CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201400016

Effect of Nanoscale Confinement on Freezing of Modified Water at Room Temperature and Ambient Pressure Sanket Deshmukh,[a] Ganesh Kamath,[b] and Subramanian K. R. S. Sankaranarayanan*[a] Understanding the phase behavior of confined water is central to fields as diverse as heterogeneous catalysis, corrosion, nanofluidics, and to emerging energy technologies. Altering the state points (temperature, pressure, etc.) or introduction of a foreign surface can result in the phase transformation of water. At room temperature, ice nucleation is a very rare event and extremely high pressures in the GPa–TPa range are required to freeze water. Here, we perform computer experiments to artificially alter the balance between electrostatic and dispersion interactions between water molecules, and demonstrate nucleation and growth of ice at room temperature in

a nanoconfined environment. Local perturbations in dispersive and electrostatic interactions near the surface are shown to provide the seed for nucleation (nucleation sites), which lead to room temperature liquid–solid phase transition of confined water. Crystallization of water occurs over several tens of nanometers and is shown to be independent of the nature of the substrate (hydrophilic oxide vs. hydrophobic graphene and crystalline oxide vs. amorphous diamond-like carbon). Our results lead us to hypothesize that the freezing transition of confined water can be controlled by tuning the relative dispersive and electrostatic interaction.

1. Introduction Water is considered to be one of the four root cosmological elements and plays an important role in diverse chemical, physical, and biological processes relevant to applications ranging from biomedical to energy technologies.[1] In its bulk form, water molecules are hydrogen-bonded to neighboring water molecules in an approximately tetrahedral geometry and form an extended hydrogen-bond network.[2, 3] The unusual properties of liquid water, such as the density maximum at 4 8C, increase in diffusivity with density, and increase in specific heat with reduction of temperature, are attributed to loss of tetrahedral order when either temperature or density are increased.[4, 5] The rapid structural evolution of the water network at femtosecond to picosecond timescales plays a key role in determining the unique properties and anomalous behavior of water.[6] The structure and dynamics of water are, however, strongly correlated to the energetics of various inter- and intra-molecular forces. In particular, the balance between short-range dispersive and long-range electrostatic contributions plays a critical role in dictating the observed structure and dynamics of water.[1, 5, 7, 8]

[a] Dr. S. Deshmukh, Dr. S. K. R. S. Sankaranarayanan Center for Nanoscale Materials Argonne National Laboratory 9700 S Cass Avenue Argonne IL-60439 (USA) E-mail: [email protected] [b] Dr. G. Kamath Department of Chemistry University of Missouri-Columbia Columbia, 65211 (USA) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201400016.

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In many emerging biomedical and energy applications, water is typically confined at the nanometer-length scale and is in direct contact with various types of interfaces.[9–11] In comparison to bulk water, the presence of a charged interface such as an oxide can alter the interatomic energetic interactions (short-range van der Waals vs. long-range electrostatic) as well as the nature of the water’s hydrogen-bond network in confined water to accommodate the distinct topology of the interface.[12] In the case of bulk water, water molecules form an extended three-dimensional hydrogen-bond network. However, at the interface, the decreased number of nearest neighbors results in the reduced probability of having a nearby acceptor water molecule to form a new hydrogen bond. In the case of bulk water, the structure and dynamics of the water molecules at any given temperature and pressure conditions depend on the balance between the short-range and long-range interatomic interactions.[1, 4, 13–15] However, there are several scenarios, in which this balance between the short-range van der Waals and long-range electrostatic interactions is likely to be perturbed. For example, when water interacts with either ionic compounds, charged chemical species, or macromolecules, the interatomic interactions are different from that of bulk water.[16] Similarly, the presence of nanoscopically confined environments,[10] the application of external fields[17] or interfaces[18] (such as oxides[19]), and so forth, might possibly lead to perturbation in the short-range and the long-range interatomic interactions between water molecules. The effect of confinement can be envisioned as being analogous to alteration in state points (pressure and/or temperature) in relation to bulk systems,[20] primarily as a consequence of the attraction/repulsion exerted on the water by the confined walls.[9] It is widely believed that the presence of charged ChemPhysChem 2014, 15, 1632 – 1642

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CHEMPHYSCHEM ARTICLES interfaces, such as oxides, can alter the intermolecular interactions of nanoscopic-confined water, however, its effect on solvation and phase behavior are not completely understood. The frustration in packing that water undergoes in the proximity of interfaces results in local density oscillations near the interface[21] or across the confined pore. This density variations of water in a confined environment can manifest itself in the form of differences in thermodynamic and kinetic properties compared to bulk water.[22] As a result, the structure and solvation dynamics of water are significantly altered and cannot be simply extrapolated from those of bulk water.[23] Although the structure and physical properties of bulk liquid water are relatively well established, a fundamental understanding of the nanoscale-confinement effects and altered intra/intermolecular energetics on the solvation behavior and the nature of freezing transition are still lacking.[1, 2, 13, 14] It has been reported that when the dimensions of the confined space approaches the range of intermolecular interactions, the freezing point of confined water is shift relative to the bulk water freezing point.[10] The shifts in freezing point and the nature of freezing transition depend on the relative strength of the fluid–wall-to-fluid–fluid interaction. There are previous studies, which have investigated freezing of water in confined environments.[11, 24, 25] In these confined environments the nature of liquid–solid freezing transitions (first order vs. continuous) and the structure of the confinement-induced phases are different from that of bulk water.[10] In the case of bulk water, there is a first-order transition between solid and liquid phases. In contrast, recent simulations by Eugene Stanley and co-workers have shown that confined water may freeze by means of both first-order and continuous phase transitions.[25] Debenedetti and co-workers have shown that in hydrophobic nanopores, for temperatures well below the bulk freezing point, it is possible to crystallize confined water through the application of high pressures.[26] The temperature of the freezing transition depends on the applied pressure and the extent of confinement. Recently, Debenedetti and co-workers have reported freezing of water under nanoconfinement when plate distances are ~ 0.6 nm.[24] The resulting crystallized structure is a bi-layer ice.[24] Similar crystallization behavior at around 240 K in the case of hydrophobic surfaces was also reported by Koga, Zeng, and Tanaka.[27, 28] They observed the formation of ice nanotubes in carbon nanotubes.[27, 28] Similarly, water under extreme confinement between quartz surfaces has been known to undergo a first-order freezing transition from a monolayer of liquid water to a quasi-two-dimensional ice at ambient conditions.[29–31] Recently, however, Alabarse et al. have suggested that although nanoscale confinement in hydrophilic pores can induce significant orientational order, the adsorbed layer is unfreezable and has a rigid (i.e. glassy) liquid-like structure.[32] Even with the application of an electric field, freezing of water is observed only when it is confined to few molecular layer thicknesses.[33] Jinesh and Frenken have used a high-resolution friction force microscope, scanning a sharp tungsten tip over a graphite surface to study the effect of confined water on tribological properties.[33] They demonstrated rapid nucleation of water between the tungsten tip and the surface caused  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org by capillary condensation and the transformation of liquid water into crystalline ice at room temperature under confinement.[34] Despite numerous investigations conducted on both bulk[1, 5, 13, 14, 35] and confined water systems[10, 11, 24, 25, 32] reports on freezing transition of liquid water into stable three-dimensional ice structures at room temperature remain scarce. Here, we report a unique freezing scenario at room temperature and ambient pressure in a nanoscale-confined environment (extending to several tens of nanometers) brought about by altering the relative strengths of inter-molecular dispersive and electrostatic forces. By using molecular dynamics (MD) simulations we show that tuning of the relative dispersive and electrostatic contributions can allow us to tailor local ordering, tetrahedrality, and solvation dynamics of nanoscopic confined water independent of the nature of the confining surfaces (hydrophilic oxides vs. hydrophobic graphene and crystalline oxide vs. amorphous diamond-like-carbon).

2. Computational Details 2.1. Potential Models Potential Model of Water Our MD simulations of simple point-charge/flexible water (SPC/Fw)[36] were performed with samples of 1000 water molecules at an initial density of 0.97 g cm3. SPC/Fw is a flexible variant of the rigid SPC model. The potential interaction, U, in the flexible SPC/Fw is a sum of various intra- and intermolecular contributions at a distance r [Eq. (1)]: UðrÞ ¼

X

Ub ðrÞ þ

bond

X

Uq ðrÞ þ

angle

X

ULJ ðrij Þ þ UES

ij allpairs

ð1Þ

The intra-molecular interaction Ub between two bonded atoms at a distance r is [Eq. (2)]: Ub ðrÞ ¼ Kb ðr  r0 Þ2

ð2Þ

where Kb is the spring constant and r0 is the equilibrium bond length. The bending interaction Uq is given by Equation (3): Uq ðrÞ ¼ Kq ðq  q0 Þ2

ð3Þ

where Kq is also a spring constant and q0 is the HOH angle at equilibrium. In the Lennard–Jones (LJ) term ULJ, rij is the separation distance between oxygen atoms on molecules i and j [Eq. (4)]: hs 12 s6 i ULJ ¼ 4 e  r r

ð4Þ

where, s and e are the scaling parameters for distance and energy. The Coulomb potential UES is given by Equation (5): UES ¼

qi qj 4 pe0 rij

ð5Þ

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where, qi and qj are the charges of atoms i and j. e0 is the effective dielectric constant and rij is the distance between atom i and j. As previously reported in several studies, the flexible SPC/Fw model is reasonably successful in describing the properties of water and the various amorphous and crystalline forms of ice.[38] The corresponding potential parameters are listed in Table 1.

Table 2. Potential energy parameters for the MgO substrate derived from the work of McCarthy et al.[40] Pair

A [kcal mol1]

1/(1) [1]

C [kcal mol1 6]

Mg–Mg O_oxide–O_oxide Mg–Ow Mg–Hw Mg–O_oxide Hw–O_oxide Ow–O_oxide

22 645 95 810 86 651 3981 46 579 8189 17 8234

4.24 4.36 4.30 3.81 4.30 3.87 4.36

1224 252 434 148 555 67 197

Table 1. Potential parameters for the SPC/Fw water model.[36] Parameter

SPC/Fw water model

qo [e] qH [e] eo [Kcal mol1] so [] Kb [Kcal mol1 2] b0 [] Kq [Kcal mol1 rad2] q0

0.82 0.41 0.1554253 3.165492 1059.162 1.012 75.90 113.24

interactions between the oxygen atoms of the water molecules and the carbon atoms of DLC and graphene sheets were modeled by using ULJ and setting eOC = 0.0749 kcal mol1 and sOC = 3.19.[42, 43]

2.2. Simulation Setups Hydrophilic Surface (MgO–Water) Potential Model of MgO Atomistic simulations are based on the Born model which assumes that ionic interactions occur through long-range electrostatic and short-range forces which can be described by using simple analytical functions.[39] The potential energy is thus a function of the distance between the ions. In addition to the Coulomb term, which describes the long-range electrostatic interactions between the ions of MgO, a Born–Meyer– Buckingham (BMB) potential is needed to describe the shortranged interactions between the ions.[40, 41] The potential energy between ions i and j separated by the distance rij owing to the charges qi and qj between the pairs of ions is thus given by Equation (6) as: 

 qi qj r VðrÞ ¼ A exp   Cr 6 þ rij 1

ð6Þ

The exponential term of the short-range potential takes into account Pauli repulsion and the r6 term accounts for any attractive dispersion or van der Waals interactions. The interactions between water and MgO were modeled by using potential parameters described by McCarthy et al.[42] The details of the potential model and the parameters used for the Buckingham potentials of the MgO substrate employed in this study are listed in Table 2.

The simulations were carried out on a periodic system comprised of MgO (100) slabs containing 1024 Mg2 + ions and 1024 O2 ions (Figure 1). The thickness of the MgO slabs was ~ 14 . The center of the unit cell [between two exposed MgO(100) slabs] was filled with water molecules. A simulation cell of ~ 34  17  72  with a water thickness of ~ 44  was used. The number of water molecules filled (~ 836 molecules) was chosen to initially equal the bulk density of water and was taken from NPT (number of particles, pressure, and temperature) equilibrated bulk water. The simulations were performed at room temperature (300 K) using a NPT (constant number of particles) ensemble. The equilibration of the system was carried out for ~ 500 ps and the remaining 1000 ps in the 1.5 ns simulation run were treated as production run for calculating the timeaveraged properties. The equations of motion were integrated by using the Verlet leap-frog scheme with a time step of 0.5 fs. The temperature was held at 300 K by using a Nose-Hoover thermostat. The Ewald summation method was used to compute the long-range electrostatic interactions. Comparisons with bulk simulations of water were also carried out. All the simulations were carried out using the DLPOLY code.[46]

Potential Model for Graphene and Diamond-Like-Carbon Interactions between carbon atoms of both diamond-like carbon (DLC) and graphene sheets were modeled using Tersoff potentials.[43] The Tersoff potential is capable of describing both sp2 and sp3 carbon bonding. This potential counts the number of neighboring atoms of a given atom and in this way controls the bond lengths and bond angles. The non-bonded  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 1. Snapshots showing initial configurations of confined water between various substrates at 300 K. a) MgO–water, b) graphene–water, and c) DLC–water.

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Simulations of Hydrophobic Surfaces (Graphene and Diamond-Like-Carbon) Simulations of water confined between hydrophobic surfaces such as graphene and amorphous diamond-like carbon were carried out at 300 K using an NPT ensemble. The simulations of water confined between DLC slabs comprised two slabs with 1354 DLC atoms which were placed at ~ 44  apart from each other (Figure 1). The center of the unit cell (between two exposed DLC slabs) was filled with ~ 836 water molecules. A simulation cell of ~ 32  17  69  with a water thickness of ~ 44  was used. In the case of simulations carried out for water confined between graphene sheets, two graphene sheets with ~ 32  17  dimensions were places at the distance of ~ 43  from each other (Figure 1). The void between these two graphene sheets was filled with ~ 836 water molecules. All the simulations were carried out by using the DLPOLY code.[44] The equations of motion were integrated by using the Verlet leapfrog scheme with a time step of 0.5 fs. The temperature was held at 300 K by using a Nose-Hoover thermostat. 2.3. Tuning Parameters and Perturbation Scenarios We introduce tuning parameters (m and l) to modify the water potential function by changing the relative strength of the electrostatic and LJ terms (Figure 2 a and b). Two perturbation scenarios were considered. In the first case, the relative weight of the dispersion and electrostatic interactions were modified by scaling l by up to 300 % of the original e while keeping s constant (Figure 2 a). In the second case, the dispersion and electrostatic interactions were modified by scaling m up to 20 % of the original s for constant e (Figure 2 b). Note that l scales the attractive and repulsive LJ terms uniformly whereas m scales them non-uniformly. For a pure LJ system, the scaling of the parameters e and s is analogous to the reduced temperature and reduced density. Such modifications have been studied in the past to evaluate the phase behavior of LJ fluids.[45–47] However, in the case of water, the presence of long-range electrostatic and the intra-molecular interactions make the situation much more complicated [Eqs. (7), (8)]: hs 12 s6 i  UðrÞ ¼ lULJ þ UES where ULJ ¼ 4 el r r hms12 ms 6 i UðrÞ ¼ mULJ þ UES where ULJ ¼ 4 e  r r

ð7Þ ð8Þ

A series of simulations were performed for nanoscopic water confined between hydrophilic surfaces such as MgO(100) slabs, hydrophobic surfacess such as graphene and DLC, as well as for bulk water (Figure 1 for initial configuration). To evaluate the effect of water model on the observed phase transition and dynamics of crystallization, we considered the above perturbation scheme for several different water models. Other water models evaluated include transferable interatomic potentials (3-point) TIP3P, modified TIP3P, SPC/E, and SPC.[34, 48, 49] All these models gave qualitatively the same behavior. Our results are independent of the water force field em 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 2. Scaling of the LJ parameters. We considered two perturbation scenarios for nanoscopically confined water. a) In the first one (weak scaling l), we varied the potential well depth e for a constant LJ diameter (s). b) In the second perturbation scenario, we varied the LJ diameter (s) for a constant potential well depth e.

ployed and illustrate that tuning the relative dispersive and electrostatic interactions allows for controlled transformations of the liquid state to glassy and ordered states of nanoscale confined water (reminiscent of hexagonal ice Ih) at room temperature.

3. Results and Discussion In the following subsections, we mainly limit our discussion to the MgO–water and the SPC/Fw–water system. Qualitatively similar results were obtained for other systems (graphene– water and DLC–water) and the same are pointed out wherever possible. 3.1. Order Map The order map based on translational and tetrahedral order parameters (see Section 1 in the Supporting Information for definitions) are used to evaluate the evolution of structural order of bulk and confined water (Figure 3 a and b). At 300 K, point A’ in Figure 3 a represents pure bulk water with a wellstructured hydrogen-bond network. An increase in the dispersive contribution relative to the electrostatic ones results in ChemPhysChem 2014, 15, 1632 – 1642

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CHEMPHYSCHEM ARTICLES a decrease in both the translational and tetrahedral ordering. The translational order (t) is strongly coupled to the orientational order, causing t to decrease strongly with q. In this regime (A’–B’ and A’–D’), hydrogen bonding determines the mutual orientation and separation between the water molecules. A minimum in the orientational order is observed at B’ (strong scaling) and D’ (weak scaling). Beyond this points, for both m and l, we observe a decrease in q with an increase in t. An increase in the dispersive contribution thus weakens the coupling between the translational and orientational order and water presents features representative of a hard-sphere liquid (C’ and E’).[2] The observed variation in the order map is consistent with previously published MD simulation studies of Lynden-Bell and Debenedetti, who observed a similar change from water to a hard-sphere liquid by scaling the dispersive interactions.[50] To investigate the effects of nanoscale confinement on molecular order, we plotted the (t, q) order map for various scaled water models in Figure 3 b. State point A represents the original state of the confined water which has slightly higher translational and tetrahedral order compared to bulk water. An ini-

www.chemphyschem.org tial increase in the dispersive contribution in the A–B and A–E regime results in a decrease in the parameters t and q; the coupling between the two order parameters is still strong. Beyond this point, the weak and strong scaling factors introduce significant differences in the molecular order. In the case of l, further increase in dispersive interactions decreases the tetrahedral order and increases translational order. This behavior is qualitatively similar to bulk water and represents a transformation from a tetrahedral to a spherically symmetric LJ fluid (point F). Scaling through m, we encounter a B–C regime wherein the behavior is similar to that seen for weak scaling. Beyond this point, however, we observe that any further increase in dispersive interactions relative to the electrostatic ones results in transformation to a highly ordered state (maximum tetrahedral and translational order). The reappearance of strong correlation between t and q in the C–D regime signifies a crystallization phase with state point D probably representing ice-like structures. 3.2. Surface Atomic Density Profiles The increased ordering in confined water at room temperature is further illustrated by using surface normal density profiles of water as a function of l and m in Figure 4. The surface normal density (1z) is defined as the number of atoms of a given type within a range of perpendicular positions in the simulation cell and normalized to the average density [Eq. (9)]: V 1ðzÞ ¼ NAdz

* X

+ dðz  zi Þ

ð9Þ

i

Here, V is the simulation cell volume, N is the number of atoms of a given type, A is the area of the interface, and zi is the distance of atom i perpendicular to the MgO substrate. d is typically the bin width (0.1 ), that is, the interval over which the atom densities are time-averaged over many configurations obtained from the MD trajectories to compute the ionic densities. As seen in Figure 4 a, weak scaling (change in l as we go from l = 1.4 to 4) results in increased layering, suggestive of high degree of translational order. Further, the peak intensities and peak widths for the highest l are broad enough for suggesting the absence of liquid–solid phase transition. On the other hand, beyond a certain threshold value (m > 1.10), the scaling by m (Figure 4 b) produces a more dramatic increase in the peak intensity (and reduction in peak width), which is indicative of a more distinct structural change. 3.3. Radial Distribution Functions

Figure 3. Order map of translational (t) versus orientational order (q) metrics for the various scaled water models in bulk and nanoscopic confined water. The lines represent evolution of the order metric upon change in the relative dispersion and electrostatic interactions for the two environments a) bulk and b) confined water. The arrows represent the direction along which the scaling factors increase for the bulk and confined water.

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The onset of crystalline nature and the associated change in the molecular order can be understood from the simulated oxygen–oxygen radial distribution function of water as shown in Figure 5 a–d. The oxygen–oxygen radial distribution function represents an average over all water molecules in the system. Figure 5 a, b shows gOO(r) for SPC/Fw bulk water at 300 K. The ChemPhysChem 2014, 15, 1632 – 1642

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Figure 4. Density profiles of water molecules perpendicular to the oxide– water interface. Effect of variation in a) the scaling factor l and b) the strong parameter m on the density distribution of nanoscopically confined water is shown.

structure is typical for a tetrahedral liquid with the second hydration shell located 1.7 times from the first neighbor distance. An increase in l, (Figure 3 a) and m, (Figure 3 b) results in the disappearance of the tetrahedral peak and in a gradual shifting of the second shell to twice the first neighbor distance, a feature characteristic of LJ fluids. In the intervening region, the transformation from tetrahedral to LJ fluid goes through an intermediate regime of minimum order (1.1 < m < 1.15). This is not surprising considering that the two types of order (tetrahedral and spherical symmetric) found in bulk water are topologically incompatible. This was also observed in the simulation studies of Debenedetti and co-workers.[48, 50] In accordance with the observed variation in the order map, the pair-wise radial

www.chemphyschem.org distribution functions (RDFs) of oxygen with oxygen in bulk water demonstrate the local order to evolve from tetrahedral to spherically symmetric, when the weight of the LJ contribution to the interatomic interaction is increased with respect to the electrostatic ones. In the case of confined water, the weak scaling of dispersive interactions (throguh l) results in a behavior qualitatively similar to bulk water (Figure 5 c); a breakdown of tetrahedral order characteristic of SPC/Fw water to a system with minimum order, eventually leading to reappearance of the characteristic order of a LJ fluid. Figure 5 d illustrates the development of crystallinity and provides direct evidence that a strong scaling (through m) of the dispersive interactions causes an initial breakdown of the tetrahedral order, which is followed by reappearance of molecular order that is reminiscent of ice-like structure (re-entrant phase). In the absence of such perturbation, Giovambattista et al. have shown in their MD simulations that confinement of water between the 0.6–1.6 nm walls can cause a first-order transition from a bi-layer liquid to a tri-layer structure characterized by a liquid (central) layer and two crystal-like layers next to the walls.[24] Thus, instead of the more commonly observed liquid-to-liquid transformations,[4, 50] the system undergoes a re-entrant freezing transition at room temperature that gives rise to intervening solid ice-like phases. The transformation of water into ice with an increase in m is further substantiated by characterization of the hydrogen-bonding lifetimes and diffusivity of the system. 3.4. Mean Square Displacements and Diffusion Coefficients

To investigate the relationship between molecular order and solvation dynamics, we show in Figure 6 the calculated dependence of the diffusion coefficient D of bulk and confined water on l and m. The increased layering in confined water results in their diffusivities being lower compared to the bulk (see also Figure S1 in the Supporting Information). In bulk water, the topological incompatibility between tetrahedral water and spherically symmetric LJ fluid results in the system going through a state of minimum order.[50] The diffusion coefficient undergoes a maximum around l = 4 and m = 1.10, which coincides with the state of minimum tetrahedral and translational order of the fluid. Further increase in l and m is associated with a drop in diffusivity, which results from an increase in the translational order of the LJ fluid. In the case of a confined Figure 5. Oxygen–oxygen radial distribution functions for the various scaled models in bulk and nanoscopic confluid, this maximum in diffusivity fined water at room temperature. Effect of a) scaling factor l and b) scaling factor m on gOO(r) in bulk water, is shifted to lower values of c) weak scaling l and d) strong scaling m effect on gOO(r) in confined water.  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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www.chemphyschem.org the potential energy requirements typical for hydrogen bonds in water. A hydrogen bond occupation number (Sij) can distinguish between the hydrogen-bonded and non-hydrogen-bonded atoms [Eq. (10)]:   Hydrogen-bond occupation number Sij ( 1 ðhydrogen  bondedÞ ¼ 0 ðnon  hydrogen  bondedÞ

Figure 6. Effect of scaling factors l and m on the diffusion coefficient of water. D is shown for different scaling factors (dispersive vs. electrostatic) for bulk and nanoscopically confined water. The dashed lines are a guide to the eye. For m > 1.10, the diffusivity drops to low values. The mean square displacement (MSDs, see also Figure S1) remains almost flat (constant) with time, indicating that water has frozen to ice.

l and m and represents an earlier onset of disorder. The diffusivity drops dramatically for m > 1.05. This indicates a significant increase in both the translational and tetrahedral order and is suggestive of a phase transformation to a crystalline phase. This is consistent with the experimental findings of Raviv et al. who found that confinement of a non-associative fluid (modified water) suppressed the translational freedom of molecules and reduced diffusivity, whereas in the case of real water, the diffusivity remained closer to bulk diffusivity for confinements above the 2–3 nm range.[11] The diffusivity variation complies with the hydrogen-bonding lifetimes. 3.5. Hydrogen-Bond Correlation Function and HydrogenBonding Lifetimes The effects of the scaling parameters m and l on the hydrogen-bonding abilities of water were studied. To represent hydrogen bonding between a pair of water molecules the following geometric criteria were used: ROO  3.6 , ROH  2.45 , and f 308.[51, 52] In Equation (6), ROO represents the distance between the oxygen of the donor and the oxygen of the acceptor water molecule. ROH is the distance between the oxygen of the acceptor water molecule and the hydrogen of the donor water molecule, which form the hydrogen bond. The angle f is the angle between the oxygen of the acceptor water molecule and the oxygen and the hydrogen of the donor water molecule (Oacceptor water···Odonor waterHdonor water). In this study, the first minimum in the corresponding RDFs of pure water was chosen as the cut-off distances, ROO and ROH. Depending on the state of the water molecules (ice-like or liquid) we used various angle criteria. For example, in the case of pure water we used f= 308 and for ice structures we used f= 1808. A hydrogen bond that is defined by using these geometric criteria fulfils  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

ð10Þ

The stability of the hydrogen bonds was determined by defining a time-dependent autocorrelation function of the state variable Sij that describes the existence or nonexistence of bonds between a selected donor–acceptor pair ij. Two types of correlation functions can be defined: the intermittent and the continuous one. In the continuous correlation case, the hydrogen-bond occupation number (Sij) is only allowed one transition from 1 to 0 when the bond between atom i and j breaks for the first time. After this first breakage of the hydrogen bond, Sij is no longer allowed to return to 1. In the intermittent correlation case, Sij(t+t0) is set to 1, if the bond between atom i and j is found to be present in the time steps t0 and t0 + t, irrespective of whether it is broken or reformed at the intermediate time [Eq. (11)] P * Sij ðt  t0 Þ  Sij ðt0 Þ+ Cx ðtÞ ¼

ij

P

Sij ðt0 Þ  Sij ðt0 Þ

ð11Þ

ij

where x corresponds to either the continuous (c) or the intermittent (i) autocorrelation function. The life time for the hydrogen bonds were defined as the time it takes the correlation functions to reach 37 % of the initial value. In this case, the correlation functions are normalized and hence, the decay time is the time taken to reach a value of 0.37. In SPC/Fw water, we observed that the lifetime of the hydrogen bonds are ~ 5–6 ps, which is reminiscent of the intermittent collective motion of water molecules, a result of extensive hydrogen-bond-network rearrangement dynamics of liquid water.[13] In bulk water, Figure 7 a and b we observe a nonmonotonic variation in the hydrogen-bonding lifetimes with an increase in l and m; the variation is more dramatic with m compared to l. An initial faster decay dynamics in the hydrogen-bond correlation function (l < 3 and m < 1.10) implies characteristics of so-called frustrated systems, such as liquid water with a disordered tetrahedral network. The minimum in hydrogen-bonding lifetimes coincides with the diffusivity maximum and corresponds to a state of minimum molecular order. Further increase in l and m restores translational order upon transition to a spherically symmetric fluid, leading to a small increase in the hydrogen-bonding lifetimes (Table 3). Although qualitatively similar variations with l were observed for confined water, we noted increased hydrogen-bonding lifetimes under confinement compared to bulk, which arise from interface proximity effects. At the interface, the decreased ChemPhysChem 2014, 15, 1632 – 1642

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water) promotes solidification by suppressing the translational freedom of molecules, whereas, in the case of real water, it tends to suppress the formation of highly directional hydrogen bonding associated with freezing.[11] In contrast, we observed a more dramatic variation in the hydrogen-bonding lifetimes for confined water when m is varied. Hydrogen bonds with average lifetimes of more than 1 ns were observed for m > 1.12 The large fraction of stable longlasting hydrogen bonds results in the onset of longrange order and signifies crystallization into a solid phase. We used the Q4 and Q6 orientational order parameters to evaluate the structure of ice.[2] These order parameters indicate whether or not the relative orientations of hydrogen bonds at individual water sites are coherently ordered. The rich polymorphism of phases of ice has been well documented through a series of X-ray diffraction and molecular dynamics studies of Figure 7. Hydrogen-bond dynamics evaluated by using correlation functions for various water under confinement.[10, 12, 15, 24, 25] Our analysis of scaled water models. Effect of weak scaling l and strong scaling m parameter on a and the orientational order of confined ice formed at b) bulk and c and d) nanoscopic confined water is shown. For confined water, an inroom temperature suggests that this phase closely crease in l results in a progressively faster decay indicating slower dynamics of hydrogen bonding, whereas an increase in m results in a non-monotonic structural variation; an inresembles the hexagonal ice (ABA).[53] Closer inspeccrease initially causes a faster decay of hydrogen-bond dynamics, whereas a slower tion of the MD trajectories (snapshots shown in Figdecay dynamics evident at higher scaling ratios (stronger dispersion forces compared to ure 8 b–c) suggests that the ice structure is comelectrostatics) suggests re-appearance of tetrahedral order. Note that the hydrogen bond prised of hexagonal ice crystals, which form hexagocorrelation functions are averaged over all molecules and typically obtained at the end of the simulation run. nal plates and columns, the top and bottom faces of which are basal planes. Our MD trajectories suggest that the hexagonal ice crystals grow in the direction of the c axis (normal to the substrate–water interface) with ice Table 3. Hydrogen-bonding lifetimes calculated for water confined benucleating on the substrate interface. As seen in the snapshots tween MgO (100) slabs. The hydrogen-bonding lifetimes are calculated presented in Figure 8 c–d, the room temperature ice we obfrom the hydrogen-bond correlation functions. tained consists of hexagonal sheets lying on top of each other. m Bulk water hydrogen-bondConfined water hydrogenTo evaluate the effect of the nature of the substrate on this ing lifetimes [ps] bonding lifetimes [ps] freezing transition, we simulated structured interfaces such as Original ~ 3.5 ~ 3.0 MgO and graphene and an atomically smooth substrate such (3.165492) as DLC. Interestingly, in all the cases, we found that nucleation 1.05 ~ 1.0 ~ 1.0 1.10 < 1.0 < 1.0 and growth of ice occured irrespective of the nature of the 1.12 < 1.0 ~ 250.0 substrate (Figure 9). 1.15 1.17

~ 1.2 ~ 1.0

~ 278.0 ~ 1000.0

l

Bulk water hydrogen-bonding lifetimes [ps]

Confined water hydrogenbonding lifetimes [ps]

Original (0.1554253) 1.47 1.94 2.90 3.86

~ 3.5

~ 3.0

~ 1.5 ~ 1.0 < 1.0 ~ 1.2

~ 1.5 ~ 1.0 ~ 2.5 ~ 3.5

number of nearest neighbor reduces the probability of having a nearby acceptor water molecule to form a new hydrogen bond. This increased lifetime of already formed hydrogen bonds near the interface translates to an increased average for the hydrogen-bonding lifetimes for confined water. This is consistent with the experimental findings of Raviv et al., who found that confinement in a non-associative fluid (modified  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

4. Discussion The physical picture which emerges from our study is as follows: At room temperature, ice nucleation is indeed a very rare event and even significant perturbations in dispersive and electrostatic interactions do not seem to enhance the probability of a nucleation event. In the presence of a foreign surface or particle to promote heterogeneous nucleation, the waterto-ice phase transition could be hypothesized as being an interface-mediated crystallization, originating from an imbalance of the repulsive and attractive terms of the forces governing the intermolecular potential. When this imbalance, a consequence of local perturbations in dispersive and electrostatic interactions, occurs near solid hydrophilic interfaces, such as an oxide, or near a hydrophobic interface, such as graphene, the substrate provides the seed for nucleation (nucleation sites) ChemPhysChem 2014, 15, 1632 – 1642

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Figure 8. Simulation snapshot illustrating the structural change in the hydrogen-bond network for confined water formed by changing the relative magnitude of the dispersion and electrostatic interaction. a) Effect of m and l on the hydrogen-bond network in nanoscopic water near an oxide surface. An increase in l results in a progressive loss of tetrahedral order to a state of minimum order. Subsequent gain of translational order results in system order evolving into a spherically symmetric one (LJ fluid). Increase in m results in a non-monotonic structural variation; an increase initially results in a loss of tetrahedral order with a subsequent re-entrant tetrahedral ordering corresponding to hexagonal ice (Ih) evident at higher scaling ratios. An increase in l for bulk water (see RDF in Figure 5) results in a non-monotonic variation, wherein the local order evolves from a tetrahedral to spherically symmetric one (LJ fluid). At intermediate values, the translational order breaks down. An increase in m results in similar qualitative variations of tetrahedral order in bulk water. b) Side view of hexagonal ice structure for a section through the center of confined water for m > 1.15. c) Top view of the same ice structure from our simulations. The view shown is along the c axis and normal to the oxide surface. d) Schematic of Ih projected onto the 1 basal plane of the hexagonal prism. The simulated structure and the schematic, show water molecules along the crystallographic c axis of two types of layers as part of the lattice structure of ice.

which could possibly lead to liquid–solid phase transition of confined water. We considered two perturbation scenarios for nanoscopically confined water. In the first one (weak scaling l), we varied the potential well depth e for a constant LJ diameter (s). The liquidto-crystalline transformation is directly related to changes in the packing density. It is well known that the depth of the potential minimum controls the packing density. For SPC/Fw confined water, the subtle balance between short-range attractive and repulsive contributions and

long-range electrostatic interactions preserves the tetrahedral order normally present in bulk solvents. For a small increase in l (< 2), the packing densities corresponding to a weakly attractive inter-particle potential (short-range repulsive interaction) are intermediates to well-dispersed or disordered systems of, and that corresponding to, tetrahedral order. When l is further increased (~ 4), deeper minimum, namely, stronger attraction, gives rise to a system with low packing density (as seen by the slight increase in mean distance in Table 4). Molecules that form ordered networks due to an increase in the attractive component of the inter-molecular potential must rearrange and increase their packing density. At the same time, the deeper the inter-molecular potential well becomes, the greater the inter-particle friction resulting from short-range repulsive terms becomes. The increased friction makes it difficult for the particles to rearrange and pack efficiently into a strongly ordered tetrahedral network (lower panel in Figure 8 a). The competition between the density lowering (increased packing efficiency) and increased friction dictates the molecular order. While a deeper potential well ensures lower packing densities and increased translational order, the increased friction prohibits crystallization into a tetrahedral ice network, even in the presence of a layered water network. In the second perturbation scenario, we varied the LJ diameter (s) for a constant potential well depth e. The constant e ensures that the inter-particle friction remains constant and essentially sets the threshold for packing efficiency to overcome the friction (see Figure 2). An initial increase in s (or m) results in density lowering and an increase in packing efficiency. This, however, is still below the threshold inter-particle friction and the system loses molecular order (both translational and tetrahedral). Further increase in m or the LJ diameter can be envisioned as a restriction within a given volume leading to an efficient packing of a given number of molecules. Once the intermolecular friction is overcome, an increase in m results in increased packing efficiency and a decrease in packing densities in comparison to that of SPC/Fw water. The lowering in density (the increase in mean distance is more prominent for m > 1.12 between the slabs as shown in Table 5) combined with in-

Figure 9. Simulation snapshot obtained at the end of 10 ns for water confined between a) graphene sheets (l = 1.0 and m = 1.17 for water model) and b) DLC (l = 1.0 and m = 1.17 for water model). Cylinders show the hydrogen-bond network.

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Table 4. Variation in the mean distance between the MgO substrates for various l. The initial distance between the two substrates is 44 Angstrom. l

Change [%]

Original 1.47 1.94 2.90 3.86

0.2 0.4 0.4 0.7 0.7

Table 5. Variation in the mean distance between the MgO substrates for various m. The initial distance between the two substrates is 44 Angstrom. m

Change [%]

Original 1.05 1.1 1.12 1.15 1.17

0.2 1.34 1.62 2.89 3.6 4.0

creased packing efficiency results in the system rearranging itself into a state analogous to super-cooled water (upper panel in Figure 8 a). Crystallization thus starts from the interface and at a temperature higher than without confinement. Upon the initial increase in dispersive interactions through the scaling factor m above the threshold, the inter-layers of water bound by the surface become less dense commensurate of a low-density, amorphous ice (upper panel in Figure 8 a). Further increase in m results in the formation of a well-ordered ice structure (hexagonal ice Ih).[35, 53]

5. Conclusions In summary, we have performed a molecular dynamics simulation study to explore the effect of systematically varying the well depth and the diameter of the interaction site (between oxygen) in water on the phase transition and fluxional properties in the vicinity of the MgO surface. We report a unique freezing scenario at room temperature and ambient pressure in a nanoscale-confined environment (extending to several tens of nanometers) brought about by altering the relative strengths of inter-molecular dispersive and electrostatic forces. Our analysis of the various dynamical and structural correlation functions including orientational order of confined ice formed at room temperature suggests that this phase closely resembles hexagonal ice. In the absence of these perturbations, that is, real water does not undergo such a transition at room temperature. Our simulations highlight the role of inter-molecular interactions of water under confinement. In this work, rather than varying the physics of the surface–water interactions (which has been extensively studied since the 1970s), we hypothesize that the effect of surface (or nanoconfinement) is to change the very nature of the water molecules themselves (through  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

the tuning of dispersion vs. electrostatic effects). We find that perturbing the short-range van der Waals interactions in the solvent interactions aids in transforming liquid water to solid water at room temperature. For confined water, an increase in l results in a progressive loss of tetrahedral order to a state of minimum order. Subsequent gain of translational order results in the system order evolving into a spherically symmetric (LJ fluid) one. In contrast, an increase in m results in a non-monotonic structural variation; an increase initially results in a loss of tetrahedral order with a subsequent re-entrant tetrahedral ordering corresponding to hexagonal ice (Ih) evident at higher scaling ratios. On the contrary, we fail to see any phase transition in bulk water at ambient conditions for similar perturbations of the van der Waals interactions in the bulk solvent. This phase transition in water at ambient conditions only occurs upon confinement of water and upon tuning of the solvent (water) repulsive and attractive interactions under ambient conditions. Thus, interestingly, bulk water and nanoconfined water respond differently to the weak and strong scaling effects. Only in nanoconfined water does the tuning result in ice nucleation. An increase in l for bulk water results in a non-monotonic variation wherein the local order evolves from a tetrahedral to a spherically symmetric one (LJ fluid). At intermediate values, the translational order breaks down. An increase in m results in similar qualitative variations of tetrahedral order in bulk water. In addition to MgO, we have carried out simulations for other substrates such as an amorphous DLC and graphene. Our simulations provide compelling evidence that there exists a sensitivity of water intermolecular structure and the nucleation of water into ice due to nanoconfinement, for both ionic surfaces (MgO) and van der Waals surfaces (DLC and graphene). When the van der Waals forces are strongly perturbed, we find crystallization of water to be independent of the nature of the substrate (hydrophilic oxide vs. hydrophobic graphene and crystalline oxide vs. amorphous DLC). Comparison of the structure and dynamics for these different surfaces imply that the nucleation of water into ice at ambient temperatures under nanoconfined environments (or close to interfaces) is possibly related to the change in intrinsic intermolecular water physics, and not simply due to the structure-imposing effects of two-dimensional interfaces. In future, it will be of interest to determine the length scales over which crystallization rate is no longer influenced by local dispersive and electrostatic perturbations and the transition approaches more bulk-like behavior. Also, whether simultaneous variation of a multi-parameter set (temperature, pressure, electric fields, dispersive and attractive terms) would make it possible to control the freezing transition including formation of various crystalline and amorphous ice under ambient conditions. Future directives would also include evaluating the role of point defects on the nucleation behavior and phase transition kinetics of confined water. Finally, it would be interesting to obtain a more quantitative molecular-level description of nucleation in confined spaces; variation in the free energy surface as a function of the degree of confinement described using metrics such as the “ordering parameter” (e.g. a characChemPhysChem 2014, 15, 1632 – 1642

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CHEMPHYSCHEM ARTICLES teristic tetrahedral ordering parameter) needs to be constructed and evaluated. Such results allow for the identification of the intrinsic dynamical effects that control the water-freezing process in confinement environments. At present, there is no experimental evidence of how such a perturbation can be brought about. This study lays the groundwork for future experiments to identify ways in which short-range interactions can be perturbed with respect to the long-range interactions.

Acknowledgements Use of the Center for Nanoscale Materials was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. The authors also thank the computational facilities provided by CNMANL, and Fusion Clusters. Keywords: computational chemistry · nanoconfinement · nucleation · phase transition · water [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

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Received: January 7, 2014 Published online on April 8, 2014

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Effect of nanoscale confinement on freezing of modified water at room temperature and ambient pressure.

Understanding the phase behavior of confined water is central to fields as diverse as heterogeneous catalysis, corrosion, nanofluidics, and to emergin...
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