Raman Measurements of Pure Hydrogen Clathrate ... - ACS Publications

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Raman Measurements of Pure Hydrogen Clathrate Formation from a Supercooled Hydrogen−Water Solution Leonardo del Rosso,†,‡ Milva Celli,† and Lorenzo Ulivi*,† †

Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy

‡

S Supporting Information *

ABSTRACT: The nucleation and growth of a solid clathrate hydrate from the liquid phase is a process that is even less understood and more difficult to study than the nucleation of a solid phase from a pure liquid. We have employed in situ Raman spectroscopy to study the hydrogen−water supercooled solution undergoing clathrate formation at a pressure of about 2 kbar and temperature of 263 K. Raman light scattering detects unambiguously the H2 molecules inside of clathrate crystallites, which change stoichiometry during growth. The spectral intensity of the hydrogen vibrational band shows the time evolution of the population of the large and small cages, demonstrating that, in the initial stages of clathrate formation, the occupation of the large cages is quite lower than its equilibrium value. From the measurement of the growth rate of the crystallites, we demonstrate that the growth of the clathrate in the liquid is a diffusion-limited process.

T

The hydrogen−water two-component system (see the phase diagram in Figure 1) exhibits a stable clathrate phase in the pressure range of 1−2 kbar and at temperatures below about −10 °C.14,15 Hydrogen clathrates have a cubic sII structure with

he mechanisms of hydrate nucleation and the kinetics of hydrate growth from water solutions has always attracted interest, both for its technological importance and its fundamental aspects.1 The authentic nucleation process, being a microscopic, nondeterministic, and time-dependent phenomenon that involves a relatively small number of molecules, hardly offers itself to a direct experimental investigation and has been either described qualitatively by different conceptual models,2−4 recently reviewed,5 or addressed by molecular simulation. This technique may provide insight into the nucleation process on space scales difficult to access experimentally, but it has to rely on empirical models for the molecular interaction.6−8 Experimentally, Raman spectroscopy is among the most effective techniques to give information at the molecular level because the vibrational frequencies of the guest molecules are sensitive to their environment (i.e., gas phase, liquid solution, or hydrate phase) and, in principle, to the molecular arrangement around them. This technique has been applied in the past to study the formation of methane (sI and sII) clathrates.9−12 In this Letter, we present the results, obtained by means of in situ Raman spectroscopy on the formation of the pure hydrogen clathrate hydrate (i.e., simple hydrogen clathrate) growing from a supercooled water−hydrogen solution at a pressure of about 2 kbar. Raman spectroscopy can detect very small solid clusters of clathrate but still quite larger, we believe, than a critical nucleus. Despite this, it can give fundamental information on the first stages of clathrate formation, especially in the case of hydrogen, where multiple occupancy of the cages and nonstoichiometric filling occur habitually. © XXXX American Chemical Society

Figure 1. Phase diagram of the water−hydrogen binary system (black15 and gray14 points), superimposed, for comparison, on that of pure water (blue lines13). Different black symbols have the same meaning as in ref 15. The large blue hexagon and the white star represent triple points. We show in red the path followed to cool our sample. Received: September 2, 2015 Accepted: October 12, 2015

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DOI: 10.1021/acs.jpclett.5b01923 J. Phys. Chem. Lett. 2015, 6, 4309−4313

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The Journal of Physical Chemistry Letters 16 small dodecahedral cages (SC) and eight large hexakaidecahedral cages (LC) per unit cell. This experiment poses some technical challenges due to the very high pressure of the sample. Initially, the optical cell, at 280 K and 1990 bar, contains the H2 gas and the liquid at equilibrium, consisting of about 2.5% H2 molar in water solution.16,17 Only the liquid is optically accessible (see the Supporting Information for details on the experiment). Subsequently, the temperature is slowly lowered at constant pressure down to 258 K, entering (for T ≃ 270 K) the supercooled solution region, without observing the phase transformation toward solid clathrate. Also, the vibrational spectra of the hydrogen molecule in solution,17 recorded during cooling, do not show any measurable difference either in the frequency position or in shape while entering into the supercooled fluid region. The path in the phase diagram is shown in Figure 1 by the red line. After reaching 258 K, the system evolution is observed (at almost constant temperature, 258−263 K) by recording several series of Raman spectra at subsequent times, observing principally the hydrogen Q1 vibrational band, but also monitoring the bending mode of liquid water, at around 1620 cm−1, and the clathrate lattice bands in the region of 150−300 cm−1. We have been able, therefore, to detect the presence, and somehow the proportion, in the probed region of the sample, of liquid water, solid clathrate, and hydrogen molecules in the form of either a gas or in solution in liquid water or encaged in the solid clathrate crystal. At the same time, our Raman results lead us to exclude a posteriori the presence of solid ice Ih at any time of the measurement. Actually, the thermodynamic parameters of the experiment were designedly chosen to avoid the stability region of ice Ih. The observation time has been longer than 200 h, up to the total transformation of the sample in solid clathrate. For the first 10 h after the start of the experiment (which we set at the time when the temperature of 258 K is reached), the recorded spectra in the hydrogen vibron region show no difference from that of the hydrogen molecules in solution, featuring a slightly asymmetric peak, about 15 cm−1 wide.17 At a time t ≃ 10 h, two shoulders start to develop on each side of the central peak and become increasingly more intense with time (Figure 2a). These shoulders sit at the same frequency as the peaks of the caged H2 molecules (see below) and demonstrate the presence, in the water solution, of solid clusters with the same cages as an sII clathrate. Later (t ≃ 18 h), the solidification of part of the sample produces a strong increase in the measured intensity but also some change in the geometry of the sample in the cell, so that the Raman signal of hydrogen gas appears in the recorded spectra. An example is in Figure 2b, where the quite intense and narrow peak at 4155 cm−1 and the shoulder at 4160 cm−1 are due to the Q1(1) and Q1(0) lines of hydrogen gas. Meanwhile, the Raman signal from liquid water in the region of the bending mode (about 1620 cm−1) disappears, providing evidence that the solid clathrate fills most of the cell, at least all of the observable part of the sample. From this moment on, the bulk solid sample is in direct contact with the high-pressure gas. This changes in part the physics of the clathrate growth because hydrogen diffusion in the solid starts now to play a role. This process, as will be clear in the following, changes the stoichiometry of the clathrate for a short time interval after t ≃ 18 h, with increased preference for filling of LC. Measurements have been taken for more than 200 h. The spectra obtained after subtraction of either the gas or the

Figure 2. Spectra collected before (a) and after (b) the solidification of most of the sample. The higher black solid line is the experimental spectrum, and the solid blue line is the spectrum of the sole hydrogen clathrate, after subtraction of the spectrum of either hydrogen in solution with water (a) or hydrogen gas (b), shown with a dashed green line.

solution hydrogen lines are consistent with the results measured from a clathrate growing from solid ice in quite similar thermodynamic conditions.18 In both cases, three peaks are evident, the first of which (at lower frequency) appears broader than the other two. It is well know from Raman spectra measured at lower temperature19,20 that a precise assignment of the peaks can be made, letting us distinguish between molecules in the SC and in LC, either alone or in pairs, triplets, or quadruplets. At low temperature, the Q1(J) band displays its structure of two distinct narrow lines.21 The same happens in many other materials containing molecular hydrogen, where the H2 rotation is almost free. Near room temperature, the rotational structure of the Q1(J) band is not observed in any material (with the exclusion of the gas at moderate pressures), and Q1(J) appears as a single band. Examples are solid hydrogen,22 the solid Ar(H2)2 compound,23,24 and hydrogen gas at high pressure, either pure25 or mixed with noble gases.26,27 Therefore, at this temperature, a single band with no rotational splitting is to be expected also for all of the hydrogen molecules in a clathrate cage with the same occupation, as it happens for the mixed THF−H2 clathrate, where the vibrational band of H2 in the small cage appears as a single band.28,29 As discussed in more detail in the Supporting Information, the observed different bands are ascribed to different cage occupations. In particular, the first band in order of increasing frequency, which is quite broader than the other two and even broader than the band due to singly occupied small cages observed in binary THF−H2 clathrates,28,29 is considered as the superposition of the band (SC1) arising from singly occupied SC and the one (LC1) due to singly occupied LC. The second and third peaks are assigned to pairs (LC2) and triplets (LC3) of hydrogen molecules contained in the LC. All of the spectra have been analyzed by a best-fit procedure to extract the contribution of the enclathrated hydrogen molecules. We have used four Lorentzian functions, with fixed frequency positions and width, plus an extra contribution, of known shape, representing either the solute molecules in 4310

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The Journal of Physical Chemistry Letters water or the hydrogen gas, for the two measurements series, respectively. To limit the number of free-fitting parameters, only an intensity factor for the extra contribution has been fitted because the spectral shape of either the solute hydrogen molecules and the hydrogen gas is well-known. Several spectra of the clathrate are reported in Figure 3, after the subtraction of

Figure 4. (a) Total integrated intensity of the clathrate spectrum (black solid squares) and intensity of each band (empty symbols: black squares, blue triangles, red circles, and green inverted triangles indicate, respectively, the intensity of the SC1, LC1, LC2, and LC3 bands). (b) The two different estimates, R′ and R″, of the large cage average occupation number NLC. NLC is always less than or equal to the minimum of the two, and its estimated behavior with time is represented by the blue thick line. In both panels, the vertical gray line at t ≃ 18 h shows the time when the solidification of most of the sample occurs (see text). Error bars represent the statistical error on the fitted parameters.

Figure 3. Spectra of the hydrogen clathrate during formation, after subtraction of the contribution of either the solute hydrogen molecules (a) or the hydrogen gas (b). In (c), the fitted components are shown. These, in order of increasing frequency, will be indicated in the following by SC1, LC1, LC2, and LC3.

the signal due either to the hydrogen in liquid water (panel a) or to the hydrogen gas (panel b). This fit procedure, as described in the Supporting Information, is actually accomplished all at once with the subtraction of the gas or liquid contribution. An example of the fitted spectrum is presented in Figure 3c. This analysis has provided the intensity of each component, which is representative of the number of hydrogen molecules in that condition if we neglect any polarizability difference for H2 in the different cages. In principle, a small difference may exist due to either local field effect19 or change of molecular bond length.30 The first effect has been extensively discussed in ref 20 (section III.A), while the bond length increase when H2 is encaged amounts to only 0.5%,31 which may produce a polarizabilty change of 0.6%,32 completely negligible given the usual accuracy of Raman intensities. The time evolution of the intensity of each band and that of the total intensity associated with the enclathrated molecules are reported in Figure 4a, up to a time of 150 h. For t > 18 h, the reported intensities have not been normalized and present some inessential instrumental fluctuations. The spectral intensity increase for t < 18 h has allowed us to measure the clathrate growth rate when the crystallites are surrounded by the liquid (see the Supporting Information). This rate result is almost the same as the delivery rate of H2 molecules to the solid crystallites when diffusing from the surface of the liquid. This is a clear demonstration that the diffusion of H2 molecules in water is the process slowing down the clathrate growth in our experimental situation. From Figure 4a, we can see that about 60 h is necessary to reach an almost complete clathrate growth, that is, about 95% of the maximum intensity. This value is in good agreement with that obtained at slightly lower pressure by other authors who have measured clathrate growth by means of neutron diffraction.33 In analogy to the analysis done on the basis of the lowtemperature spectra,20 we have estimated the hydrogen

occupation of the SC and LC and studied its evolution during clathrate formation. We indicate with IS the intensity of the band arising from singly occupied SC (SC1) and with I1, I2, and I3 the intensity of the bands LC1, LC2, and LC3, arising from molecules in LC, respectively, alone, in pairs, or in triplets. Because the number of SC is twice the number of the LC, the quantity R′, given by R′ = 2

I1 + I2 + I3 N = LC IS NSC

(1)

represents the ratio of the average number of molecules per each LC (NLC) to the average number of molecule in each SC (NSC). If we assume that each SC is singly occupied (NSC = 1), then R′ = NLC, but in general, we may consider that during clathrate formation, there may be empty small cages; therefore, NSC ≤ 1 and NLC ≤ R′. An alternative and independent way of estimating NLC has been described in ref 20. Indicating with Lm, with m = 1−4 as the fraction of large cages containing m molecules (with some Lm being possibly equal to 0), we have that the intensity Im of each band is proportional to mLm, so that the quantity R″, defined as 4

R″ =

∑m = 1 mLm 4 ∑m = 1 Lm

=

I1 + I2 + I3 + I4 1

1

1

I1 + 2 I2 + 3 I3 + 4 I4

(2)

is equal to NLC in the hypothesis that the number of empty large cages, L0, is zero. In any case, if L0 > 0, we have that 4

4

m=1

m=0

∑ Lm < ∑ Lm, and therefore, NLC ≤ R″. We have then the possibility to measure experimentally two quantities, R′ and R″, each of which is an upper bound for NLC and that coincide 4311

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The Journal of Physical Chemistry Letters

speculate on the nucleation phase, because the size of the sample probed by the Raman technique is much larger that a critical nucleus, we can conclude that the clathrate formation from liquid starts with a preferential filling of small cages. The growth rate of crystallites in the liquid is slow because of the slow diffusion of H2 molecules in water. On the contrary, observing the growth of a sample whose surface is in contact with the hydrogen gas, we have measured a much faster growth and a preferential filling of the large cages. We stress also the different equilibrium stoichiometry between the hydrogen clathrate at 263 K and the one analyzed at 20 K in ref 20. This is due to the different thermodynamic path followed for the synthesis of this latter sample, which, after a growth at the same temperature, experiences a cooling under pressure down to 77 K. The cooling under pressure apparently impacts positively on the hydrogen content, that is, the hydrogen equilibrium stoichiometry is dependent on temperature, increasing at low temperature at constant pressure.

when no empty cages, large or small, are present in the structure, that is NLC ≤ min{R′ , R″}

(3)

It is reasonable to assume that when R′ ≃ R″, also NLC ≃ R′ ≃ R″ and that, in general, NLC ≃ min{R′,R″} . As a consequence, if R″ > R′ ≃ NLC, some empty large cages are present in the sample, and alternatively, if R′ > R″ ≃ NLC, some small cages are empty. The time evolution of R′ (black dots) and R″ (red squares) is reported in Figure 4b. For large times, at equilibrium, the two quantities coincide and have a value R′ ≃ R″ ≃ NLC ≃ 2. During clathrate formation, in the liquid phase, NLC ≃ R′ is sensibly lower than the asymptotic value and grows with time, until the moment (t ≃ 18 h) that we observe the sudden start of the fast clathrate growth. This moment is indicated by a vertical thick gray line in Figure 4 and corresponds to a change of geometry and a radical change in the kinetics of clathrate growth. For larger times, as a matter of fact, the high-pressure gas gets in contact with the already formed solid clathrate, allowing for a much faster diffusion of the gas into the sample compared to the situation when the observed clathrate particles were in contact only with water, with a limited amount of hydrogen gas in solution. Just after this moment, NLC reaches its asymptotic value, while the behavior of R′ and R″, with R′ > R″, indicates an occupation number less than one for the SC that lasts for about another 5 h. The interpretation of these results is as follows. During the first 18 h, we have measured clathrate particles, probably of mesoscopic size, growing from the liquid solution. This is demonstrated by the fact that the region probed by the laser beam is all below the meniscus. In this time, the clathrate is deficient of hydrogen in the large cages, which have, at the beginning, an average occupation number even less than 1. This observation suggests that the clathrate grows from nuclei that arise from an organization of water molecules around one hydrogen molecules forming a small cage. The growth in this phase is hindered by the shortage of hydrogen in solution, which is, in this thermodynamic region, of about 2.5% molar ratio with respect to water, while the solid clathrate, with the stoichiometry measured in this work, contains 23% H2 molecules with respect to water molecules.17 These results can be compared with those relative to methane hydrates.12 In the latter, before the crystallization, the system seems to assume an amorphous phase, but with the small cages that appear before the large ones, hence playing a central role in the first stage of growth. Similar information on cage occupancy during the first stages of clathrate formation has been obtained also for xenon clathrates, by means of NMR spectroscopy.34,35 The comparison with the methane or xenon clathrates is anyhow limited to this fact due to the possibility of multiple occupation of the LC by the hydrogen molecules. Subsequently, when the solid grown in the cell starts to be in contact with gas, the kinetics of growth is strongly sped up, presumably by a much larger diffusion rate in the solid than that in the liquid. In this phase, the LC, which present hexagonal faces larger that the only pentagonal ones of the SC, are filled rapidly with H2 molecules up to equilibrium, and the clathrate grows rapidly, leaving some small cage empty. In conclusion, our data shed new light on the growth of pure hydrogen clathrate from the liquid, presenting Raman spectra obtained in situ at almost 2000 bar and 263 K, at different times during growth and at the final equilibrium. Even if we cannot

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b01923. Experimental details with the description of the scattering cell, discussion of the band assignment and detailed description of the fitting procedure, description of a simple model for the calculation of the diffusion rate of the molecules in the liquid, and comparison with the growth rate of the clathrate grains (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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