International Conference on Gas Hydrates (ICGH) (6th : 2008)

MOLECULAR DYNAMICS STUDY ON STRUCTURE-H HYDRATES Englezos, Peter; Ripmeester, John A.; Alavi, Saman; Susilo, Robin 2008-07-31

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  MOLECULAR DYNAMICS STUDY ON STRUCTURE-H HYDRATES      Robin Susilo, Saman Alavi, and John A. Ripmeester* Steacie Institute for Molecular Sciences  National Research Council Canada 100 Sussex Drive, Ottawa, ON, K1A 0R6  CANADA  Peter Englezos Department of Chemical & Biological Engineering  University of British Columbia 2260 East Mall, Vancouver, BC, V6T 1Z3 CANADA   ABSTRACT The  presence  of  structure H (sH) methane  hydrate  in natural  environments, in  addition to the well-known structure-I (sI) and II (sII) hydrates, has recently been documented. Methane in the presence of condensates (C5-C7) forms sH hydrate at lower pressure than the sI hydrate. Thus, the occurrence  of  sH  methane  hydrate  is  likely  to  have  both  beneficial  and  negative  practical implications. On the negative side, in the presence of condensate, sH hydrate may form and plug gas transmission pipelines at lower pressures than sI hydrate. On the other hand, sH hydrate can be  synthesized  at  lower  pressures  and  exploited  to  store  methane.  The  existence  of  natural hydrates containing sH hydrate may also be expected in shallow offshore areas. There are at least 26 large guest molecules known as sH hydrate formers and each of them produces a sH hydrates with  different  properties.  The  hydrate  stability,  the  cage  occupancies  and  the  rates  of  hydrate formation  depend  on  the  type  of  large  molecule  selected.  Consequently,  it  is  essential  to understand  how  the  host  and  the  guest  molecules  interact.  Studies  at  the  molecular-level  are therefore indispensable in providing information that is not obtainable from experiments or too costly  to  acquire.  Free  energy  calculations  are  performed  to  determine  the  relative  stability among different sH hydrate systems and the preferable cage occupancy. The latter would give indications  of  how  much  methane  gas  can  be  stored  in  the  hydrate.  The  interaction  of  guest molecule inside the hydrate cage is also investigated. The results are related to the physical and chemical properties of gas hydrates observed from the experiments or reported in the literature.  Keywords: Gas storage, clathrates, structure-H, methane, natural gas  INTRODUCTION Gas  hydrates  are  inclusion  compounds  that  are formed both naturally and artificially, when water molecules  and  suitable  guest  molecule(s)  are  in contact  at  low  temperatures  and/or  high  pressure conditions  [2].  The  selectivity  of  hydrate  cages toward  guest  molecule(s)  and  the  gas  holding potential in hydrates have attracted many scientists to  investigate  this  compound  for  energy  and environmental  applications  [3].  It  is  therefore important  to  understand  thermodynamic  and kinetic  properties  of  gas  hydrates.  This  work focuses  on  structure  H  (sH)  hydrates  where  its occurrences  in  nature  has  been  reported  recently [4]  and  can  be  utilized  as  a  promising  methane storage medium [5-7]. This structure possesses the largest  cage  among  all  hydrate  structures  (sI,  sII, and  sH)  and  requires  two  different  sized  guest molecules  to  stabilize  the  crystal  [8].  In  the  sH hydrate the large cages are occupied by large guest molecules whereas the smaller cages are filled with smaller  molecules  such  as  methane,  xenon,  or carbon  dioxide,  which  by  themselves,  are  known as  typical  sI  hydrate  formers.  The  smaller * Corresponding author: Phone: +1 613 998 2011 Fax: +1 613 998 7833 Email: ?Reprinted with permission from [1]. Copyright [2008], American Institute of Physics?   molecules  (e.g.  methane)  may  also  occupy  the large cage of sH hydrate with multiple occupancy, although this has been reported only at extremely high pressures and is not practical [9,10]. The large guest  molecule  is  also  known  as  a  LMGS  [11]. Interestingly, the sH hydrates with the large guest molecule (LMGS) form at lower pressures than the corresponding  sI  hydrates.  However,  the  both  the large and small guest molecules have low affinity with water. As a result, three separate phases: a gas phase, a non-aqueous liquid (LMGS) phase, and an aqueous  phase  are  typically  present,  which complicate the system. All molecules have to be in contact for the sH hydrate to form.   Earlier  experimental  studies  employing  both macroscopic techniques (gas uptake [12,13], fluid phase  equilibria  [14],  calorimetric  [15])  and microscopic  techniques  (X-Ray  diffraction,  NMR and  Raman  spectroscopy  [15,16])  on  methane storage in sH hydrates at our laboratories revealed that the formation rates and methane occupancies differ  among  the  three  LMGS  studied:  tert-butyl methyl  ether  (TBME),  neo-hexane  (NH),  and methyl-cyclohexane  (MCH).  The  initial  hydrate formation  rate  from  solid  ice  powder  (without stirring)  [13,16]  and  liquid  water  with  efficient mixing by agitation [12] were found to increase in the  order:  MCH<NH<TBME.  The  system  with TBME  showed  the  fastest  initial  hydrate  growth rate which is consistent with the fact that TBME is much  more  soluble  in  water  than  NH  and  MCH [14]  and  TBME  wets  ice  much  better  than  the other  two  liquids  [16].  Surprisingly,  the  hydrate composition  determined  by  solid-state  NMR spectroscopy  and  the  gas  content  measured  by decomposing  the  clathrate  revealed  that  the methane  content  with  TBME  was  the  smallest, followed  by  NH  and  MCH  [15].The  methane pressure required to form a stable sH clathrate with TBME  is  also  higher  than  with  NH  or  MCH [17,18].  Moreover,  the  system  with  TBME  showed  a slower hydrate transformation during the formation from  melted  ice  particles  whereas  the  other  two systems  (NH  and  MCH)  proceeded  quickly towards full hydrate conversion as the temperature was ramped above the ice-point [13]. Contrary to previous  findings  [11,12],  TBME  is  not  the  best LMGS  because  the total time required  to convert ice/water fully into clathrate is actually longer and the  methane  content  is  also  less  than  for  the NH/MCH systems.   The  experimental  measurements  and  observations could  not  explain  why  the  sH  hydrate  formation rate  and  methane  content  vary  with  LMGS.  It  is unknown  whether  different  methane  occupancy values  observed  are  due  to  thermodynamics, kinetics  or  a  combination  of  both.  Hence,  a molecule level study via molecular dynamics (MD) is  indispensable  for  gaining  insights  on  hydrate properties. Free energy calculations are performed to determine the sH hydrate stability and methane occupancy  dependence  on  LMGS  and  pressure. The preference of methane molecules for different cages (512 or 435663) is also studied. In addition, the structures  of  hydrate  phase  with  LMGS  is examined.  The  implications  of  these  molecular level  studies  on  hydrate  stability  and  kinetics  are discussed.    COMPUTATIONAL METHODOLOGY  The  DL_POLY  molecular  dynamics  simulation package version 2.14 was employed in this study [19].  The  simulations  were  performed  with  the NPT ensemble using the Nos?-Hoover thermostat-barostat algorithm [20,21] and the modification of Melchionna et al. [22] with thermostat and barostat relaxation  times  of  0.5  and  2.0  ps,  respectively. The equations of motion were solved by using the Verlet leapfrog algorithm with a time step of 1 fs [23,24]. The simulations were performed for a total time of 100 ps where the initial 30 ps was used to equilibrate the system.   A 3?3?3  replica  of  the  sH  hydrate  unit  cell  with 36.99  ?  36.99  ?  29.76  ?3  initial  dimensions  and periodic  boundary  conditions  is  used  as  the simulation  cell  for  the  hydrate  phase.  The  water oxygen  atom  positions  are  obtained  from  the crystallography  of  sH  hydrate  [25-27].  The hydrogen  atoms  were  distributed  at  the  oxygen sites subject to the constraints of the ice rules [28] via a Monte Carlo simulation. The sH unit cell has 34 water molecules arranged in one large 20-sided (51268)  cage,  two  ?medium?  sized  12-sided  cages (435663), and three small 12-sided cages (512) and can be represented by (S)3(M)2(L)1?34H2O, where S, M, and L represent the small, medium, and large cages,  respectively.    Methane  molecules  occupy both small and medium  sH cages, whereas larger   molecule  guest  substance  (LMGS)  molecules  are placed  in  the  large  hydrate  cages.  The  LMGSs studied  are  tert-butylmethylether  (TBME),  neo-hexane  (NH)  and  methyl-cyclohexane  (MCH). Guest molecules are initially placed at the center of the cages and equilibrated before collecting data.                                        Figure  1.  LMGS  employed  in  this  study:  TBME (top),  NH  (middle)  and  MCH  (bottom).  The charges  and  Lennard-Jones  parameters  for  the atoms are given in Table 1.  The van der Waals interactions among guest-guest and  guest-host  molecules  are  based  on  the Lennard-Jones  (12-6)  potential  with  a  cut-off distance  of  13  ?.  Long-range  electrostatic interactions  were  calculated  using  the  Ewald summation  method  [23,24]  with  a  precision  of 1?10-6.  Coulombic  interactions  between  point charges qi and qj located on the atomic nuclei i and j are used to model the electrostatic intermolecular interactions.  The  standard  combination  rules, 2)(jjepsilonepsilonepsilon = and sigmaij = (sigmaii+sigmajj) /2 are used to derive Lennard-Jones potential parameters between unlike atom-type force centers i and j from the values of the  parameters  between  similar  atom  types.  The intermolecular potential is given by,  summationsummation-= > braceexbracerightbtbraceexbracerightmidbracerighttpbraceexbraceleftbtbraceexbraceleftmidbracelefttp +bracketrightexbracketrightexbracketrightbtbracketrighttpbracketleftexbracketleftexbracketleftbtbracketlefttpparenrightexparenrightexparenrightbtparenrighttpparenleftexparenleftexparenleftbtparenlefttp-parenrightexparenrightexparenrightbtparenrighttpparenleftexparenleftexparenleftbtparenlefttp= 11 0644)(NiNi ijjijijijijij rqrinterV piepsilonsigmaepsilon   (1).  Atom (assignment)  Molecule  q (e)  iisigma  (?) a iiepsilon  (kJ/mol) a O  H  C1 (C3) H1-H3 (H1) O (OS) C2 (C3) C3-C5 (C3) H4-H12 (HC) C1 (C3) C2 (C3) C3-C4 (C3) C5-C6 (C3) C7 (C3) H1-H3 (HC) H4 (HC) H5-H6 (HC) H7-H8 (HC) H9-H10 (HC) H11-H12 (HC) H13-H14 (HC) C1-C3 (C3) C4 (C3) C5 (C3) C6 (C3) H1-H12 (HC) H13-H14 (HC) C b H b water water TBME TBME TBME TBME TBME TBME MCH MCH MCH MCH MCH MCH MCH MCH MCH MCH MCH MCH NH NH NH NH NH NH CH4 CH4 -0.8476 +0.4238 0.1027 0.0256 -0.5405 0.7721 -0.3474 0.0701 -0.3848 0.3597 -0.0520   0.0441 0.0265 0.0765 -0.0722 -0.0110 -0.0050 -0.0231 -0.0150 -0.0174 -0.3298 0.6173 0.0564 -0.1818 0.0475 -0.0362 -0.572 +0.143 3.166 0.000 3.3996 2.4714 3.0000 3.3996 3.3996 2.6496 3.3996 3.3996 3.3996 3.3996 3.3996 2.6495 2.6495 2.6495 2.6495 2.6495 2.6495 2.6495 3.3996 3.3996 3.3996 3.3996 2.6495 2.6495 3.3500 2.6100 0.6502 0.0000 0.4577 0.0657 0.7113 0.4577 0.4577 0.0657 0.4577 0.4577 0.4577 0.4577 0.4577 0.0657 0.0657 0.0657 0.0657 0.0657 0.0657 0.0657 0.4577 0.4577 0.4577 0.4577 0.0657 0.0657 0.4257 0.0718 a The intermolecular potential parameters between unlike atoms are determined from combination rules. b From the Murad and Gubbins potential [29].   Table 1. Atomic charges and Lennard-Jones interaction parameters used in MD simulations.    C1 C2 C3  C4 C5 O H1 H2 H3 H4 H5 H6 H9 H8 H7 H12 H11 H10 C1 C3 H1 H8 H2 H3 C2 C4 C5 C6 H5 H4 H6 H7 H9 H13 H13 H11 H10  H12 H1 H2 H3 C1  C2 C3  C4  C7 C5  C6 H5 H7  H9 H12 H14 H13 H4 H10 H11 H6 H8   Free  energy  calculations  were  performed  to determine  the  relative  stability  of  sH  hydrates  at several  methane  occupancies  and  pressures. Initially,  all  small  and  medium  cages  in  the simulation  cell  are  fully  occupied  by  methane molecules.  Subsequently,  in  each  stage  methane molecules  are  removed  or  annihilated  randomly from both cages to reduce the methane occupancy. The  number  of  methane  molecules  annihilated from the simulation cell, x are 14, 27, 41, 54, and 68 which correspond to 0.9, 0.8, 0.7, 0.6, and 0.5 methane occupancy of the small and medium cages in the simulation cell, respectively. Two additional simulations  were  conducted  with  methane molecules  removed  only  from  the  small  cages  or only  from  medium  cages.  This  is  to  determine whether  there  is  any  energetic  preference  for  the methane  molecule  to  occupy  a  particular  type  of cage. The methane removal from the hydrate phase at temperature T and pressure p is represented by,  hydrate [(n+x) CH4] arrowright hydrate [(n) CH4]    + x CH4 (fluid)         (2),                                     where n and x are integers representing the number of  methane  molecules  that  remain  in  the  hydrate and  the  number  of  methane  molecules  randomly removed from the hydrate, respectively. Chemical equilibrium is established between the two phases when  methanes  in  the  hydrate  and  fluid  phases have  the  same  chemical  potential.  The  total  free energy change for the methane elimination reaction in  Eq.  (2)  is  deltaGtotal  =  Gfluid  +  (Gn  ?  Gn+x),  where Gfluid  is  the  free  energy  of  methane  in  the  fluid phase  and  (Gn+x  ?  Gn)  is  the  free  energy  of  n methane molecules in the hydrate phase.   For methane in the fluid phase, the free energy is the sum of ideal gas and residual contribution,  ))lnpqpxkTGresidmethanefluid?rho+parenrightexparenrightexparenrightbtparenrighttpparenleftexparenleftexparenleftbtparenlefttp=                          (3),  where rho(T, p) is the methane gas density, qmethane is the partition function for methane internal degrees of  freedom  and  ?resid(fluid)  is  the  residual  (or excess)  chemical  potential  of  fluid  methane  at  T and  p.  The  residual  chemical  potential  is determined  from  direct  calculations  from  MD simulations by using the thermodynamic relation,  ( ) ( )] dpp igresid integral -1 ,     (4),  where  ( )  is  fluid  molar  volume  calculated from MD simulations and Vig = RT / p  is the ideal gas  molar  volume  at  the  same  pressure  and temperature.  The  free  energy  of  methane  in  the  hydrate  phase (Gn+x ? Gn) can be written as,  ECresidmethanenGpqpxkTGdelta+parenrightexparenrightexparenrightbtparenrighttpparenleftexparenleftexparenleftbtparenlefttp=+ ))ln?rho           (5),  where  rho(hydrate,T,p)  is  the  density  of  methane confined in the simulation cell and ?resid(hydrate) is the  residual  chemical  potential  for  a  methane molecule  from  the  hydrate  phase.  The ?resid(hydrate)  will  be  obtained  by  using  the method of thermodynamic integration as discussed in  later  section.  The  entropy  correction,  EC  is free energy associated with the possible ways for distributing n methane molecules among a total of n + x small and/or medium cages in the simulation cell,  ( )parenrightexparenrightexparenrightbtparenrighttpparenleftexparenleftexparenleftbtparenlefttp +=delta!!lnxxkTGEC              (6).  The  total  free  energy  change  for  the  methane annihilation  reaction  in  Eq.  (2),  is  the  difference between the free energies of methane in the fluid phase and methane in the hydrate phase,  ECresidGpppxkTGdelta+parenrightexparenrightexparenrightbtparenrighttpparenleftexparenleftexparenleftbtparenlefttp=))))ln??rhorho                (7).  The  methane  residual  chemical  potential  in  the hydrate  phase,  ?resid(hydrate,T,p)  is  calculated  by using thermodynamic integration [23] based on the Kirkwood  coupling  parameter  method  [30,31]. This  technique  has  been  used  in  previous  free energy  calculations  of  guest  substitution  and annihilation  in  hydrate  [32-34].  The  potential energy of the hydrate system can be written as [32],    )2121 lambdavdWelecnxn U+    (8),  where lambda1 couples the electrostatic interactions and lambda2 couples the van der Waals interactions of the x guests  in  the  cages  to  the  rest  of  the  hydrate [(n)CH4] system.   The annihilated methane molecules with lambda1 = lambda2 = 0 no  longer  interact  with  each  other  or  with  other remaining particles in the simulation, but remain in the  hydrate  simulation  cell  volume  as  ideal  gas molecules  at  the  density  of  the  hydrate.  The residual  clathrate  chemical  potential  is  calculated from, integralintegral==partialdiffpartialdiff+partialdiffpartialdiff=10110202221121)))lambdalambdalambdalambdalambdalambdalambdalambda?NpTNpTUdUdp   (9).  The  derivates  of  the  total potential U(lambda1,  lambda2)  with respect  to  the  lambdai  are  evaluated  numerically  with values of lambdai between 0 and 1 in small increments [33] and these functions are used in calculating the integrals of Eq. (11).   The  positions  and  orientations  of  the  large  guest molecule  (LMGS)  inside  the  large  sH  cages  are examined. The atomic trajectories from MD were recorded  at  every  0.2  ps  interval  for  1000 snapshots where each snapshot consists of 27 unit cells.  The  analysis  was  done  per  each  cage  per snapshot to find unusual guest-host interactions.    RESULTS AND DISCUSSION Preference of methane for occupying sH cages Free  energy  calculations  were  performed  to determine whether there is small or medium cage preference  for  methane  molecule  occupancy. Methane  molecules  from  the  hydrate  cages  were removed from the small cages, medium cages, or randomly from both small and medium cages. The different  contributions  to  the  free  energies  for removing 20% of the methane molecules from the clathrate are summarized in Table 2. The residual clathrate contribution to the free energy increases slightly if the methane is removed only from one particular type of cage. Moreover, there is a small entropic  penalty  when  removing  methane  only from  one  particular  cage.  The  total  free  energy calculation indicates that random methane removal from  both  small  and  medium  cages  is  preferred over removal from only one type of cage. Hence, methane  molecules  are  removed  randomly  from both  small  and  medium  cages  in  subsequent simulations.    thetaCH4  clathfluidkTrhorholn x?resid (fluid,T,p) -deltaG EC -x?resid (hdy,T,p) deltaG total Small  -8.2  -0.3  -4  +19  +7 Medium  -8.2  -0.3  -3  +18  +7 Random  -8.2  -0.3  -5  +16  +3  Table  2.  The  contributing  free  energies  per  unit cell of removing 20% of methane molecules at 274 K and 2 MPa. All values are in kJ/mol.  Methane occupancy dependence on LMGS  The  residual  free  energy  contribution  from  the hydrate  -x?resid(hydrate,T,p)  increases  linearly upon  removing  methane  from  the  small  and medium  cages  of  sH  hydrate  for  all  the  three LMGS  at 274 K and 2 MPa  as plotted in Fig. 2. The  hydrate  residual  free  energy  calculations  at higher  pressures  (6  and  10  MPa)  show  similar trends. The linearity shows that there are no strong collective interactions associated with the methane guests  in  small  and  medium  cages.  The  hydrate lattice  is  less  stable  when  the  small  and  medium cages are empty.   1.0 to 0.9 1.0 to 0.8 1.0 to 0.71.0 to 0.6 1.0 to 0.5MCHNHTBME817273441916253242916243443051015202530354045----????res (hydrate) / kJ/molMethane occupancy Figure 2. The residual hydrate free energy per unit cell at 2 MPa and 274 K.  Experimentally,  it  is  observed  that  the  methane occupancy  from  the  sH  hydrate  depends  on  the LMGS  [15].  The  solid  state-analysis  with  NMR   spectroscopy indicated that the small and medium cage  occupancies  increased  as  follows:  TBME (~77%)  <  NH  (~88%)  <  MCH  (~90%).  Similar cage  occupancy  values  were  also  reported  from single  crystal  diffraction  studies  [35].  If  the methane  occupancy  dependence  on  LMGS  were driven  by  thermodynamics,  the  hydrate  residual free  energy  values  obtained  from  the  simulation should  increase  following  the  same  trend  as  the measurements. However, as shown in Fig. 2, there is no noticeable difference in residual free energy among  all  LMGS  studied  within  the  simulation uncertainties.    This discrepancy may be related to the difference in  the  experimental  kinetics  of  methane incorporation during the hydrate formation for the different  LMGSs  [13].  The  simulations  are performed  under  equilibrium  conditions  whereas the  hydrates  were  not  synthesized  under  constant temperature  and  pressure  conditions.  This  can  be an  explanation  for  the  discrepancy  between  the experiments and the equilibrium MD simulations. The hydrate is not formed at equilibrium although it may be expected to be at equilibrium when it is collected  at  the  end  of  the  experiment  and  the measured small/medium methane occupancies may be  influenced  by  the  formation  kinetics.  The change in the kinetics profile for the TBME system may be attributed to the structures of aqueous and hydrate phase in the presence of LMGS as will be discussed in later section.   Methane occupancy dependence on pressure At  given  pressures  and  temperatures,  methane molecules  partition  between  the  gas  and  hydrate phases. The methane molecules removed from the hydrate lattice enter the gas phase as shown in Eq. (2).  The  averaged  residual  chemical  potential  for the  hydrate  and  the  total  free  energies  of  the system at pressures ranging from 2 MPa to 10 MPa are plotted in Fig. 3. The residual hydrate energy is independent  of  pressure  and  LMGS  but  the relationship  between  the  total  free  energy  and methane  occupancy  is  pressure  dependent  due  to the  fluid  contributions  to  the  total  free  energy, which  is  negative  at  low  pressures  but  become more positive at higher pressures. Hence, the total free  energy  is  fully  dependent  on  the  cage occupancy and pressure.   -55152535450.5Cage occupancydeltadeltadeltadeltaGTotal / kJ/mol Figure  3.  The  residual  hydrate  and  total  free energies per unit cell at 274 K and 2-10 MPa.   At  the  lowest  pressure  (2  MPa)  close  to  ambient pressure, the simulation predicts that the total free energy of the reaction shown in Eq. (2) is negative only when the hydrate cages go from full methane occupancy to ~90% methane occupancy. This is in good  agreement  with  the  experimental  cage occupancies for NH and MCH systems [15]. Thus, less than full methane occupancies in the hydrate cages are favored near ambient conditions, as also observed  in  natural  sI  hydrate  samples  [36-38]. Further  removal  of  methane  molecules  from  the hydrate to the gas phase leads to an increase in the total  free  energy  that  eventually  decreases  the hydrate  stability  and  ultimately  decomposes  the hydrate. At higher pressures, the total free energy of  methane  annihilation  increases  quickly,  which indicates that full cage occupancies are preferred at high  pressure.  This  observation  is  in  good qualitative  agreement  with  the  idea  of  the Langmuir  isotherms  for  gas  adsorption  which emphasize that higher pressure increases methane occupancy.  Hydrate cages structure with LMGS It  is  well-known  that  water  molecules  form  a hydration  shell  (cavity)  when  solvating  a  solute. The  aqueous  solution  structure  study  reveals  that there  is  a  strong  attraction  between  TBME  and water  molecules  that  lead  to  the  formation  of  a hydrogen  bond  between  oxygen-TBME  and hydrogen-water  [39].  Accordingly,  the  solvation cavity is distorted and the water molecules have a preferred orientation in comparison to the solution with hydrophobic solutes. A higher energy barrier may  be  required  to  break  the  hydrogen  bond between  TBME  and  water  in  order  to  form  the ( )res  10 MPa 6 MPa 2 MPa   hydrate  cage.  As  a  result,  the  rate  of  hydrate formation with TBME is the slowest when hydrate is grown from melted ice in a non-stirred system. On  the  other  hand,  the  undistorted  water  cavity surrounding  the  hydrophobic  solute  provides structural template required to form hydrate. Hence, the  hydrate  formation  proceeds  towards  complete conversion  when  the  temperature  ramping  is applied and no mass transfer resistance is present. However, it is unknown if the H-bond between the guest and host-water is present in the hydrate phase.  The guest-host interactions may also be associated with  hydrate  host-lattice  stability,  dielectric relaxation,  activation  energy  for  water  dynamics and  the  occupancy  of  the  cages.  Guests  such  as ether  or  ketone  molecules  may  be  able  to  inject Bjerrum defects into the hydrate lattice by forming hydrogen  bonds  with  cage  water  molecules  [40]. Consequently,  strong  interactions  between  the guest  and  host  water  molecules  may  cause  the hydrate  cage  to  rotate  faster  and  reduce  their motional  activation  energy.  However,  there  is  no direct evidence on defect formation on gas hydrate, especially for sH hydrate.   Careful  examinations  of  hydrate  lattice  structures obtained  from  MD  support  the  hypothesis  that  a defect formation is possible with TBME. No defect was  seen  when  NH  or  MCH  was  used  as  the LMGS.  However,  the  host-water  molecule  may change  its  orientation  towards  the  NH  guest, although it is very rarely seen and it occurs only at high  temperatures  (>250  K).  The  large  cage structure  for  the  TBME  system  with  and  without defect is shown in Fig. 4. The cage is illustrated in two  viewing  side:  the  top  and  the  front  side  at  a radial distance of ~8 ? from the cage center.   The  top  view  is  on  the  a-b  plane  looking  down along the c-axis. The front view is on the a-c plane looking  through  the  b-axis.  Upon  looking  down from  the  top,  the  large  cage  consists  of  two hexagonal rings. The ring at the center represents two  hexagonal  faces  on  the  poles  sides  (top  and bottom) and the other one on the outside represents six  hexagonal  faces  on  the  equatorial  plane.  The outside ring looks like a perfect 12-sided from the top-view  when  no  defect  is  seen.  However,  a distortion on the outside ring is seen as marked by the  yellow  dashed  ellipse  due  to  hydrogen  bond that  is  formed  between  ether-TBME  and  host-water molecule.  NO DEFECT DEFECTcaabcaab Figure 4. TBME molecule in the large cage of sH hydrate may or may not induce lattice defect.  The  front  view  provides  better  illustration  on  the hydrate cage structure. As seen on the lower part in Fig.  4,  each  hexagonal  faces  on  the  equatorial plane (six in total) is connected to a medium cage which  shares  the  square  face.  When  no  defect  is formed, all square faces are seen from all the six hexagonal faces. This square face is the boundary between  neighboring  medium  cages  that  are attached  to  the  same  large  cage.  However,  this square  face  is  altered  when  a  defect  forms.  A hydrogen bond is missing on the host-cage due to the  stronger  attraction  from  the  ether-TBME. Consequently,  two  medium  cages  appear  as  one larger cage. Hence, it is expected that the hydrate cage is less  stable  and  less  effective  in  enclosing the  methane  molecules.  This  is  evident  from  the hydrate  phase  diagram  [17,18]  and  methane content/cage occupancy measurements [15].   CONCLUSIONS Molecular  dynamics  simulations  are  employed  to understand  the  molecular-level  properties  of  sH methane  hydrate  with  the  large  guest  molecules (LMGS). The methane occupancy dependence on LMGS and pressure is investigated. The structure of  hydrate  cage  is  also  examined.  Energetically, the  hydrate  lattice  becomes  more  stable  when  all the  cages  are  fully  occupied.  However,  the negative free energy contribution from methane in the  gas  phase  at  low  pressures  near  equilibrium conditions  limits  the  methane  occupancy  in  the hydrate  cages  and  not  all  of  the  cages  are  fully   occupied  by  methane.  This  is  in  good  agreement with methane occupancies of nature and synthetic hydrate  samples.  Full  methane  occupancy  is favored  at  higher  pressures.  Contrary  to experiments, methane occupancy dependence with LMGS was not observed in this study. This may be due to kinetic effects during the synthesis that are not  taken  into  account  in  the  equilibrium  MD simulation. Finally, a defect formation on the large cage  is  observed  when  TBME  is  used  as  the LMGS.    The  defect  may  destabilize  the  hydrate lattice and limit the methane occupancies.   ACKNOWLEDGEMENTS The  financial  support  from  Natural  Sciences  and Engineering  Research  Council  of  Canada (NSERC)  is  greatly  appreciated.  Robin  Susilo gratefully  acknowledges  financial  support  from Canada Graduate Scholarship (CGS).   REFERENCES [1]  Susilo R, Alavi S, Lang S, Ripmeester JA, Englezos P. Molecular dynamics study of structure H clathrate hydrate containing methane and large guest molecules. J. Chem. Phys.; accepted for publication (March, 2008). [2] Davidson DW. Gas hydrates, In Water: a comprehensive treatise, edited by Frank F. Plenum Press, New York, 1973. [3] Koh CA, Sloan ED. Natural gas hydrates: Recent advances and challenges in energy and environmental applications. AIChE J. 2007; 53: 1636-1643. [4]  Lu H, Seo YT, Lee JW, Moudrakovski I, Ripmeester JA, Chapman NR, Coffin RB, Gardner G, Pohlman J. Complex gas hydrate from the Cascadia margin. Nature. 2007; 445: 303-306. [5]  Englezos P, Lee JD. 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