Anisotropic Lattice Expansion of Structure H Clathrate Hydrates

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Anisotropic Lattice Expansion of Structure H Clathrate Hydrates Induced by Help Guest: Experiments and Molecular Dynamics Simulations Kotaro Murayama,† Satoshi Takeya,‡ Saman Alavi,†,§ and Ryo Ohmura*,† †

Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-Ku, Yokohama, 223-8522, Japan National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8565, Japan § Department of Chemical and Biological Engineering, University of British Columbia, Vancouver V6T 1Z3, Canada ‡

S Supporting Information *

ABSTRACT: The structure H (sH) clathrate hydrates of neo-hexane with argon, krypton, and methane help gases are synthesized to study the effect of the help gas on the crystal lattice structure. Powder X-ray diffraction (PXRD) measurements on these hydrates were performed for temperatures in the range of 93−183 K, and the a-axis and c-axis lattice constants and the small and medium sH cage occupancies were determined. The PXRD results show that the a-axis lattice constants of the three clathrate hydrates are close in magnitude, but at each temperature, for the caxis lattice constants c(CH4) > c(Kr) > c(Ar). Parrinello−Rahman molecular dynamics (MD) simulations were performed on the three sH clathrate hydrate phases. The PXRD observed trends in the a-axis and c-axis lattice constants at different temperatures were reproduced by the simulations. The dynamics of the small cage guests are characterized by the velocity autocorrelation functions. The experiments and computations show the complex interplay of the molecular size and interaction energies in determining the lattice structure and stability of even relatively simple clathrate hydrates of nonpolar, hydrophobic molecules.

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molecule guest substance (LMGS) occupying the 51268 cage, and the second is a small “help gas”, such as methane, xenon, or H2S which is required to stabilize the small cages (512 and 435663 cages). The sH clathrate hydrates generally form under milder conditions than the other structures. The sH hydrates of a large number of LMGSs have been synthesized3−6 and suggested for applications as storage media for natural gas7 and hydrogen,8,9 CO2 capture,10 and working materials for heat pump/refrigeration systems.11 Using equilibrium phase stability, powder X-ray diffraction (PXRD), and molecular dynamics simulations, we recently studied the pressure−temperature stability conditions and lattice constants of a number sH clathrate hydrates of LMGSs with CH4 as the help gas.4 Tezuka et al. focused on the effect of size and shape of LMGSs on the thermodynamic stabilities of the sH hydrates with a specified small-molecule guest, CH4.6 The effects of small guest on the stability of the sH hydrates have not been investigated. In this work, we study possible connections between size and interaction strengths of the help gas in the sH hydrate with the unit cell lattice constants and cage expansion/shrinkage. We selected the spherical CH4, Ar, and Kr as help guest gases and in the present

INTRODUCTION

Clathrate hydrates are ice-like crystalline inclusion compounds that form when water is compressed with a wide range of substances. The size and chemical structure of the guest substances determine the variant of hydrate crystallographic structures that is formed. The main canonical clathrate hydrate structures designated as structure I (sI), structure II (sII), and structure H (sH, Figure 1) are formed as guest size increases.1,2 Clathrate hydrates can form with more than one type of guest molecule, and indeed the formation of sH hydrates requires two different guest substances: the first is a relatively large

Figure 1. (a) Crystal structure model of structure H hydrate and the cages consisting of the structure H hydrate unit cell: (b) pentagonal dodecahedron (512), (c) irregular dodecahedron (435663), and (d) icosahedron (51268). © 2014 American Chemical Society

Received: June 13, 2014 Revised: August 22, 2014 Published: August 22, 2014 21323

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stoichiometric amount for NH needed to occupy all large cages of structure H hydrate for the amount of water given (an sH unit cell consists of one large cage per 36 water molecules). This ratio of water to NH is determined through trial and error. The hydrate sample made from this ratio contained less ice and solid NH. The vessel was then immersed in the temperaturecontrolled bath equipped with a PID-controlled heater and a cooler set. The temperature inside the vessel was kept at 275 K. The air was purged from the vessel by repeating the procedure of pressurization with CH4 to 0.4 MPa and depressurization to atmospheric pressure three times. CH4 gas was supplied from a high-pressure cylinder through a pressure-regulating valve until the pressure in the vessel increases to 3.0 MPa to avoid the formation of simple CH4 sI hydrate. The subcooling temperature (ΔTsub = Teq − Tex, where Teq is the equilibrium temperature and Tex is the temperature of forming hydrates) was 6 K. Kr gas was supplied to 1.7 MPa, and Ar gas was to 9.0 MPa after pressurization and depressurization with each gas. The subcooling temperatures were both 9 K for these gases. The driving force for the hydrate formation may be expressed in terms of the pressure. The normalized pressures, defined as Pex/Peq where Pex is the pressure forming hydrates and Peq is the equilibrium pressure, were about 2.1, 3.0, and 2.7 for the system with CH4, Ar, and Kr, respectively. During hydrate formation in the vessel, a line connecting the vessel and CH4 supply cylinder was intermittently closed. Upon hydrate formation, when the pressure decreased to the equilibrium pressure of sH hydrate formed with each gas and NH, the vessel was recharged with each gas to the initial pressure and repeated until no further pressure reduction was observed. The inside of the vessel was continuously agitated at 400 rpm after hydrate nucleation. Nearly complete conversion of water to hydrate was obtained when no further pressure reduction was observed. After the pressure stabilized, the vessel was subsequently removed from the temperature-controlled bath and immediately immersed in a liquid nitrogen bath. After the temperature in the vessel decreased below 200 K, the vessel was removed from the liquid nitrogen pool and quickly disassembled. Then, the lower part of the vessel containing the hydrate sample was again placed in a liquid nitrogen pool, and the hydrate sample was obtained from the vessel. The hydrate sample was subjected to PXRD measurements after storing in a container kept at a temperature below 90 K. For the PXRD measurements, the hydrate sample was finely powdered in a nitrogen atmosphere at a temperature below 100 K. The fine-powdered hydrate samples were toploaded on a copper (Cu) specimen holder. PXRD measurements were done using Cu−Kα radiation by a θ/2θ step scan mode with a step width of 0.02 degree (40 kV, 40 mA; Rigaku model Ultima III). Here, the parallel beam optics was employed for the PXRD measurement to avoid shift in the 2θ angles of diffraction. To eliminate further systematical errors, LaB6 as an external standard reference (NIST Standard Reference Material 660a) was also measured. Analysis of the lattice constants was done by a full-pattern fitting method using the Rietveld program RIETAN-FP.23 Cage occupancies for the small and medium cages were analyzed by the Rietveld method, which were performed using the crystal structure of the NH with CH4 hydrate determined by the ab inito powder X-ray diffraction method24 as the initial model. For each analysis on cage occupancy, the help gas molecules were fixed at centers of small and medium cages. The full occupancy for NH in large cages is assumed since the large sH cages are not stable when empty and analyzed in an earlier study.24

work do not consider the effect of shape anisotropies of the help gas molecules on the lattice constant and sH phase stability. The effects of guest species on the stability and properties of clathrate hydrate inclusion compounds have been widely studied.4,6 The traditional method of assessing the effects of guests on the stability of the hydrate phase is through the use of the van der Waals−Platteeuw theory.12 This theory assumes that the guest species reside in specific clathrate hydrate water cages with known structure and interact with the cage water molecules through an averaged potential energy function. Recent studies show that this picture is incomplete and only applies to a family of clathrate hydrates with small and inert guests. Factors such as hydrogen13−16 and halogen bonding of the guests with the cage water molecules,17−20 mutual effects of the small cage guests on hydrogen bonding of the large cage guests,14 migration of guests between cages,21,22 and distortion of the shape of large cage guests for their incorporation into cages6 are not predicted by the traditional approaches, and these factors can influence the temperature/pressure stability range and guest occupancies of the clathrate hydrate phase. In this work, we aim to study the effect of different help gas molecules, namely, CH4, Ar, and Kr, on the properties of the sH hydrate phase. For this purpose, we have chosen the neohexane (NH, (CH3)3CCH2CH3)) as the LMGS. The NH guest is nonpolar and does not undergo large changes in geometry (as a result of changes in dihedral angles of the molecule) upon encapsulation in the large (51268) sH cages of the hydrate phase. In the present study, in the sH clathrate hydrate with NH as the LMGS, we measure the dependence of the lattice constants and thermodynamic stability of the hydrate phase on the molecular sizes of the small and medium cage help-gas molecules CH4, Ar, and Kr. Lattice constants for the sH clathrate hydrates are measured by PXRD and calculated using Parrinello−Rahman molecular dynamics (MD) simulations. The experimentally observed changes in the lattice constants are related to the size, interaction energies, and dynamics of the small cage guests in these hydrate phases from the MD simulations.

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EXPERIMENTAL AND COMPUTATIONAL METHODS The three hydrate crystal samples for PXRD measurements were synthesized in a high-pressure vessel from mixtures of distilled water, neo-hexane (NH, C6H14); pure CH4 (0.9999 mole fraction certified purity; Takachiho Chemical Industrial, Co., Ltd.); argon (0.999999 mole fraction certified purity; Taiyo Nissan, Co., Ltd.); and krypton (0.99999 mole fraction certified purity; Tokyo Gas Chemicals, Co., Ltd.). The LMGS was purchased from Sigma-Aldrich with minimum purity of 99.0 mol %. Hydrate crystal samples for PXRD measurements were prepared with liquid water, a LMGS liquid, and CH4/Ar/Kr gas using a high-pressure cylinder. The main component of the apparatus was a stainless steel cylindrical vessel with inner volume of 200 cm3 which is equipped with a magnetic stirrer to agitate the fluids and hydrate crystals inside the vessel. The vessel was immersed in a bath filled with aqueous ethylene glycol solution. Each experimental run is commenced by placing 35 cm3 of liquid water and 14.4 cm3 of NH liquid in the vessel. The molar ratio of liquid water and NH is about 17.9:1. The amount of NH is about 1.9 times larger than the 21324

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pressure for all three small cage guests. These conditions are consistent with those of the PXRD measurements. Unit cell lattice constants were determined after the simulations.

In the molecular dynamics simulations, the initial coordinates of the water oxygen atoms in the sH clathrate unit cell for the simulations were taken from the clathrate X-ray crystallography structure.25 The initial positions of the water hydrogen atoms about the oxygen atoms were assigned to be consistent with the ice rules while simultaneously minimizing the total energy and dipole moment of the unit cell.26 In the simulations, a 3 × 3 × 3 replica of the sH hexagonal unit cell with 918 water molecules is used. The center of mass of NH (from the optimized gasphase structure) and CH4/Ar/Kr helper gas molecules were initially placed in the center of the respective cages according to the experimentally determined PXRD occupancies. Guest structures and positions in the cages equilibrate during the simulation. The initial, gas-phase structures of the NH large guest molecule were determined by quantum chemical structural optimization using the Gaussian 03 suite27 and the B3LYP/6311++G(d,p) level of theory. The intermolecular van der Waals potentials between atoms i and j on different molecules are modeled as a sum of Lennard-Jones (LJ) and electrostatic point charge interactions ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj σij σij V (rij) = ∑ 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ 4πε0rij i,j ⎣⎝ ij ⎠

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RESULTS AND DISCUSSION The PXRD profiles for the sH hydrates of NH with CH4, Kr, and Ar at 93 K are given in Figure 2. The crystal structure of all

(1)

where σij and εij are the distance and energy parameters of the ij pair of atoms separated by a distance of rij, and qi and qj are the electrostatic point charges on the atoms. Water molecules in the clathrate were modeled using the TIP4P/ice four-charge model,28 while the large cage guest molecules are allowed flexibility and their intra- and intermolecular potential interactions were modeled with the general AMBER force field (GAFF).29 The Guillot and Guissani potential was chosen for methane,30 and potentials Ar and Kr are taken from Hirschfelder, Curtiss, and Bird.31 The values for the parameters σii and εii for selected atom types used in the simulations are given in Table S1 of the Supporting Information. For potentials between unlike atoms, standard combination rules, εij = (εiiεjj)1/2 and σij = (σii + σjj)/2, are used. Partial electrostatic charges on the atoms of the structurally optimized NH guest molecules were calculated using the “charges from electrostatic potential grid” (CHELPG) method32 implemented in the Gaussian 03. The point charges qi on the water and optimized large cage NH guest molecules are given in Table S1 (Supporting Information). Nonisotropic constant pressure/temperature NpT (Parrinello−Rahman)33,34 molecular dynamics simulations on periodic simulation cells were performed using the DL_POLY software program version 2.2035 with pressure and temperature regulated using the modified Nosé−Hoover thermostat/ barostat algorithm33,34 and thermostat and barostat relaxation times of 0.2 and 1.0 ps, respectively. The Verlet leapfrog algorithm was used with a time step of 1 fs. Long-range electrostatic interactions were calculated using the Ewald summation method,33,34 and all intermolecular interactions in the simulation box were calculated within a cutoff distance of Rcutoff = 13.0 Å. All systems were initialized by running an isotropic NpT simulation for 500 ps at the temperature and pressure of interest. Afterward, a nonisotropic NpT simulation was performed for an additional time of 500 ps with the first 200 ps used for temperature-scaled equilibration. Simulations were run at 90, 120, 150, and 190 K temperatures and 1 bar

Figure 2. Powder X-ray diffraction spectrum for the sH binary hydrate of neo-hexane and CH4 (a), Kr (b), and Ar (c) at 93 K. The tick marks in the lower part represent the calculated peak positions for the structure H (sH) hydrate and hexagonal ice (Ih). The differences between measured and modeled spectra are shown as light lines for each hydrate.

the hydrates tested in the present study is identified to be the hexagonal sH. It was also calculated by Rietveld method using PXRD data that the sH hydrates of NH with CH4, Kr, and Ar contained 3, 3, and 17 wt % ice, respectively. The experimentally estimated occupancies of the 512/435663 cages from the PXRD analysis are 0.8/0.8, 0.9/0.8, 0.8/0.8 for CH4, Kr, and Ar, respectively. These occupancies could not be quantitatively confirmed by other techniques, but an earlier study suggested that the cage occupancies estimated using the same procedures were consistent with the results of 13C NMR and single-crystal structure analysis with 10% of deviation.24 The values of the a-axis and c-axis lattice constants of the sH hydrates measured at temperatures in the range of 93−183 K are given in Table 1 and shown in Figure 3. The sH NH hydrate with CH4 has the largest values of the c-axis lattice constant, and the sH NH hydrate with Ar has the smallest values of the c axis lattice constant at each temperature. The values of the a axis lattice constants in all three sH NH clathrate hydrates show similar values. 21325

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suggest that the cage occupancies of these clathrate hydrates are almost identical. However, the molecular radii of CH4 (calculated from the C−H bond length and van der Waals radius of hydrogen), Kr, and Ar are 2.2, 2.02, and 1.88 Å, respectively.37 Figure 3 shows that the c axis lattice constants increase as the help gas guest molecule radii become larger. The lattice constant dependence on the molecular volume of the LMGS was previously reported by Takeya et al.24 for ten LMGSs (isopentane, NH, pinacolone, pinacolyl alcohol, adamantine, methylcyclohexane, 2-methyltetrahydrofuran, 2methylcyclohexanone, 3-methyltetrahydropyran, and 4-methylcyclohexanone). As the molecular volume of LMGS increases, the c-axis lattice constant increases. In our previous PXRD and MD study,6 we also reported the increase of the c-axis lattice constant and the decrease of the a-axis lattice constant when the volume of the LMGSs becomes larger for 2-methylbutane, 2,2-dimethylbutane, 2,3-dimethylbutane, methylcyclopentane, pinacolone, and methylcyclohexane. The largest and smallest value of the a-axis lattice constant in six sH hydrates was reported to be 12.190 and 12.134 Å, respectively, which is a difference of 0.056 Å. The largest and smallest value of the caxis lattice constant was 10.031 and 9.971 Å, respectively, a difference of 0.060 Å (see Table S2 of the Supporting Information). In the present study, the c-axis lattice constants also increase as the molecular volume of the small cage guest increases from Ar to CH4. In contrast to the decrease in the a-axis lattice constant with increasing molecular volume of LMGS,6,38 the PXRD measurements (and MD simulations, see below) of the present study show that the a-axis lattice constant shows little variability with changing the gaseous guest substances in the small cages. In the present study, the range of variation of the aaxis lattice constant for sH NH hydrates with CH4, Kr, and Ar guests is 0.026 Å which is smaller than half of the range of variation of the a-axis lattice constant (which is 0.056 Å), in the case of changing the LMGS in sH hydrates with CH4 in the small cages. In comparison, the difference between the largest and smallest value of the c-axis lattice constant in the sH NH hydrates for different small help gas guests is 0.076 Å which is 0.016 Å larger than the range of variation for the c-axis lattice constant, which is 0.060 Å, with changing the LMGS. The range of expansion of the sH hydrate unit cell lattice constants is different depending on whether the molecular volumes of the small or large molecule guest substances are changing.

Table 1. Lattice Constants (Å) for Binary sH Clathrate Hydrates of NH with Methane, Argon, and Krypton Measured by PXRD Measurements and NpT Calculated from Nonisotropic Constant Pressure−Temperature Molecular Dynamics Simulations at Different Temperatures and Pressuresa

help gas/ temperature CH4 93 100 108 123 138 153 168 Ar 93 100 108 123 138 153 168 183 Kr 93 100 108 123 138 153 168 183

lattice constants

lattice constants

measured by PXRD/Å

calculated by MD/Å

a/Å

c/Å

help gas/ temperature

a/Å

c/Å

CH4 90 120 150 190

12.14 12.16 12.18 12.22

9.99 10.01 10.02 10.04

12.165 12.167 12.171 12.179 12.188 12.199 12.213

10.002 10.003 10.005 10.009 10.015 10.020 10.028

12.164 12.168 12.172 12.180 12.189 12.200 12.210 12.217

9.928 9.930 9.931 9.936 9.941 9.946 9.953 9.961

90 120 150 190

12.15 12.17 12.20 12.23

9.93 9.94 9.95 9.98

12.166 12.170 12.173 12.179 12.187 12.197 12.205 12.215

9.980 9.981 9.983 9.986 9.990 9.997 10.000 10.004

90 120 150 190

12.13 12.16 12.18 12.22

9.97 9.99 10.00 10.03

a

The uncertainty in the experimentally measured lattice constants is 0.001 Å and the computed lattice constants is 0.03 Å or less.

The lattice constant of sI, sII, and sH clathrate hydrates generally depends on the size, structure, and cage occupancy of the guest molecules under isothermal conditions.21,36 In the binary sH NH clathrate hydrates, the PXRD measurements

Figure 3. Lattice constant a and c of sH hydrates with temperature from (a) the experimental results between 93 and 183 K determined from PXRD and (b) MD results. The empty symbols show the lattice constant a, and filled symbols show the lattice constant c: (●) methane; (■) krypton; (▲) argon. The computed error bars for the lattice constants are 0.03 Å or less. 21326

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small (roughly 1%) discrepancies between experimental and computed lattice constants. The effect of help gas guest occupancy on the a-axis and caxis lattice parameters is determined in Figure 4 where we

In Figure 3, the slope of the temperature variation of the experimental a-axis lattice constants is greater than that of the caxis lattice constants for each help gas. We can say that the thermal expansivity for the CH4, Kr, and Ar hydrates along the a-axis of the lattice (4.6 × 10−5, 4.2 × 10−5, and 5.0 × 10−5 Å· K−1, respectively, at 150 K) is larger than that of the c-axis (3.2 × 10−5, 2.9 × 10−5, and 2.9 × 10−5 Å·K−1, respectively, at 150 K) direction. The difference in the thermal expansivity of the lattice constants of the sH hydrate in the a-axis and c-axis directions was reported by Takeya et al.,38 and it is stated that the plastic difference of the lattice parameters depends on the molecular size of LMGS. From the present study, it is determined that the difference of thermal expansivity of the a- and c-axes also depends on the small guest substance. The computationally determined a-axis and c-axis lattice constants of the binary sH clathrate hydrates with the experimental small and medium cage occupancies are also plotted in Figure 3. The agreement with the experimental values is very good, and the ordering of the c-axis lattice constants for CH4, Kr, and Ar agrees with experiment. Similar to the experiments, in the MD results, the variability of the caxis lattice constants between the three sH NH hydrates is significantly greater than the range of variability of the a-axis lattice constants. The origin of the different behavior of the aand c-axes of the unit cell is captured by the MD simulations. The different sizes and interaction strengths of the small cage guests (see Table S1 of the Supporting Information) and anisotropic expansion/shrinkage of the hexagonal sH unit cell, reflected in the structure shown in Figure 1, reproduce the observed behavior. An explanation for the different ranges of variation of the a and c lattice constants for sH hydrate with the different small cage guests may be made with reference to the sH unit cell structure model shown in Figure 1. The small guests occupy the 512 and 435663 cages of the sH unit cell. The square and hexagonal faces of the 435663 cages of sH have water O−O−O angles that deviate most from the ideal hydrogen bonding angle for water molecules and would have the weakest hydrogen bonding strength. These faces are arranged parallel to the c-axis direction. It is reasonable to assume that when larger guests such as CH4 are incorporated into the 435663 cages these cages expand along the c-axis direction as this would primarily involve a lengthening of the weak hydrogen bonds in that direction. Any expansion in the a-axis direction would involve a lengthening of water−water hydrogen bonds in pentagonal faces of the 512 and 435663 cages. These latter hydrogen bonds are stronger, leading to smaller expansion along the a-axis. Better agreement is seen between the simulated lattice constants and experimental results at higher simulation temperatures (between 160 and 200 K). The low-temperature simulations underestimate the experimental lattice constant values. As a result, the computationally determined thermal expansivity for the three sH NH hydrates is somewhat larger than the experimental values. This could be related to the fact that the TIP4P/ice potential was parametrized to produce coexistence curves of different solid ice phases in the temperature range of ∼180−270 K.28 At lower temperatures, a different parametrization of the water potential may lead to better agreement with the low-temperature sH hydrate lattice constants. Additionally, at low temperatures below 150 K, quantum mechanical effects for the water and guest dynamics (particularly for the lighter CH4 guest) may contribute to the

Figure 4. Computed a and c lattice constants for binary sH hydrates with methane, krypton, and argon + neo-hexane between 90 and 190 K with experimental (full lines) and 100% (dashed lines) small and medium cage occupancies.

compare the predicted values of the lattice constants with the experimental occupancies and with results of MD simulations with full occupancy of the 512 and 435663 cages. Interestingly, computed lattice constants for hydrates with fully occupied small and medium cages have smaller a-axis lattice constants but larger c-axis lattice constants. In each sH NH hydrate, the differences between the a-axis and c-axis lattice constants in the experimental and full occupancies are about 0.01 Å. In previous work,21 we studied the effect of the small cage guests on the structure and hydrogen bonding in the structure binary structure sII THF hydrate with CO2, H2S, CH4, and Xe small cage guests. Similar to the present case, the order of the lattice constants for the binary sII clathrate hydrates was determined to be a(CO2) > a(Xe) > a(CH4) ≈ a(H2S) > a(empty small cages), which corresponds to the order of the effective size of these small cage guest molecules. In the sII THF binary hydrate with CO2, with a decrease in occupancy of the small cages by CO2, a decrease in the lattice constant was observed. To further understand the effect of the small and medium cage guests on the hydrate structures and energetics, we plot the unit cell configuration energy (total potential energy) as a function of temperature for the three hydrates in Figure 5 with values given in Table S3 of the Supporting Information. The configurational energy of the Ar hydrate is the least negative value, which is consistent with Ar atoms having the smallest Lennard-Jones well depth, ε(Kr) = 0.3306 > ε(CH4) = 0.2940 > ε(Ar) = 0.2380 (in kcal·mol−1units; see Table S1 of the Supporting Information). In all cases, the hydrates with full small and medium cages have more negative configurational energy, implying attractive guest−water interactions between the help gas molecules and water molecule in the 512 and 435663 cages of the hydrate phase. The order of the lattice constants (Figure 3 and Table 1) is consistent with the size ordering of the three small cage guests (Table S1, Supporting Information) and is different than the order of the configurational energies. However, the experimental equilibrium pressures of hydrate formation given at two 21327

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Figure 6. Velocity autocorrelation functions of sH small and medium cage guests methane, krypton, and argon from simulations at 150 K.

Figure 5. Total calculated configurational energy per unit cell for binary sH hydrates with methane, krypton, and argon + neo-hexane between 90 and 190 K with experimental small and medium cage occupancies (full lines) and small and medium cages 100% filled (dashed lines).

radius of the three guests, and Figure 6 shows the largest rattling frequency. To further understand the effect of help guests on the host structure of structure H hydrates, structure refinement of cages and distribution and cage occupancies of guest molecules using diffraction techniques will be useful. Further refinement of the PXRD pattern and analysis of the MD results will show the details of the cage expansions for the different small cage guests.

temperatures in Table 239 are consistent with the order of the configurational energies. The binary sH NH hydrate with Ar Table 2. Equilibrium Pressure of Hydrate Formation for the sH Hydrates of Neo-Hexane with Methane, Argon, and Krypton Help Gas Molecules at Two Temperaturesa

a

help gas

T/K

Peq/MPa

T/K

Peq/MPa

CH4 Ar Kr

276.0 276.0 276.0

1.60 3.50 0.72

278.0 278.0 278.0

2.02 4.50 0.24

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CONCLUSIONS Structure H clathrate hydrates of neo-hexane with argon, krypton, and methane help gases are synthesized to study the effect of the help gas on the crystal lattice structure of clathrate hydrates. Powder X-ray diffraction (PXRD) measurements on these hydrates were performed for temperatures in the range of 93−183 K, and the a-axis and c-axis lattice constants and the two small sH cage occupancies were determined. The PXRD results show that the a-axis lattice constants of the three clathrate hydrates are close in magnitude, but at each temperature, the c-axis lattice constants differ in the order c(CH4) > c(Kr) > c(Ar). These results suggest anisotropy in the compressibility of the sH clathrate hydrates where the solid is less compressible along the a-axis direction of the unit cell than the c-axis direction. At T = 93 K, the guest occupancies for the 512/435663 cages from the PXRD studies are estimated to be 0.8/0.8, 0.9/0.8, and 0.8/0.8 for CH4, Kr, and Ar, respectively. Parrinello−Rahman molecular dynamics (MD) simulations were performed on the three binary sH clathrate hydrate phases using the experimental help gas occupancies. The observed trends in the a-axis and c-axis lattice constants at different temperatures were reproduced by the MD simulations and are related to the size parameter of the small molecule guests. The molecular dynamics configurational energy (total potential energy) of the three hydrate phases was also determined and seen to correlate with the ε parameters of the guest molecules and the experimentally determined thermodynamic stability of these hydrates as determined by the pressure of formation. The experiments and computations of this work show the complex interplay of the details of the molecular structure and energetics in determining the lattice structure and stability of even relatively simple clathrate hydrates of nonpolar, hydrophobic molecules. In cases where the large cage guests have flexible structures and the LMGS/help gas interact through hydrogen bonding with the cage water molecules, other

Experimental details are given in ref 39.

has the highest pressure of formation at each temperature and the least negative configurational energy in the simulations. The binary sH NH hydrate with Kr has the lowest pressure of formation and the most negative configurational energy. The stability of the hydrates, as measured by the pressure required to synthesize each hydrate at a certain temperature, correlates well with the MD configurational energy and ε parameter for each small cage guest. The dynamics of the help gas guest molecules in the three sH NH binary hydrates are compared by plotting the normalized velocity autocorrelation functions (VACFs) VACF(t ) =

⟨vi(t ) ·vi(0)⟩ ⟨vi(0) ·vi(0)⟩

(2)

at 150 K in Figure 6. In eq 2, vi(t) is the velocity of the small cage guest molecule i in the simulation at time t, and vi(0) is the corresponding velocity of the molecule at time 0. The brackets indicate an ensemble average over all molecules in the simulation. The VACF gives a measure of the change in magnitude and direction of the velocities of the small cage molecules as they move in the small cages and undergo collisions with the cage walls. The CH4 molecule has the largest vibrational (rattling) frequency inside the sH cages, followed by Ar and Kr which have rattling frequencies similar in magnitude. The size and strength of interaction with the cage water molecules both affect the vibrational frequencies of the guests. As seen in Table S1 (Supporting Information), CH4 has the largest effective 21328

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complication factors will enter the prediction of the lattice constants and phase stability.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.

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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 study was supported by a Keirin-Racing-based researchpromotion fund from the JKA Foundation and by JSPS KAKENHI Grant Number 25289045.

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REFERENCES

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