bonded OH Stretch in Halide−Water Clusters. The Importance of Charge Transfer. J. Am. Chem. Soc. 2000, 122, 6278− 6286. (34) Robertson, W. H.; Johnson, M. A.; Myshakin, E. M.; Jordon, K. D. Isolating the Charge-Transfer Component of the Anionic H Bond via Spin Suppression of the Intracluster Proton Transfer Reaction in the NO−·H2O Entrance Channel Complex. J. Phys. Chem. A 2002, 106, 10010−10014.
the results are about a factor of 2 larger for the ice interfaces. The side of the interface nearest the ice phase tends to have positively charged water molecules, while the other side closer to the vapor or liquid phase have negatively charged molecules. Charge transfer thus provides another mechanism for the electrostatic properties of ice surfaces. This effect could influence the binding of ions to the interface and would produce a small tendency to attract cations to the surface of ice at the disordered, or quasi-liquid, layer. The hydrogen bond pattern and charge transfer amounts could be changed by the presence of ions or other particles,70 leading to subtle effects at the interface. This will be the focus of future studies.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Science Foundation under contract number CHE-0611679. This material is based upon work supported by the Louisiana Optical Network Initiative (LONI) and by the National Science Foundation under the NSF EPSCoR Cooperative Agreement No. EPS1003897, with additional support from the Louisiana Board of Regents. A.J.L. gratefully acknowledges support from the State of Louisiana Board of Regents.
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