Article pubs.acs.org/JPCA
Does Hydrophilicity of Carbon Particles Improve Their Ice Nucleation Ability? Laura Lupi and Valeria Molinero* Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, United States
ABSTRACT: Carbonaceous particles account for 10% of the particulate matter in the atmosphere. Atmospheric oxidation and aging of soot modulates its ice nucleation ability. It has been suggested that an increase in the ice nucleation ability of aged soot results from an increase in the hydrophilicity of the surfaces upon oxidation. Oxidation, however, also impacts the nanostructure of soot, making it difficult to assess the separate effects of soot nanostructure and hydrophilicity in experiments. Here we use molecular dynamics simulations to investigate the effect of changes in hydrophilicity of model graphitic surfaces on the freezing temperature of ice. Our results indicate that the hydrophilicity of the surface is not in general a good predictor of ice nucleation ability. We find a correlation between the ability of a surface to promote nucleation of ice and the layering of liquid water at the surface. The results of this work suggest that ordering of liquid water in contact with the surface plays an important role in the heterogeneous ice nucleation mechanism.
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INTRODUCTION The formation of ice in the Earth’s atmosphere strongly influences the radiative properties of clouds.1,2 Aerosols of various origins are major contributors to the heterogeneous nucleation of ice.1−3 Aerosols display a broad range of freezing efficiencies, quantified by the difference between the heterogeneous and homogeneous freezing temperature, ΔTf = Tf − Tfhomo.1,3−13 Carbon particles are a major component of atmospheric aerosols, constituting 10% of the tropospheric particulate matter.1,14,15 Soot, consisting of graphitic carbon particles, is a main component of carbon aerosols and can promote the heterogeneous nucleation of ice with a wide range of freezing efficiencies, 0 < ΔTf < 16 K.1,16−25 Carbonaceous particles age in the atmosphere through oxidative processes that have been shown to significantly increase the particles hydrophilicity.26 Some studies found that oxidation of aerosols is related to their ability to nucleate ice.18,26−35 The role of oxidation, however, is still debated, as other experiments indicate that oxidation does not impact freezing.20,30 It has been proposed that increase in the hydrophilicity of soot is correlated with higher nucleation ability,18 but this is still controversial.18,20,30−33 Oxidation, however, leads to complex transformations in soot that not only modulate the hydrophilicity but also modify the nanostructure of the particles.36 In separate work we investigated the role of soot nanostructure (size and curvature of the graphitic lamellae) on modulating the freezing temperature of water.37 We found that changes in soot nanostructure alone could account for the full range of freezing efficiencies observed in experiments. The goal of this work is to investigate how the freezing efficiency of carbon surfaces is modulated by hydrophilicity, defined by the contact angle of liquid water with the surface. © 2014 American Chemical Society
We use molecular dynamics simulations to determine the heterogeneous freezing temperatures of ice in the presence of model graphitic surfaces with a wide range of hydrophillicities and for which the nanostructure is kept constant. Crystallization of water through molecular simulations is challenging because nucleation is a rare event. The study of nucleation requires very long simulations or the use of advanced simulation techniques to sample rare events. In this work we use the coarse grained model of water mW that allows for 180 times more efficient simulations than atomistic models of water with Ewald sums.38 The mW water model reproduces the structures of liquid water, ices, and amorphous solid water.38−55 It has been shown to correctly predict the homogeneous nucleation of ice from bulk water,41−43,49,52,54 solutions,47 nanodroplets,53,56 and in nanopores.40 Recently, it has been used to investigate heterogeneous nucleation of ice from liquid water in contact with pure graphitic surfaces of a wide range of sizes and radius of curvature.37 Here we investigate water freezing in contact with two families of flat graphitic surfaces in which the hydrophilicity is increased either by homogeneously tuning the water−carbon interaction or by decorating the graphitic surface with hydrophilic hydroxyl-like sites. These are not meant to represent realistic surfaces of atmospheric carbon, for which the structure and functionalization upon oxidation has not yet been established,57−62 but two distinct ways of controlling the contact angle to establish whether that variable correlates with the ice freezing temperatures. Our results show Special Issue: Kenneth D. Jordan Festschrift Received: December 3, 2013 Revised: February 14, 2014 Published: February 17, 2014 7330
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a slab of water molecules of a bulk simulation of liquid water at 298 K.44 The width of the interface of the rough surfaces, 0.14 nm, as measured by the t90−10, is half the width of a water molecule.40 Simulation Settings. Molecular dynamics simulations were carried out with LAMMPS.68 The velocity Verlet algorithm was used to integrate the equations of motion of water with a time step of 10 fs for the bulk systems and 5 fs for systems with an open water/vacuum interface. A smaller time step is required in the latter because of the faster motions of water molecules at an open interface. Periodic boundary conditions were applied in the dimensions corresponding to the surface plane for the simulation cells with droplets or slabs, and in the three dimensions for bulk systems. The simulations of water droplets and slab were performed in the NVT ensemble; the NPT ensemble was used for the systems without water/vacuum interfaces. Temperature and pressure were controlled using Nose−Hoover thermostat and barostat with relaxation times 0.5 and 2.5 ps, respectively. Cooling ramps at 1 K/ns were performed to investigate the crystallization of water. This is the fastest cooling rate that leads to crystallization of ice in simulations with mW water in the presence of graphitic surfaces.37 We estimated the error bars in the freezing temperatures by performing 5 independent quenching simulations for each system, for a total of 90 cooling simulations. Isothermal simulations were carried out at temperatures ranging from 218 to 300 K; a period of at least 5 ns equilibration preceded each production runs. Analysis. The freezing temperature, Tf was determined as the onset of increase in the fraction of ice during quenching simulations. Layering of water at the surface was determined from isothermal simulations by integrating the density distribution functions of mW molecules along the direction normal to the surface. To avoid surface effects in the case of water droplets, layering was computed only for the water molecules in a cubic box at the center of the droplet. The contact angles for each surface were calculated according to ref 69: the density profiles of droplets containing 5241 water molecules were computed and averaged over 20 ns long isothermal simulations at 298 K. The contact angles θ between the liquid droplet and the surface were computed by fitting the density profile to a second order polynomial and computing the tangent at the surface (i.e., zero height).69 Contact angles for temperatures ranging from 300 and 220 K do not show a noticeable dependence on temperature. We verified that the contact angle is independent of droplet size for droplets with more than 2000 water molecules. Bond orientational order parameters ql70 of order l = 3 and 6 were used to identify ice and ice-like order. q6 identifies a variety of crystals, including ice,49 while q3 is more selective for identification of ice and icelike structures.40,52 The order parameters q6 and q3 for a given water are defined by ql = ((4π/(2l + 1))∑lm=−l|ql̅ m|2)1/2, where ql̅ m = (1/NB)∑iN=B1Ylm(θi(r), ϕi(r)) is averaged over the number of bonds, NB, of molecule i to each of its near neighbors, defined as those water molecules within a cutoff distance given by the first minimum of the water−water radial distribution function, 0.35 nm. Ylm(θi(r), ϕi(r)) are the corresponding spherical harmonics of rank l and m, where θi(r) and ϕi(r) are the polar angles of the water−water bond.70 The order parameter q670 was used to identify total ice; a cutoff value of 0.58 was used to distinguish between ice and supercooled liquid water. A cutoff distance of 0.35 nm between water molecules with q6 > 0.58 was used to identify the largest ice cluster. Ice-
that hydrophilicity modulates the freezing efficiency of carbon surfaces but in opposite directions for the two families of surfaces. This indicates that knowledge of surface hydrophilicity is not sufficient to predict heterogeneous freezing temperatures. We find that roughness of the surface has a detrimental effect on its ice nucleation ability, irrespective on whether the surface is hydrophilic or hydrophobic. Finally, we observe a correlation between nucleation ability and layering of liquid water at the surface, suggesting that the ordering of interfacial water is important for the heterogeneous nucleation mechanism.
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METHODS Force Fields. The interaction between water molecules was represented by the monatomic water model mW, which does not have hydrogen atoms or electrostatic interactions.38 The mW model represents each water molecule as a single particle able to form tetrahedral hydrogen bonded structures encouraged by three-body nonbonded interactions that penalize nontetrahedral water−water−water angles. The mW water molecules interact through a sum of pairwise and three-body contributions described by the functional form of the Stillinger−Weber (SW) potential.63 Water does not form hydrogen bonds with graphitic carbon; therefore, we use only the two-body term of the SW potential to represent the interaction between water molecules and the carbon atoms of the graphitic surfaces. The size σ = 0.32 nm of the water− carbon interaction is the standard used in atomistic models to reproduce water−carbon distances.64−66 The strength of the water−carbon interaction was tuned to obtain graphitic surfaces with different degree of hydrophilicity. The water−carbon interaction parameters for bare graphite, ε = 0.13 kcal/mol, are those that reproduce the experimental contact angle for graphite, 86°.74 The other constants in the water−carbon potential are the same as those in ref 63. Carbon−carbon interaction potentials do not need to be defined because the surface atoms are fixed, i.e., their equations of motion are not integrated. We also investigated water in contact with a rough hydrophilic surface, in which the interaction of the surface particles with water were identical to water−water interactions, and water in contact with a smooth atomless wall interacting with water with a Lennard-Jones 9−3 with σ =0.356 nm and ε = 1.3 kcal/mol. Systems. We investigated the nucleation of ice on atomically flat graphitic surfaces with various degrees of hydrophilicity, a smooth Lennard-Jones surface, and an atomically rough hydrophilic surface. The results for the latter surface were compared with those for an atomically rough surface with the same hydrophobicity as graphite.37 The graphitic surfaces were built with the Visual Molecular Dynamics (VMD) package.67 Bare graphite was represented as a single layer of carbon atoms, periodic in the plane of the surface. Periodic surfaces with dimensions 5 × 5 nm2 were in contact with bulk water (4096 molecules). The average separation between the surfaces confining the water slab was 5 nm. Water droplets (5528 molecules) were studied over 16 × 16 nm2 periodic graphitic surfaces. The hydrophilicity of the surface was modified in two ways: (i) heterogeneously decorating the bare graphite surface (ε = 0.13 kcal/mol) with a square grid of hydroxyl groups positioned approximately every ΔOH = 1, 2, 4, and 8 nm; this was achieved by replacing atom carbons by mW water molecules; (ii) homogeneously tuning the water−carbon attraction to ε = 0.12, 0.13, 0.16, 0.18, and 0.2 kcal/mol. The rough surface was obtained immobilizing 7331
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chemically homogeneous flat surface to the water deposited on it.71,72 The contact angles of water droplets on the two types of surfaces are shown in Figure 2. The hydrophilicity of the surface increases with the increase in density of hydroxyl groups or an increase in water−carbon attraction. All the graphitic surfaces of this study promote the heterogeneous nucleation of ice: the crystallization temperatures of ice on the carbon surfaces are higher than the temperature of homogeneous ice nucleation (Figure 2B,D). Tf of mW water on the model graphite is 12 ± 3 K higher than the temperature of homogeneous nucleation, in excellent agreement with experiments that indicate that unoxidized carbon surfaces have a Tf ≈ 16 K above the homogeneous limit.1,16,17 Figure 3 illustrates the process of heterogeneous ice freezing on the surface decorated with hydroxyl groups every 1 nm. The dependence of the freezing temperatures with hydrophilicity is opposite for the hydroxyl-decorated and interactiontuned sets of surfaces. The freezing temperature of water decreases with the hydrophilicity of the surface in the case of the decorated surfaces, and it increases with hydrophilicity for the surfaces with tuned water−carbon attraction. These results indicate that the hydrophilicity of the surface is not by itself a good predictor for its ability to promote the nucleation of ice. The hydrophilicity of the surface, however, could play an indirect role on the nucleation of ice by increasing the hygroscopicity of the carbon particles. Ordering of Water at the Surface Is Correlated to Ice Nucleation Ability. In the previous section we showed that carbon surfaces with a wide range of hydrophilicities promote the heterogeneous nucleation of ice. In what follows we investigate the effect of the surfaces on the structure of liquid water. Our aim is to identify relevant microscopic variables that correlate with the ice nucleation ability of the surfaces and that can be tested as reaction coordinates for heterogeneous ice nucleation in future studies. The water molecules layer at all the graphitic surfaces of this study. The density profile of water as a function of the distance from the surfaces is shown for representative surfaces in the upper panel of Figure 4. The degree of order can be quantified by the layering, L = ∫ z0bulk((ρ(z)/ρbulk) − 1)2dz, which measures the deviation of the local water density ρ(z) at distance z from the surface from the average bulk density ρbulk of water, integrated over all the density profile. The integration spans from the surface (z = 0) to a distance zbulk for which the water density plateaus to the bulk value (zbulk = 1.5 nm in the present calculations; see density profile in Figure 4). Water layering has been previously reported for water at 298 K in contact with graphene using ab initio73,74 and atomistic75 simulations. Our simulations indicate that layering is already present at room temperature and increases with supercooling.37 We find a correlation between water layering L at the carbon surfaces and ice nucleation efficiency ΔTf (Figure 4 lower panel): water crystallizes at higher temperatures on surfaces that induce more layering. We considered two additional surfaces: a flat soft atomless Lennard-Jones (LJ) surface and a hydrophilic atomically rough surface. The results for the hydrophilic rough surface in this study are identical to those for a hydrophobic rough surface in ref 37. The LJ surface yields layering L and ice freezing temperature Tf similar to those of the decorated carbon surface with ΔOH = 1 nm. The hydrophilic and hydrophobic rough surfaces did not produce layering of water molecules and did not promote heterogeneous nucleation of ice. These results support the existence of a
like ordering of water at the surface was evaluated from isothermal runs using the order parameter q3.70 We verified that the two order parameters predict the same trends, and the selection of one over the other does not affect the conclusions of this work. The order at the surface has been evaluated separately for water molecules in the first layer from the surface, in the second layer, and in the bulk. The layers were identified from the density distribution function: the first layer between 0 and 0.4 nm and the second layer between 0.4 and 0.8 nm. The bulk has been identified as the region further than 1.5 nm from the surface.
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RESULTS AND DISCUSSION Hydrophilicity of Carbon Surfaces Is Not a Good Predictor of Ice Freezing Temperatures. In order to elucidate whether there is a correlation between wetting of the surface by liquid water and its ability to promote ice nucleation, we investigated the freezing of water in contact with the two sets of flat graphitic surfaces described in Methods. The first set consisted of graphite surfaces modified with hydroxyl groups replacing carbon atoms every approximately ΔOH = 1, 2, 4, and 8 nm. Figure 1 shows a droplet on top of a graphitic surface
Figure 1. Determination of the contact angle between liquid water and the surface. The upper panel shows the density profile of water droplets on top of graphite (red circles) and a graphitic surface decorated with hydrophilic groups every ΔOH = 1 nm (blue circles). The contact angles θ were computed as in ref 69 from the tangent at the surface of a second order polynomial that fits the density profile (black lines). The lower panel shows a snapshot of the simulation box for a water droplet (blue balls) on top of the graphitic surface (gray balls) decorated with hydrophilic groups (red balls) every ΔOH = 1 nm.
decorated with hydroxyl groups every ΔOH = 1 nm. The hydroxylated surfaces of this study should not be considered realistic representations of oxidized carbon surfaces, for which actual distribution of functional groups is not yet known.57−62 Although oxidation of graphite would also involve a loss of surface planarity,36 we here conserve the planarity of the surface as the effect of curvature on ice freezing temperatures has been independently evaluated in a separate paper and found to decrease the ice nucleation ability of the surface.37 The second set of surfaces encompasses bare graphitic surfaces with different strengths ε of the water−carbon interaction. These surfaces can be realized in experiments by depositing graphene on metallic substrates such as Cu or silica, which tune the hydrophilicity of graphene surfaces while still providing a 7332
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Figure 2. Contact angles and ice freezing efficiency of modified graphitic surfaces. (A, C) Contact angles measured for liquid droplets containing 5528 water molecules at 298 K. The contact angle for the surface with water−carbon attraction ε = 0.2 kcal/mol could not be measured because water spreads, indicating that the contact angle of water on that surface is close to zero. The contact angle of water on graphite (86°) is shown as a black band for reference. (B,D) Freezing efficiency, ΔTf = Tf − Tfhomo, of the surfaces as obtained from quenching simulations at 1 K/ns, the fastest cooling rate that leads to ice crystallization on these surfaces. The homogeneous ice nucleation temperature of mW water is Tfhomo = 201 ± 1 K, and the freezing efficiency of bare graphite, shown with a black band, is ΔTf = 12 ± 3 K. We found the freezing temperature of bulk water and droplets in contact with each surface to be identical.
To quantify the degree of ice-like order of water in contact with the surfaces we calculated the value of the order parameter q3,70 which is a measure of tetrahedral order around individual water molecules. The average value of q3 is 0.46 in bulk water at 300 K and reaches a value of 0.67 in ice. Figure 6 shows the average q3 for the first and second layers of interfacial water, as well as bulk water, for temperatures ranging from 218 to 300 K. The tetrahedral, ice-like ordering of bulk water increases, unsurprisingly,39,42 on cooling. The average q3 of the second and farther layers is essentially the same as in bulk water. For the first layer, there is a significant enhancement of ice-like ordering at the flat surfaces, but not at the interface of the rough ones. Interestingly, the increase in ordering in the first layer does not seem to be a function of the distance to the heterogeneous freezing temperature, T−Tf, but rather of the absolute temperature T. These results suggest that tetrahedral ordering of the first water layer in contact with flat surfaces is not able to discriminate between different surfaces in their ability to nucleate ice. We conjecture that the rare formation of bilayer patches of hexagons (i.e., the fluctuations in the second layer) may be associated to the nucleation of ice. The elucidation of the actual ice nucleation coordinate, however, requires the analysis of hundreds of unbiased trajectories and will be the object of future studies.
Figure 3. Heterogeneous nucleation of ice on OH-decorated graphite surface. Snapshots along a crystallization simulation of a cell containing ∼5000 water molecules in contact with OH-decorated surface with ΔOH = 1 nm. The graphitic surface is shown with gray balls, OH-like groups with red balls, liquid water is shown with blue dots, and the largest ice cluster with blue sticks.
correlation between ordering of liquid at the surface and heterogeneous nucleation ability, and the lack of correlation between hydrophilicity of the surface and freezing temperature. The increase in layering on cooling is accompanied by an increase in the planar ordering of the first water layer in contact with the flat surfaces. Fluctuating patches of hexagons develop in the first two layers of water in contact with the flat surfaces (Figure 5), but not on top of the rugged surfaces, irrespective of their hydrophilicity. The patches of bilayer hexagons result from the overlay, in registry, of hexagons of the first and second layers. The patches of hexagons in the first layer in contact with the surface are significantly larger and longer lived than in the second layer. Transient patches of bilayer hexagons are created and annihilated in the first two bilayers during the induction time that precedes the formation of the critical ice nucleus on graphite.37 We find the same phenomenology for the modified graphitic surfaces of the present study.
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CONCLUSIONS We used molecular dynamics simulations to assess whether the hydrophilicity of carbon surfaces is a good parameter in controlling the ice crystallization temperatures. The hydrophilicity of the surface was tuned following two different procedures: (i) decorating the graphite surface with OH-like groups and (ii) increasing the water−carbon attraction. The simulations indicate that all modified graphitic surfaces 7333
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Figure 4. Layering of liquid water at the surfaces correlates with ice nucleation ability. Upper panel: Water density profiles at 230 K for bare graphite (black line), modified water−carbon attraction surface with ε = 0.18 kcal/mol (purple line), LJ surface (brown line), and hydrophilic water-like rigid slabs (green line). The density profile of ice formed on the bare graphite is shown with a cyan line, the splitting of the peaks evidence that water oxygens are not in plane. Lower panel: Layering of liquid water on all surfaces at 230 K. Green symbols are used for hydrophobic37 and hydrophilic rough surfaces (their values overlap), brown circle for the LJ surface, red circles for OHmodified carbon surfaces (in order of increasing freezing efficiency: ΔOH = 1, 2, 4, and 8 nm), purple circles for water−carbon attraction modified surfaces (in order of increasing freezing efficiency: ε = 0.12, 0.16, 0.18, and 0.2 kcal/mol), and black triangle for the graphite surface.
Figure 5. Structure of interfacial water in contact with a modified graphitic surface with ΔOH = 1 nm. Upper panels show the front view of the simulation boxes; in the left panel, only the first layer of water molecules at the surfaces is shown, and in the right panel, only the second layer is shown. Carbon atoms of the surface are shown with gray balls, OH-like groups with red balls, and water as blue sticks that connect neighbors within 0.35 nm. In the lower panels, both first and second layers are shown to highlight the presence of bilayer hexagonal patches (showing the surface in the left panel, and hiding it for clarity in the right panel). There is no apparent alignment between the water molecules and the surface atoms, indicating that the surface does not template the formation of ice.
promote heterogeneous nucleation of ice and ordering of liquid water at the surface. We found that an increase in hydrophilicity of the OH-decorated surfaces anticorrelates with an increase in freezing temperature, while hydrophilicity is correlated with freezing temperature for the surfaces with tuned water−carbon attraction. We conclude that the hydrophilicity of the surface is not in general a good predictor for heterogeneous ice nucleation ability. Oxidation of atmospheric soot and carbonaceous aerosols increases their hygroscopicity and hydrophilicity, and it also alters their nanostructure and chemistry. The specific way in which oxidation affects the structure and functionalization of carbon has not yet been elucidated. Knowledge of the actual nanostructure and spatial distribution of chemical groups in soot and other atmospheric carbon particles is critical for an accurate prediction of the ice nucleating ability of these aerosols. Layering of liquid water at the surface correlates with the ability of carbon particles to promote ice nucleation. Hydrophobic and hydrophilic atomically rough surfaces do not induce layering and do not promote heterogeneous nucleation of ice. Ice-like order in interfacial liquid water appears as fluctuating patches of bilayer hexagons on the carbon surfaces. These domains of bilayer hexagons were not observed on the
atomically rough surfaces. We find that the ice-like order of liquid water in the first layer of all modified graphitic surfaces is noticeably higher than the order of bulk liquid water. The order of the first layer of water on graphite reaches a value comparable to that in ice as the temperature approaches the corresponding Tf. Interestingly, already in the second layer of water on all graphitic surfaces, the order is the same as in bulk water. Our results suggest that the formation of bilayer patches of hexagons in interfacial water, which may serve as precursors for the formation of the ice nuclei, is mostly limited by fluctuations in the structure of the second layer. Nucleation pathways in which the formation of semiordered regions act as precursors of crystallization have been proposed for homogeneous nucleation in a variety of systems including ice,42,47,76,77 clathrate hydrates,78−80 colloids,81 and hard spheres.77,82,83 We conjecture that patches of bilayer hexagons may play a similar role in the heterogeneous nucleation of ice at graphitic surfaces. Our results strongly suggest that layering and ordering of interfacial liquid water plays an important role in the mechanism of heterogeneous nucleation of ice. Surface sensitive spectroscopies, which provide microscopic information on the order of interfacial liquid water, could be used for the diagnosis of the ice-nucleating ability of carbon surfaces and other atmospheric particles. 7334
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neous nucleation of ice on carbon surfaces will be the focus of future work.
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AUTHOR INFORMATION
Corresponding Author
*(V.M.) E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Sarah D. Brooks for discussions and Matı ́as Factorovich for the code to compute the contact angles. This work was supported by the National Science Foundation through awards CHE-1125235 and CHE-1309601. We acknowledge the Center for High Performance Computing at the University of Utah for technical support and allocation of computer time.
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Figure 6. Temperature dependence of ice-like ordering of interfacial liquid water. Order parameter q3 averaged over the water molecules in the first layer (circles) and second layer (diamonds) from the surfaces. Black symbols are for graphite, which has ΔTf = 12 ± 3 K. Red symbols are for the OH modified surface with ΔOH = 1 nm, which has ΔTf = 6 ± 2 K. Purple symbols are for the graphitic surface with higher water−carbon attraction ε = 0.18 kcal/mol, which has ΔTf = 18 ± 2 K. Green symbols correspond to the hydrophilic rugged surface, which does not heterogeneously nucleate ice. The wide gray line indicates the average values of q3 for bulk water. Note that q3 of the first layer on graphite reaches a value comparable to the order in hexagonal ice (0.67) on approaching Tf.
REFERENCES
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Layering of liquid water is a robust feature of water in contact with graphitic surfaces and has been previously reported in simulations of graphene surfaces using ab initio simulations73,74 and classical simulations with atomistic models.75 The mW water model correctly predicts the structures of liquid, amorphous, and ice phases38−55 and the mechanisms of homogeneous nucleation and growth of ice;40−43,49,52−54,56 hence, we expect the predictions of this work to be valid for other water models and for real water in experiments using similar model surfaces. It should be noted that a correlation between layering or ordering of interfacial liquid water and ice freezing is not restricted to carbon surfaces: layering of liquid water has been reported to occur in molecular simulations of good ice nucleating surfaces, kaolinite84 and on AgI,85 and a recent experimental study using sum frequency spectroscopy reveals a correlation between increased ice-like order of liquid water at the surface of dust particles coated with sulfuric acid and an increase in ice crystallization temperatures.86 Even simple systems such as colloids,87 hard spheres,88−90 and Jagla particles,91 which do not have hydrogen bonds or the anisotropic interactions of water, display a correlation between layering at a surface and heterogeneous crystallization. These results suggest that layering and interfacial ordering may facilitate heterogeneous nucleation in a wide class of liquids. There may be mechanisms responsible for heterogeneous nucleation of water and other substances that do not involve layering. The ice nucleation ability of long-chain alcohol monolayers, for example, has been ascribed to templating of the ice structure by the underlying ordered surface.92,93 The formation of ice on the model carbon surfaces of this study, however, does not involve templating by the surface. The elucidation of the detailed nucleation pathway for heteroge7335
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