Molecular Dynamics Simulations of Ice Growth from Supercooled

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Molecular Dynamics Simulations of Ice Growth From Supercooled Water When Both Electric And Magnetic Fields Are Applied Hui Hu, Hua Hou, and Baoshan Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp304266d • Publication Date (Web): 28 Aug 2012 Downloaded from http://pubs.acs.org on September 1, 2012

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of Ice Growth From Supercooled Water When Both Electric And Magnetic Fields Are Applied

Hui Hu,

Hua Hou,*

Baoshan Wang*

College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, 430072, People's Republic of China

[Revised, submitted to J. Phys. Chem. C]

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ABSTRACT: TIP4P/2005 force-field based classical molecular dynamics simulations were employed to investigate the microscopic mechanism for the ice growth from supercooled water when the external electric (0 − 109 V/m) and magnetic fields (0 − 10 Tesla) are applied simultaneously. Using the direct coexistence ice/water interface, the anisotropic effect of electric and magnetic fields on the basal, primary prismatic, and the secondary prismatic planes of ice Ih has been calculated. It was revealed for the first time that the solvation shells of supercooled water could be affected by the cooperative electric and magnetic fields. Meanwhile, the self diffusion coefficient is lowered and the shear viscosity increases considerably. The critical electric and magnetic fields to accelerate ice growth on the prismatic plane are fairly low (ca. 106 V/m and 0.01 Tesla). In contrast, the basal plane is hardly affected unless the fields increase to the order 109 V/m and 10 Tesla. Rotational dynamics of water molecules might play an important role in ice growth with the applied external fields. Density functional theory with the triple numerical all-electron basis set was used to reveal the electronic structures of the basal and primary prismatic planes of ice Ih with respect to the anisotropic effect of ice growth.

Keywords: Supercooled water; Ice growth; Electric field; Magnetic field; TIP4P/2005 water model.

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1. INTRODUCTION

Ice accretions on high-voltage overhead power lines and insulators create many problems and even disasters during winter storms in the cold and temperate regions.1 In contrast to the common ice growth process, there are three distinct features concerning the electric power systems: supercooled environment due to various frozen precipitations such as freezing drizzle, freezing rain, and hoar frost, strong electric field, and strong magnetic field.2 Using the density functional theory and the all-electron basis set and slab model, we have calculated the multilayer adsorption / dissociation mechanism of water molecules on the α-Al2O3 surface.3 It was found that the highly ordered ice-like structure, which might act as the nucleation of ice, is formed on the hydroxylated Al2O3 surface. In this work we have investigated the subsequent ice growth from supercooled water on the ideal ice Ih basal and prism surfaces using the force-field based molecular dynamics (MD) simulation technique in order to gain further insight on the ice accretion phenomena. Major concern of the current work is the potential importance of strong electric and magnetic fields applied to the icing process under supercooled conditions (e.g., temperatures below the freezing point).

Electric field effects on the structures and energetics of (H2O)n (n=2-15) clusters have been studied at the B3LYP/cc-pVTZ level of theory.4 The external electric field tends to increase the strength of the inter-cluster hydrogen bonds. Maerzke and

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Siepmann studied the effects of an applied electric field on the vapor-liquid equilibria of water using the Gibbs ensemble Monte Carlo simulations based on the TIP4P water model.5 In the temperature range 350 − 550 K, the radial distribution functions of liquid water show very little change but the orientational ordering increases greatly when the electric field is on the order of 109 V/m.

The structure of supercooled water at 250 K was studied using classical molecular dynamics (MD) simulations with the electric fields up to 109 V/m.6,7 It was suggested that strong electric fields significantly affect the dynamics of liquid water, for instance, inducing spatial anisotropy, stronger hydrogen bonds, and slower self diffusion. Moreover, electrofreezing of liquid water at 250 K has been simulated using the TIP4P and SPC/E force fields, resulting in the structure of ice Ic.8,9

The effect of magnetic field on the structure of room-temperature water has been subjected to numerous studies as well. Applying an increasing magnetic field to water can reduce critical supercooling and prompt equilibrium solidification when the strength of the magnetic field increases.10 Magnetic fields can also affect the van der Waals bonding,11 melting transition,12 self-diffusion, internal energy, entropy,13 viscosity,14 and formation of hydrogen bonds of pure water.15 It was reported that the coordination numbers of hydrogen bonds for liquid water at 300 K increase very slightly from 3.47 to 3.48 under magnetic fields from 0 to 10 T, respectively, using a flexible F3C water model.16 Moreover, a new ice phase could be formed from liquid

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water in the nanoscale hydrophobic confinement at an anomalously high freezing temperature of 340 K under a homogeneous external magnetic field of 10 T using the same water model.17 There is few report related to the effect of magnetic field on the structure of supercooled water up to date.

Although it is accepted that electric and magnetic fields can affect the structures and properties of liquid water, to our best knowledge, neither experimental nor theoretical study is available on supercooled water and ice growth from supercooled water when both strong electric and magnetic fields are applied simultaneously. This work represents the first effort to gain some insights on the above question in line with our final goal of mimicking the ice accretion on high-voltage power lines. Moreover, the present work is motivated by an interesting question that the electric and magnetic fields exert either opposite or additive effect on the structure of supercooled water and the subsequent ice accretion process. Force-field based MD simulations have been carried out in the time scale of a few nanoseconds. Structures and dynamics of the supercooled water and ice growth have been analyzed carefully and the results are reported herein.

2. COMPUTATIONAL METHODS

Many potential models for water molecules have been developed although none

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of them is capable of reproducing all the properties of water and ice phases. Several common water models have been carefully calibrated by Vega et al.18 It was concluded that the TIP4P/2005 model shows the best performance for water and ice simulations, including critical temperature, surface tension, density, melting point, thermal expansion coefficient, hydrogen-bond structure, self-diffusion coefficient, and so on. Therefore, we chose the TIP4P/2005 force field in the current MD simulations.

TIP4P/2005 is a rigid non-polarizable model described by a single Lennard-Jones (LJ) site and three charges.19 Note that it is unclear whether a flexible or a polarizable model for water is required for a correct description of the influence of the external fields. Kiselev and Heinzinger have shown that no significant difference could be observed for flexible or rigid water models as electric field strengths up to 1010 V/m.20 Moreover, adding flexibility to a rigid model has not been recommended because it does not improve its quality rather introducing even worse artifacts.21

Many ice/water interface models have been suggested since the pioneer work by Karim and Haymet.22 Fernandez et al. calculated the melting point of ice Ih for common water models from direct coexistence of the solid-liquid interface.23 The direct coexistence model has been verified to perform very well for the interface simulations. A similar direct coexistence model with vacuum slab was employed by

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Carignano et al. to study the ice growth kinetics from supercooled water on both the secondary prismatic plane (1 2 10) and the basal plane (0001) of ice Ih in the temperature range 255 − 275 K.24 It was found that the freezing is much faster on the prismatic plane than on the basal plane, which is in reasonable agreement with the experimental observation. The direct coexistence ice/liquid interface has been employed in the present work to simulate the ice growth from supercooled water in the presence of strong external fields. The main advantage is that the NPT molecular dynamics simulation could be carried out. Although it is hard to obtain the absolute kinetic rate of ice growth, the direct coexistence method has been useful to provide unique information about the dynamics of crystal growth.25

A box of 432 water molecules was first simulated at 250 K with NPT ensemble and three-dimensional periodic boundary condition. Temperature was controlled using a Nose thermostat and the virtual mass of 500 is set for heat bath.26 Pressure was controlled at one atmosphere using a Parrinello-Rahman barostat with the virtual mass of 50 for piston.27 Long-range Coulomb interaction was calculated using the Ewald summation with a Fourier space cutoff of 30. The cutoff for short-range Lennard-Jones intermolecular potential was set at the distance of half the smallest box length. The Newton’s equation of motion has been integrated using the fifth-order Gear's predictor-corrector algorithm with a time step of 0.2 fs. The Hamiltonian is well conserved during the simulation as the energy of the simulation cell drifts with a slope of 0.002 kcal/mol/ns. After 2 ns equilibrium, additional 2 ns

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production run was carried out and the data were collected every 0.1 ps for analysis. A larger simulation cell containing 3456 (e.g., 2×2×2 supercell) water molecules has been examined preliminarily for the size effect.

Ice growth from supercooled water was simulated using the direct coexistence solid/liquid interface at 240 K, corresponding to about 10 K supercooling (The recommended melting point for TIP4P/2005 water is 250.5 K).23 The ice Ih unit cell containing 432 TIP4P/2005 water molecules, which satisfies the rules of Bernal and Fowler with zero net dipole moment, zero net quadrupole moment, and randomness of hydrogen bonding, was build using a home-made Fortran program on the basis of the methodology proposed by Hayward and Reimers.28 Subsequently, the matching liquid water box was constructed through successive melting of the ice cell. The ice Ih unit cell and water box was equilibrated for 1 ns before they were joined together directly with respect to three contacting surface, namely, basal {0001}, prismatic {10 1 0}, and the secondary prismatic plane {1 2 10}. Finally, the pre-equilibrated direct coexistence solid/liquid interfaces involving 864 water molecules were employed as the starting configurations for the NPT simulations with the parameters mentioned above. The typical sizes of the simulation boxes depend on the specific ice/water interfaces, namely, 26.9 × 23.6 × 43.3, 23.4 × 22.1 × 55.5, and 22.1 × 35.4 × 34.5 (Å3) for the basal, prismatic, and secondary prismatic planes, respectively.

It is worth noting that the ice growth might depend greatly on the initial

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configuration of the solid/liquid contacting interface. In order to eliminate such an uncertainty, the atomic configurations and velocities of the equilibrated ice/water cells for three coexistence surfaces have been saved and copied when they are employed to study the effects of various electric and magnetic combinations.

It has been shown experimentally that icing rate in the alternating electric field is nearly equal to that in the positive static fields.2 Therefore, homogenous positive static electric field (E) in the range 0 − 109 V/m was considered. However, the induced magnetic field (B) related to the high-voltage conductors has not been well established. The order of magnitude of B was estimated using the relationship B = E / c, where c is velocity of light. As a result, four combinations of E and B, namely, 106 // 0.01, 107 // 0.1, 108 // 1, 109 // 10 (in units of V/m and Tesla, respectively), have been applied along the z-axis of the simulation cells. The external electric field was implemented as an additional force, F = q ⋅ E, where F is the force induced by the electric field, q is the charge of each atom. Implementing an external homogeneous magnetic field pointing in the z direction into the MD simulations was carried out using the Larmor oscillation of frequency, Ω = qB / m, to follow the sprialling motion of the particles. The acceleration on each particle is a(t) = −Ω Ω× v(t), where v(t) is the time-dependent velocity.29

In order to clarify the interaction of the isolated water molecules with the ice Ih surfaces, which might dominate the anisotropic dynamics behavior of ice growth,

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density functional theory (DFT), as implemented in the DMol3 program,30 was employed. Electron exchange and correlation energies were calculated using Becke-Lee-Yang-Parr (BLYP) with the all-electron triple numerical polarized (TNP) basis sets.31,32 It has been calibrated that the BLYP/TNP level of theory shows a good performance in the calculation of the structures and energetics of various water clusters and ice phases.3,33 The ice Ih unit cells used in the above MD simulations are too large to be affordable for the BLYP/TNP calculation. A 16-molecule supercell model of ice Ih, as suggested by Morrison and coworkers, has been used for our purpose.34 It is worth noting that such an ice model presents proton disorder while still obeying the Bernal-Fowler ice rules. The basal {0001} and the primary prismatic {10 1 0} surfaces of ice Ih were cleaved and the vacuum slabs were set as large as 20 Å in order to avoid interaction between periodic images. Atomic coordinates of the unit cells and surfaces have been fully optimized using the Broyden-Fletcher-Goldfarb-Shanno

(BFGS)

method

within

the

delocalized

coordinates. The convergence criteria are enforced to 10-5 au for energy, 0.002 au/Å for force, and 0.005 Å for maximum displacement. A 3×3×1 k-points meshes were chosen to ensure convergence of the DFT total energy.

3. RESULTS AND DISCUSSION

A. Liquid water at 250 K. The calculated properties for liquid water at 250 K,

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including density, thermal expansion coefficient, viscosity, heat of vaporization, and self-diffusion coefficient, are summarized in Table 1. The theoretical results are in good agreement with the corresponding experimental data,35-41 which is an evidence on the good performance of the TIP4P/2005 model for supercooled water.42 The calculated density of 0.982 g/cm3 is about one percent smaller than the value of 0.991 g/cm3 obtained previously via Monte-Carlo simulation.19 The MC production run was only 0.375 ns and the present MD production run is 2 ns. With the same simulation time, a slightly larger density, i.e., 0.987 g/cm3 was obtained.

Shear viscosity of liquid water is worth a further note. Recently, Gonzalez and Abasca have shown that TIP4P/2005 is the best model to evaluate shear viscosity of water at room temperature.43 As shown in Table 1, shear viscosity appears to be extremely sensitive to the MD simulation time used in the statistical analysis, fluctuating from 1.6 cP (1 ns) to 7.6 cP (2 ns) whereas the experimental value is 5.2 cP. The shear viscosity was calculated using the autocorrelation function (ACF) of the off-diagonal components of the stress tensor with the Green–Kubo formula. Although it is determined predominantly by the short time ACF (e.g., 0 − 3 ps), the long-time ACF tail (e.g., as long as 4 ns) have significant contributions as well.

When the electric and magnetic fields are applied to liquid water, the calculated properties do not change significantly until the external fields increase to as high as 109 V/m and 10 Tesla. The density decreases to 0.932 g/cm3, which is close to that

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of ice Ih within the same external fields (0.921 g/cm3). The self-diffusion coefficient, calculated using the Einstein equation from the mean-square-displacement of the center mass of water, is lowered by one order of magnitude. The shear viscosity increases by a factor of six. In contrast, the changes of thermal properties such as heat of vaporization and thermal expansion coefficient are only marginal.

Radial distribution function of OH (gOH) with the external fields of 109 V/m // 10 Tesla are compared to that at zero field and to that for the ice Ih. As shown in Figure 1, the gOH profile with the external field applied exhibits apparent difference from the zero-field gOH starting from 3.5 Å, corresponding to the third solvation shell and beyond. Evidently, the external field induces liquid water to be orientational ordering. The first and second solvation shell shows very little change regarding to the peak positions in the radial distribution functions. However, the peak at 1.8 Å increases from 1.98 to 2.26 and the second peak becomes a little narrower in the external fields. Consequently, as shown in Figure 1, the running coordination numbers for hydrogen bonds with the external fields are larger than those without fields for the first solvation shell (e.g., rOH < 2.5 Å). For the second solvation shell and more distant molecules, the running coordination numbers for hydrogen bonds with the external fields are smaller than those without fields. Note that the gOH profile of liquid water in the presence of the field does now show the details that appear in the gOH of ice. In fact, the formation of ice configuration has never been observed from the simulated trajectories.

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In order to clarify the respective contributions of electric and magnetic fields, two MD simulations on the liquid water at 250 K with the isolated electric (E = 109 V/m) or magnetic fields (B = 10 Tesla) applied have been performed. The running coordination numbers for hydrogen bonds were calculated and compared to those with the combined fields in Figure 2. Evidently, the effect of magnetic field is only marginal even at 10 Tesla because the running coordination number is almost identical to that at zero fields. In contrast, the electric field changes the structure of liquid water significantly, increasing the number of hydrogen bonds for the first solvation shell by roughly as much as 5% and decreasing the number of hydrogen bonds for the second solvation shell and beyond by as much as 12%. When the electric and magnetic fields are applied together, the running coordination numbers are always in between those with the isolated electric and magnetic fields. The cooperative effect of electric and magnetic fields on the structure of supercooled water shed a new light on the ice accretion mechanism.

The rotational dynamics of water molecules at 250 K were examined through the auto-correlation function: C (t ) = P2 [u (0) u (t )] , where u(t) is the body-fixed unit vector along the inertial principal axis of water molecular at time t and P2(x) denotes the second Legendre polynomial. As shown in Figure 3(A), the autocorrelation function in the range 0 // 0 − 108 V/m // 1 Tesla can be described by a single-exponential function. The rotational dynamics approaches to the equilibrium ∞

rapidly within 100 ps. The rotational time ( τ = ∫ C (t )dt ) for the liquid water at zero 0

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fields was estimated to be 5.8 ps, which is in good agreement with previous theoretical result of 5.6 ps.44 The time constants for the applied fields up to 108 V/m // 1 Tesla are in the range 10 − 23 ps, showing a normal rotational relaxation in accordance with Debye theory. When the external fields increase to 109 V/m // 10 Tesla, the rotational autocorrelation function changes suddenly, exhibiting an initial decay around 50 ps and a much slower decay of as large as 300 ps, which is about two orders of magnitude longer than that of water at zero field. The respective influence of electric or magnetic fields on the rotational time is illustrated in Figure 3(B). The rotational time for the applied magnetic field of 10 Tesla increases to 31.4 ps, which is about six times longer than that for the zero field. If only the electric field is applied, the rotational motion of water molecules is constrained effectively as indicated by a large time constant of 81.6 ps. This could be readily understood because the external fields tend to align the atomic charges along the field direction. In addition, it appears that there is cooperativity of the effect of these two types of fields. Moreover, it is worth noting that the rotational motion of water is anisotropic at higher temperatures as suggested by the NMR experimental measurements.45

B. Ice growth on the secondary prismatic plane {1 2 10}. It is well known that the secondary prismatic plane is the fastest surface for ice growth. Preliminary MD simulation shows that neither density nor structure of ice Ih has observable change when the external fields are applied. The ice growth process from supercooled water at 240 K was characterized by monitoring the total energy, i.e.,

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the sum of potential and kinetic energies, as shown in Figure 4. Apparently, the total energies show fluctuations to some extent. The sudden change of slope exhibits melting process of ice near the growing boundary. Some small plateaus in the middle part of the curve indicate the simultaneous icing and melting. The similar fluctuation behavior has been observed in previous MD simulations.23 The existence of a plateau at the end of the curve denotes the complete freezing of all water molecules. However, after visual inspection of the MD trajectories, it was found that the crystallization is not perfect because a small number of defective molecules do not accommodate into the ideal crystal structure, as implied by the slightly higher density (0.925 g/cm3) of the simulated ice Ih cell than the experimental value of 0.921 g/cm3.

In view of Figure 4, ice growth from supercooled water could be accelerated when the external electric and magnetic fields are applied. The profound uptake effect occurs when the fields increase to 107 V/m // 0.1 Tesla and the ice growth rate was estimated to be 4 Å/ns. For the higher fields at 108 V/m // 1 Tesla, the ice growth rate is about 3 Å/ns, which is close to that for the 107 V/m // 0.1 Tesla fields within the statistical errors. As mentioned above, the liquid water is little disturbed by the external fields until 109 V/m // 10 Tesla. The apparent acceleration of ice growth from supercooled water at 107 V/m // 0.1 Tesla implies that the {1 2 10} solid/liquid interface is more readily affected by the external fields than the bulk liquid. Unfortunately, when the external fields increase to 109 V/m // 10 Tesla, the

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simulation cell is broken rapidly. The reason might be two-folds: numerical instability of the MD simulation exists; the direct coexistence interface between the secondary prismatic plane of ice Ih and supercooled water becomes unstable under extremely strong electric and magnetic fields.

Radical distribution functions of OH for the ice phase and the liquid layer were calculated separately using the last 1 ns trajectory. The results are shown in Figure 5 for comparison. In view of the shapes and positions, the RDF profiles of the solvation shells for the liquid layer are analogous to those for the ice phase.46 The RDF profile with the 106 V/m // 0.01 Tesla fields is slightly below that without external field, whereas the RDF profiles with stronger fields are well above that without field. This behavior is in accordance with the changes of the total energy as mentioned above. In comparison with the isolated ice Ih, the H-bond network for ice phase does show some response to the fields especially in view of the second and third solvation shells. After checking the MD trajectories, it was found that the simultaneous melting of the ice phase, which is induced by the heat released from the freezing of water on the solid/liquid interface,23-25 occurs when the ice growth from supercooled water is accelerated significantly by the strong external fields. The rotational time for the liquid water molecules was calculated to be 20 ps, which is nearly the same as that for the bulk water. Therefore, the external fields up to 108 V/m // 1 T do not impose observable change on the rotational dynamics of water molecules during ice growth on the secondary prismatic plane.

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It should be noted that the faster crystallization of supercooled water in the presence of the strong fields is caused not only by the field-dependent kinetic effect and dynamics of the freezing water molecules but also by the thermodynamic driving force, i.e., the change in the melting temperature of water due to the fields. The apparent icing acceleration within the strong fields could be an additive result of the two effects. Currently, we are unable to assess which effect is predominant because the melting temperatures with the electric and magnetic fields have to be determined using either free energy calculations19 or solid-liquid coexistence simulations.23 This part of work is very time-demanding and the results will be presented separately.

C. Ice growth on the primary prismatic plane {10 1 0}. Temporal total energies of the simulation cells for ice growth on the prism surface of ice Ih are shown in Figure 6. Even with relatively low external fields such as 106 V/m // 0.01 Tesla, the growth process finishes within 5 ns, as indicated by the plateau tail of the total energies and the final cell density of 0.925 g/cm3. In contrast, the ice growth is still ongoing in the absence of external field. The ice growth rate for the 106 V/m // 0.01 Tesla fields was estimated to be 3 Å/ns, while those for the stronger fields increase to about 5~6 Å/ns. Analogous to the secondary prismatic plane, the simulation cell involving the primary prismatic plane becomes unstable when the external electric and magnetic fields increase to 109 V/m and 10 Tesla, respectively.

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Trajectories and RDF profiles of OH for the liquid water and ice layers demonstrate that the water molecules are well aligned into the ice Ih lattice through hydrogen bonds when both electric and magnetic fields are applied. The rotational autocorrelation functions for the liquid layer (namely, the 432 water molecules to be frozen) on the primary prismatic plane of ice indicate that the rotational relaxation time is only 2 ps, which is shorter than that on the secondary prismatic plane of ice by nearly one order of magnitude (See Figure S1 in the Supporting Information). Consequently, the ice growth on the primary prismatic plane of ice Ih could be dominated by the fast rotational dynamics of water molecules, which is promoted by the external electric and magnetic fields.

D. Ice growth on the basal plane {0001}. Temporal total energies of the simulation cell for the ice growth on the basal plane of ice Ih are shown in Figure 7. Even though the external electric and magnetic fields increase to 108 V/m and 1 Tesla, the icing process is still incomplete within 5 ns simulations. The total energy continues to decrease and there is no clear plateau near the end of the trajectories. Recently, Rozmanov and Kusalik reported an investigation of temperature dependence of crystal growth of the basal face of hexagonal ice using the TIP4P/2005 force field without fields.54 The growth rate at 240 K, i.e., 10 K supercooling below the melting temperature, was found to be in the range 0.5 − 1 Å /ns, depending on the system sizes employed in the simulations, in accordance with the experimental growth rate of less than 1 Å/ns.55 In the presence of strong electric

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and magnetic fields, for instance, 108 V/m and 1 Tesla, the ice growth rate on the basal face of ice Ih was estimated to be about 4 Å/ns.

When the external fields increase to 109 V/m and 10 Tesla, the simulation cell is stretched abnormally after 2 ns production run. Fortunately, the MD run with 5×108 V/m for electric field and 5 Tesla for magnetic field has been successful. The ice growth from supercooled water is promoted significantly by the external fields. The growth rate was estimated to be about 10 Å/ns, which is higher than that without the fields by nearly one order of magnitude. The freezing process is complete within 4 ns, as indicated by the definitive plateau near the end of simulation and by the final cell density of 0.922 g/cm3. The RDF profiles of OH obtained from the last 1 ns trajectory prove that the whole liquid water phase freezes into ice Ih. The rotational relaxation time for all the water molecules in the liquid layer is about 100 ps, indicating that the rotational orientation of water on the basal plane is fairly slow. Therefore, the icing process on the basal solid/liquid interface is dominated probably by self-diffusion of water molecules. Meanwhile, it seems that the critical external fields required to accelerate ice growth from supercooled water have some correlations with the rotational dynamics of the liquid phase.

E. First-Principles BLYP/TNP Calculations. Although the TIP4P/2005 force-field water model has been successfully used to simulate the phase diagram, equation of state, surface tension, vapror/liquid interfacial coexistence, transport

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coefficients, shear viscosity, and critical properties of water and supercooled water,19,23,42,43,47-53 the validation of TIP4P/2005 for the ice/liquid interfacial simulation is still an open question. In fact, little is known for the ice/liquid interface experimentally and theoretically. Before more extensive investigations on the ice/water interface (e.g., force-field and statistical time-scale dependence of the coexistence model) have been done, the present MD simulations should be taken with caution. Therefore, it is invaluable to explore the electronic structure characteristics of different surfaces of ice relevant to the anisotropic behavior of ice growth using the first-principles methods.

The basal and prismatic surfaces of ice Ih show quite different growth behavior in the direct coexistence with the supercooled water. Moreover, the prismatic solid/liquid interface is more sensitive to the electric and magnetic fields than the basal interface. Plots of the density of states (DOS) for the basal and prismatic surfaces of ice Ih at 0 K are shown in Figure 8. Evidently, DOS for the prismatic surface is generally higher and all the peaks are closer to the Fermi level than that for the basal surface. As a result, the prismatic surface could be more sensitive to the external fields. This feature has been further supported by the electrostatic potential (ESP) distributions of the two surfaces along the z-axis as shown in Figure 9. The prismatic surface involves two well-separated ESP peaks located at about 0.28 (the surface water layer) and 0.19 (the second water layer), while the two ESP peaks for the basal surface are overlapped at around 0.2. It is conceivable that the prismatic

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surface of ice Ih should be more preferable to be polarized by the external electric and magnetic fields. Therefore, the relatively low external fields might lead significant alternation of the ice growth on the prismatic plane, which supports the results obtained from the above MD simulations.

In addition, the ice growth from supercooled water should be relevant to the hydrogen bonding interaction of the isolated water molecule with the ice surface. Various binding modes have been explored to obtain the most stable hydrogen bonding structures when one isolated water molecule is absorbed on the basal or prismatic surfaces of ice Ih. For the prismatic surface, the absorbed water molecule forms two hydrogen bonds with the surface O and H atoms. One of HO bonds of the absorbed water molecule is directed outward the surface. For the basal surface, the stable structure involves three hydrogen bonds. Two HO bonds of the isolated water molecule form two hydrogen bonds with the surface O atom. The oxygen atom of the isolated water forms the third hydrogen bond with the surface H atom. The different interaction structures of water molecule with the prismatic and basal surfaces might be a clue to understand the rotational dynamics of water as observed in the MD simulations. Interestingly, in view of the binding energies, the absorbed structure on the prismatic surface is even more stable than that on the basal surface by 1.0 kcal/mol because of the shorter hydrogen bonding distances of the former. Furthermore, the energetic route for the absorbing process was obtained through partial optimizations with the fixed distance between the isolated water molecule

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and the surfaces. The potential energy curve for the prismatic surface is steeper than that for the basal surface. Therefore, the ice growth is thermodynamically preferable on the prismatic surface of ice Ih. It is in agreement with the experimental and theoretical observations that the prismatic plane is a faster surface for ice accretion than the basal plane.24 A first-principle MD simulation would be highly desired to clarify the details of the anisotropic effect for the ice growth from supercooled water at specific interfaces when the external fields are applied.

4. CONCLUSIONS

Ice growth from supercooled water has been examined using molecular dynamics simulations with the TIP4P/2005 force field when the cooperative electric and magnetic fields are applied simultaneously. For liquid water, the hydrogen bond structures and physical properties can be changed considerably when the external fields increase to 109 V/m and 10 Tesla. Viscosity increases by a factor of six and the self diffusion coefficient decreases by one order of magnitude. Electric field can play a significant role to the hydrogen bonding structures of liquid water but the effect of magnetic field is only marginal.

The growth of ice from supercooled water can be affected when both strong electric and magnetic fields are applied simultaneously. However, the critical

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strength of the fields, at which the cooperative effect of the two fields leads to any observable change of the ice growth rates in a 5 ns simulation of the TIP4P/2005 water model, depends greatly on the solid/liquid interface. For {0001}, {10 1 0}, and {1 2 10} surfaces of ice Ih, the external fields start to play a significant role at 5×108 V/m // 5 T, 106 V/m // 0.01 T, and 107 V/m // 0.1 T, respectively. Both diffusion and rotational dynamics of liquid water molecules are of importance during ice growth.

Density of states, electrostatic potential, and hydrogen bonding interactions of the ice Ih surfaces are relevant to the anisotropic ice growth induced by the external fields. First-principles calculation supports that the prismatic plane is a preferable surface for ice growth with respect to the basal surface. Moreover, the calculation supports that the prismatic plane should be more sensitive to the external fields than the basal surface.

For the typical electric and magnetic fields combination, namely, 106 V/m // 0.01 Tesla over the high-voltage power lines, ice accretion from supercooled water might be accelerated at least on the prismatic plane of ice. It has been shown that the multilayer water absorption on the hydroxylated Al2O3 surface leads to a prism-terminated ice structure. The present work may stimulate further investigations of the ice accretion mechanism from supercooled water when both strong electric and magnetic fields are applied.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Phone: (86)27-6875-6347.

ACKNOWLEDGMENT Financial support was provided, in part, by the Key Projects in the National Science & Technology Pillar Program during the Eleventh Five-Year Plan Period (No. 2009BAA23B01-1-A). We thank the anonymous referee for his/her valuable comments and constructive suggestions to the manuscript.

Supporting Information Available Figure S1 shows the rotational autocorrelation functions for the liquid water layer on the (100) and (110) surfaces of ice Ih. This information is available free of charge via the Internet at http://pubs.acs.org.

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Table 1. Computed properties for liquid water at 250 K and 1 atmosphere for various concerted external electric (E, in V/m) and magnetic fields (B, in Tesla) pairs. The experimental data are listed in parenthesis. κT, viscosity, and self-diffusion coefficients were calculated using 1 ns and 2 ns production-run data, respectively. See text for discussion.

E // B ρ (g/cm3) a

105κT (MPa-1) b

Viscosity ∆vH (cP)

109D (m2/s) d

(kcal/mol) c

0 // 0

106 //

0.987±0.012

72.8 - 71.9 (64.5,

1.6 - 7.6

10.6

0.337 - 0.338 (0.341,

(0.991)35

70.4)36,37

(5.2)38

(11.0)39

0.372)40, 41

0.979±0.011

62.5 - 65.4

7.1 - 6.4

10.6

0.324 - 0.313

0.980±0.011

63.3 - 61.0

3.6-7.3

10.6

0.316 - 0.337

0.980±0.011

70.8 - 66.7

10.7 - 6.4

10.6

0.357 - 0.341

0.932±0.026

70.0 - 68.1

36.4

- 11.9

0.036 - 0.052

0.01 107 // 0.1 108 // 1 109 10

/

66.0

a

Density. bThermal expansion coefficient. cHeat of vaporization. dSelf-diffusion coefficient.

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Figure Captions

Figure 1. Radial distribution functions of OH (gOH) and the running coordination numbers (NOH) for liquid water at 250 K. Black line: zero fields. Red line: 109 V/m // 10 Tesla fields. Dashed line: ice Ih (220 K, ref 45). Insert: partial running coordination numbers between 1.75 and 3.0 Å.

Figure 2. Running coordination numbers of OH for liquid water at 250 K. Dots: zero fields. Blue line: magnetic fields only with B = 10 Tesla. Green line: electric fields only with E = 109 V/m. Red line: with combined E//B = 109 V/m // 10 Tesla.

Figure 3. Rotational autocorrelation function of liquid water at 250 K with the applied electric and magnetic fields. (A) Black: zero fields. Green: 106 V/m // 0.01 Tesla. Blue: 107 V/m // 0.1 Tesla. Cyan: 108 V/m // 1 Tesla. Red: 109 V/m // 10 Tesla. (B)

Black: zero fields. Green: with 109 V/m electric field only. Blue: with 10 Tesla

magnetic field only. Red: with 109 V/m and 10 Tesla fields simultaneously.

Figure 4. Temporal total energies for the icing of supercooled water on the secondary prismatic plane of ice Ih at 240 K. The applied electric and magnetic fields (E//B) are labeled in the units of V/m and Tesla, respectively.

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Figure 5. Radial distribution functions of OH for liquid layer and ice phase for the ice growth on the secondary prismatic plane. Black: zero fields. Red: 106 V/m // 0.01 Tesla. Green: 107 V/m // 0.1 Tesla. Blue: 108 V/m // 1 Tesla. Dashed line: for the isolated ice Ih at zero fields.

Figure 6. Temporal total energies for the icing of supercooled water on the primary prismatic plane of ice Ih at 240 K. The applied electric and magnetic fields (E//B) are labeled in the units of V/m and Tesla, respectively.

Figure 7. Temporal total energies for the icing of supercooled water on the basal plane of ice Ih at 240 K. The applied electric and magnetic fields (E//B) are labeled in the units of V/m and Tesla, respectively.

Figure 8. Density of states for the basal plane (black line) and the primary prismatic plane (red line) of ice Ih calculated at the BLYP/TNP level of theory.

Figure 9. Electrostatic potential (ESP) of the basal plane (black line) and the primary prismatic plane (red line) of ice Ih along the z fractional coordinates of the unit cells calculated at the BLYP/TNP level of theory. The Fermi energy levels for the two planes are shown as horizontal lines.

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Figure 1.

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Figure 2.

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Figure 3.

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Figure 4.

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Figure 5.

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Figure 6.

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Figure 7.

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Figure 8.

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Figure 9.

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TABLE OF CONTENS GRAPHIC

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Radial distribution functions of OH (gOH) and the running coordination numbers (NOH) for liquid water at 250 K. Black line: zero fields. Red line: 109 V/m // 10 Tesla fields. Dashed line: ice-1h (220 K, ref 45). Insert: partial running coordination numbers between 1.75 and 3.0 Å. 316x213mm (96 x 96 DPI)



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Running coordination numbers of OH for liquid water at 250 K. Dots: zero fields. Blue line: magnetic fields only with B = 10 Tesla. Green line: electric fields only with E = 109 V/m. Red line: with combined E//B = 109 V/m // 10 Tesla. 312x218mm (96 x 96 DPI)


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Rotational autocorrelation function of liquid water at 250 K with the applied electric and magnetic fields. (A) Black: zero fields. Green: 106 V/m // 0.01 Tesla. Blue: 107 V/m // 0.1 Tesla. Cyan: 108 V/m // 1 Tesla. Red: 109 V/m // 10 Tesla. (B) Black: zero fields. Green: with 109 V/m electric field only. Blue: with 10 Tesla magnetic field only. Red: with 109 V/m and 10 Tesla fields simultaneously. 155x226mm (96 x 96 DPI)



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Temporal total energies for the icing of supercooled water on the secondary prismatic plane of ice-1h at 240 K. The applied electric and magnetic fields (E//B) are labeled in the units of V/m and Tesla, respectively. 167x209mm (96 x 96 DPI)


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Radial distribution functions of OH for liquid layer and ice phase for the ice growth on the secondary prismatic plane. Black: zero fields. Red: 106 V/m // 0.01 Tesla. Green: 107 V/m // 0.1 Tesla. Blue: 108 V/m // 1 Tesla. Dashed line: for the isolated ice-1h at zero fields. 164x215mm (96 x 96 DPI)



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Temporal total energies for the icing of supercooled water on the primary prismatic plane of ice-1h at 240 K. The applied electric and magnetic fields (E//B) are labeled in the units of V/m and Tesla, respectively. 167x211mm (96 x 96 DPI)


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Temporal total energies for the icing of supercooled water on the basal plane of ice-1h at 240 K. The applied electric and magnetic fields (E//B) are labeled in the units of V/m and Tesla, respectively. 169x216mm (96 x 96 DPI)



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Density of states for the basal plane (black line) and the primary prismatic plane (red line) of ice-1h calculated at the BLYP/TNP level of theory. 304x211mm (96 x 96 DPI)


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Electrostatic potential (ESP) of the basal plane (black line) and the primary prismatic plane (red line) of ice1h along the z fractional coordinates of the unit cells calculated at the BLYP/TNP level of theory. The Fermi energy levels for the two planes are shown as horizontal lines. 303x211mm (96 x 96 DPI)



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TABLE OF CONTENS GRAPHIC 159x119mm (96 x 96 DPI)


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Molecular Dynamics Simulations of Ice Growth from Supercooled

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