Dynamics of hydrogen guests in ice XVII nanopores
Leonardo del Rosso, Milva Celli, Daniele Colognesi, Svemir Rudic, Niall J. English, Christian J. Burnham, Lorenzo Ulivi
DDynamics of hydrogen guests in ice XVII nanopores
Leonardo del Rosso, Milva Celli, ∗ Daniele Colognesi, ∗ SvemirRudi´c, Niall J. English, Christian J. Burnham, and Lorenzo Ulivi † ISC–CNR, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy ISIS Facility, STFC Rutherford Appleton Laboratory,Chilton, Oxfordshire OX11 0QX, United Kingdom School of Chemical and Bioprocess Engineering,University College Dublin, Belfield, Dublin 4, Ireland (Dated: September 26, 2018)The present high-resolution inelastic neutron scattering experiment on ice XVII, containing molec-ular hydrogen with different ortho/para ratio, allows to assign the H motion spectral bands torotational and center-of-mass translational transitions of either para - or ortho -H . Due to its struc-ture, ice XVII confines H molecules to move in spiral channels of molecular size. Reported datademonstrate that H molecules rotate almost freely in these nanometric channels, though showinglarger perturbation than in clathrate hydrates, and perform a translational motion exhibiting twolow frequency excitations. The agreement between experimental spectra and corresponding molec-ular dynamics results clearly enables to portray a picture of the confined motions of a hydrophobicguest within a metastable ice framework, i.e. ice XVII. PACS numbers: 78.70.Nx, 82.75.-z, 63.20.Pw
Ice XVII is a newly discovered form of solid water ob-tained from the so-called C -phase of the H -H O binarycompound, quenched at a temperature T = 77 K andambient pressure, after letting the hydrogen moleculesdiffuse out of the crystal . It is a pure water crys-tal, metastable at ambient pressure if maintained below130 K. Its crystal structure is intrinsically porous andpresents accessible channels where hydrogen moleculeshave been located during the production and where othermolecules (belonging to hydrogen or another gas) canbe absorbed again, confined in an essentially one dimen-sional geometry . The diameter of these channels, mea-sured from the center of the oxygen atoms, is about 6.10˚A. This exotic and low-density water crystal adds to thelist of solid structures of water possibly stable at negativepressure .The study of the dynamics of hydrogen moleculesin nano-confinement, that is intrinsically quantum-mechanical, is of great importance from both a practicaland fundamental point of view. In hydrogen clathratehydrates, which possess a similar chemical composition,although a different structure and stoichiometry, the hy-drogen molecules confined in nearly spherical cages per-form an almost free rotation and a deeply non-harmoniccenter-of-mass (CoM) vibrational motion (rattling), bothof which have been experimentally investigated by inelas-tic neutron scattering and Raman scattering . Inthis paper we discuss the results of a combined experi-mental and simulation study on the dynamics of the H guests in D O ice XVII and of the D O host lattice.Samples for the present Inelastic Neutron Scattering(INS) experiment were produced at ISC–CNR using D Oand H , as described in Ref. 1. This isotopic composi-tion is chosen in order to exploit the intrinsic advantageof the large incoherent neutron scattering cross-sectionof the proton (compared to both D and O), thus allow- ing for a relatively simple access to the self dynamicsof molecular hydrogen. Measurements have been per-formed at T = 15 K on TOSCA, a high energy res-olution (∆ E ) spectrometer at ISIS (UK) characterizedby 1 . (cid:46) ∆ E/E i (cid:46) . E i being the incom-ing neutron energy. Raw time-of-flight data have beentransformed into energy-transfer spectra, taking into ac-count both the correction for the kinematic factor andthe normalization for the incoming neutron flux.We have measured the spectra for three different gas-charged samples and one reference sample of pure deuter-ated ice XVII. Initially, we probed the material as pre-pared, i.e. the metastable H -D O compound in the C phase, quenched at low temperature and ambient pres-sure. This material, as for structure and composition,does not differ much from ice XVII when refilled withH , apart for small possible nitrogen impurities whichdo not give visible signal in this experiment. After athermal treatment at about 120 K that removes all theguests molecules (described in Ref. 1), we have recordeda spectrum of pure deuterated ice XVII at T = 15K. Subsequently, we have measured two spectra of iceXVII loaded, respectively, with normal ( n -H ) and para -enriched hydrogen ( p -rich H ). Due to the limited work-ing pressure of our aluminum sample cell, a quite lowtemperature (i.e. T = 20 K) has been chosen for the gasloading processes. According to previous work , thisproduces ice XVII with a H /D O molar ratio of about25%, that is, half filling of the H crystallographic sites.Measured spectra, before any analysis, are shown inFig. 1 on a logarithmic horizontal axis. Many featuresdue to translational and librational excitations of the lat-tice are already recognizable in the spectrum of emptyice XVII (blue line). The other two spectra from thehydrogen-charged samples (black n -H , red p -rich H ),present, in addition, several narrow and intense bands a r X i v : . [ c ond - m a t . o t h e r] N ov due to the molecular hydrogen dynamics. The two mainH -molecule rotational features are readily identified inthe spectrum and assigned, namely the strong J = 0 → para -hydrogen ( p -H ), i.e. a triplet at (cid:39)
14 meV, and the J = 1 → ortho -hydrogen ( o -H ) around 29 meV.For the identification of the CoM excitations a sub-traction procedure is applied, similar to that describedin Ref. 5. First, the hydrogen contribution was obtainedsubtracting the weak reference spectrum (i.e. that ofempty ice XVII plus aluminum cell, adjusted by consid-ering self-shielding attenuation). The resulting H spec-trum can be modeled considering the neutron scatteringcross section for the two hydrogen-molecule spin isomers,and its dependence on the rotational transitions . Afterneglecting the coherent part of the neutron scattering,the double differential scattering cross-section becomesproportional to the self part of the dynamical structurefactor for the CoM motion, S self ( Q, ω ), and can be writ- E (meV) J = 1 → o -H ) J = 0 → p -H ) I n t en s i t y ( a r b . un i t s ) FIG. 1. (Color online) Bottom panel: INS spectrum ofdeuterated ice XVII. Top panel: the two upper traces are thespectra of ice XVII refilled with normal (black line) and para-enriched (red line) hydrogen. Blue line represents the samespectrum as in the bottom panel replotted here for an easiercomparison. All spectra have been recorded at T = 15 K.The logarithmic horizontal scale implies that the width of thebands in different spectral regions are not readily comparableby eye. ten as : d σd Ω dω = k f k i S self ( Q, ω ) ⊗ (cid:88) JJ (cid:48) δ ( ω − ω JJ (cid:48) ) ν ( J, J (cid:48) , Q ) , (1)where k i and k f stand for the initial and final neutronwavevectors, respectively, ω is simply (cid:126) − E , and thesymbol ⊗ represents a convolution product. This ex-pression holds whenever the hypothesis of decouplingbetween rotational and CoM motions is satisfied. TheDirac delta functions reported in the previous equationare centered at the rotational transition energies, (cid:126) ω JJ (cid:48) ,while ν ( J, J (cid:48) , Q ) (called molecular form factor) dependson both the momentum transfer Q and the rotationaltransition J → J (cid:48) undergone by molecule. Therefore theexpected neutron spectrum is made of a comb of CoMexcitations, replicated and shifted by the energy of anypossible rotational excitation of the single molecule. Themolecular form factors ν ( J, J (cid:48) , Q ) can be easily calculatedassuming either a rigid rotor or a rotating harmonicoscillator model.Molecular hydrogen trapped in ice XVII channels is anon-equilibrium mixture of o -H and p -H , in a concen-tration which is essentially invariant in time, being theconversion rate extremely low. At the low temperaturevalues typical of the present experiment, only the lowestrotational state for each species is populated (namely, J = 0 for p -H and J = 1 for o -H ) and so few transi-tions contribute to the spectrum in the frequency regionof interest, namely the rotationally-elastic J = 1 → J = 1 → o -H , plus the in-elastic transition J = 0 → p -H . We remark that the J = 0 → p -H molecule, being weightedby the mere coherent cross section, does not contributeappreciably to the observed spectrum. As a consequence,we assume that the spectral intensity recorded in the en-ergy range below 10 meV is solely due to ortho molecules.Being the strong J = 0 → p -H , we can extract, by a linear combination of thetwo measured spectra (samples with n -H and para -richH ), the spectra of pure p -H and o -H , represented inFig. 2.This decomposition enables to highlight two intensebands due to the translational excitations of the moleculeCoM, which appear at low energy in the spectrum of o -H , as combinations with the rotationally elastic J = 1 → a and b in thefigure, are quite broad (about 4.0 and 3.5 meV respec-tively). Band a is asymmetric, extending from 2.2 to 6.2meV, while b has a more symmetrical shape. The po-sition of these band is estimated at 2 . . a (cid:48) b (cid:48) for o -H ,(bottom panel) and a (cid:48)(cid:48) b (cid:48)(cid:48) for p -H (top panel).In the inset of Fig. 2 we show the fitting of the J = 0 → o -H J = 1 → b'a'ba E (meV) J = 0 → b''a'' I n t en s i t y ( a r b . un i t s )
10 15 20 25 a'' p -H FIG. 2. (Color online) Spectra of pure p -H (top panel) andpure o -H (bottom panel). The two observed CoM excitationsare marked with a and b , while we use a (cid:48) , b (cid:48) , and a (cid:48)(cid:48) , b (cid:48)(cid:48) for thecombinations of these excitations with J = 1 → J = 0 → J = 0 → a (cid:48)(cid:48) mode. rotational line, exhibiting three separated components.The splitting of the rotational band into a triplet, com-monly observed for hydrogen molecules in a confined ge-ometry, is due to the lifting of the threefold degeneracyof the J = 1 rotational level, as consequence of the poten-tial energy anisotropy with respect to the orientation ofthe H molecule. This rotational triplet is nicely fittedby the sum of three Gaussians, whose energy positionsare 13.05, 14.16, and 15.59 meV. Comparing these val-ues with those measured for the same transition of H in clathrate hydrates (namely, 13.64, 14.44, and 15.14meV), we observe here a larger splitting (i.e. 2.54 meVinstead of 1.50 meV) proving a stronger potential energyanisotropy.This fitting procedure also highlights the extra inten-sity due to the a (cid:48)(cid:48) band. Concerning the CoM transla-tional motion of the hydrogen molecule inside the chan-nel, even though this has a spiral shape it can be pic-tured as locally cylindrical. Therefore two vibrationalfrequencies are expected, the lower corresponding to thevibration along the cylinder axis, say z , and the higherto the xy degenerate mode. This is the way we have as- signed the a and b bands, observed in the spectra. In or-der to verify this assignment, we have performed classicalmolecular dynamics (MD) and calculated the spectrumof the CoM motion.MD computation was performed at T =50 K, withwater potential model TIP4P-2005 and Alavi’s H model , using Partridge-Swenke and Morse intramolec-ular flexibility for water and H , respectively. The aver-age structure of empty ice XVII is known from accurateRietveld refinement of neutron diffraction data and isdescribed by the space group P
22. Less certain butat any rate very similar is the structure of the samplescontaining H . A neutron diffraction measurement on therecovered C phase determined a lower symmetry spacegroup ( P et al. , fromX-ray diffraction measurements in a diamond anvil cell,recently claimed to have determined that also the highpressure phase C exhibits a hexagonal P
22 structure.The differences between the atomic coordinates of thetwo structures are numerically minimal, but are substan-tial to determine the potential energy shape for one H molecule hypothetically located in the channel, as clearlydiscussed in Ref. 2. Specifically, the ice lattice configu-ration based on the lower symmetry space group P molecule pereach hexagonal unit cell.For the MD calculation aimed to study the CoM dy-namics, we start from an initial configuration made by384 water molecules, located on the lattice sites of a su-percell 4 × × P
22. The as-sumed lattice constants are a = 6 .
326 ˚A and c = 6 .
080 ˚Afor the hexagonal cell (corresponding to an orthorhombiccell 6 . × . × .
080 ˚A ). The O atoms of the watermolecules in the supercell are placed on their crystallo-graphic positions. However, the D atoms in deuteratedice XVII are configurationally disordered. Different ran-dom distributions of the framework water deuterons weregenerated by a computer routine, each consistent withthe Bernal-Fowler ice rules and the periodic boundaryconditions outside the supercell. A proton configurationwith a negligible dipole moment was selected for use infurther calculations.The spectra calculated for the H CoM motion areshown in Fig. 3, assuming full hydrogen loading (i.e.3 H molecules for primitive cell) or half loading, (i.e.randomly filling half of the H sites). The comparisonwith the experimental values shows a semi-quantitativeagreement, considering that our samples are in a situ-ation close to half filling. The disagreement of the lowfrequency value can be easily imputed to the approxima-tions (classical motion, empirical interaction potentials,structural model etc.) in the computation and, partly, tothe large uncertainty of the experimental band energy. Itis interesting to note that, by increasing the loading, thelow energy mode essentially disappears and the intensityof a mode at higher energy increases. This supports theassignment of the modes at about 7 meV and 23 meV
21 327.1 23 full H loading half H loading M D s pe c t r u m ( a r b . un i t s ) E (meV)
FIG. 3. (Color online) Spectra of the CoM velocity autocor-relation function, obtained by MD calculation, for completelyhydrogen filled (black line) and randomly half-filled (magentaline) ice XVII. Symbols mark the positions of the maxima ofeach curve. to the motion along and across the spiral channels, re-spectively. The energy of the mode along the channels ismuch more sensitive to the amount of loading, which isvery reasonable.By means of the same MD computation, we have calcu-lated the D-projected density of phonon states (DoPS),which is compared in Fig. 4 with the same quantity ex-tracted from our neutron scattering spectra. The analysisof the experimental data has been done analogously towhat presented in Ref. 24. The first steps are straight-forward and consist in the subtraction of the empty con-tainer contribution and the correction for self-shieldingattenuation, operated via the analytical approach sug-gested by Agrawal . Multiple scattering contaminationsmade of two inelastic scattering events have been foundto be practically negligible in the energy transfer intervalof interest (i.e., 2 meV < E <
100 meV). Finally, in or-der to determine and remove the multi-phonon terms inthese spectra, we have used a well-known self-consistentprocedure already tested with positive experience on anumber of systems. Such a procedure, performed in theframework of the incoherent approximation, would havebeen totally justified for a polycrystalline H O-based ma-terial and would have led directly to the proton-projecteddensity of phonon states, due to the much larger cross-section, and lower mass, of the H nucleus than that ofthe O nucleus. For a deuterated sample like ours, how-ever, the rationale of this approximation is based onwell-established results obtained on various forms of D Oice .Despite the various approximations involved (i.e. apurely incoherent, harmonic, isotropic, and single-sitetreatment of the multi-phonon terms), the results reveala satisfactory convergence of the method, allowing fora sound extraction of the one-phonon component of theself-dynamic structure factor, and, finally, for the evalua- G D ( E ) ( m e V - ) E (meV) empty D O ice XVII full H loading half H loading FIG. 4. (Color online) Experimentally determined (lowerpanel) and calculated (upper panel) density of phonon states,projected on the deuteron nucleus. The calculation has beenperformed for different hydrogen filling. Experimental dataare derived from the spectra in Fig. 1 (bottom panel). tion of the deuterium-projected density of phonon statesin ice XVII, G D ( E ), which is reported in Fig. 4. It isworth noting that, in order to obtain an accurate resultfrom a quantitative point of view, the oxygen contribu-tion to the experimental estimate of G D ( E ) has been dulyevaluated and subtracted. This contribution has beenfound to be fully negligible in the librational part of thespectrum, while in the lattice phonon part it turned outto amount to 27.7 % of the deuterium one. Due to thefact that the lattice-phonon corresponds to a rigid mo-tion of D O molecules as single units, then the D and Ocontributions to the density of phonon states in the corre-sponding spectral zone exhibit exactly the same spectralshape and so the aforementioned corrections to G D ( E )can be simply performed by scaling the intensity of thelattice part of G D ( E ) (in the energy transfer range from0 to 42 meV) by the factor 0.783, obtained by taking intoaccount the different cross section of D O molecule andD nucleus.The calculated DoPS does not depend appreciably onthe hydrogen loading, and shows some bands originatedby different vibrational modes. By looking at Fig. 4, onecan observe that the lattice phonons region (i.e.,
E < G D ( E ) is different from what can be observed inbasically all other ice forms , but is quite similar to thelattice band in deuterated sII clathrate hydrate (filledwith Ne) , even though the cleft of the main acousticpeak seems less deep and more asymmetric in ice XVII.In the librational region (i.e. 45 meV < E <
90 meV),one also notes some differences between G D ( E ) of iceXVII and that of sII clathrate hydrate. In particular,the first steep peak, located at about 50 meV, appearsmore asymmetric and centered at a slightly lower fre-quency in ice XVII, followed by a dip, at around 60 meV,which looks shallower and less pronounced. Altogetherthe comparison with the computed G D ( E ) shows a rea-sonably good agreement, similar to what obtained forclathrate hydrates of various structures, as discussed inRefs. 28 and 29.In this work we have accurately measured the quan-tum dynamics of a single H molecule in the confined ge-ometry of one single nanometric ice XVII channel. Thesplitting of the rotational and translational bands is aconsequence of the water environment, whose anisotropyappears stronger than in the clathrate hydrate confine-ment. As for the CoM translational dynamics, the com-parison between the measured spectra and the MD calcu-lations supports the identification of the lowest frequency band as the vibration along the channel direction, whilethe higher mode corresponds to the motion across thespiral channel. Both frequencies are significantly influ-enced by the hydrogen loading, but this dependence israther more marked for the vibration along the channel.The present data about the guest motion, together witha substantial agreement between the measured and cal-culated D-projected DoPS of the host molecules, allowto characterize the main features of the vibrational dy-namics of this novel inclusion compound. ACKNOWLEDGMENTS
We gratefully thank Mr. Andrea Donati for hisskillful technical support in the sample preparation.We acknowledge the PRIN project ZAPPING, number2015HK93L7, granted by the Italian Ministry of Edu-cation, Universities and Research (MIUR). This workhas been performed within the Agreement No.0018318(02/06/2014) between STFC and CNR, concerning col-laboration in scientific research at the spallation neutronsource ISIS ∗ present affiliation: Istituto di Fisica Applicata “Nello Car-rara”, IFAC–CNR † present affiliation: Istituto di Fisica Applicata “Nello Car-rara”, IFAC–CNR; and Michigan Technological University,Houghton, MI, (USA); e-mail: [email protected] L. del Rosso, M. Celli, and L. Ulivi, Nat. Commun. ,13394 (2016). L. del Rosso, F. Grazzi, M. Celli, D. Colognesi, V. Garcia-Sakai, and L. Ulivi, J. Phys. Chem. C , 26955 (2016). Y. Huang, C. Zhu, L. Wang, X. Cao, Y. Su, X. Jiang,S. Meng, J. Zhao, and X. C. Zeng, Sci. Adv. , e1501010(2016). E. D. Sloan,
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