Structure of the IceâClathrate Interface - ACS Publications - American

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Structure of the Ice−Clathrate Interface Andrew H. Nguyen,† Matthew A. Koc,†,‡ Tricia D. Shepherd,‡ and Valeria Molinero*,† †

Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, United States Westminster College, 1840 South 1300 East, Salt Lake City, Utah 84105, United States

‡

S Supporting Information *

ABSTRACT: Clathrate hydrates are crystals in which water molecules form hydrogen-bonded cages that enclose small nonpolar molecules, such as methane. In the laboratory, clathrates are customarily synthesized from ice and gas guest under conditions for which homogeneous nucleation of hydrates is not possible. It is not known how ice assists in the nucleation of clathrate hydrates or how ice forms on clathrate hydrate in the case of self-preservation. There is no lattice matching between any plane of ice and clathrate hydrates; therefore, an interfacial transition layer has to form to connect the two crystals. Here, we use molecular dynamic simulations to study the structure of ice−clathrate interfaces produced by alignment and equilibration of the crystals, competitive growth of ice and clathrate from a common solution, nucleation of hydrate in the presence of a growing ice front, and nucleation of ice in the presence of clathrate hydrates. We find that the interfacial transition layer between ice and clathrate is always disordered and has a typical width of two to three water layers. Water in the interfacial transition layer has tetrahedral order lower than either ice or clathrate and higher than liquid water under the same thermodynamic conditions. The potential energy of the water in the interfacial transition layer is between those in liquid water and the crystals. Our results suggest that the disordered interfacial transition layer could assist in the heterogeneous nucleation of clathrates from ice and ice from clathrates by providing a lower surface free energy than the ice−liquid and clathrate−liquid interfaces.

1. INTRODUCTION Gas clathrate hydrates are crystalline inclusion compounds in which water molecules form polyhedral cages that surround small nonpolar molecules, such as methane.1 Clathrate hydrates are important for a variety of fields ranging from energy production to carbon capture and transportation of natural gas from remote sources.2,3 Methane hydrates occur naturally in the seafloor and the permafrost and are estimated to be the most abundant reserve of hydrocarbon energy in our planet.4,5 Methane hydrate can protect itself from further decomposition by the formation of an ice layer on its surface.6−13 This phenomenon, called self-preservation, occurs at temperatures just below 273 K, and is important for the transportation and storage of natural gas as crystalline solid. In the laboratory, clathrate hydrates are synthesized from ice and guest gas.8,14−18 It is not yet understood how ice forms on clathrate hydrates in the case of self-preservation or how clathrate hydrates nucleate from ice. The nucleation of hydrates on ice has been carried out at temperatures as high as 270 K.8,14 The self-preservation of clathrate by the formation of ice on the clathrate surface9,12,19,20 occurs at temperatures from 242 to 271 K. Close to 270 K, the rate of homogeneous nucleation of either ice or clathrate hydrates is negligible;21,22 hence, formation of ice on clathrate or clathrate on ice must be initiated by heterogeneous nucleation. Some possibilities are the existence of structural matching between some crystal faces of ice and clathrates, or the presence of an interfacial layer between the two crystals that © XXXX American Chemical Society

decreases the free energy of the interface, lowering the nucleation barrier. Clathrates and ice are tetrahedrally coordinated water crystals. It would be plausible that water molecules of ice and clathrate be directly hydrogen bonded to each other. The structure of water at the ice−clathrate interface, however, is not known. Subbotin and co-workers used molecular simulations to investigate the ice−clathrate interface produced by embedding a nanosphere of clathrate hydrate into a sheet of hexagonal ice and letting the structure relax using a conjugate gradient optimization.23,24 They found that the interfacial layer between ice and clathrate has an anomalously high local density and increased local pressure. Pirzadeh and Kusalik nucleated clathrate hydrate in the presence of ice in nonequilibrium molecular simulations and found that ice was connected to the clathrate hydrate via coupled 5- and 8-member water rings.25,26 They proposed that the 5−8 water rings supported the formation of cage-like solids, which would facilitate the nucleation of an amorphous clathrate hydrate.25,26 These studies provide some insights into the structure of the ice− clathrate interface. The quasi-liquid water layer that exists at the ice surface has been conjectured to be the locus for nucleation of clathrate Received: November 24, 2014 Revised: January 15, 2015

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DOI: 10.1021/jp511749q J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C hydrates from ice and guest gas.27−29 The quasi-liquid layer is a disordered interfacial region between ice and gas or vacuum that forms at temperatures below the melting temperature of ice, and has been characterized in experiments and simulations.30−37 It has been experimentally determined that clathrate hydrates nucleate at the ice−gas8,14−18 and solution− gas36,38−45 interfaces. This, however, could be due to reactant availability and mass transport limitations, and not necessarily due to a lower barrier for nucleation at the interface. Sloan and Fleyfel27 proposed a kinetic mechanism for clathrate nucleation from ice in which formation of clathrate hydrate occurs at the ice−gas interface. They proposed that a transient liquid water layer between the ice and gas phases (i.e., the quasi-liquid or premelted layer) would allow for the diffusion of gas molecules into the ice and be responsible for the nucleation of clathrate hydrates. Molecular simulations, however, indicate that the width of the disordered layer and the ice−vacuum and ice− methane interfaces is narrower than the smallest clathrate cage for temperatures 2 K below the melting point of ice,30,32,46 and when it becomes wider on approaching the ice melting point, its structure does not show an increased tetrahedral order or methane solubility that would favor the nucleation of hydrates.32 On the other hand, distinct clathrate polymorphs can grow from each other, a process called cross-nucleation, without producing a disordered layer between the two crystals.47−49 A seamless transition between clathrate polymorphs can occur if the two crystals share a common plane, and an ordered, crystalline interfacial transition layer connects the two crystals when the clathrate polymorphs do not share a common plane.48,49 Layers of hexagonal and cubic ice I can also grow seamlessly on top of each other and with very small energy cost, as these two ice I polymorphs share a common plane.50−55 It is not known whether clathrate hydrates can seamlessly transition into ice, or vice versa, a question that is of high relevance for understanding the mechanism of clathrate nucleation from ice and of nucleation of ice from clathrates in self-preservation. Silicon, like water, forms sI and sII clathrates.56−59 Recent experimental studies have shown promising results in the formation of silicon clathrates on silicon diamond wafer by thermal decomposition of NaSi film.60−65 Kume et al.60 and Ohashi et al.61 were able to selectively grow sI or sII silicon clathrates depending on the exposed face of the silicon diamond substrate. It was suggested that the underlying symmetries of the diamond silicon faces could lead to preferential growth of a silicon clathrate film of either the sI or sII polymorphs.61,64 The preferential growth of sI or sII raises an interesting question about the role of lattice and domain matching, and the underlying symmetry of the crystal planes, on the formation of clathrate hydrates. Lattice matching refers to the one-to-one matching of lattice constants between substrate and film. In the case of water crystals, the difference in the lattice constants of sI clathrate (a = 12.0 Å)1 and hexagonal ice (a = 4.5 Å and b = 7.34 Å)66 indicates that there is no lattice matching between these crystals. This is also the case for sII clathrate and ice and for silicon clathrates and diamond silicon. Domain matching is the matching of integral multiples of lattice planes between two crystals.67,68 Growth of a thin film on a substrate where there is a large misfit in lattice constants can occur via domain matching.67−72 For instance, a 20% misfit can be accommodated such that four planes (unit cells or lattice spacings) of the new film match with five planes of the substrate.67 One important feature of domain matching is that

the strain due to the difference in lattices is relaxed within one to two monolayers.67,68,70−72 It is not known whether these interfacial layers between the two crystals are ordered or disordered. Silicon clathrate and silicon diamond lattices have the same silicon−silicon bond lengths but no lattice matching. Ohashi et al. concluded that there is no epitaxial growth of silicon clathrate on diamond silicon (100) or (111) surfaces.61 The sI and sII silicon clathrates grown on the diamond substrates were polycrystalline.60,61 The order of silicon at the interface between the clathrate and the diamond lattices is not known. Analogously to the silicon case, water−water bond lengths in ice and clathrate hydrates are essentially identical. This poses the question of what is the structure of the interface between ice and clathrate, and whether the interfacial transition layer between ice and clathrate is ordered or disordered. To our knowledge, there have been no reports of the molecular structure of the ice−clathrate interface except for the identification of 5−8 membered rings by Pirzadeh and Kusalik. 25,26 In this work, we use molecular dynamic simulations to investigate the structure of the interface between hexagonal ice and sI methane clathrate, because of their importance for understanding the synthesis and self-preservation of methane hydrates.6−8,12,20,73 Experimental and simulation studies have suggested that sI hydrate exposes the (110) and (100) faces as it grows from solution.61,64,74 The (110) face of sI clathrate is the slowest growing plane. The (110) plane at the clathrate−solution interface does not have exposed hexagonal water rings, and it is more rugged than the (100) exposed plane.75 Figure S1 (Supporting Information) shows the sI (110) plane and the orientations of the hexagonal water rings, which are not parallel to the exposed plane. The (100) face is the other slow growing plane of sI clathrate hydrate, with planar hexagonal water rings perpendicular to the exposed plane.76 Here we use molecular dynamics simulations to study the structure of interfaces between the (110) and (100) planes of sI clathrate hydrate exposed to the basal, prismatic, and secondary prismatic planes of hexagonal ice, as well as the interfaces formed by competing nucleation of ice and clathrate from a common solution, from the nucleation of clathrate hydrates in the boundary layer of an advancing ice front, and from the nucleation of ice in the presence of clathrate hydrates. There is no lattice matching between clathrate and ice; therefore, an interfacial transition layer must separate the two crystals. We find that this transition layer is disordered for all combinations of crystal faces studied. Water in the disordered interfacial transition layer has higher tetrahedral order and lower potential energy than bulk water under the same thermodynamic conditions. The thickness of the disordered interfacial transition layer varies from two to three water layers. Our results suggest that the high tetrahedral order and low potential energy of the disordered interfacial transition layer could be responsible for the stabilization of the interface of the clathrate in contact with ice compared to the interface of clathrate or ice in contact with liquid, and may favor the heterogeneous nucleation of clathrates on ice and ice on clathrates.

2. MODELS AND SIMULATION METHODS A. Force Fields and Simulation Settings. Water was modeled using the mW water model, a monatomic model with short-range three-body tetrahedral “hydrogen-bonding” interactions.77 We considered two guests for the clathrate hydrates, M and MS. M has properties intermediate between carbon B


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with 4096 water molecules (43.5 Å × 53.1 Å × 57.7 Å) exposing the basal face is in contact with a block of sI clathrate with 5750 water molecules (58.02 Å × 58.02 Å × 58.02 Å) exposing the (100) plane, with the water hexagons in the ice and clathrate surface aligned as indicated above. Prismatic (57.3 Å × 52.6 Å × 45.6 Å) and secondary prismatic (46.5 Å × 57.7 Å × 53.1 Å) planes were aligned with the (100) plane of sI hydrate as mentioned above. We evaluate the energy of the system as a function of the distance between ice and clathrate. The I0 aligned and minimized ice−clathrate interface is prepared by arranging the crystals of ice and clathrate at 2.7 Å, the approximate distance between O−O bonds in water crystals, and followed by the minimization of the energy. Details about the selection of separation distances are discussed in section A of the Results and Discussion section. I0 was simulated at 200 K, well below the melting temperatures of mW ice (274 K)77 and empty sI hydrate (245 K)85 because the ice−clathrate system constructed this way does not fully fill the simulation cell (it has crystal/vacuum interfaces). The simulation of the I0 interface was performed in the NVT ensemble for 10 ns with fixed periodic boundary conditions. We fill the clathrate cages with M guest (melting temperature of the filled hydrate is 307 K78,79), which allows us to equilibrate the system for 10 ns to 240 K without melting of any of the two crystals. The vacuum surrounding the crystals in the simulation cell is subsequently filled with a water−M solution with a concentration of ∼5% mol of M, resulting in a (92.4 Å × 93.8 Å × 140.2 Å) simulation cell containing 38323 mW waters and 1736 M guests. This large system is evolved in the NpT ensemble at 260 K and 500 atm for 10 ns, which allows the ice and clathrate to grow and to form a more extended ice−clathrate interface that spans through the periodic simulation cell. We call this system and interface I1. We prepare the I2 system by melting the 20 Å central region containing the ice−clathrate interface in I1 by heating this region at 400 K for 0.5 ns while keeping the rest of the atoms fixed, subsequently regrowing the crystals at 260 K, followed by equilibration for 10 ns. The I3 system is obtained by evolving the I2 system at 200 K for 10 ns. Twenty cycles of linear temperature ramps exerting heating (255−265 K) and cooling (265−255 K) at a rate of 1 K/ns are used to anneal the clathrate−ice interface obtained from the I3 interface. Then, we simulate the ice−clathrate interface in the NpH ensemble for 10 ns to equilibrate the ice−clathrate interface. ii. Competing Growth of Ice and Clathrate. A simulation cell is created with dimensions 70 Å × 120 Å × 70 Å. The system contains 18729 particles (17881 mW and 848 M). The bottom 15 Å in the y-direction of both cells is initially a slab of pre-equilibrated hexagonal ice, Ih, and the top 7 Å in the ydirection of both simulations is initially a slab of preequilibrated M gas. The hexagonal ice exposes the secondary prismatic plane to the solution. The center of the simulation cells contains pre-equilibrated water−M saturated solution and a sI clathrate crystallite with a radius of 20 Å, taken from a simulation of ref 82. This system is used to create the clathrate−ice interface at different temperatures for the competing growth of clathrates and ice. The initial configuration of the simulation cells involves four phases (ice, solution, clathrate, guest fluid) and two components, and are not in thermodynamic equilibrium. The concentration of the solution is initially 1 guest for every 21 waters, lower than the ratio of 1 guest for every 5.75 water molecules in sI clathrate. The melting temperature of ice in the

dioxide and methane.78 M is represented by a single particle that interacts through a two-body Stillinger−Weber potential with σM−M = 4.08 Å and εM−M = 0.34 kcal/mol and σw−M = 4.05 Å and εw−M = 0.24 kcal/mol. The solubility and hydration of M in mW and the melting temperatures and thermodynamic properties of sI and sII clathrate hydrates were presented in refs 78−80. Due to the higher solubility in water of M compared to methane, it is more amenable to clathrate growth than a lower solubility, more methane-like particle.21,48,78,81,82 The MS guest is even more soluble than M and was characterized in ref 78. We use MS as a guest for the nucleation of clathrate hydrates in the presence of an advancing ice front. The MS guest has a water−MS characteristic size of σw−MS = 3.90 Å and a water− MS interaction strength of εw−MS = 0.3 kcal/mol.78 The MS− MS interaction strength and characteristic size are the same as those between M guests. The MS guest was only used in the clathrate hydrate nucleation with a growing ice front, while all other simulations were performed with the M guest. Molecular dynamics (MD) simulations are carried out using LAMMPS.83 Due to the absence of fast molecular rotational modes in the coarse-grained models, the equations of motion are integrated with the velocity Verlet algorithm using 10 fs time steps.77 For aligned ice−clathrate interfaces, ice nucleation in the presence of clathrate hydrates, and clathrate hydrate nucleation in the presence of a growing ice front (see descriptions in section 2B), the temperature and pressure are kept with the Nosé−Hoover barostat and thermostat with damping constants of 5 and 1 ps, respectively. For the competing growth of ice and clathrate (see details in section 2B), the Nosé−Hoover barostat and thermostat have damping constants of 25 and 5 ps, respectively. B. Systems. In order to examine the ice−clathrate interface, we produce ice−clathrate interfaces by four methods: (i) by alignment of hexagonal rings in the surface of the two crystals, followed by minimization and/or equilibration of the two-phase system, (ii) by competing growth of clathrate and ice from a water−guest solution in the presence of each other, (iii) by clathrate hydrate nucleation induced by a growing ice front, and (iv) ice nucleation in the presence of clathrate hydrates. These systems are described in detail in what follows. i. Aligned Ice−Clathrate Interfaces. We build several interfaces with the goal of determining the distance of domain matching between different planes of ice and sI clathrates, and to study the structure of these interfaces when relaxed and equilibrated under several thermodynamic conditions. To find the distances of domain matching, we overlay a large simulation cell consisting of multiple unit cells of the basal plane of hexagonal ice (36 × 36 × 2 unit cells) over the (100) plane of sI clathrate (30 × 30 × 2 unit cells) using VMD.84 Large simulation cells of the secondary prismatic plane (32 × 32 × 2 units cell) and prismatic plane (32 × 32 × 2 units cell) of hexagonal ice are overlaid with the (100) plane of sI clathrate. The plane of interest is exposed perpendicular to the z-axis. The (100) plane of sI clathrates exposes planar hexagonal water rings.48 We rotate the ice plane by 30° increments around the z-axis while keeping the clathrate plane fixed. The ice−clathrate system is arranged such that a maximum number of the (nonplanar) hexagonal rings of the basal hexagonal of ice Ih line up with the hexagonal rings in the (100) plane of sI clathrate. The same alignment method is used for the prismatic and secondary prismatic planes. The periodicity is determined by identifying the recurring domains in superimposed ice and clathrate planes. Next, we create a system where a block of ice C


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The Journal of Physical Chemistry C presence of the M guest fluid at 500 atm is 272 ± 1.4 K,32 and the melting temperatures of sI and sII M hydrates at that pressure are 307 ± 2 and 303 ± 1 K, respectively.78 Due to the small size of the clathrate crystallite we use (2 nm radius), the clathrate would melt at temperatures greater than approximately 270 K.82 Because we specifically want to study the ice− clathrate interface, the molecules in the 15 Å slab of ice are fixed (i.e., their equations of motion are not integrated during the simulations), ensuring the formation of an ice−clathrate interface even under thermodynamic conditions for which all ice should transform into clathrate hydrate. The clathrate grows at the expense of the guest bubble, resulting in a three-phase system at the end of the simulation: clathrate, ice, and solution. All competing growth simulations are performed in the isothermal−isobaric (NpT) ensemble at 500 atm with periodic boundary conditions. The competing growth simulations are studied at various temperatures ranging from 250 to 270 K. The length of competing growth simulations at each temperature is 10 ns. Twenty-four cycles of linear temperature ramps exerting heating (255−265 K) and cooling (265−255 K) at a rate of 1 K/ns are used to anneal the clathrate−ice interface obtained from the competing growth simulations. The high and low temperatures of the ramp are selected to ensure the annealing of the ice−clathrate interface without melting either crystal. Starting from the annealed system, we simulate the ice− clathrate system at 255, 265, 268, and 270 K in the NpT ensemble for 1 ns. Then, we simulate the ice−clathrate interface in the NpH ensemble for 10 ns to equilibrate the ice− clathrate interface. We refer to the ice−clathrate system at 268 K followed by NpH equilibration as the competing growth (CG) system. iii. Clathrate Hydrate Nucleation in the Presence of a Growing Ice Front. We prepare three systems initially containing three phases (ice, supersaturated water−guest solution, and guest gas). Each of these systems exposes different ice planes to the supersaturated solution: basal (cell dimensions: 91 Å × 106 Å × 360 Å), prismatic (288 Å × 106 Å × 115 Å), and secondary prismatic (91 Å × 331 Å × 115 Å). Each simulation cell contains 105524 mW waters and 5068 MS guests, with a 30 Å slab of ice exposing the desired plane to a 2% mol MS solution phase, and a slab of MS guests that contacts on one side of the periodic simulation cell the solution and on the other the clathrate. These simulation cells are used for the nucleation of clathrate hydrates with an advancing ice front, in an approach similar to the one employed by Pirzadeh and Kusalik.26 At each hexagonal plane, a 50 ns simulation of clathrate hydrate nucleation is performed at 260 K and 100 atm. iv. Ice Nucleation in the Presence of sI Clathrate Hydrate. We prepare two systems exposing different planes of sI clathrate to liquid water. The (100) plane is obtained directly form the unit cell. The (110) plane is prepared by the following method. We construct a large simulation cell of sI clathrate by replicating a unit cell: 8 × 8 × 8. We rotate this large simulation cell by 45° around the z-axis in order to expose the (110) plane perpendicular to the x-axis. We cut a small cell (29.5 Å × 29.5 Å × 62.13 Å) from the large system such that the small cell can be replicated without overlapping of the atoms or producing gaps in the clathrate structure. Two systems are created exposing the (100) and (110) planes to solution. The (100) plane contains 9936 mW in the clathrate phase and 19872 mW in the solution phase, while the (110) plane consists of 8832 mW in the clathrate and 26496 mW in the liquid. Simulations

for both the (100) and (110) planes are performed at 1 atm and at three different temperatures: 200, 205, and 208 K. These temperatures are selected because they are close to the homogeneous ice nucleation temperature of mW water, which is 202 ± 2 K.86 At these temperatures, the ice nucleates spontaneously in solution and grows to form ice−clathrate interfaces. The ice−clathrate interfaces are further evolved for 20 ns at 240 K and 1 atm. C. Identification and Characterization of Liquid, Ice, and Clathrate. We use the CHILL+ algorithm to identify molecules with the local order of either liquid or crystals.87 Water in hexagonal ice has three staggered water−water bonds and one eclipsed water−water bond, while it has four staggered water−water bonds in cubic ice.88,89 In clathrate hydrates, each water molecule forms four eclipsed water−water bonds.87 CHILL+ identifies the staggered (S) and eclipsed (E) water− water bonds from the correlation of orientational order of a water molecule with its four closest neighbors. CHILL+ identifies cubic and hexagonal ice and clathrates up to temperatures close to the melting point.87 The CHILL+ algorithm allows for the identification of clathrate and ice during nucleation and growth processes.87 D. Characterization of the Ice−Clathrate Interface. We characterize the ice−clathrate interface through the following measures: the density of direct contacts and mediated contacts between ice and clathrate, the tetrahedral order of the four closest neighbors to each water molecule, and the thickness of the interfacial transition layer (ITL) between the two crystals. Throughout this study, we define ice as hexagonal (3S+1E), cubic (4S), or interfacial ice (either 3S+0E and with at least one first neighbor with more than one S bond, or 2S+0E or 2S+1E and with at least one first neighbor with more than two S bonds), while clathrate is defined as clathrate (4E) and interfacial clathrate (3E).87 Molecules identified as ice or clathrate have four neighbors in the first coordination shell. We classify the contact between molecules in the ice and clathrate as direct and mediated or indirect contacts. A molecule in the clathrate experiences direct contact with ice when it is within 3.5 Å of a water molecule classified as ice. Likewise, an ice molecule within 3.5 Å of a clathrate molecule is classified as having a direct contact to clathrate. The indirect or mediated contact occurs when a water molecule identified as liquid (i.e., no ice and no clathrate) is within 3.5 Å of both clathrate and ice. Indirect contact could double count direct contacts of ice or of clathrate in which the liquid, ice, and clathrate are within 3.5 Å of each other. The density was computed as the number of direct or mediated contacts normalized by the area of the simulation cell most parallel to the ice−clathrate interface. The tetrahedral order parameter of each water molecule i is defined as90 q t (i ) = 1 −

3 8

3

4

2 ⎛ 1⎞ ⎜cos θ + ⎟ ijk ⎝ 3⎠ k=j+1

∑ ∑ j=1

(1)

where θijk is the angle subtended by the central particle i and two of its four closest neighbors j and k. The tetrahedral order indicates the deviation from perfectly tetrahedral angles and ranges from 0 (random distribution) to 1 (perfectly tetrahedral). We average the tetrahedral order and potential energy of the water molecules over 3 Å slices of the simulation cells to characterize the order in the clathrate, ice, and interfacial transition layer. The average potential energy of the D


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The Journal of Physical Chemistry C water molecules includes the water−water interaction and water−guest interaction. The results of averaging are similar for bin sizes of 1 or 3 Å. We report the latter because it produces a smoother curve. The average tetrahedral order and potential energy for water is obtained using a 10 ns simulation of 4096 mW waters at 260 K and 100 atm. We find that 1 and 500 atm yield essentially the same tetrahedral order and potential energy for water at 260 K. The thickness of the ITL is determined from the full width at half-maximum of the density profile of molecules identified as clathrates, ice, and liquid using the CHILL+ algorithm. An alternative measure of the thickness is computed from the distance d such that 90% of the molecules in the interfacial transition layer mediate contacts between ice and clathrate. We compute the percent of the interfacial transition layer that is identified by varying this distance within 3.5 Å < d < 8 Å. The width Δ of the ITL is determined by the equation ΔMC = 2d − σW, where σW = 3.5 Å is the width of a water molecule. σW is subtracted to avoid counting the width of the molecules on the crystals as contributing to the ITL. We use the ring identification algorithm of Matsumoto et al. from ref 91 to find 5-, 7-, and 8-membered water rings in the configurations obtained from the simulations. From the identity of the water molecules in each ring, we identify coupled 5−7 rings and coupled 5−8 rings. The coupled rings share an edge, i.e., a connected pair of water molecules.

Figure 1. Alignment of the basal plane of hexagonal ice and the (100) plane of sI clathrate. Panel A shows the overlap of the basal plane of hexagonal ice (red sticks represent the water−water bonds) with the (100) plane of sI clathrate (cyan sticks). Panel B displays the position of the water molecules (represented as balls, same color code as panel A) for the same interface. The black circles mark the overlap in hexagonal water rings between ice and clathrate.

clathrate is shown in Figure S3 of the Supporting Information. Different from the basal plane, the secondary prismatic and prismatic planes display clusters of aligned hexagonal water rings with the clathrate plane. In what follows, we investigate whether these clusters of aligned rings impart extra order or stabilization to the ice−clathrate interface. The stabilization of the interface should depend on the energy and extent of hydrogen bonding between water molecules in the ice and clathrate surfaces. To assess these quantities, we first vary the distance between rigid ice and clathrate crystals and find the minimum in potential energy as a function of the separation distance. We find a minimum in the potential energy at a distance of 1.3 Å between the outer layers of the two crystals (Figure S2 of the Supporting Information). As there is no significant structural matching between the two crystals, it should not be surprising that a separation of 2.76 Å, the approximate distance between O−O bonds in water crystals, does not correspond to the minimum energy. The average potential energy of the water molecules at the interface after minimization of the energies is 2.83 kcal/mol higher than in ice at 1.3 Å, and even higher for 2.7 Å (Figure S4 of the Supporting Information). The enthalpy of melting of ice is 1.26 kcal/mol for mW77 (1.436 kcal/mol in experiments92); hence, the energy of the interfacial water is even higher than that in the liquid, and it may not be unexpected for the interfacial transition layer to relax to a liquid-like or disordered state after the interface is properly equilibrated. The extent of the hydrogen bonding between clathrate and ice can be measured through the density of direct contacts, defined as a water molecule of ice within 3.5 Å of a water molecule in the clathrate, or vice versa. Figure 1B shows that, even for the aligned interface, there is significant mismatch between the positions of the water molecules on the ice and clathrate sides of the interface. We call the aligned ice−clathrate system with the crystals of ice and clathrate at 2.7 Å “I0”. We verify that the results that follow are identical if the starting interface is at other distance, as pressure and not volume is kept constant in the equilibration. We examine the density of direct contacts for the I0 aligned interfaces between the (100) plane of sI clathrate and the basal, prismatic, and secondary prismatic planes of hexagonal ice after minimization of the energy, letting all water molecules find their local optimum position. After minimization, the surface density of water molecules in the ice surfaces increases in the order secondary prismatic (6.0 nm−2)

3. RESULTS AND DISCUSSION A. The Interface between Clathrate and Ice Is Disordered. An interfacial transition layer (ITL) must form between clathrate and ice, as there is no common plane between these water crystals. The question is whether the ITL is ordered, as the one existing between sI and sII clathrate hydrates,48,49 or disordered. We examine the overlay of crystal planes of hexagonal ice and sI clathrate to determine if there is a possibility of structural matching between the tetrahedrally coordinated lattices of these water crystals. The slowest growing planes are those most exposed in a crystal. We first consider one of the slowest growing planes of sI hydrate, the (100) plane, and of hexagonal ice, the basal plane. We first build “aligned ice−clathrate systems” in which a maximum density of hexagonal water rings of the clathrate and ice surfaces are in registry (see section 2B), and investigate this interface under several conditions. The two crystal surfaces do not match under any condition of rotation or translation of the crystals: there is no lattice matching between clathrate and ice. This is illustrated in Figure 1. Although there is no lattice matching between ice and clathrate, domain matching is possible. Each ice plane results in a different domain matching distance with sI clathrate. Figure 2 shows large simulation cells used to find the distances of domain matching DDM between the (100) plane of sI hydrate and the basal and secondary prismatic planes of hexagonal ice. DDM between the basal plane of ice and the (100) plane of sI hydrate are 30.9 Å along the x-axis and y-axis. The DDM between the sec-prismatic plane of hexagonal ice and sI clathrate is 30.9 Å along the x-axis and 72.10 Å along the y-axis. If the structure of the ice−clathrate interface were ordered, crystalline as the one between clathrate polymorphs, then the lattice parameters of the ITL should be equal to the DDM, resulting in a repeating ITL unit cell with hundreds of atoms and probably a very complex structure. Domain matching between the prismatic plane of ice and the (100) plane of sI E


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clathrate molecule (Table S1, Supporting Information). The fraction of water molecules at the clathrate surface that are in direct contact with an ice molecule is slightly higher, between 35 and 45% (Table S1, Supporting Information). The poor matching between the water positions in the planes of the two crystals, the low density of direct contacts between water molecules in ice and clathrate, and the high potential energy of the minimized ice clathrate interface are consistent with the observation of a disordered interfacial transition layer between ice and clathrate. To investigate the possibility of an ordered interfacial transition layer after equilibration of the interface, we prepared three ice−clathrate interfaces (I1, I2, and I3, see the Models and Simulation Methods section) from the I0 interface discussed above. The I1 interface is obtained by equilibrating I0 at 260 K. The I2 interface was obtained by melting a 20 Å slab of the ice−clathrate interface in I1 and regrowing the crystals at 260 K. The I3 interface was prepared by evolving I2 at 200 K. Table 1 displays the density of direct contacts of Table 1. Density of Direct and Mediated Contacts of the Interfacial Transition Layer of Three Aligned Ice−Clathrate Interfaces

aligned ice−clathrate interfaces

density of direct contacts of ice molecules (nm−2)

density of direct contacts of clathrate molecules (nm−2)

density of mediated contacts (liquid in contact with both ice and clathrates) (nm−2)

I1 (260 K) I2 (260 K) I3 (200 K)

2.1 ± 0.3 2.1 ± 0.2 3.0 ± 0.3

2.6 ± 0.2 2.7 ± 0.2 3.6 ± 0.3

2.9 ± 0.4 2.9 ± 0.3 3.3 ± 0.3

clathrate and ice for I1, I2, and I3. I1 and I2 produce a similar result even though we melted and recrystallized the I2 interface. The interface at 200 K, I3, has a higher density of direct contacts than I1 and I2. Equilibration of the I3 interface at 1 and 500 atm yields similar results: the disorder in the interfacial transition layer is not due to the pressure used in simulations. I1, I2, and I3 produce a similar result for the density of contacts between ice and clathrate mediated by a liquid water molecule (which we call mediated contacts and report in Table 1; Figure S5 of the Supporting Information shows the distribution of mediated contacts at the I3 interface). All of the aligned ice− clathrate systems obtained through matching of hexagons on the two surfaces followed by minimization and further equilibration produced a disordered interfacial transition layer. Annealing of the ice−clathrate interface at low temperature increases the density of direct contacts between clathrate and ice but still does not result in an ordered interfacial transition layer between these water crystals. This can be seen in Figure 3, which shows the interface in I3, the aligned system with the highest density of direct contacts between clathrate and ice. The interfacial transition layer between ice and clathrate is disordered. B. The Interfacial Transition Layer Is Two to Three Water Molecules Thick. Figure 4 shows the density profile of water classified as ice, clathrate, and liquid-like (i.e., structurally no ice and no clathrate but not necessarily highly mobile) along the axis perpendicular to the interface for the interface equilibrated at 260 K (I1) and at 200 K (I3). We determine the thickness of the interfacial transition layer from the full width at half-maximum (fwhm) of the liquid-like component of

Figure 2. Domain matching between hexagonal ice and sI clathrate. Panel A overlays the basal plane of hexagonal ice (red bonds) and the (100) plane of sI clathrate (cyan bonds). The yellow circles signal the overlaid hexagons in the surface of the two crystals, and the black arrows, the distance of domain matching, DDM = 30.9 Å. Panel B overlays the secondary prismatic plane of hexagonal ice and the (100) plane of sI clathrate. Color coding and symbols as in panel A. In this case, domain matching has a rectangular cell with DDM = 72.1 Å and 30.9 Å.

< prismatic (6.7 nm−2) < basal (7.6 nm−2) planes, and it is 7.2 nm−2 for the (100) plane of sI clathrate. The surfaces that have the closest water densitiesbasal of ice and (100) of sI hydrate or prismatic of ice and (100) of sI clathratehave the highest fraction of direct contacts (see Table S1 in the Supporting Information). We find, however, that the density of the direct contacts is not correlated with the density of aligned hexagonal water rings in Figure 1. The aligned hexagonal water rings do not result in direct contacts (i.e., hydrogen bonds) between ice and clathrate after minimization of the interface. Most of the molecules of clathrate and ice at the surface are in contact with disordered water, and not with water molecules of the other crystal. For any of the three ice surfaces, less than one-third of the ice molecules are in direct contact (within 3.5 Å) of a F


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Figure 4. Density profile of water molecules, averaged over 3 Å slices perpendicular to the ice−clathrate interface. The green, blue, and red curves represent the density of the clathrate hydrate, ice, and interfacial transition layer (ITL), respectively. The solid line represents the I1 ice−clathrate interface at 260 K, while the dashed line represents the I3 ice−clathrate interface at 200 K. The density of the interfacial transition layer overlaps with the ones of ice and clathrate because the surface is rough.

To provide an alternative measure of the thickness of the ITL that is less sensitive to the curvature of the surface, we also estimated the thickness of the interface from the number of liquid mediated contacts between ice and clathrate. Figure 5

Figure 5. Percent of water molecules of the ITL within distances d of both ice and clathrate. The curves correspond to the aligned interfaces I0 (violet), I2 (blue), and I3 (green) and two competing growth simulations, CG1 (black) and CG2 (red). The crossing of these curves with the dashed black line signals that 90% of the ITL has been accounted for up to that distance d. The aligned interfaces are narrower than the competing growth ones.

Figure 3. Interfacial transition layer between the basal plane of hexagonal ice and the (100) plane of sI clathrate in I3, obtained by melting of 2 nm around the initial interface and regrowth at 260 K and then evolved at 200 K. This interface has the highest density of direct contacts between ice and clathrate (Table 1). (A) View of the I3 ice− clathrate system perpendicular to the interface. The blue sticks represent water−water bonds in ice, green in clathrate, and red sticks with balls the disordered interfacial transition layer. (B) Front view of the interfacial transition layer. The blue and green beads represent water molecules in the ice and clathrate, respectively, in direct contact with the clathrate and ice on the other side, respectively. Red beads represent water molecules that are liquid-like (no ice and no clathrate but not necessarily high mobility) in the interfacial layer. The interfacial transition layer is disordered. Extensive annealing of the I3 interface by heating and cooling did not result in a significant change in the structure of the ice−clathrate interface.

shows the percentage of molecules in the ITL that are within a distance d of both an ice molecule and a clathrate molecule. By varying the minimum distance to produce a contact between water molecules in the disordered layer and in the crystals from 3.5 to 8 Å, we capture all the water molecules in the interfacial transition layer. A distance d = 5.5 Å of liquid water molecules to both ice and clathrate accounts for 90−98% of the water molecules in the interfacial transition layer. Subtracting a water diameter of the ice and clathrate (see the Models and Simulation Methods section), the thickness of the ITL is ΔMC = 7.5 Å. Both the use of the fwhm of the density profiles and of the minimum distance to account for at least 90% of water in “mediated contacts” with ice and clathrate result in comparable widths of the ITL, approximately two to three molecules thick.

the disordered layer in Figure 4. We found thicknesses of Δfwhm = 11.5 and 8 Å for the I1 and I3 interfaces, respectively. The overlap of the density profiles of the disordered layer and the crystals is partly due to the roughness and curvature of the interface. This may result in an overestimation of the intrinsic width of the disordered layer. G


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The Journal of Physical Chemistry C C. The Interfacial Transition Layer Has Higher Tetrahedral Order and Lower Potential Energy than Liquid Water. The average potential energy and tetrahedral order along the axis perpendicular to the aligned ice−clathrate interfaces I0, I1, and I3 are shown in Figure 6. In all cases, the

Figure 6. Profiles of (A) average potential energy and (B) tetrahedral order parameter as a function of the position of the water molecules in the axis perpendicular to the interfacial transition layer. Green, blue, and red shades represent the regions of clathrate hydrates, ice, and the disordered interfacial transition layer (ITL), respectively. The violet, black, and cyan curves correspond to the aligned ice−clathrate interface at 200 K (I0), the aligned interface equilibrated at 260 K (I1), and the aligned interface re-equilibrated at 200 K (I3), respectively. The dashed black lines indicate the average potential energy and tetrahedral order of liquid water at 260 K and 500 atm. The disordered layer has higher tetrahedral order and lower potential energy than liquid water under the same conditions.

Figure 7. The disordered ITL contains coupled 5−7 and 5−8 water rings. (A) Coupled 5−7 and 5−8 rings at the disordered ITL of the I3 interface. The 5-membered rings are not shown (they mostly belong to the ice or clathrate surface). The 7-membered rings are shown in cyan sticks (cyan balls signal the water molecules in the edges shared with pentagonal rings), and the 8-membered rings are shown in gray (gray balls signal the water molecules in the edges shared with pentagonal rings). The rest of the water classified as liquid at the ice− clathrate interface is shown with red sticks and balls. (B) Detail of the 5−8 ring within the black circle in panel A, showing the pentagonal ring in purple. (C) Detail of the 5−7 ring within the yellow circle of panel A (colors as in parts A and B).

energy of the disordered interfacial transition layer is higher than that in the crystals but lower than that in liquid water. Similarly, the tetrahedral order of the water molecules in the ITL is also lower than that for clathrate and ice but higher than that for liquid water at the same temperature. The tetrahedral order of the ITL is higher than that for liquid water. There is also a higher density at the interface of motifs such as the coupled 5−7 and 5−8 rings, where the 5-membered rings share an edge (a pair of water molecules) with 7membered or 8-membered rings. These coupled rings have been previously reported to occur at the surface of ice,93−97 on defects related to the existence of cubic and hexagonal order in an ice layer,50−55 and between ice and clathrate.26 Pirzadeh and Kusalik nucleated clathrate hydrate in the presence of ice, and found that coupled 5−8 water rings connected ice and clathrate hydrate.25,26 On the basis of these results, they proposed that the 5−8 water rings could support the nucleation of amorphous clathrate hydrate.25,26 In agreement with their results, we find that the disordered interfacial transition layer between clathrate and ice of I3 contains coupled 5−7 rings and 5−8 rings (Figure 7). The 5−7 and 5−8 coupled rings are arranged such that the 7- and 8-membered rings are located within the disordered ITL,

whereas the 5-membered rings are made of water molecules that are classified as either interfacial ice or clathrate. Although ice does not have 5-membered rings, 5−7 coupled rings have been observed as defects at the surface of ice and during melting.93,94 We find that the ratio of 5−8 to 5−7 coupled rings at the ice−clathrate interface is about 5:1, and that the water molecules involved in these coupled rings represent a small fraction of the ice−clathrate interface (Figure 7). The density of 5−8 and 5−7 rings is even lower in bulk liquid water, where their ratio is about 1:1 in pure water and 2:1 under conditions of very high methane supersaturation. In conclusion, there is an enhancement of 5−8 rather than 5−7 rings at the ice−clathrate interface compared to liquid water, with a preponderance of the 5−8 rings. These rings do not fully pave the interface. In the next section, we show that, in agreement with the results of ref 26, our simulations show coupled rings connecting small clathrate nuclei to the surface of ice. The extent by which these rings decrease the free energy of the ice−clathrate interface is an important question that deserves further study. H


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The Journal of Physical Chemistry C D. Ice−Clathrate Interfaces Obtained by Competing Growth or Nucleation Are Also Disordered. With the goal of assessing whether ordered interfacial transition layers could be formed under conditions different from those of the aligned interfaces discussed above, we investigate the ice−clathrate interfaces in three additional systems obtained through (a) competing growth of ice and clathrate from a common solution, (b) nucleation of clathrate hydrates induced by an advancing ice front, and (c) nucleation of ice in the presence of clathrate. We expose different planes of ice and clathrate to form a variety of ice−clathrate interfaces. We simulate the competing growth of ice and clathrate from solution in the presence of each other at temperatures between 250 and 270 K for which both crystals are more stable than the liquid. Panel A of Figure 8 shows a representative initial

Here, the sI clathrate does not expose any defined crystallographic plane, such as the (100) plane of sI clathrate in sections 3A and 3B. In all cases, the resulting interface between ice and clathrate is disordered. In order to make the interface of the competing growth (CG) systems more ordered, we anneal the CG system grown at 260 K through four cycles of heating from 255 to 265 K and cooling back to 255 K, followed by a short equilibration at 268 K and 500 atm with the NpT ensemble, and then 20 ns of NpH simulation. The annealed interface is thinner and less curved but still remains disordered (Figure 9). The annealed ITL has a

Figure 9. The interfacial transition layer of the annealed competing growth (CG) interface is disordered: (A) ice (blue), clathrate (green), and liquid-like interface (red) after annealing; (B) liquid-like water molecules of the two disordered interfacial transition layers. The interfacial transition remains disordered after 200 ns of further annealing and equilibration.

Figure 8. Competing growth of clathrate hydrate and ice. Panel A shows the initial configuration at 260 K and 500 atm (ice with cyan, clathrate with blue, methane-like guests with white balls, liquid water hidden). Panel B shows the same system after 3 ns, where a curved ice−clathrate interface has been established. Further growth of clathrate results in consumption of the guest bubble, leaving only ice and clathrate, separated by a disordered interfacial transition layer.

slightly higher tetrahedral order than the non-annealed ITL, and in both cases, the tetrahedral order is slightly lower than that for the aligned interfaces discussed above but still between the value for bulk liquid water and the crystals. Annealing improves the structure of the clathrate hydrate by diminishing the halo87 surrounding the clathrate crystal. As a result, it increases the tetrahedral order and decreases the potential energy of the disordered interfacial transition layer. The width of the annealed ITL is ΔMC = 10.5 Å, about one water diameter broader than that for the aligned ice−clathrate interfaces (Figure 5). Table 2 demonstrates that annealing the competing growth (CG) system results in higher tetrahedral order than the nonannealed system at 260 K. The increase in tetrahedral order of the disordered layer seems to be associated with the reduction of the clathrate halo surrounding the sI clathrate crystallite. We now examine the ice−clathrate interface created via the nucleation of clathrate hydrates induced by an advancing ice f ront. We grow ice at 260 K and 100 bar exposing the basal, prismatic, and secondary prismatic faces to the water−guest solution. The advance of the ice front increases the supersaturation of the MS guest at the ice boundary layer, resulting in the nucleation and growth of clathrate hydrate (Figures 10 and 11), as predicted by Poon and Peters.98 The MS guest has the same size as the methane-like M guest but significantly higher solubility in water and produces a clathrate with a higher melting point (Tm of sI 338 K),78 which facilitates the nucleation. Clathrate nucleation occurs when the concentration of MS in the layer close to the

configuration of the periodic simulation cell containing an ice slab exposing secondary prismatic planes to a saturated water− guest solution that contains a sI clathrate crystallite, and to a slab of guest fluid. These systems have initially four phases but only two components, so they can only be in equilibrium at the specific temperature and pressure of the ice + water-rich solution + clathrate + vapor quadruple point. The growth rate of the crystals depends on the driving force and, for the clathrate, also on the availability of guest. The contribution to the driving force due to supercooling is proportional to the degree of supercooling, ΔT = Tm − T. For the guests of this study, the driving force at 500 atm is higher for clathrate growth because its melting point (Tm = 307 K80) is significantly higher than the one for ice (Tm = 272 K32). The growth of the hydrate, however, is limited by the transport of the guest to the clathrate−solution interface (growth leads to depletion of guest at the crystal interface because the solubility of guest in water is lower than that in the clathrate). The clathrate crystallite grows at all temperatures considered, between 250 and 270 K, while ice only grows at temperatures up to 265 K (see Figure S6 in the Supporting Information). At temperatures below 265 K, ice grows faster than clathrate, while at higher temperatures the faster growth rate of clathrate prevents further formation of ice. I


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Table 2. Average Tetrahedral Order Parameter for Ice, Clathrate, Disordered Layer for Competing Growth, Annealed System, and Nucleationa system 260 260 260 260 260

K K K K K

competing growth (secondary prismatic) annealing of competing growth (secondary prismatic) nucleation (secondary prismatic) nucleation (prismatic) nucleation (basal)

ice 0.95 0.95 0.94 0.95 0.95

± ± ± ± ±

clathrate 0.01 0.01 0.01 0.01 0.01

0.89 0.93 0.88 0.91 0.90

± ± ± ± ±

0.01 0.01 0.02 0.02 0.02

liquid-like ITL 0.78 0.82 0.76 0.76 0.76

± ± ± ± ±

0.01 0.01 0.02 0.02 0.02

liquid 0.73 0.73 0.73 0.73 0.73

± ± ± ± ±

0.01 0.01 0.01 0.01 0.01

a

Values were averaged over the last 2 ns of the simulation. Error bars were computed from 500 ps block averages. Exposed ice plane indicated between parentheses.

Figure 11. Nucleation of clathrate hydrate near the surface of the basal plane of hexagonal ice at 260 K and 100 atm. Ice shown with blue sticks, liquid water with red points, and clathrate clusters with green sticks. Clusters of a few water molecules identified as clathrate-like are normal fluctuations of liquid water. Guest molecules are hidden to facilitate the visualization of the water rings. 7- and 8-Membered water rings are shown with cyan and gray sticks, respectively. Cyan beads signal water molecules shared by the 5- and 7-membered rings, and gray beads represent water molecules shared by the 5- and 8membered rings. The coupled 5−8 rings anchor the clathrate nuclei to the ice surface.

Figure 10. Nucleation of clathrate hydrate due to the advancing ice front exposing the secondary prismatic face to a supersaturated solution at 260 K and 100 atm results in an interface between ice and amorphous clathrate. Panels A and B represent configurations of the initial and final (after 50 ns) states of the system. Ice is shown in cyan, clathrate in blue, liquid-like interface in red, guest molecules as gray balls, and liquid water in the solution hidden. The box encloses the region of the ice−clathrate interface. The pyramidal (2021) plane of hexagonal ice is in contact with the amorphous clathrate. Additional simulation time results in the flattening of the ice−clathrate interface, as shown in Figure S7 (Supporting Information).

crystal, as previously reported in other simulations of nucleation at high driving force.26,79,99,100 The amorphous clathrate contains many voids and defects, which makes the calculation of a thickness of the ITL challenging. The tetrahedral order of the ITL between the advancing ice front and the nucleated clathrate is lower than that for the aligned and competing growth interfaces, and close to the tetrahedral order of the liquid phase. We attribute the lower tetrahedral order of the disordered interfacial transition layer in this case to the amorphous nature of the clathrate. Longer simulation times and annealing would be required for the amorphous clathrate to become more crystalline. However, we expect that the ice− clathrate interface would not be thinner than the two to three water layers observed for the aligned I0 or I3 interfaces even after extensive simulation time and annealing. After we extend the simulation of Figure 10B for an additional 50 ns, the

ice surface reaches 3.6% mole fraction. The details of the nucleation of the clathrate hydrate at the ice boundary layer will be discussed in a separate publication. In agreement with the results of the fully atomistic simulations of ref 26, 5−7 and 5−8 coupled rings anchor the incipient clathrate nuclei to the ice surface (Figure 11). These coupled rings, however, still represent a small fraction of the interfacial transition layer between ice and clathrate after the interface has fully developed. The clathrate that results from the nucleation and growth of clathrate in the ice boundary layer is amorphous; it has the characteristic clathrate cages but not the long-range order of the J


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The Journal of Physical Chemistry C interface becomes flatter (Figure S7, Supporting Information), decreasing the interfacial area and exposing the secondary prismatic plane of hexagonal ice to the clathrate. Nonetheless, the ice−clathrate interface is still disordered. Our results indicate that the crystallinity of the clathrate hydrate affects the tetrahedral order of the disordered interfacial transition layer. However, regardless of the orientation of the ice front, a disordered interfacial transition layer forms between ice and clathrate. Lastly, we investigate the nucleation of ice in the presence of empty sI clathrate hydrate by exposing either the (110) or (100) planes to supercooled liquid water at 200, 205, and 208 K. The (110) plane is the slowest growing face of sI clathrate hydrate,76,103 while the (100) plane is the other slowly growing sI clathrate face.76,103 The temperatures were selected such that ice nucleation occurs within a few nanoseconds at 200 K for a system with 4096 mW waters in ref 86. Here the initial liquid phase contains ∼20000−25000 mW water molecules. Figure 12

homogeneous nucleation of ice within the liquid phase. The result is, as for the other cases, a disordered interfacial transition layer (see Figure S8, Supporting Information). Growth of ice in the presence of the (100) plane of sI clathrate also displays these coupled 5−8 water rings. Figure 13 shows the coupled 5−

Figure 13. Coupled 5−8 water rings connect the ice nucleus to the (110) plane of sI clathrate. The color scheme is as in Figure 11, without showing liquid water. Coupled 5−8 water rings form at the surface of the clathrate. The coupled water rings appear to anchor the ice to the sI clathrate surface, similar to the observation in Figure 11. The number of these coupled 5−8 water rings, however, constitutes a small fraction of the water at the interface between the two crystals. The coupled 5−8 rings were also observed to anchor the ice to the (100) plane of sI clathrate.

8 water rings connecting the ice to the (110) plane of sI clathrate. Same as seen for the nucleation of clathrates in the presence of an advancing ice front (Figure 11), these coupled 5−8 water rings represent a small fraction of the interfacial water between ice and clathrate. We investigate the evolution of the ice−clathrate interface obtained by nucleation of ice in the presence of guest-free clathrates when these two-phase systems are warmed to 230 K and 240 K, below the melting point of the guest-free clathrates (Tm = 245 and 252 K for empty sI and sII, respectively85). Ice continues to grow at the expense of the empty clathrate, resulting in the disappearance of the clathrate within 20 ns. The disordered interfacial transition layer mediates the solid−solid transition from clathrate to ice. The molecular mechanisms and rates of transformation between ice and clathrate, and the role of guests in that process, are important issues that deserve further study.

Figure 12. Nucleation of ice in the presence of sI clathrate hydrate exposing the (110) plane. Panels A−D show snapshots along a simulation trajectory at 205 K in which the empty sI clathrate (green) grows while ice (blue) nucleates and grows from the liquid. Liquid water molecules (red) are not shown in panels A, B, and C. The ice critical nucleus forms at about 1 nm of the surface of the clathrate. The resulting interfacial layer between clathrate and ice is disordered.

4. CONCLUSIONS In this work, we investigate the structure of ice−clathrate interfaces obtained through molecular dynamics simulations with mW and methane-like guests. We use four methods to obtain the interfaces: (i) alignment of the ice and clathrate to maximize the overlap of hexagons in the two surfaces of the two crystals, (ii) competing growth of ice and clathrate from a common solution, (iii) nucleation of clathrate hydrates in the presence of growing ice fronts, and (iv) nucleation of ice in the presence of clathrate hydrates. In all cases, a disordered

illustrates the nucleation of ice in the presence of sI clathrate exposing the (110) plane to solution. The critical ice nucleus forms within 15 Å of the (110) plane of sI clathrate. The resulting ice−clathrate interface is disordered (panel D of Figure 12). In the simulations starting with the sI clathrate exposing the (100) plane to supercooled water, we observe first cross-nucleation from sI into sII clathrate, followed by K


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interfacial transition layer forms between ice and clathrate, regardless of the faces exposed by the crystals. Because of the different local orders at the ice and clathrate surfaces, even when these crystals are optimally aligned, less than 40% of the interfacial crystal molecules make direct “hydrogen bonding” contact to the crystal on the other side of the interface. The rest of the contacts between ice and clathrate are mediated by liquid-like water molecules (we refer to these molecules as liquid-like based on their local order, not on their mobility). Our analysis indicates that coupled 5−7 and 5−8 water rings, that previous works25,26 and this work find to be involved in the anchoring of small clathrate nuclei to the ice surface (and vice versa), represent only a small fraction of water molecules in the interfacial transition layer (ITL) between ice and clathrate. The water molecules in the interfacial transition layer have higher tetrahedral order and lower potential energy than in liquid water, although the difference to liquid water almost vanishes when the clathrate phase is itself disordered (amorphous). The thickness of the disordered ITL is typically two to three water molecules. While the simulations provide no support for an ordered ITL between ice and clathrate, that scenario cannot be fully discarded without an exhaustive search of crystalline ITLs that bind to both ice and clathrate. It should be noted, however, that the repeated unit of an ordered interfacial transition layer cannot be smaller than the areas of domain matching between ice and clathrate planes, which involve hundreds of interfacial atoms. We expect that the large repeating unit of a putative ordered ITL along with the poor matching of the surfaces would hinder the formation of an ordered interface between ice and clathrate. The nucleation of clathrate hydrates from ice8,14 and of ice from clathrate hydrate in the case of self-preservation9,12,19,20 has been reported to occur under conditions of low thermodynamic driving force, which are inconsistent with homogeneous nucleation mechanisms.21,22 Within the framework of classical nucleation theory, this indicates that the surface free energy of the ice−clathrate interface (γIC) is lower than the surface free energies of the clathrate−liquid (γCL) or ice−liquid (γIL) interfaces (we note that γCL21,82 and γIL22,102,103 are almost equal). The lower potential energy of the water at the ice−clathrate interface compared to the solution supports this scenario. Future studies should explicitly compute the interfacial free energy of the disordered ice−clathrate interface, a key quantity to establish how effectively ice and clathrates can promote the nucleation of the other crystal.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation through award CHE-1012651. We gratefully acknowledge the Center of High Performance Computing of the University of Utah for allocation of computing time and technical support.

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REFERENCES

(1) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press/Taylor-Francis: Boca Raton, FL, 2007. (2) Sum, A. K.; Koh, C. A.; Sloan, E. D. Clathrate Hydrates: From Laboratory Science to Engineering Practice. Ind. Eng. Chem. Res. 2009, 48, 7457−7465. (3) Koh, C. A.; Sloan, E. D.; Sum, A. K.; Wu, D. T. Fundamentals and Applications of Gas Hydrates. Annu. Rev. Chem. Biomol. Eng. 2011, 2, 237−257. (4) Zhang, X.; Hester, K. C.; Ussler, W.; Walz, P. M.; Peltzer, E. T.; Brewer, P. G. In Situ Raman-Based Measurements of High Dissolved Methane Concentrations in Hydrate-Rich Ocean Sediments. Geophys. Res. Lett. 2011, 38, L08605. (5) Sloan, E. D., Jr. Fundamental Principles and Applications of Natural Gas Hydrates. Nature 2003, 426, 353−363. (6) Takeya, S.; Ripmeester, J. A. Anomalous Preservation of CH4 Hydrate and Its Dependence on the Morphology of Hexagonal Ice. ChemPhysChem 2010, 11, 70−73. (7) Kuhs, W. F.; Genov, G.; Staykova, D. K.; Hansen, T. Ice Perfection and Onset of Anomalous Preservation of Gas Hydrates. Phys. Chem. Chem. Phys. 2004, 6, 4917. (8) Kuhs, W. F.; Staykova, D. K.; Salamatin, A. N. Formation of Methane Hydrate from Polydisperse Ice Powders. J. Phys. Chem. B 2006, 110, 13283−13295. (9) Falenty, A.; Kuhs, W. F. “Self-Preservation” of CO2 Gas Hydrates–Surface Microstructure and Ice Perfection. J. Phys. Chem. B 2009, 113, 15975−15988. (10) Sun, D.; Shimono, Y.; Takeya, S.; Ohmura, R. Preservation of Carbon Dioxide Clathrate Hydrate at Temperatures Below the Water Freezing Point under Atmospheric Pressure. Ind. Eng. Chem. Res. 2011, 50, 13854−13858. (11) Takeya, S.; Ripmeester, J. A. Dissociation Behavior of Clathrate Hydrates to Ice and Dependence on Guest Molecules. Angew. Chem., Int. Ed. 2008, 47, 1276−1279. (12) Takeya, S.; Shimada, W.; Kamata, Y.; Ebinuma, T.; Uchida, T.; Nagao, J.; Narita, H. In Situ X-Ray Diffraction Measurements of the Self-Preservation Effect of CH4 hydrate. J. Phys. Chem. A 2001, 105, 9756−9759. (13) Takeya, S.; Yoneyama, A.; Ueda, K.; Mimachi, H.; Takahashi, M.; Sano, K.; Hyodo, K.; Takeda, T.; Gotoh, Y. Anomalously Preserved Clathrate Hydrate of Natural Gas in Pellet Form at 253 K. J. Phys. Chem. C 2012, 116, 13842−13848. (14) Rivera, J. J.; Janda, K. C. Ice Particle Size and Temperature Dependence of the Kinetics of Propane Clathrate Hydrate Formation. J. Phys. Chem. C 2012, 116, 19062−19072. (15) Kuhs, W. F.; Klapproth, A.; Chazallon, B. Chemical Physics of Air Clathrate Hydrates; Physics of Ice Core Records; Hokkaido University Press: Hokkaido, Japan, 2000; pp 373−392. (16) Staykova, D. K.; Kuhs, W. F.; Salamatin, A. N.; Hansen, T. Formation of Porous Gas Hydrates from Ice Powders: Diffraction Experiments and Multistage Model. J. Phys. Chem. B 2003, 107, 10299−10311.

ASSOCIATED CONTENT

S Supporting Information *

Figure S1 shows the orientation of the hexagonal water ring at the (110) plane of sI clathrate. Figure S2 shows the potential energy as a function of the distance between the aligned crystals of ice and clathrate. Table S1 shows the density of direct contact in section 3A. Figure S3 shows the domain matching between the (100) plane of sI with the prismatic plane of hexagonal ice. Figure S4 shows the potential energy of the minimized aligned ice−clathrate interface. Figure S5 displays direct and mediated contacts at the I3 interface. Figure S6 shows the competing growth of ice and clathrate at temperatures ranging from 250 to 270 K. Figure S7 illustrates the flattening of the ice−clathrate interface after further simulation of the system shown in Figure 10. Figure S8 shows the ice nucleation in the presence of the (100) plane of sI clathrate. L


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