Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 6475−6479
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Diffusion of Water Molecules in Quantum Crystals Brendan Moore, Pavle Djuricanin, and Takamasa Momose* Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1, Canada
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S Supporting Information *
ABSTRACT: With the use of solid parahydrogen in matrix isolation spectroscopy becoming more commonplace over the past few decades, it is increasingly important to understand the behavior of molecules isolated in this solid. The mobility of molecules in solid parahydrogen can play an important role in the dynamics of the system. Water molecules embedded in solid parahydrogen as deposited were found to be mobile at 4.0 K on the time scale of a few days. The diffusion at this temperature must be due to quantum tunneling in solid parahydrogen. The diffusion dynamics were analyzed based on the theory of nucleation. The concentration dependence on the diffusion rate indicates that there might be correlated motion of water molecules, a signature of quantum diffusion. We find that both water monomers and water dimers migrate in solid parahydrogen and provide insight into the behavior of molecules embedded in this quantum crystal.
M
atoms27 and Li atoms28 in solid parahydrogen diffuse only at an elevated temperature of 4.3−4.4 K, which is interpreted as thermal diffusion. CH3F molecules were also found to migrate in normal hydrogen at 4.2 K,29 but the diffusion mechanism has not been discussed. Because the use of parahydrogen for matrix isolation spectroscopy has increased over the past 2 decades, understanding the physical stability of embedded molecules in a parahydrogen lattice is of increasing importance. Here, we report our recent findings on the diffusion of water molecules and its clusters in solid parahydrogen at 4.0 K as evidenced by the growth of water clusters30 (H2O)n of n = 3−6 over a few days. Parahydrogen gas was prepared by converting orthohydrogen to parahydrogen by a method described in ref 31. Hydrogen gas (Praxair Canada Inc., 99.99% purity) was flowed through a magnetic catalyst (FeOH)O cooled to 13 K by a closed-cycle refrigerator. This converted the hydrogen gas into 99.95% purity parahydrogen, which was then stored in a cylinder for use. The H2O/parahydrogen mixtures with a H2O concentration of 600, 1200, 1800, and 2400 ppm were prepared by mixing a cylinder prefilled with H2O gas at a certain pressure with the parahydrogen gas. In this study, we employed rapid vapor deposition9 to grow a parahydrogen crystal on a cold substrate. Parahydrogen gas was deposited at a flow rate of 20 ccm onto a wedged BaF2 window (Pier Optics Co., Ltd., 25 mm diameter, 2 mm mean thickness) held by a copper holder with indium and cooled by a closed-cycle Gifford−McMahon refrigerator (Sumitomo Heavy Industries, Ltd., SRDK-205). At the beginning of each crystal growth, pure parahydrogen layers were grown on the substrate for 10 min. Then, a mixed gas of H2O/parahydrogen was deposited for about 90 min. The thickness of each sample
atrix isolation is a technique used to stabilize atoms and molecules in a cryogenic inert medium for spectroscopic studies.1−3 Because the embedded species are frozen in the cryogenic environment and well-isolated from other species, it is particularly suited for the study of reactive species such as free radicals.4 Rare gas solids such as Ne and Ar crystals have been used as the medium for matrix isolation spectroscopy for many years. In the 1990s, solid parahydrogen crystals5−10 were introduced as a medium for matrix isolation. Due to the large zero-point motion of the molecules about their equilibrium positions, these quantum hosts provide more free space for embedded species than other solids, resulting in almost free quantized rotational motion10 as well as a diminished cage effect.8,11−13 While matrix isolation is a technique to stabilize and confine atoms and molecules in a medium, molecules trapped in parahydrogen matrices may migrate through the lattice due to the quantum nature of solid parahydrogen. Indeed, the diffusion of orthohydrogen in solid parahydrogen has been observed by NMR,14 which has been attributed to resonant ortho−para conversion.15 The diffusion of hydrogen atoms has also been studied by ESR16,17 as well as IR spectroscopy,12,18−20 where it was proposed that the diffusion occurs via reactive tunneling.16,17 On the other hand, the diffusion of impurity HD molecules was observed21−23 and was attributed to quantum tunneling.21 In quantum crystals such as solid hydrogen, there is a significant overlap of the wavefunctions of molecules on neighboring lattice sites, which allows defects such as vacancies or impurities to exchange positions with nearest-neighbor molecules. It has been predicted that the defects in quantum crystals will become delocalized and move through the crystal in a coherent manner.24,25 A non-Arrhenius-type temperature dependence on the diffusion rate of HF molecules in solid parahydrogen26 suggests that the diffusion is caused by tunneling assisted by vacancies. On the other hand, Br © 2018 American Chemical Society
Received: September 24, 2018 Accepted: October 30, 2018 Published: October 30, 2018 6475
DOI: 10.1021/acs.jpclett.8b02943 J. Phys. Chem. Lett. 2018, 9, 6475−6479
Letter
The Journal of Physical Chemistry Letters ranged between 650 and 880 μm, estimated from the intensity of the Q1(0) + S0(0) transition of solid parahydrogen.32 The BaF2 window temperature was kept at 4.2 ± 0.5 K during deposition. After the deposition, each sample was left on the window for up to 100 h at a temperature of 4.05 ± 0.05 K (or 4.2 ± 0.05 K) while measuring IR spectra. No annealing was done in order to minimize the initial concentration of large water clusters. We found that the thickness of the hydrogen crystal was reduced by less than 10% over 100 h due to sublimation of solids into the vacuum at 4.0 K. We confirmed that the growth of water clusters reported in this Letter was not affected by the sublimation of parahydrogen within 100 h. We did not observe any difference in the rate of decrease/increase of water clusters for n ≥ 2 even if we covered the water containing hydrogen crystals with additional pure parahydrogen layers such that the evaporated part did not contain any water molecules. Optical measurements were carried out using an FT-IR spectrometer (Bruker, IFS 125HR), equipped with an MIR globar light source and a KBr beam splitter. A liquid-nitrogencooled MCT detector was used for IR detection. Spectra were collected from 700 to 7600 cm−1 with 0.2 cm−1 resolution. The MIR source was redirected away from the sample between scans, exposing the sample to IR only during data collection in order to minimize the effect of the MIR source on any diffusion. In order to check the effect of the MIR source, we also recorded spectra while samples were exposed to the MIR source for the entire experiment. The black traces (a) in Figure 1 show infrared spectra of H2O in solid parahydrogen for initial H2O concentrations of (I) 1200 and (II) 2400 ppm, as examples. At these concentrations, we observed infrared peaks corresponding to
water clusters (H2O)n of n = 2−6 in addition to peaks corresponding to H2O monomers.33 The assignments are based on work by Fajardo and Tam.30 It is seen that peaks corresponding to clusters with n ≥ 2 are increased upon increasing the initial H2O concentration in the mixture. Larger clusters such as the pentamer are seen only in a sample at higher H2O concentrations. It was also observed that the cluster populations in the matrix were changing over time. Traces (b) (blue) and (c) (red) in Figure 1 are spectra taken at 50 and 80 h, respectively, after each deposition, with minimum MIR exposure time. It is seen that the dimer ((H2O)2) peaks have decreased while larger cluster peaks corresponding to n = 3−6 have increased. In a sample of 2400 ppm of H2O, peaks corresponding to both the cyclic form and the cage form of the water hexamer ((H2O)6) were clearly seen after 50 h. The increase in larger cluster peak areas over time must be a result of the diffusion of H2O molecules in solid parahydrogen at 4.0 K. In order to analyze the temporal behavior of each cluster, we focused on the temporal changes of intensities up to the tetramer, whose spectral peak areas were obtained through integration of the infrared spectra. We will discuss the temporal changes of larger water clusters (n ≥ 5) in a separate paper. The temporal changes of each cluster peak for the sample with (A) 600 and (B) 2400 ppm are shown in Figure 2. The integrated windows for each cluster are listed in the Supporting
Figure 1. FTIR spectra of H2O in solid parahydrogen at 4.0 K for initial H2O concentrations of (I) 1200 and (II) 2400 ppm (multiplied by a factor of 0.5). The sample was exposed to the MIR light only during spectral recording. (a) Black trace: spectrum taken immediately after deposition. (b) Blue trace: 50 h after deposition. (c) Red trace: 85 h after deposition. The assignments are based on ref 30. Notations are as follows: cyc-Tri: the cyclic form of (H2O)3; cycTetra: the cyclic form of (H2O)4; cyc-Penta: the cyclic form of (H2O)5; cyc-Hexa: the cyclic form of (H2O)6; and cage-Hexa: the cage form of (H2O)6. Sharp downward peaks in the region of 3500− 3850 cm−1 are due to water vapor in the spectrometer.
Figure 2. Temporal behavior of the integrated area of each cluster peak of a sample with the initial H2O concentration of (A) 600 and (B) 2400 ppm. (a) Red open circle: (H2O)2, (b) black open triangle: cyclic-(H2O)3, (c) blue open square: cyclic-(H2O)4, and (d) green open circle: cyclic-(H2O)5. The y-axis is normalized to the dimer intensity at t = 0. The dashed lines are based on the fitting with Scheme 1, and the solid lines are those with Scheme 2. 6476
DOI: 10.1021/acs.jpclett.8b02943 J. Phys. Chem. Lett. 2018, 9, 6475−6479
Letter
The Journal of Physical Chemistry Letters Information (SI). It is seen that the dimer peaks decreased exponentially, while the trimer peaks initially increased but decreased after ∼50 h. In Figure 2B, the pentamer peaks continuously increased but increased more slowly than those of smaller clusters. These changes indicate that the size of the water clusters grows over a few days. The model that we used for analysis of the temporal behavior is a special case of the discrete Smoluchowski coagulation equation34 dNk 1 = dt 2
k−1
concentrations, which indicates that the water dimer is also mobile in solid parahydrogen. The rate constants ka obtained from the fitting are listed in the SI. Using the relation of ka = β1,a[H2O], the aggregation kernel β1,a can be evaluated. Figure 3 plots the aggregation
∞
∑ βi ,k− iNN i k − i − ∑ βi , k NN i k i=1
Scheme 2
i=1
(1)
where Nk is the concentration of water clusters (H2O)k and βi,k is the aggregation kernel. This model assumes that the cluster dissociation rate is negligible and that the rate of each clustering reaction is diffusion-controlled in the environment. The simplest model that we employed is the one in which only the water monomer is mobile in the solid parahydrogen at 4 K or βi,k = 0 for all i ≥ 2 in eq 1. Because the concentration of the dimer and larger clusters was estimated to be less than 10% of the concentration of the monomer and the change of monomer intensity was a few % at most over the course of the measurements, we assumed that the monomer decay is expressed by an exponential function with a small rate constant. The model has also been discussed as a multistep nucleation model.35 The growth of the size of the water clusters is given by Scheme 1.
Figure 3. Concentration dependence on the aggregation kernels β1,a. Red closed circle: (H2O)2(a = 2) for k2a; black closed triangle: (H2O)3 (a = 3); and blue closed square: (H2O)4 for the sample with limited MIR light exposure. The dashed lines are the fitted curve with a function of β1,a = Ax−αa with a = 2 (red), 3 (black), and 4 (blue). The best-fitted values are α2 = 0.85(22), α3 = 1.34(12), and α4 = 1.43(13). The red open circle, black open triangle, and blue open square are those for the samples with full MIR exposure for a = 2, 3, and 4, respectively.
Scheme 1
In this case, the rate equation in eq 1 reduces to kernel as a function of concentration in ppm. In order to convert from the rate constants ka to the aggregation kernel β1,a, we used the molar volume of solid parahydrogen of 23.06 cm3 mol−136 and assumed that the distribution of monomer water (H2O) is uniform in the solid. The obtained kernel values are, for example, 6.1(3) × 10−31 and 2.7(2) × 10−31 m3 s−1 for (H2O)3 in the sample with initial H2O concentrations of 600 and 1200 ppm, respectively. These values are about the same order of magnitude as the diffusion rate of HF in solid parahydrogen reported by Ooe et al.26 In Figure 3, the aggregation kernels are shown for samples that were kept at either 4.0 or 4.2 K and for both continuous (open markers) and minimized MIR light exposures (filled markers). The kernel for the sample with 600 ppm under continuous MIR exposure was significantly larger than the one for minimized MIR exposure. The diffusion observed here was clearly affected by the phonon excitation of solid parahydrogen by the MIR light source as in the case of HF diffusion.26 The mutual aggregation rate constant βi,k is proportional to the diffusion coefficient, D, of water molecules. What we observe in Figure 3 is that the diffusion coefficient is approximately inversely proportional to the concentration of water molecules. In general, the self-diffusion coefficient, D, in a dilute solution or in solids has been treated as either independent of concentration or linearly proportional to the concentration.37−40 On the other hand, it has been discussed that the diffusion coefficient of impurities in quantum crystals, or impuritons, depends on the concentration, x, as x−1 for
d[(H 2O)a ] = ka − 1[(H 2O)a − 1] − ka[(H 2O)a ] (2) dt where the rate constant ka is related to the concentration of the water monomer [H2O] and the aggregation kernel β1,a as ka = β1,a[H2O]. The solution of the differential equation in eq 2 is given in the SI. It was found that Scheme 1 was sufficient for modeling the cluster population temporal behavior for an initial water concentration of 600 ppm, as shown with the dashed lines in Figure 2A. However, when concentrations above 600 ppm are considered, this model insufficiently describes the temporal behavior of water clusters. The dashed lines shown in Figure 2B represent the deviation of fitted curves based on Scheme 1 from the actual behavior of the dimer, trimer, and tetramer at the 2400 ppm initial H2O concentration. For example, Scheme 1 predicts a delay in the increase in the tetramer population at early times, whereas the actual data show a rapid increase immediately following deposition. This deviation of the model indicates that assuming that only the monomer is mobile may be incorrect. When the mobility of the dimer to form the tetramer is included in the model, as shown in Scheme 2, the agreement improves. The sold lines in Figure 2B show the fitted curves with the new model of the tetramer temporal behavior including the dimer mobility. The solution of the rate equations corresponding to Scheme 2 is given in the SI. The agreement is clearly better than that of Scheme 1 for larger initial H2O 6477
DOI: 10.1021/acs.jpclett.8b02943 J. Phys. Chem. Lett. 2018, 9, 6475−6479
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noninteracting particles, while x−4/3 for interacting particles as a result of correlated motions of quantum particles.25 The concentration dependence shown in Figure 3 is x−1.34(12) for β1,3 and x−1.43(13) for β1,4, which may indicate that the diffusion of water molecules in solid parahydrogen can be treated as correlated quantum particles in quantum crystals. On the other hand, the concentration dependence for the dimer (k2a in Scheme 2) is x−0.85(22). Because the concentration dependence on the kernel for the dimer is not significant enough to determine the parameter α well, it would be necessary to measure the kernels at lower concentrations in order to discuss the parameter α for the dimer quantitatively. The interaction between a water molecule and a hydrogen molecule is on the order of 350 K,41 while the binding energy between the hydrogen molecules in solid hydrogen is only 5 K. Furthermore, the size of a water molecule (a few Å) is on the same order as the lattice constant of solid hydrogen (3.7 Å).36 Therefore, diffusion due to interstitial migration or direct exchange between the positions of a water molecule and a hydrogen molecule by quantum tunneling would be very slow as a result of the localized wavefunction of water molecules. This can explain the observed diffusion time scale of a few days. Another possible mechanism is the diffusion assisted by quantum exchange of vacancies in solid hydrogen. It is known that solid parahydrogen films grown by rapid vapor deposition9 contain both hcp and fcc crystal structures.42 The existence of a metastable fcc structure indicates that the crystal films are highly nonequilibrium. In addition, a detailed X-ray study showed that the structural characteristics of solid hydrogen are significantly affected by doping impurities.43 These facts suggest that the number of vacancies or lattice defects is significantly larger than the thermal population in a doped crystal, which could accelerate the diffusion of water in solid parahydrogen crystals.40 We did not detect any direct evidence of the change of crystal structures between fcc and hcp based on the infrared absorption of hydrogen crystals. Further studies, especially detailed studies on the temperature dependence and MIR irradiation effects, are necessary to understand the mechanism of impurity diffusion in solid parahydrogen. In summary, we have observed that H2O molecules in solid parahydrogen migrate at 4.0 K in samples grown by rapid vapor deposition. In addition to the diffusion of water monomers, it was seen that water dimers may also be migrating. This dimer migration is particularly important at higher water concentrations. The concentration dependence of the diffusion constant indicates that the diffusion of water may be described by those of correlated particles in quantum crystals.
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Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Takamasa Momose: 0000-0001-8976-1938 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by a National Science and Engineering Research Discovery Grant in Canada and funds from the Canada Foundation for Innovation for the Centre for Research on Ultra-Cold Systems (CRUCS) and Chirality Research on Origins and Separation (CHIROS) at UBC.
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REFERENCES
(1) Norman, I.; Porter, G. Trapped Atoms and Radicals in a Glass ‘Cage’. Nature 1954, 174, 508. (2) Broida, H. P.; Pellam, J. R. Phosphorescence of Atoms and Molecules of Solid Nitrogen at 4.2 K. Phys. Rev. 1954, 95, 845−846. (3) Whittle, E.; Dows, D. A.; Pimentel, G. C. Matrix Isolation Method for the Experimental Study of Unstable Species. J. Chem. Phys. 1954, 22, 1943−1943. (4) Jacox, M. E. The spectroscopy of molecular reaction intermediates trapped in the solid rare gases. Chem. Soc. Rev. 2002, 31, 108−115. (5) Oka, T. High-Resolution Spectroscopy of Solid Hydrogen. Annu. Rev. Phys. Chem. 1993, 44, 299−333. (6) Fajardo, M. E.; Tam, S.; Thompson, T. L.; Cordonnier, M. E. Spectroscopy and reactive dynamics of atoms trapped in molecular hydrogen matrices. Chem. Phys. 1994, 189, 351−365. (7) Momose, T.; Uchida, M.; Sogoshi, N.; Miki, M.; Masuda, S.; Shida, T. Infrared spectroscopic studies of photoinduced reactions of methyl radical in solid parahydrogen. Chem. Phys. Lett. 1995, 246, 583−586. (8) Momose, T.; Shida, T. Matrix-Isolation Spectroscopy Using Solid Parahydrogen as the Matrix: Application to High-Resolution Spectroscopy, Photochemistry, and Cryochemistry. Bull. Chem. Soc. Jpn. 1998, 71, 1−15. (9) Fajardo, M. E.; Tam, S. Rapid vapor deposition of millimeters thick optically transparent parahydrogen solids for matrix isolation spectroscopy. J. Chem. Phys. 1998, 108, 4237−4241. (10) Momose, T.; Hoshina, H.; Fushitani, M.; Katsuki, H. Highresolution spectroscopy and the analysis of ro-vibrational transitions of molecules in solid parahydrogen. Vib. Spectrosc. 2004, 34, 95−108. (11) Momose, T.; Fushitani, M.; Hoshina, H. Chemical reactions in quantum crystals. Int. Rev. Phys. Chem. 2005, 24, 533−552. (12) Yoshioka, K.; Raston, P. L.; Anderson, D. T. Infrared spectroscopy of chemically doped solid parahydrogen. Int. Rev. Phys. Chem. 2006, 25, 469−496. (13) Huang, C.-W.; Lee, Y.-C.; Lee, Y.-P. Diminished cage effect in solid p-H2: Infrared spectra of ClSCS, ClCS, and ClSC in an irradiated p-H2 matrix containing Cl2 and CS2. J. Chem. Phys. 2010, 132, 164303. (14) Amstutz, L. I.; Thompson, J. R.; Meyer, H. Observation of Molecular Motion in Solid H2Below 4.2 K. Phys. Rev. Lett. 1968, 21, 1175−1177. (15) Oyarzun, R.; Van Kranendonk, J. Quantum Diffusion in Solid Hydrogen and Deuterium. Phys. Rev. Lett. 1971, 26, 646−648. (16) Kumada, T.; Sakakibara, M.; Nagasaka, T.; Fukuta, H.; Kumagai, J.; Miyazaki, T. Absence of recombination of neighboring H atoms in highly purified solid parahydrogen: Electron spin resonance, electron-nuclear double resonance, and electron spin echo studies. J. Chem. Phys. 2002, 116, 1109−1119. (17) Kumada, T. Experimental determination of the mechanism of the tunneling diffusion of H atoms in solid hydrogen: Physical
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b02943. Solution to the differential equations for Scheme 1 and 2, table summarizing the rate constants ka for various conditions, table summarizing calculated IR intensities of water clusters, and table summarizing the integrated windows for each cluster (PDF) 6478
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The Journal of Physical Chemistry Letters exchange versus chemical reaction. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 4959−4. (18) Fushitani, M.; Momose, T. A study on diffusion of H atoms in solid parahydrogen. Low Temp. Phys. 2003, 29, 740−743. (19) Wonderly, W. R.; Anderson, D. T. Reactions of Atomic Hydrogen with Formic Acid and Carbon Monoxide in Solid Parahydrogen II: Deuterated Reaction Studies. J. Phys. Chem. A 2014, 118, 7653−7662. (20) Balabanoff, M. E.; Ruzi, M.; Anderson, D. T. Signatures of a quantum diffusion limited hydrogen atom tunneling reaction. Phys. Chem. Chem. Phys. 2018, 20, 422−434. (21) Edwards, C. M.; Sullivan, N. S.; Zhou, D. Quantum Diffusion of HD Impurities in Solid Hydrogen. Phys. Scr. 1987, T19B, 458−461. (22) Zhou, D.; Edwards, C. M.; Sullivan, N. S. Quantum diffusion of vacancies and impurities in solid hydrogen. Phys. Rev. Lett. 1989, 62, 1528−1531. (23) Kisvarsanyi, E. G.; Sullivan, N. S. Quantum tunneling in solid D2and solid.H2. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51, 3462−3468. (24) Andreev, A. F.; Lifshitz, I. M. Quamtum theory of defects in crystals. Sov. Phys. JETP 1969, 29, 1107−1113. (25) Andreev, A. F. Diffusion in quantum crystals. Sov. Phys. Usp. 1976, 19, 137−148. (26) Ooe, H.; Miyamoto, Y.; Kuma, S.; Kawaguchi, K.; Nakajima, K.; Nakano, I.; Sasao, N.; Tang, J.; Taniguchi, T.; Yoshimura, M. Diffusion of hydrogen fluoride in solid parahydrogen. J. Chem. Phys. 2013, 138, 214309−7. (27) Kettwich, S. C.; Pinelo, L. F.; Anderson, D. T. Synthesis and infrared characterization of Br−HBr and Br−DBr entrance channel complexes in solid parahydrogen. Phys. Chem. Chem. Phys. 2008, 10, 5564−5573. (28) Pinelo, L. F.; Klotz, E. R.; Wonderly, W. R.; Paulson, L. O.; Kettwich, S. C.; Kubelka, J.; Anderson, D. T. Solid Parahydrogen Infrared Matrix Isolation and Computational Studies of Li-(C2H4)m Complexes. J. Phys. Chem. A 2018, 122, 985−991. (29) Abouaf-Marguin, L.; Vasserot, A. M. Infrared spectroscopy of solid normal hydrogen doped with CH3F and O2 at 4.2 K: CH3F:O2 complex and CH3F migration. Low Temp. Phys. 2011, 37, 357−362. (30) Fajardo, M. E.; Tam, S. Observation of the cyclic water hexamer in solid parahydrogen. J. Chem. Phys. 2001, 115, 6807. (31) Tom, B. A.; Bhasker, S.; Miyamoto, Y.; Momose, T.; McCall, B. J. Producing and quantifying enriched para-H2. Rev. Sci. Instrum. 2009, 80, 016108. (32) Tam, S.; Fajardo, M. E. Single and Double Infrared Transitions in Rapid-Vapor-Deposited Parahydrogen Solids: Application to Sample Thickness Determination and Quantitative Infrared Absorption Spectroscopy. Appl. Spectrosc. 2001, 55, 1634−1644. (33) Fajardo, M. E.; Tam, S.; DeRose, M. E. Matrix isolation spectroscopy of H2O, D2O, and HDO in solid parahydrogen. J. Mol. Struct. 2004, 695−696, 111−127. (34) Smoluchowski, M. V. Drei Vortrage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen. Zeitschrift fur Physik 1916, 17, 557−585. (35) Allnatt, A. R.; Jacobs, P. W. M. Theory of nucleation in solid state reactions. Can. J. Chem. 1968, 46, 111−116. (36) Souers, P. C. Hydrogen Properties for Fusion Energy; University of California Press: Berkeley, CA, 1986. (37) Akcasu, A. Z. Temperature and concentration dependence of diffusion coefficient in dilute solutions. Polymer 1981, 22, 1169−1180. (38) KopsWerkhoven, M. M.; Pathmamanoharan, C.; Vrij, A.; Fijnaut, H. M. Concentration dependence of the selfdiffusion coefficient of hard, spherical particles measured with photon correlation spectroscopy. J. Chem. Phys. 1982, 77, 5913−5922. (39) Heitjans, P.; Kärger, J. Diffusion in Condensed Matter; SpringerVerlag: Berlin Heidelberg, 2005. (40) Mehrer, H. Diffusion in Solids, Fundamentals, Methods, Materials, Diffusion-Controlled Processes; Springer-Verlag: Berlin Heidelberg, 2007.
(41) Hodges, M. P.; Wheatley, R. J.; Schenter, G. K.; Harvey, A. H. Intermolecular potential and second virial coefficient of the water− hydrogen complex. J. Chem. Phys. 2004, 120, 710−720. (42) Tam, S.; Fajardo, M. E.; Katsuki, H.; Hoshina, H.; Wakabayashi, T.; Momose, T. High resolution infrared absorption spectra of methane molecules isolated in solid parahydrogen matrices. J. Chem. Phys. 1999, 111, 4191−4198. (43) Galtsov, N. N.; Prokhvatilov, A. I.; Shcherbakov, G. N.; Strzhemechny, M. A. Properties of solid hydrogen doped by heavy atomic and molecular impurities. Low Temp. Phys. 2003, 29, 784− 787.
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