Cage occupancies in nitrogen clathrate hydrates from Monte Carlo simulations Vincent Ballenegger Institut UTINAM, Univ. Bourgogne-Franche-ComtÃľ, UMR CNRS 6213, 16, route de Gray, 25030 BesanÃğon Cedex, France E-mail: [email protected] Abstract Their exploitation could be combined with the sequestration of carbon dioxide, in the form of Comparisons of Gibbs ensemble Monte Carlo CO2 hydrate on the seafloor, to help keeping the simulations with experimental data for the cage concentration of this global warming gas under occupancies in N2 clathrate hydrates are per- control.2 Nitrogen molecules were found to act formed to assess the accuracy of such simu- as a promoter in the N2âĂŞassisted CH4 CO2 lations, to refine the effective potentials em- exchange reaction.3 Since flue gas mixtures con- ployed, and to help interpret recently measured tain a mixture of N2 and CO2, a deep under- large cage over small cage occupancy ratios standing of mixed N2 CO2 clathrates, and also [Petuya et al., J. Phys. Chem. C 122, 566 pure N2 and CO2 clathrates as reference sys- (2018)]. Different sets of interaction potentials tems, is important for this technology. Air for N2 N2,N2 H2O and H2O H2O interac- clathrates, containing N2,O2 and other trace tions are considered. Some of them fail to re- gases, are found on Earth below ice caps at a produce the known experimental fact that some depth of 1000 m or more. They are of particu- large cages are doubly occupied at 273 K and lar interest as they contains relics of our ancient high pressures. The best agreement between atmosphere up to 420 kyr back. N2 clathrates simulations and experiments is obtained when may also be present in comets and in some plan- using a new N O interaction potential derived ets or their satellites of our solar system.4,5 in this work by averaging an ab-initio potential There exist 3 clathrate structures at low pres- energy surface for the N2 H2O dimer. sures: two cubic ones (sI, sII) and a hexag- 1 onal one (sH). N2 clathrates crystallize in a Introduction cubic structure: the structure I is kinetically arXiv:1905.02453v1 [physics.chem-ph] 7 May 2019 favoured, while the sII is the thermodynami- cally stable structure if the pressure is not too A gas clathrate hydrate is a form of crystalline high (a transition to sH is observed at the high ice where the water molecules form a solid net- pressure 0.85 GPa).6–8 The unit cell of the sI work with small and large cavities that encap- crystal contains 46 water molecules forming 8 sulate guests.1 This molecular structure is sta- cages: 2 small and 6 large ones. The unit cell ble at high pressure and/or low temperature. of sII contains 136 water molecules forming 24 Methane (clathrate) hydrates have been found cages: 16 small cages and 8 large cages (these in natural gas pipelines, deep sea sediment and large cages are slightly bigger than in sI). Struc- permafrost regions. They are considered to be ture II is promoted by the ability of the small an enormous possible future energy resource.1 1 17,21 molecule N2 to fill in the numerous small cages using molecular dynamics (MD). van Klav- of this structure. eren et al. have shown also that a N2 hy- The cage occupancies θS and θL of small (S), drate with sII at high pressure remains mechan- respectively large (L), cages in a clathrate is an ically stable even for the case of a full double important quantity for practical applications: occupancy of the large cages.19 In those MD they determine the gas storage capacity (see simulations, the number of guest N2 molecules e.g. Ref.9 for hydrogen storage) and intervene is fixed beforehand and no attempt was made also in the calculation of phase equilibria in- to quantify the thermodynamical stability of volving clathrates.1,10 Occupancies in a nitro- a phase with full or partial double occupa- gen clathrate have been measured, at 273 K and tion. The Monte Carlo (MC) method over- pressures up to 1000 bar using powder neutron comes this difficulty because MC moves with in- diffraction and Rietveld refinement by Chazal- sertion/deletion of guest molecules allow the av- lon and Kuhs11 for both sI and sII. They discov- erage cage occupancy of the simulated clathrate ered that some large cages in sII can be doubly to converge automatically towards its value occupied at pressures above ≈ 300 bar. An ad- at thermodynamical equilibrium. A grand- ditional measurement at 1093 bar and 268:2 K canonical Monte Carlo (GCMC) calculation of in a sI nitrogen clathrate was performed by Qin cage filling in a N2 clathrate has been performed and Kuhs;12 it also shows some double occu- by Klapproth et al.,18 who found an unsatis- pancy of the large cages: θL = 111:9 ± 0:8% factory agreement: simulations strongly over- while θS = 98%. Yet another measurement in a estimated the occupancy when using the sim- sII clathrate at 150 bar and at a lower temper- ple point charge (SPC) water model.1 Patt et ature 258:15 K gave: θL = 121:8 ± 0:6% and al. performed GCMC simulations of N2, CO 13 θS = 96:7 ± 0:3%. Occupancy ratios θL/θS and mixed N2 CO clathrates but only at low have moreover been measured at pressures up temperatures (50, 100 and 150 K) and they did to 200 bar and for temperatures down to 150 K not compare quantitatively with experimental by Petuya et al.6 The latter authors used an- data.22 Their calculations suggest that experi- other technique, Raman spectroscopy, which ments performed on the single-guest N2 and CO does not provide separately the occupancies of clathrates might be sufficient to get information large and small cages, but only their ratio. on the corresponding mixed clathrates. The purpose of the present paper is to per- In the present work, the Gibbs ensemble form Monte Carlo simulations to determine the Monte Carlo (GEMC) technique is employed occupancy of cages in N2 clathrates at thermo- because of its convenience: the experimental dynamical equilibrium for the same conditions pressure and temperature are direct input pa- as in the previous experiments. This will en- rameters for the simulation and the volume of able us to assess the agreement between simu- the simulated clathrate adjusts itself automati- lations and experiments for a wide range of con- cally to the imposed pressure. This can be con- ditions covering both single and multiple occu- trasted with grand-canonical MC simulations pancy regimes for the cages, and to help inter- where the volume is fixed (and must hence be pret the recently measured occupancy ratios6 in adjusted manually when varying the pressure) terms of separate occupancies θL and θS. No- and where the pressure of the gas is not con- tice that similar comparisons but for the sim- trolled directly but must be deduced from its pler methane clathrate, which forms in struc- fugacity by using an appropriate equation of ture I and which does not show any multiple state. occupancy of cages, have been done by several 1This overestimation was probably due in part to 14–16 authors. their assumption of a rigid water framework. Only few simulations results for a N2 clathrate can be found in the literature.17–22 Horikawa et al., and later van Klaveren et al., have studied the dynamical behavior of encaged N2 molecules 2 Computational details sociated with each N atom. Its parameters (see Table 1) are very close to the model X1 Isobaric-isothermal Gibbs ensemble Monte of Murthy et al.29 that was used in the sim- Carlo simulations were performed with the ulation study by Klapproth:18 the geometric open-source MCCCS Towhee simulation pro- and LJ parameters are almost identical, but gram23 (version 7.2.0) to compute the cage oc- the latter model differs by the fact that it fea- cupancies θS and θL for pressures and tempera- tures no point charge but a point quadrupole tures where experimental data points are avail- of strength −3:91 × 10−40 C m2 located on the able. In this ensemble two simulation boxes are center of mass (that strength is considered to held at the same constant pressure P and tem- be an adjustable parameter in the X1 model perature T , while the total number of water and and results from a best fit to a wide range of nitrogen molecules across both boxes, is also properties). The Etters model involves 6 in- constant. One box represents the N2 clathrate teraction sites: a repulsion-dispersion interac- crystal and the other the nitrogen gas phase. tion site on each N atom and 4 Coulomb inter- Some additional GCMC simulations were per- action sites along the axis of the molecule at formed with the open-source DL_MONTE-2 the positions ±0:847 and ±1:044 Å, i.e. further simulation code;24 their results were consistent away than the N atoms which are at positions with those of Towhee. ±0:547 Å. Similarly to van Klaveren et al., we have modified slightly the electrostatic descrip- Molecular models tion to reduce the number of interaction sites to 3 and to match the experimentally observed A classical description of the interaction poten- quadrupole moment [−4:7 × 10−40 C m2]. The tials between water and guest molecules has repulsion-dispersion interaction potential in the been used. Short-range and dispersion in- Etters model was obtained from a refitting of ab teractions were computed as a sum of pair- initio calculations to better match experimen- wise Lennard-Jones (LJ) or Buckingham (also tal data for the second virial coefficient and for known as Exp-6) interactions between interac- condensed phases of N2.