in Hydrogen−Ice Clathrate by - American Chemical Society

J. Phys. Chem. B 2007, 111, 12097-12102

12097

Rotation and Diffusion of H2 in Hydrogen-Ice Clathrate by 1H NMR Lasitha Senadheera† and Mark S. Conradi*,†,‡ Departments of Physics and Chemistry, Washington UniVersity in St. Louis, One Brookings DriVe, Saint Louis, Missouri 63130 ReceiVed: June 11, 2007; In Final Form: August 17, 2007

A recently reported hydrogen-ice clathrate carries up to four H2 in each large cage and one H2 in each small cage. We report pulsed proton NMR line shape measurements on H2-D2O clathrate formed at 1500 bar and 250 K. The behavior of the two-pulse spin-echo amplitude with respect to the nutation angle of the refocusing pulse shows that intramolecular dipolar broadening, modulated by H2 molecular reorientations, dominates the line width of the ortho-H2. Dipolar interaction between H2 guests and host D atoms explains the echo variation with the relative phases of the pulses. From 12 to 120 K, the line width varies as 1/T, demonstrating that the three sublevels of J ) 1 are split by a constant energy, . The splitting arises from distortion in the otherwise high-symmetry cages from frozen-out D2O orientational disorder. Above 120 K, further line-narrowing signals the onset of H2 diffusion from cage to cage. At the lowest temperature, 1.9 K, the spectrum has Pake powder doublet-like features; the doublet is not fully developed, indicating a broad distribution of order parameters and energies .

Introduction Clathrate hydrates are inclusion compounds in which guest molecules are encapsulated by a solid, crystalline host lattice of ice (H2O) molecules. There are three main kinds of naturally occurring hydrates known as sI (bcc cubic), sII (diamond cubic), and sH (hexagonal).1 It had been believed that hydrogen molecules (H2) were too small to stabilize the clathrate structure until H2 clathrate hydrate was first discovered2 in 2002. This discovery has created much interest among hydrogen storage researchers because hydrogen clathrate hydrate is viewed as a novel way of storing hydrogen.3 X-ray and neutron diffraction studies2,4 have shown that H2 and H2O form sII clathrate at high pressure (∼2 kbar) and low temperature (∼250 K); each unit cell has 16 pentagonal dodecahedron (512) small cages, eight hexakaidecahedron (51264) relatively large cages, and 136 water molecules. It was reported that hydrogen molecules in the clathrate hydrate are in free rotation and interact with each other or with H2O molecules through van der Waals forces.2,3 Four H2 molecules and one H2 molecule can occupy each large and small cavity, respectively, representing 3.77 wt % of H2 of the total system mass;4,5 earlier reports claimed the possibility of occupying two H2 molecules per small cage.2,6 We note that diffraction-derived cage occupancies are, in general, averages of statistical quantities. We are interested in exploring the basic physics of enclathrated H2 guest molecules using nuclear magnetic resonance (NMR). NMR has been used in H2-THF-H2O clathrate (THF is the promoter molecule tetrahydrofuran) to identify and confirm the presence of H2 molecules in the clathrate,7-9 but none of these have studied the dynamics of the H2 guest molecules. We report here the first systematic NMR investigation of H2 guests in H2-D2O clathrate hydrate. In this Article, we focus primarily upon 1H NMR line shapes at temperatures * Corresponding author. E-mail: [email protected]. † Department of Physics. ‡ Department of Chemistry.

from 160 to 1.9 K; the line shape data reveal the nature of the reorientation and diffusion motions of the H2. At the outset, we note the uniquely quantum mechanical aspects of molecular H2.10 There are two species of H2 molecules called ortho-hydrogen (o-H2) and para-hydrogen (p-H2) due to the requirement that the total wavefunction, a product of nuclear spin and molecular rotational wavefunctions, be antisymmetric under exchange of the two spin-1/2 protons (fermions). The o-H2 has total nuclear spin-1 (triplet state) and rotational states with odd quantum numbers J ) 1, 3, 5, ..., whereas p-H2 has nuclear spin-0 (singlet state) with rotational states J ) 0, 2, 4, .... Only o-H2 is detectable with NMR due to its nonzero nuclear magnetic moment. The unusually small moment of rotational inertia of the H2 molecule, due to the small mass and short H-H bond length, is reflected in the large rotational constant, B/kB ) 85.6 K; the energy of each level is EJ ) BJ(J + 1). Therefore, all H2 molecules in the clathrate hydrate at our temperatures occupy primarily the lowest states, J ) 0 (para) and J ) 1 (ortho).10 Hydrogen equilibrated at room temperature is 75% o-H2; at lower temperatures, the equilibrium concentration C0 of o-H2 decreases. Thus, C0 is 50% at 80 K and less than 1% at 20 K. In general, ortho-para conversion10 is a slow process requiring days in the bulk solid and much longer for comparatively isolated H2 molecules. Experimental Methods Before attempting NMR measurements, we confirmed the formation of H2 clathrate hydrate following the procedure of ref 5. Ground D2O ice (99.9%) was exposed to H2 gas (99.99% purity) at 1500 bar at about 250 K in a stainless steel pressure vessel with an internal thermocouple and an attached pressure transducer. After 3 h, the pressure vessel was cooled to 77 K, and then the excess gas was evacuated. We note that the clathrate does not decompose (or decomposes only slowly) into a vacuum at this temperature. We subsequently calculated the amount of enclathrated H2 by warming to room temperature and measuring

10.1021/jp074517+ CCC: $37.00 © 2007 American Chemical Society Published on Web 10/05/2007

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the pressure of the H2 gas released into the known volume. The result was consistent with previous reports,5 ∼3.5 wt %. A homemade high-pressure NMR probe with a berylliumcopper pressure vessel was used for forming the clathrate and then performing in-situ NMR experiments. In the already chilled, high pressure BeCu NMR cell, crushed D2O ice was placed inside a chilled glass tube 1 cm long and 5 mm diameter, capped with Teflon; a small hole allowed H2 in and out of the glass tube. A two-turn solenoid NMR rf coil was used with an electrical feedthrough adapted from ref 11. We followed the same procedure as above to prepare our H2-D2O sample in the NMR probe. D2O was selected as the host so the only proton NMR signals are from the H2. NMR line shapes were recorded at temperatures from 160 to 1.9 K at 354 MHz (8.32 T field strength), using a homemade pulsed NMR spectrometer and a Kadel flow dewar. The temperature was determined from a thermocouple (above 150 K) and a factory-calibrated carbonin-glass resistance thermometer. All line shape data were highly reproducible for the same sample, with little variation among samples. Spectra were obtained as the Fourier transforms of free induction decays (FIDs), typically excited by 90° pulses. For the broadest lines, a pulse of 1 µs duration, a much smaller nutation angle, was used for its broad excitation bandwidth. The deadtime following the rf pulse was small, about 1 µs; the acquired signals were extrapolated back to zero time12 prior to Fourier transformation. At the high field and low temperatures used, the signal-to-noise ratio was high. Results and Discussion The temperature dependences of the NMR free induction decays (FIDs) and frequency domain line shapes of the H2D2O clathrate hydrate are shown in Figure 1. Data below 77 K were taken upon repeated cooling and warming runs, and no differences in line shape were observed at a given temperature. The data above 77 K were taken on warming, which eventually decomposed the sample near 160 K. We observed a single, unstructured NMR line (Figure 1b) at all temperatures above 10 K. The exception is the line at 151.4 K, which has a distinct narrow spike superimposed on a broader resonance. Despite the presence of one-third of the H2 molecules in the singly occupied small cages and two-thirds in the quadruply occupied large cages, there is no clear evidence in the line shapes for these two distinct components. This suggests that the environments of H2 molecules in the large and small cages are not sufficiently different to permit distinguishing them. For example, the chemical shifts of H2 in the two environments are predicted to be within 0.1 ppm.13 At high temperatures such as 77 K, where we usually started the NMR measurements, the lines are Lorentzian-like in shape and broaden continuously as temperature is decreased. Below about 8 K, the broad single line starts to evolve toward the Pake powder doublet, similar to that observed in orientationally ordered bulk solid H2 below 1 K.14-16 Even at the lowest temperature we reached, 1.9 K, the Pake powder doublet is not fully developed. Specifically, the shoulders expected at (164 kHz are rounded, the expected cusps at (82 kHz appear merely as ledges, and there is a remnant central line. The frequency width of the doublet (measured between cusps, or here ledges) is approximately 164 kHz at 1.9 K, which is very close to that in bulk solid hydrogen in the orientationally ordered phase.14-16 The NMR line width is mainly determined by the intramolecular dipole-dipole interactions of each hydrogen molecule. An isolated pair of spins-1/2, as already mentioned, forms spin-0

Figure 1. (a) NMR free induction decays (FIDs) and (b) Fourier transform line shapes of H2 molecules in H2-D2O clathrate as a function of temperature. Arrows in (b) at 1.9 K show the width of the characteristic doublet.

(para) and spin-1 (ortho) states; only the spin-1 states give NMR signals. With mutual dipolar interaction (intramolecular), the composite spin-1 is fully equivalent to a single spin-1 with quadrupolar interaction (e.g., 2D, 6Li, 14N). The spin echo behavior of this spin-1 system under the pulse sequence 90Xτ-θφ (i.e., refocusing pulse of nutation angle θ applied at rf phase φ relative to the x-axis) applied at the resonance frequency is well known.17 For φ ) 0 (so-called xx phasing), the echo amplitude SXX is 0, whereas for φ ) 90° (so-called xy phasing), the echo amplitude SXY is maximum. As a function of the refocusing pulse nutation angle θ, the echo is predicted to be maximum for θ ) 90° and zero for θ ) 180°. As shown in Figure 2a, the maximum and minimum of the experimental echo amplitude SXY at 17 K are found at θ values of 90° and 180°, respectively. The nonzero echo amplitude at θ ) 180° is presumably due to the inhomogeneity of the applied rf field, so that the 180° nutation condition does not occur simultaneously throughout the sample for any pulse duration. From this agreement with theory, it is apparent that the dephasing and line width result primarily from the intramolecular dipole interaction within each H2 molecule. The dependence of the echo amplitude on the relative phases of the two rf pulses is presented in Figure 2b as a function of 2τ. Extrapolating to zero τ, one sees that SXX is nearly zero and SXY is large, in agreement with the above prediction. However, at all nonzero τ, SXX is no longer zero, and eventually (beyond 2τ ) 200 µs) SXX and SXY become essentially equal. Beyond 200 µs, both echo amplitudes decrease due to T2 processes; we believe intermolecular H-H dipole interactions control this decay.

Diffusion of H2 in Hydrogen-Ice Clathrate

Figure 2. (a) Echo amplitude generated by 90X-τ-θY (SXY) as a function of second nutation angle θ, where τ is the delay between the two pulses and subscripts X and Y denote the phases of the pulses. (b) Absolute values of echo amplitudes SXY (from 90X-τ-90Y) and SXX (90X-τ-90X) versus echo time 2τ. The long-time decay of the echoes is characterized by spin-spin relaxation time T2. All of these data were recorded at 17 K for H2-D2O clathrate hydrate. Dashed lines represent extrapolations. The solid curves are guides for the eyes.

Meyer et al.17,18 considered the variation of the echo amplitudes, SXX and SXY, as a function of resonance offset ∆ω between the rf pulse sequence (i.e., spectrometer carrier frequency) and the spin-1 system (here, the spin frequency is defined as the mean of the frequencies of the two ∆m ) 1 transitions). They find that the variation of SXY is proportional to cos2(∆ωτ) and SXX proportional to sin2(∆ωτ). Clearly, for short τ and/or ∆ω ) 0, this returns the well-known on-resonance result that SXX ) 0 and SXY is maximum. Indeed, neglecting T2 decay processes, SXY is equal to the amplitude of the FID, so the XY echo is a full-amplitude refocused FID. In our system, unlike-spin dipole interactions between the 2D spins of the D2O host and the o-H2 spins can be regarded as generating a distribution of hydrogen resonance-frequency offsets ∆ω; we recall that resonance offset and unlike-spin dipole interactions are both linear in the Iz (hydrogen nuclear spin) operator, so they produce identical effects. The width of the distribution of phase angles ∆ωτ is proportional to τ. Hence, for small, nonzero τ, the width of the distribution makes SXX ∝ 〈sin2(∆ωτ)〉 nonzero. For large τ, the averages of sine-squared and cosinesquared become equal ()1/2), explaining why SXX and SXY are equal for sufficiently large τ. Indeed, a reasonable extrapolation (see Figure 2b, dashed curves) of the large τ amplitudes to τ ) 0 yields one-half the extrapolated amplitude of SXY (for small τ). Thus, the echo amplitude data of Figure 2 are consistent with the following hierarchy or ranking of dipole interactions: The intramolecular H-H coupling is the largest and so controls the dephasing and line width. The host-guest D-H coupling controls the relative amplitudes of the XX and XY echoes as a function of τ. The intermolecular (host-host) H-H coupling results in the observed T2 decay of the echo envelope.

J. Phys. Chem. B, Vol. 111, No. 42, 2007 12099 To better understand the line width of H2 in the H2-D2O clathrate, we first consider a hypothetical H2 molecule with orientational coordinates and dynamics treated classically. The dominant line-broadening interaction is intramolecular H-H dipolar interaction, as demonstrated above. As compared to a very rapidly and isotropically reorienting molecule, which would have a limiting line width of zero, there are two ways for line width to develop: slowing of the reorientations and existence of a preferred direction. The relaxation and motional narrowing theory of BPP15,19 treats the first case. The molecular reorientational motions are described by a correlation time τc, which describes the (assumed exponential) decay of the autocorrelation of second-order spherical harmonic functions of orientation. Thus, τc is approximately the time for a molecule to rotate by π/2. Provided one remains in the line-narrowing regime, τc∆ωRL , 1 (where ∆ωRL is the rigid lattice or no-rotation NMR line width), the observed line width ∆ω is approximately ∆ω = (∆ωRL)2τc. Slowing of the reorientation (increasing τc), as generally occurs in liquids with decreasing temperature, results in increasing line width. This is an accurate description of most classical, bulk liquids. The second scenario for development of line width is the presence of a favored direction.20 Examples include molecules in a liquid crystalline phase21 (where the favored axis is the directrix) and molecules adsorbed on a surface.22 In both cases, the orientational probability distribution function (opdf) is nonspherical, in contrast with the isotropy of a bulk ordinary liquid. When the opdf is non-spherical, the molecule spends more time at some orientations than others. Thus, the time average of (3 cos2 β - 1)/2, where β is the angle between the H-H molecular axis and the static magnetic field, becomes nonzero; this results in a nonzero intramolecular dipole interaction and a nonzero NMR line width, even if the molecule rotates very rapidly. For a powder system, in which the locally favored direction occurs equally in all orientations relative to the static field, the line width will be proportional to σ, the order parameter. Here, σ is

1 σ ) 〈3 cos2 θ - 1〉 2

(1)

where θ is the instantaneous angle between the H-H axis and the locally favored (or symmetry) direction. Here, we have assumed the local opdf exhibits cylindrical symmetry about the favored direction. Limiting cases are σ ) 0, which can arise from a spherical opdf (vanishing orientational order), and σ ) 1, the case of molecules aligned only along the favored direction. If all molecules have the same value of σ, the spectrum of the hypothetical classical H2 will be a Pake powder doublet, with frequency width scaled by σ. The orientational states of o-H2 must be treated quantum mechanically, of course.10 In our system, the weakness of the H2-D2O interactions indicates that, for our temperature range below 160 K, the H2 molecules are confined to the three sublevels of J ) 1. The higher odd-J states are at least 860 K higher in energy, so that they are essentially unavailable, either for thermal excitation or for admixing into the J ) 1 states. Quantum mechanically, the reorientation rate is described by Γ, the transition rate between the three sublevels;23 here, we assume the three such rates are all equal. When Γ is approximately equal to ω0 (NMR precession frequency), one expects a maximum in the longitudinal relaxation rate 1/T1; this is analogous to the classical condition ω0τc ≈ 1. The three sublevels of J ) 1 have a very small (negligible) molecular Zeeman interaction with the static field,15 just a few

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millikelvins at the present field strength. Much larger is the interaction with neighbors and the environment (crystal field splitting).14 This interaction results in an energy splitting  between the lowest level and the average of the other two; residence in this lowest level is the quantum version of the classical condition “pointing in the favored direction”.24 If the locally favored direction is z, the quantum orientational order parameter25 σ is

1 σ ) 〈2 - 3J 2z 〉T 2

(2)

where the 〈...〉T symbol implies expectation values in the three states followed by appropriate thermal (Boltzmann) weighting at temperature T. Here, Jz represents rotational angular momentum along the favored direction; we assume axial symmetry, which means the other levels (*z) have essentially equal energies. As in the classical case, the NMR spectrum with a single value of σ less than 1 will be the rigid-lattice (σ ) 1) spectrum (a Pake powder doublet, for a powder sample), scaled in frequency width by factor σ. In detail, we assume no exact degeneracies of the three levels exist, so that the components of angular momentum are quenched and the spin-rotation interaction therefore has no effect.14,15 We note that sole occupation of the favored level (with Jz ) 0, the Jz state) results in σ ) 1, so a full width Pake powder doublet. In general, σ is nonzero only when the three sublevels of J ) 1 are unequally occupied (we note the trace of (2 3Jz2) is zero). For completeness, we note that this full width spectrum has only two-fifths the width expected classically from the known H-H bond length.14,15 This factor is a result of the angular width of the J ) 1 states (qualitatively, motional averaging is built into the wavefunction itself):

〈J |21 (3 cos θ - 1)|J 〉 ) 52 2

z

z

(3)

We now turn to apply these concepts to the line width data of Figure 3. First, we note that T1 passes through a deep minimum of about 24 ms as a function of temperature near 10 K (data not shown), demonstrating that the transition rate Γ between the three levels is near ω0 (here 2.2 × 109 s-1) at 9 K. This is much larger than ∆ωRL (about 106 s-1, see width of Pake-like spectrum at 1.9 K), revealing unambiguously that slowing of the molecular reorientations is not the source of line broadening, at least above 10 K. The observed T1 suggests Γ ∝ T2, which implies that Γ remains larger than the static line width at all of our temperatures (T g 1.9 K). Thus, the line width must be understood in terms of the order parameter σ, the favored orientation picture of eq 2. We note that the line shape is never a scaled version of the full-width Pake powder doublet (see Figure 1b). This indicates that, at each temperature, there is not a unique value of σ, but a distribution of σ values (presumably, a different σ for each molecule or at least for the molecules in each cage). The line width is proportional to 1/T from 12 to 120 K, a remarkably wide range, as shown by the curve through the data in Figure 3a. If the energy splitting  for a given o-H2 were constant over this temperature range, and  remained small as compared to kBT, then the population in the lowest level would be

pz =

(

1 2 1+ 3 3kBT

)

(4)

Figure 3. (a) Temperature dependence of full width at half-maximum (fwhm) of the H2 NMR line of H2-D2O clathrate hydrate. The solid curve, (fwhm) × T ) 8.9 × 105 Hz K, indicates line width is inversely proportional to the temperature from 12 to 120 K. Departure from 1/T dependence is evident at high (T > 120 K) and low temperatures (T < 10 K). (b) Selected, normalized spectra at 14, 22, 30, 66, 87, 94, and 109 K, all in the 1/T region. Each spectrum is normalized to the same peak height and fwhm (frequency axis scaled by fwhm) for comparison. The spectra are quite similar; the outermost ones are labeled by temperature. For temperatures between 22 and 94 K, the normalized spectra are nearly identical and are not labeled.

from the high-temperature expansion of the Boltzmann factor. The excess population, which is the source of line width here, follows /kBT and is similar to the per-spin magnetization in a Curie-law paramagnet. Thus, the NMR line width should vary as 1/T. This signature in the data from 12 to 120 K demonstrates that the energy splitting  of the three J ) 1 levels does not change over this temperature range. Further, the distribution of σ values (for example, see spectrum at 1.9 K in Figure 1b where a central line coexists with Pake doublet-like features) reflects the distribution of splittings, . Not only does the line width of the resonance vary as 1/T from 12 to 120 K, the shape of the line is nearly constant over this range, once the frequency axis is scaled by the fwhm, as presented in Figure 3b. This is the expected result if the energy splittings  remain temperature-independent so that all of the values in the distribution of order parameter σ scale as 1/T. We regard the constant shape in Figure 3b as a stricter test of the assumption of constant energy splitting . What is the source of the energy splittings  and their broad distribution? We note that the large and small cages have idealized symmetries Td (43m) and Th (3m), respectively; these are sufficiently high symmetries that no splitting of the J ) 1 states can result. Again, admixture of higher-J states must be extremely small, because of the large energy differences. However, the D2O molecules in the cage walls have random

Diffusion of H2 in Hydrogen-Ice Clathrate orientations, just as in ordinary ice-Ih.26,27 That is, the D position along any O-O line segment obeys Pauling’s ice rules, with the D atom covalently bonded close to one O atom and hydrogen-bonded to (more distant from) the other O atom. The result of the frozen-in disorder of D-atom positions (equivalently, frozen orientations of D2O) is that each cage has a lower symmetry than the idealized cage. Position disorder of the host D-atoms can thus generate a splitting  of the three J ) 1 levels. Also, because of the random nature of the disorder,28,29 one expects a distribution of  values, as observed. The effects of D-atom disorder on guest methyl group tunneling and on spherical top molecules have been measured.30,31 The rotational and center-of-mass oscillatory states have been examined computationally for one or more H2 in the small and large clathrate cages.32-34 For a single H2 in a small cage,32 the energies of the three J ) 1 states are 0, 39, and 87 K in the center-of-mass ground states. Thus, at or below 13 K, the lowest of these levels would be occupied greater than 95%. Yet the experimental spectrum in Figure 1 at 10 K shows no hint of the Pake-doublet features that would result from such complete population of the lowest level. We note that the above discussion applies only to the one-third of H2 molecules in small cages; quantitative predictions for the large cages are not available. We also note that the theoretical energy splittings of the J ) 1 levels were obtained for only two realizations of the disordered host D-atom positions, out of the many possible configurations. We have implicitly assumed that what matters to the splitting  is the symmetry of the cage, and not the (much lower) symmetry of a particular “pocket”, where the H2 could sit away from the cage center, against the cage wall. That is, we have assumed the single H2 in each small cage is able to move throughout the interior of the cage, sampling all of the pockets and volume in a time short as compared to the NMR time scale, 1/∆ω. For the four H2 occupying each large cage, the hydrogens of which have been pictured as fitting into the cage in a tetrahedral configuration,4 the H2 must roll over each other and again rapidly sample the entire cage interior. We see these as the only way for  to remain temperature independent over the wide range of temperatures. Specifically, the observation of constant energy splittings  from 12 to 120 K requires, on the NMR time scale and across the full temperature range, either (1) each H2 samples all of the available sites in its cage or (2) each H2 remains at a fixed site, one or the other, exclusively. If a typical molecule went from “single pocket” to “all available sites” with increasing temperature, the result would be a decrease in the effective  and a departure from the observed 1/T line width. We rule out case 2 because of the weakness of H2 physisorption: it is not plausible that H2 could remain immobilized up to 120 K. Another potential source of the splitting  is orientationdependent H2-H2 interaction. The walls separating nearest neighbor cages are only one layer of D2O thick. Thus, the H2 orientation in one cage can couple through wall distortions to H2 in the next cage. We believe this indirect effect on the H2 orientational states is secondary and much smaller than the direct effect of D-atom disorder. With decreasing temperatures below 12 K, the line width increases more slowly than 1/T. This is not unexpected, as the line width is no longer small as compared to its limiting Pake powder doublet value. This is the value that would attain with all of the population residing in the lowest sublevel. Clearly, the high-temperature expansion of the Boltzmann factor (eq 4) is no longer applicable below 12 K. The spectrum of Figure 1b

J. Phys. Chem. B, Vol. 111, No. 42, 2007 12101 at 1.9 K is not a fully developed Pake powder doublet. The outer steps are very rounded (despite the very short 1 µs excitation pulse and wide bandwidth receiver), the expected cusps at (82 kHz appear only as ledges, and there is a prominent central line. All of this points to a distribution of the order parameter σ, with substantial weighting for σ values smaller than unity. The close agreement between the width of the Pake doublet features here and in orientationally ordered bulk solid H214-16 supports our contention that the rotational states here are nearly pure J ) 1 states with negligible admixtures of J ) 3, 5, ... (see expectation value in eq 3). Above 120 K, the line width in Figure 3 falls below the 1/T curve that describes the data from 12 to 120 K. The rapidity of this decrease suggests the onset (on the NMR time scale) of a thermally activated motion that results in motional averaging. One possibility is that the H2 diffuses from cage to cage; given the different crystal fields of the cages (from the random, frozenin D-atom position disorder), the H2 resonance would be narrowed. We note that H2 rapidly leaves our clathrate sample, going into the vacuum, near 160 K upon warm-up. Thus, it appears reasonable that H2 cage-to-cage motion becomes visible on the time scale of the reciprocal of the line width (1/∆ω, 17 µs) at 120 K. Cage-to-cage diffusion requires vacant and/or under-occupied cages; in H2-D2O clathrate, the occupancy does not appear to be complete at these temperatures.4 A second avenue for narrowing is onset of D-atom motion (equivalently, D2O reorientation). If sufficiently rapid, this motion would time-average the crystal field in each cage to the high symmetry of the idealized cage, so the splitting  of the three levels would go to zero (time average). Such motion has been reported in tetrahydrofuran-H2O clathrate, becoming evident as line-narrowing of the H2O host resonance at 185 K.28,29 We note this clathrate has the sII structure, like H2D2O, but the tetrahydrofuran molecules occupy only the large cages, with the small cages remaining empty. The 185 K onset is substantially hotter than our 120 K line-narrowing onset, so we believe that cage-to-cage H2 hopping drives the narrowing, not D2O reorientations. Alavi and Ripmeester35 have used electronic structure calculations to determine the energy barriers for H2 molecules to pass through the hexagonal throat connecting two large cages, and pentagonal throat connecting two small cages. They find 5-6 and 25-29 kcal/mol, respectively. Our line-narrowing data above 120 K cover too small a range to allow for an activation energy to be determined directly. Instead, we have used that the hopping rate of H2 molecules is approximately 105 s-1 (line width before narrowing, in rad s-1) at the onset of motional averaging at 120 K. The attempt frequency is estimated as 1012 s-1 (chosen to be a bit smaller than typical vibration frequencies, to account for the fraction of under-occupied cages). With these values, the activation energy is 3.8 kcal/mol, just a bit smaller than the calculated value for hops between large cages. We note the calculation treated the cage wall as rigid; inclusion of cage atomic-relaxation (flexibility) would reduce the calculated barrier.35 We note that motion between large cages should narrow the resonance only of (nominally) two-thirds of the H2 molecules that reside there. The one-third of molecules in small cages are expected to have much slower diffusion, because of the much larger barriers to motions between small cages as well as between small and large cages.35 Our limited data do not reveal whether the H2 in small cages indeed diffuse more slowly than H2 in large cages. However, the distinctly two-component

12102 J. Phys. Chem. B, Vol. 111, No. 42, 2007 spectrum at 151.4 K in Figure 1b is at least suggestive of a coexistence of diffusionally mobile and immobile hydrogen molecules. Conclusions The proton NMR line shape of o-H2 molecules in H2-D2O clathrate is controlled below 120 K by the reorientational motions. The dependence of the two-pulse spin echo amplitude on the nutation angle of the second pulse demonstrates that intramolecular dipole interactions are responsible for the line width. The unlike-spin dipole interactions between the o-H2 guests and 2D of the host satisfactorily account for the echo behavior with respect to the relative phases of the rf pulses. Over the wide temperature range from 12 to 120 K, the line width is proportional to 1/T, demonstrating the constancy of the energy splitting  between the three J ) 1 levels. The high symmetries of the idealized cages indicate that the splittings  arise from the frozen, random D-atom positions (equivalently, frozen D2O orientations) that lower the cage symmetries. The random nature of these crystal fields provides a natural explanation for the observed distribution of orientational order parameters σ and energy splittings . Above 120 K, additional line-narrowing is observed and attributed to diffusion of H2 from one cage to the next. Below 8 K, the proton NMR spectrum gradually evolves toward a Pake powder doublet. However, even at 1.9 K the Pake features are not fully developed, providing direct evidence of the distribution of order parameters σ. Acknowledgment. We acknowledge research support from NSF grant DMR-0400512. Partial support was provided by DOE grant DE-FG02-06ER46256. We appreciate helpful conversations with L. Gelb and A. E. Carlsson. We appreciate the comments and literature references suggested by a reviewer. References and Notes (1) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker: New York, 1998. (2) Mao, W. L.; Mao, H.-K.; Goncharov, A. F.; Struzhkin, V. V.; Guo, Q.; Hu, J.; Shu, J.; Hemley, R. J.; Somayazulu, M.; Zhao, Y. Science 2002, 297, 2247-2249. (3) Mao, W. L.; Mao, H.-K. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 708-710. (4) Lokshin, K. A.; Zhao, Y.; He, D.; Mao, W. L.; Mao, H.-K.; Hemley, R. J.; Lobanov, M. V.; Greenblatt, M. Phys. ReV. Lett. 2004, 93, 125503.

Senadheera and Conradi (5) Lokshin, K. A.; Zhao, Y. Appl. Phys. Lett. 2006, 88, 131909. (6) Patchkovskii, S.; Tse, J. S. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 14645-14650. (7) Lee, H.; Lee, J.-W.; Kim, D. Y.; Park, J.; Seo, Y.-T.; Zeng, H.; Moudrakovski, I. L.; Ratcliffe, C. I.; Ripmeester, J. A. Nature 2005, 434, 743-746. (8) Florusse, L. J.; Peters, C. J.; Schoonman, J.; Hester, K. C.; Koh, C. A.; Dec, S. F.; Marsh, K. N.; Sloan, E. D. Science 2004, 306, 469-471. (9) Strobel, T. A.; Taylor, C. J.; Hester, K. C.; Dec, S. F.; Koh, C. A.; Miller, K. T.; Sloan, E. D. J. Phys. Chem. B 2006, 110, 17121-17125. (10) Silvera, I. F. ReV. Mod. Phys. 1980, 52, 393-452. (11) Schouten, J. A.; Trappeniers, N. J.; Goedegebuure, W. ReV. Sci. Instrum. 1979, 50, 1652-1653. (12) Brady, S. K.; Conradi, M. S.; Majer, G.; Barnes, R. G. Phys. ReV. B 2005, 72, 214111. (13) Alavi, S.; Ripmeester, J. A.; Klug, D. D. J. Chem. Phys. 2005, 123, 051107. (14) Reif, F.; Purcell, E. M. Phys. ReV. 1953, 91, 631-641. (15) Abragam, A. Principles of Nuclear Magnetism; Clarendon Press: Oxford, 1961. (16) Harris, A. B.; Meyer, H. Can. J. Phys. 1985, 63, 3-23. (17) Yu, I.; Washburn, S.; Meyer, H. J. Low Temp. Phys. 1983, 51, 369-400. (18) Clarkson, D.; Qin, X.; Meyer, H. J. Low Temp. Phys. 1993, 91, 119-151. (19) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Phys. ReV. 1948, 73, 679-712. (20) Walton, J. H.; Conradi, M. S. Phys. ReV. B 1990, 41, 6234-6239. (21) Suryaprakash, N. Concepts Magn. Reson. 1998, 10, 167-192. (22) Kubik, P. R.; Hardy, W. N. Phys. ReV. Lett. 1978, 41, 257-260. (23) Conradi, M. S.; Fedders, P. A.; Norberg, R. E. In Pulsed Magnetic Resonance: NMR, ESR, and Optics. A Recognition of E. L. Hahn; Bagguley, D. M. S., Ed.; Clarendon: Oxford, 1992. (24) Conradi, M. S. Phys. ReV. B 1983, 28, 2848-2851. (25) Sullivan, N. S.; Edwards, C. M.; Lin, Y.; Zhou, D. Can. J. Phys. 1987, 65, 1463-1470. (26) Hobbs, P. V. Ice Physics; Oxford University Press: London, 1974. (27) Fletcher, N. H. The Chemical Physics of Ice; Cambridge University Press: Cambridge, 1970. (28) Garg, S. K.; Davidson, D. W.; Ripmeester, J. A. J. Magn. Reson. 1974, 15, 295-309. (29) Davidson, D. W.; Garg, S. K.; Ripmeester, J. A. J. Magn. Reson. 1978, 31, 399-410. (30) Ripmeester, J. A. J. Chem. Phys. 1978, 68, 1835-1840. (31) Ripmeester, J. A.; Ratcliffe, C. I.; Cameron, I. G. J. Phys. Chem. B 2004, 108, 929-935. (32) Xu, M.; Elmatad, Y. S.; Sebastianelli, F.; Moskowitz, J. W.; Bacˇic´, Z. J. Phys. Chem. B 2006, 110, 24806-24811. (33) Sebastianelli, F.; Xu, M.; Elmatad, Y. S.; Moskowitz, J. W.; Bacˇic´, Z. J. Phys. Chem. C 2007, 111, 2497-2504. (34) Sebastianelli, F.; Xu, M.; Kanan, D. K.; Bacˇic´, Z. J. Phys. Chem. B 2007, 111, 6115-6121. (35) Alavi, S.; Ripmeester, J. A. Angew. Chem., Int. Ed. 2007, 46, 1-5.