6th International Conference on Gas Hydrates

NEUTRON SCATTERING MEASUREMENTS OF THE HYDROGEN DYNAMICS IN CLATHRATES HYDRATES. Ulivi, Lorenzo; Celli, Milva; Giannasi, Alessandra; Zoppi, Marco; Ramirez-Cuesta, A.J. 2008-07-01

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   NEUTRON SCATTERING MEASUREMENTS OF THE HYDROGEN DYNAMICS IN CLATHRATES HYDRATES   Lorenzo Ulivi,**** Milva Celli, Alessandra Giannasi, Marco Zoppi Istituto dei Sistemi Complessi, CNR Via Madonna del Piano 10, 50019, Sesto Fiorentino ITALY  A. J. Ramirez-Cuesta Rutherford Appleton Laboratory, ISIS Facility Chilton, Didcot, Oxon, OX11 0QX, U.K    ABSTRACT The hydrogen molecule dynamics in tetrahydrofuran-H2-H2O clathrate hydrate has been studied by high-resolution inelastic neutron scattering and Raman light scattering. Several intense bands in the neutron spectrum are observed that are due to H2 molecule excitations. These are rotational transitions,  center-of-mass  translational  transitions  (rattling)  of  either  para-  or  ortho-H2,  and combinations  of  rotations  and  center-of-mass  transitions.  The  rattling  of  the  H2  molecule  is  a paradigmatic example of the motion of a quantum particle in a non-harmonic three-dimensional potential well. Both the H2 rotational transition and the fundamental of the rattling transition split into triplets. Raman spectra show a similar splitting of the S0(0) rotational transition, due to a significant anisotropy of the potential with respect to the orientation of the molecule in the cage. The comparison of our experimental values for the transition frequencies to a recent quantum mechanical calculation gives qualitative agreement, but shows some significant difference.  Keywords: gas hydrates, hydrogen clathrates, neutron scattering, Raman spectroscopy.                                                         * Corresponding author: E-mail: lorenzo.ulivi@isc.cnr.it NOMENCLATURE E, energy [meV] J, rotational quantum number of H2 molecule 2Hm , H2 molecular mass [kg] HDm  HD molecular mass [kg] p-H2, para-hydrogen o-H2, ortho-hydrogen sII, cubic structure II of clathrate-hydrates ( , )CMself Q w   Self  dynamic  structure  factor  of  the center of mass T, Temperature [K] or [?C] THF, tetrahydrofuran (C4H8O) TDF, deuterated tetrahydrofuran (C4D8O)   INTRODUCTION The  search  for  efficient  hydrogen-storage materials  has  led  to  an  increased  interest  in hydrogen  clathrate-hydrates  [1].  Hydrogen molecule has long been thought to be too small to stabilize  any  of  the  clathrate  structures  [2],  until 1999,  when  it  was  demonstrated  that, using high pressure,  a  simple  H2  clathrate  could  be  formed [3].  This  compound  require  about  2000  bar  of pressure to be produced at T ? 273 K [1],[4], but the synthesis pressure can be significantly lowered by adding tetrahydrofuran (THF), to form a THF-H2-H2O  binary  clathrate  [5],[6],  still  capable  of storing  appreciable  amount  of  molecular hydrogen.  Understanding  the  forces  between  the H2  molecule and the host material is a key issue Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008.  for  a  rational  design  of  clathrates  as  hydrogen storage  materials.  We  have  been  engaged  in  this task using spectroscopic techniques, like inelastic neutron  scattering  (INS)  and  Raman  light scattering  experiments,  performing  experiments aiming  to  shed  some  light  on  the  microscopic dynamics of the molecule trapped in the cage [7]. In this paper we present results, obtained with both techniques,  on  binary  THF-hydrogen-water clathrates. The crystal structure of this compound is  cubic  (sII),  with  136  H2O  molecules,  sixteen (small)  dodecahedral  cages  and  eight  (large) hexakaidecahedral cages in the unit cell [1],[5],[8]. The THF and H2 molecules are hosted in the large and  small  cages,  respectively.  Recent  reports indicate  that  only  one  H2  molecule  is  hosted  in each of the small cages [9],[10],[11].   SAMPLE PREPARATION We  prepared  the  samples  for  this  study  at  ISC-CNR  using  D2O  and  completely  deuterated tetrahydrofuran  (TDF)  in  stoichiometric proportion (17:1 mol), either starting from a liquid D2O-TDF mixture, and freezing it in the presence of H2 gas at various pressures and T ? +2 ?C, or adding the H2 gas, at about 800-1000 bar and T ? -10  ?C,  to  the  pre-formed  D2O-TDF  clathrate, ground  as  a  fine  powder.  This  second  procedure led to a higher H2 content in the sample. Raman spectra can assess the quality of samples, both for what concern H2 content and presence of different phases, as, for example, ice. Spectra are shown in Fig. 1.  The  hydrogen  content  increases  if  the synthesis pressure is increased, and if the sample is prepared  from  the  solid  (THF-D2O  clathrate) instead  of  the  liquid.  Raman  spectroscopy  could allow  also  a  quantitative  measurement  of  the  H2 content of clathrates, by calibrating the intensity of the rotational S0(0) and S0(1) H2 lines against the lattice  band  located  around  200-300  cm-1.  By comparing  these  Raman  intensity  data  with  gas release  measurements  from  the  same  sample  we were  able  to  obtain  quantitatively  consistent results.    NEUTRON SCATTERING RESULTS Inelastic  Neutron  Scattering  (INS)  measurements were  performed  on  the  TOSCA  spectrometer  at ISIS,  the  pulsed  neutron  source  at  Rutherford Appleton  Laboratory,  U.K..  Incoherent  INS  is  a powerful technique for studying the self dynamics of  hydrogen  in  materials.  By  this  technique,  we take  advantage  of  the  large  incoherent  scattering cross-section  of  the  proton,  which  is  almost  two orders of magnitude greater than the average value of  the  other  nuclei.  In  the  energy  range  of  our interest  (?3.5  ?  E/meV  ?  ?120)  the  TOSCA spectrometer is characterized by a resolving power DE/E ? ?1.8%, that is not much different from an optical  Raman  spectrometer.  Four  different samples  were  measured  in  this  experiment.  One consisted of a simple D2O-TDF clathrate with no hydrogen.  Its  spectrum  is  considered  as  a background  in  the  analysis.  Two  other  samples 200 300 400 500 600 700 800 900Raman intensity (arb. units)Frequency shift (cm-1)D2O + TDF + H2liquid 50 barT = 20 KD2O + TDF + H2liquid 1000 barT = 20 KD2O + TDF + H2solid 1000 barT = 20 KFigure 1 Raman spectra of hydrogen clathrates obtained with different procedures, i.e. starting from  the  solid  or  the  liquid,  with  H2  gas  at different  pressures.  The  two  (broad  and structured) lines at about 354.4 and 587.0 cm-1correspond  to  the  rotational  S0(0)  and  S0(1) transitions of the H2 molecule, while the band between 200-300 cm-1 is due to lattice modes of the clathrate structure. The lines between 730-930 are due to the THF molecules enclosed in the large cages of the structure. In the figure the different  spectra  are  labeled  according  to  the preparation  procedure,  while  T  refers  to  the temperature  at  which  the  Raman  spectra  have been collected. contained H2 at different ortho-para concentrations (in the following referred to as o-rich sample and p-rich  sample)  and  one  sample  contained  HD. Once  the  clathrate  is  formed,  the  ortho-para conversion  rate  is  very  low.  For  the  samples prepared  starting  from  the  solid,  gas-release thermodynamic  measurements  gave  results consistent  with  the  hypothesis  of  single  H2 occupancy  of  the  totality  of  the  small  cages. Conversely, using the other preparation technique (i.e. adding H2 gas to the freezing liquid mixture) the  H2  content  of  the  clathrates  turned  out  much lower.  Raman  measurements  performed  at  ISC-CNR,  before  and  after  the  neutron  experiment, provided the determination of the ortho-para ratio in  the  two  D2O-TDF-H2  clathrates.  The  o-H2 content resulted 53 % and 48 % for the o-rich and p-rich  sample,  respectively.  All  neutron measurement were performed at T=20 K. Details  of  the  experiment  and  data  analysis  are presented  in  Ref. [7].  In  summary,  from  each  of the  H2-clathrate  spectra,  the  weak  background spectrum  of  the  simple  TDF-D2O  clathrate  has been subtracted, to extract the bands related to the dynamics  of  the  single  H2  molecule  in  the dodecahedral clathrate cage. The two spectra, we have  measured  with  the  ortho-rich  and  para-rich samples, are significantly different. By a weighted difference, it was possible to extract the spectra for pure  o-H2  and  pure  p-H2.  These  are  shown  in Fig. 2. The resulting spectra are now substantially different, since the neutron scattering cross section is different for o-H2 and p-H2, and depends on the rotational transitions [12]. Neglecting the coherent part  of  the  scattering,  on  account  of  the overwhelming incoherent scattering length for the proton, the analysis is quite simple. The expected spectrum results from the superposition of several replicas  of  the  center  of  mass  (CM)  dynamical structure  factor  ( , )CMselfS Q w ,  one  for  each (significant) rotational transition of the molecule, shifted  by  the  rotational  transition  energy  of  the molecule.  In  other  words,  each  rotational transition,  that  is  present  in  the  spectrum,  is followed  by  its  combinations  with  all  possible center-of-mass  excitations.  On  the  other  hand, ( , )CMself Q w   itself  should  consist  of  a  spectrum  of lines, since it pertains to a localized motion of a quantum  particle  in  a  (non-harmonic)  potential well (rattling). Since INS is not subject to selection rules,  all  transitions  to  molecular  rotational  and CM vibrational (rattling) states are allowed, even though those rotational transitions for which only the  coherent  cross  section  for  the  proton contributes are very weak, and are not observed. In details, at the low temperature of the experiment, only the lowest rotational states (i.e. J = 0 for p-H2 and HD, and J = 1 for o-H2) are populated. For o-H2,  the  only  rotational  transitions  contributing significantly  to  the  spectrum  in  the  observed frequency  region  are  the  elastic  J  =  1  ?1  and inelastic J = 1 ? 2 transitions. For p-H2 only the inelastic  transition  J  =  0  ?  1  gives  a  non-negligible  contribution,  (the  elastic  J  =  0  ?  0 transition, weighted by the coherent cross section, turns  out  very  weak,  and  is  not  observed).  With reference  to  Fig 2,  in  the  p-H2  spectrum,  we observe  the  intense  band  due  to  the  rotational transition J = 0 ? 1 at 14.5 meV. In addition, the combination  of  the  rotation  with  the  rattling fundamental  and  with  the  first  overtone  of  the rattling motion give rise to the two bands located respectively at about 25 and 36 meV. In the o-H2 spectrum, the elastic J = 1 ? 1 is outside the range of the instruments; the structured band at about 10 meV  represents  the  main  contribution  and originate from the combination of the elastic J=1 0 10 20 30 40 50 60 rotation J = 1 ? 2+ rattling fundamentalrotation J = 0 ? 1+ rattling 1st overtonerotation J = 0 ? 1+ rattling fundamentalrotationJ = 1 ? 2rattling1st overtonerotationJ = 0 ? 1rattlingfundamental o-H2p-H2 Neutron Energy Loss / meV S(Q,w) / arb. units Figure 2. The INS spectra of the o-H2 and p-H2molecule  excitations,  obtained  by  difference from the measured spectra of the ortho-rich and para-rich samples. The main bands are indicated in the figure, and discussed in the text.  ?  1  rotational  transition  with  the  fundamental rattling transition of the o-H2 molecule. The band at about 22 meV is the first overtone of the rattling excitation. In addition, the pure rotation line J = 1 ?  2  is  present  at  about  29  meV,  as  well  as  its combination  with  the  rattling  fundamental.  The spectrum  of  HD  (see  Fig. 3),  on  the  other  hand, shows  both  the  fundamental  rattling  and  the rotational band, since for this molecule the neutron scattering cross sections for the J = 0 ? 1 and J = 0  ?  0  transitions  are  of  the  same  order  of magnitude,  being  proportional  to  the  incoherent proton cross section [12]. It is interesting to discuss the fine structure of the rotational  band  of  p-H2  at  about  14  meV,  of  the rattling band of o-H2 at about 10 meV and of both bands  of  HD,  which  are  shown  in  Fig. 3.  Both bands  are  split  into  three  components.  The splitting of the fundamental of the rattling mode is due to the anisotropy of the potential energy with respect  to  the  direction  of  the  CM  displacement from the center of the cage. The cage shape, as it results from the structural measurements [8], [13], is  indeed  quite  anisotropic,  with  the  20  oxygen atoms located at three different distances from the center. On the other hand, the splitting of the J = 0 ?  1  rotational  transition  into  a  triplet  is  a consequence  of  the  anisotropy  of  the  potential energy  with  respect  to  the  orientation  of  the  H2 molecule.  We  have  fitted  each  band  with  three Voigt  functions  (with  a  Gaussian  width  fixed  by the  instrumental  resolution),  obtaining  values  for the  energy  reported  in  [7].  It  is  interesting  to discuss  the  difference  due  to  the  different  mass and moment of inertia of H2 and HD. The ratio of the  average  HD  rotational  energy  (11.54  meV) with the same quantity for H2 (14.41 meV) is 0.80, to  be  compared  with  an  expected  value  of 3/4=0.75, for free rotors. An anisotropic potential can  indeed  influence  the  average  value  of  the rotational energy, in addition to the removal of the degeneracy. Considering the rattling frequency, we notice  that,  changing  from  H2 to HD, the energy scales  neither  with  the  square  root  of  the  mass ratio  2 2 3 0.816H HD = =  (as we would expect for  an  harmonic  motion)  nor with the mass ratio 22 3 0.667H HD = =  (which is the value expected for a square well potential). Thus the potential well for  the  H2  molecule  in  the  cage  appears  as intermediate between these two limiting cases, i. e. more flat than a parabola in the center of the cage evolving  towards  hard  repulsion  walls increasing the distance from the center. A recent calculation of  some  of  the  lower  energy  levels  of  one  H2 molecule  in  the  dodecahedral  clathrate  cage  [14] predicted  a  splitting  into  a  triplet  of  both  the rattling fundamental and the rotational transition, as  we  have  experimentally  observed.  The calculated energy levels for both o-H2 and p-H2 are represented  in  Fig.  3  with  violet  vertical  arrows. For  the  rattling  transition  (o-H2)  the  calculated splitting  (3.52  meV  maximum  separation) reproduces  quantitatively  the  experimental  one, i.e. 3.73 meV, but, on the average, the calculated energy underestimates the experimental one. In the case  of  the  rotational  transition  (p-H2),  the calculation  strongly  overestimates  the  splitting (7.51 vs. 1.50 meV). Therefore, the pair potential model used in [14] seems to largely overestimate the  actual  anisotropic  forces  on  the  hydrogen molecule.   p-H2  S(Q,w) / arb. units  o-H2 neutron energy loss / meV   6 8 10 12 14 16 18 20   HDFigure 3. Detail of the spectra of p-H2, o-H2 and HD. The fine structure of the rotational band (p-H2 and HD) and of the rattling band (o-H2 and HD) is evident. Each band is fitted with three Voigt  functions.  The  blue  vertical  lines  mark the energy of the transitions calculated in Ref. [14]  RAMAN LINE SHAPE We  present  in  Fig. 4  the  shape  of  the  H2  S0(0) Raman  rotational  line  measured  in  D2O-TDF-H2 clathrate. Analogously to the splitting observed for the J = 0 ? 1 line of p-H2 in the neutron spectrum, the  S0(0)  line  presents  a  structure  that  can  be attributed  to  the  presence  of,  at  least,  three components. The width of this line (? 16 cm-1) is of the same order of magnitude to that observed in the  neutron  spectrum  (?  18  cm-1).  This  indicates that the influence of the anisotropic potential (with respect  to  the  orientation  of  the  H2  molecule)  is similar  for  the  J  =  1  as  for  the  J  =  2  state.  The Raman line is compared to that measured in solid H2.  From  this  comparison  we  observe  that  the perturbation to the free rotation of the H2 molecule in  the  clathrate  cage  is  slightly  stronger  than  in solid H2, but still is a small perturbation (compare the  width,  ?  18  cm-1,  with  the  energy  of  the rotational state, 354 cm-1). In addition, we observe that the average frequency of both rotational lines is  smaller  in  clathrates  than  for  the  isolated molecule. This may be ascribed to the presence of attractive interactions between H atoms and H2O molecules  of  the  cage,  which  tends  to  increase slightly  the  internuclear  H2  distance,  and consequently to decrease the rotational frequency. The  increase  in  the  interatomic  distance  is however very small, and it can be estimated to be about  0.6  %.  A  comparison  with  a  theoretical computation is possible also in this case. In Fig. 4 we have reported the J = 2 rotational energies of the H2 molecules calculated in Ref. [15]. Similarly as  the  J  =  1  case  (see  Fig. 3),  the  calculation overestimate  the  splitting  of  the  rotational sublevels,  probably  as  a  consequence  of  an overestimation of the anisotropy of the interaction potential.   CONCLUSIONS Our  INS  spectra  disclose  most  aspects  of  the quantum dynamics of a single H2 molecule in the confined geometry of a water clathrate nanocavity. The fundamental transition for the rattling motion has  an  average  energy  of  9.86  meV,  and  is  split into a triplet with a separation of about 3.7 meV. The rotational transition that would appear at 14.7 meV  for  an  isolated  molecule,  is  slightly downshifted  at  14.4  meV,  and  is  also  split  into three  components  separated  by  1.5  meV. Comparison  of  both  the  neutron  and  the  Raman data  with  recent  theoretical  values  [14]  [15] indicates  that,  while  the  assumed  isotropic potential  and  the  assumed  CM  anisotropy reproduce satisfactorily the experimental data, the anisotropy with respect to the orientation of the H2 molecule  is  overestimated  in  the  model.  The splitting of the rotational and translational bands is a  consequence  of  the  anisotropy  of  the environment  that  should  be  modeled  with  an accuracy greater than that attained until now, if a direct information on the basic interaction between H2 and H2O molecules is to be obtained. Besides the  transition  energies, it would be interesting to calculate also the intensities of the neutron spectral bands.  This  can  be  done  by  the  knowledge  not only  of  the  eigenvalues,  but  also  of  the eigenvectors, for the H2 CM motion. Some results in this direction have been obtained [7].   ACKNOLEDGEMENTS The Cooperation Agreement No.01/9001 between CNR  and  CCLRC,  the  Grant  from  Firenze-Hydrolab  by  the  Ente  Cassa  di  Risparmio  di Firenze are gratefully acknowledged.   320 330 340 350 360 370 380 390 TDF-D2O clathrate solid n-H2 solid p-H2 H2 gas Xu et al. (2007)S0(0) H2Raman intensity (arb. units)Frequency shift (cm-1)Figure 4. S0(0) Raman line of the H2 molecule measured on a sample of THF-D2O-H2 clathrate (black  line  with  solid  dots)  compared  to  that measured  in  solid  n-H2  (red solid line) and in  p-H2  (green  solid  line)  [16].  The  dark  green arrow  represents  the  isolated  molecule transition  frequency  [17],  while  the  violet vertical  arrows  are  the  results  of  a  quantum-mechanical calculation [15]. REFERENCES [1] Mao WL, Mao HK, Goncharov AF, Struzhkin VV, Guo Q, Hu J, Shu J, Hemley RJ, Somayazulu M,  Zhao  Y.  Hydrogen  clusters  in  clathrate hydrate. Science 2002, 297: 2247-2249.  [2] Sloan ED and Koh CA. Clathrate Hydrates of Natural  gases.  3rd  ed.,  New  York:  Taylor  and Francis, 2008.  [3]  Dyadin  YA,  Larionov  EG,  Manakov  AY, Zhurko FV, Aladko EY, Mikina TV and Komarov VY.  Clathrate  hydrates  of  hydrogen  and  neon. Mendeleev Commun. 1999, 9: 209-210. [4]  Lokshin  KA  and  Zhao  Y.  Fast  synthesis method and phase diagram of hydrogen clathrate hydrate. 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