Next Article in Journal
Reference Data by Player Position for an Ice Hockey-Specific Complex Test
Next Article in Special Issue
A Review of Reactor Designs for Hydrogen Storage in Clathrate Hydrates
Previous Article in Journal
An Unsupervised Generative Adversarial Network-Based Method for Defect Inspection of Texture Surfaces
Previous Article in Special Issue
Intra-Cage Structure, Vibrations and Tetrahedral-Site Hopping of H2 and D2 in Doubly-Occupied 51264 Cages in sII Clathrate Hydrates from Path-Integral and Classical Molecular Dynamics
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Applied Sciences
Volume 11
Issue 1
10.3390/app11010282
applsci-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Hydrogen Inter-Cage Hopping and Cage Occupancies inside Hydrogen Hydrate: Molecular-Dynamics Analysis

by
Yogeshwaran Krishnan
1,
Mohammad Reza Ghaani
1,*,
Arnaud Desmedt
2 and
Niall J. English
1,*
1
School of Chemical and Bioprocess Engineering, University College Dublin, Dublin 4 Belfield, Ireland
2
Institut des Sciences Moléculaires UMR5255 CNRS-Univ, Bordeaux, F-33405 Talence, France
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2021, 11(1), 282; https://doi.org/10.3390/app11010282
Submission received: 30 October 2020 / Revised: 15 December 2020 / Accepted: 21 December 2020 / Published: 30 December 2020
(This article belongs to the Special Issue Hydrogen Storage in Gas Hydrates)
Browse Figures
Versions Notes

Abstract

:
The inter-cage hopping in a type II clathrate hydrate with different numbers of H2 and D2 molecules, from 1 to 4 molecules per large cage, was studied using a classical molecular dynamics simulation at temperatures of 80 to 240 K. We present the results for the diffusion of these guest molecules (H2 or D2) at all of the different occupations and temperatures, and we also calculated the activation energy as the energy barrier for the diffusion using the Arrhenius equation. The average occupancy number over the simulation time showed that the structures with double and triple large-cage H2 occupancy appeared to be the most stable, while the small cages remained with only one guest molecule. A Markov model was also calculated based on the number of transitions between the different cage types.

1. Introduction

Hydrogen is a non-polluting fuel, and it is viewed as a promising substitute for fossil fuels and clean fuel that might be on the horizon. When it ignites, it simply conveys water vapour into the atmosphere, not in any way like non-sustainable power sources, such as oil, vaporous petroleum, and coal, i.e., fuels that contain carbon and produce carbon dioxide (CO2) or carbon monoxide (CO), including a higher extent of carbon outpourings, nitrogen oxides (NOx), and sulphur dioxide (SO2). Non-sustainable power sources, in a like manner, release ash particles into the earth, which is significantly contributing to global warming. Global warming has also risen to severe levels due to huge emissions of CO2 into the atmosphere due to the heavy dependence of people on limited fossil fuels as energy resources [1,2,3]. Among several alternative fuel sources, hydrogen (H2) has gained focus because it provides primary advantages and meets ideal fuel requirements [4], and is also one of the most promising and vital fuels for the future [5].
Hydrogen is great, significantly copious, and renewable, economical fuel and packs imperativeness per unit mass like some other exorbitant empowers. H2 can be used for power generation, transportation and heating as a highly efficient fuel [6].
The major issue with this fuel is its storage, since it ought to be taken care of like other compacted gases. Hydrogen is regularly stored in three methods, i.e., compression, liquefaction (changing the phase from gas to liquid), and as a solid material [7,8].
Clathrate hydrates are inclusion compounds which incorporate guest molecules inside the polyhedral cages of the host framework, which is made up of hydrogen-bonded water molecules [9]. Within the clathrate lattice, water molecules form a network of hydrogen-bonded cavity structures that enclose the guests, the latter generally comprising single or mixed low-molecular-diameter gases and/or organic compounds (e.g., methane, tetrahydrofuran(THF)) [10,11,12,13,14,15].
In recent years, clathrate hydrates have generated much interest in the study of hydrogen storage, as a possible future energy-storage medium. Molecular dynamics (MD) has been significant in advancing our understanding in hydrate science at the atomistic level of insight. This has added to our understanding of clathrate hydrates’ thermodynamic properties and their possibilities for energy stockpiling, especially of hydrogen. Indeed, these MD methodologies might be deployed to a greater degree in the coming decade, as what appears computationally ‘heroic’ today may turn out to be routinely available in the hydrate simulation network in the medium-term future [16,17,18]. During much of the 20th century, it had been suspected that the molecular size of hydrogen was too small to confer appreciable thermodynamic stabilisation to clathrate hydrates [10,19], although more recent investigations in the past 20 years or so show that a large degree of H2 (perhaps up to around 5 wt %, albeit with some uncertainty) can be accommodated in cubic structure II clathrate hydrates under higher-pressure conditions (i.e., at pressures of around 1 GPa and higher at ambient temperature conditions) [20,21]. Understandably, this revelation has provoked significant examination into clathrate hydrates as potential hydrogen storage materials [20,21,22,23,24].
Given this great, and well-justified, interest in hydrogen hydrates as a hydrogen-storage material, in the present study, we are motivated by unresolved, open questions pertaining to both H2 inter-cage diffusivity and cage occupancies, which have a substantial bearing on hydrates as a viable energy-storage medium. Inter-cage hopping is a phenomenon in which the guest molecule (D2 or H2) will move from one cage to another cage, for example, small to small, or small to large, or large to large. Indeed, in order to obtain better insights into the different aspects of the inter-cage hopping of the guest molecules inside a clathrate hydrate, we have scrutinised the cage-to-cage molecular hopping movement of H2 molecules inside a stable hydrate as a function of temperature, whilst also studying cage occupancies and activation-energy profiles. In order to assess potential isotopic effects in these cage-hopping phenomena, the behaviour of a deuterium (D2) molecule was also studied in this work.

2. Computational Details

Hydrogen molecules were placed in a 2 × 2 × 2 sII-clathrate supercell with a box size of 3.42 nm on each side, with 51264 large cages (i.e., with 12 pentagonal faces and 4 hexagonal ones) and small-cage 512 dodecahedra (each composed of 12 water pentamers). The Periodic Boundary Condition (PBC) was applied for the x, y and z directions. The calculation was performed in four different configurations, with each large cage holding one to four (1, 2, 3 and 4) molecules as a guest, and each small cage holding only one molecule as a guest. The other set of four calculations was performed using D2 molecules as the substitute for H2 molecules. The parameters for both calculations were the same; however, the D2 is a stable isotope of hydrogen, i.e., D2 contains one proton and one neutron, and H2 contains only one proton. In order to properly reproduce the experimental gas-phase quadrupole moment of H2 and D2, the same intermolecular potential parameters were used as in previous MD investigation of sII hydrogen hydrate [25]. A Lennard-Jones 12-6 with a 6.8 Å cut-off was implemented, whilst the smooth particle-mesh Ewald method [26] was used to handle the long-range electrostatics. The selected four-site water model, TIP4P/2005, was also used in many simulation studies on hydrate structures [27,28]. The velocity Verlet algorithm was used for the molecular dynamics (MD) simulations with a time step of 3.33 fs using the canonical NVT ensemble, featuring a Nosé–Hoover relaxation time of 5 ps, for a total time of 50 ns [29]. The trajectories were performed at nine different temperatures: 80 K, 100 K, 120 K, 140 K, 160 K, 180 K, 200 K, 220 K and 240 K. All of the simulations were performed in the GROMACS 5.1 package [30,31,32,33,34]. The sII-clathrate lattice [25] was used in our calculations, and it is shown in Figure 1.
The diffusion coefficients (D) [35] of the H2 and D2 molecules were calculated by the limiting-slope analysis of the mean squared displacement (MSD) for the entire temperature range—from 80 K to 240 K—at intervals of 20K (see Figures S1 and S2, Supporting Information). The travel of the H2 and D2 molecules inside the clathrate–hydrate structure, facilitated by inter-cage hopping migration [36,37,38], was analysed and captured as Markov-chain models [39]. It is important to realize that not all states will make a significant contribution to the configurational properties of the system. In order to accurately determine the properties of the system in the finite time available for the simulation, it is important to sample those states that make the most significant contributions. This is achieved by the generation of a Markov chain.

3. Result and Discussion

The calculated diffusion coefficients at the different temperatures for each of the simulated systems are presented in Figure 2; for the H2 and D2 systems, the values are tabled in Tables S3 and S4, respectively (see SI). The clathrate hydrates are of special interest because they are less dense than regular ice and, under negative pressure, are expected to be stable [29,40,41,42,43,44,45]; the density of the clathrate hydrate is also less in low temperatures, and the density increases with the temperature, as shown in the Table S4 (see SI). The diffusion coefficient is a physical constant dependent on the molecule size and other properties of the diffusing substance, as well as on temperature and pressure. The diffusion coefficient increases with the temperature, as can be expected for thermally-activated Brownian motion. The diffusion coefficient can be connected to the temperature by the Arrhenius expression, in which the amount of existing potential barriers (activation energy) plays the main role. In the double occupancy configuration, the diffusion coefficient does not change in low temperatures, and it has higher D values in high temperatures from 200 K to 240 K compared to the single occupancy. The triple occupancy showed higher D values than the single and double occupancies. Indeed, this is not unexpected, in that there are more frequent guest–guest collisions inside cages, which propel and push them to rearrange themselves dynamically, and leads to a greater propensity for a ‘momentum kick’ to hop to a neighbouring cage (with Newton’s Third Law providing equal and opposite pairwise reaction-kick forces on the other guests). This phenomenon of ‘crowding out’ becomes even more pronounced for quadruple occupation, and this same increase of the self-diffusivity is also seen in Figure 2.
The activation energy for each system was derived based on the different D values at different temperatures using the Arrhenius equation (Figure S3b,d), and the values are summarized in the Table 1 for both the hydrogen and deuterium systems. The calculated energy barrier (Ea) for the diffusion inside the bulk hydrate structure revealed that the inter-cage hopping in the model with four occupancies is more favorable, from a thermodynamic point of view, for both the H2 and D2 systems. Despite the statistically significantly different diffusion coefficient for H2 and D2, the activation energies for both systems are almost similar. This similarity shows that the dynamics of the water molecules in the hydrate structure are the controlling parameters during the hopping process, and they do not depend greatly on the traveling gas type. Such an observation is confirmed by recent experimental results obtained on the H2 long-range diffusion in gas hydrate-containing H-bond defects. In such ionic hydrates, the H2O relaxation occurs on a shorter timescale than hydrates without H-bond defects [46,47], facilitating cage deformation [48]; thus, the H2 diffusion is measured to be faster than in the same hydrate without H-bond defects [49].
The most probable origin of a lower activation energy for the higher-occupancy systems is the deformation of the cage due to the increased cage occupancy. Figure 3 represents the average cage radius for small and large cages, and the increase in the radius in going from triple to quadruple occupation is clearly evident, with the increasing temperature serving to exaggerate this cage stretching further (see SI Figure S3. The extent of the deformation also becomes more evident at high temperatures, with Figure 3 showing larger cage-radius deviations for higher occupancies and temperatures; there is greater distortion to the cages, which is sometimes anisotropic, as hexagonal rings, in particular, flex and stretch to allow the passage of cage-hopping H2 and D2 molecules, which increase in frequency at higher temperatures and cage occupancies owing to the greater amplitude of guest–guest collisions.
The cage occupancies for both the large and small cages were calculated for all of the simulated systems over the full simulation time at different temperatures, and are reported in Figure 4. At all of the temperatures for both the H2 and D2 containing models, in the case of the 1, 2 and 3-occupancy systems, the average occupancy for small cages was found to be less than one, whilst the large cages contain a higher number of guest molecules with respect to the starting structure. Instead, a system with four guest molecules in large cages exhibits a cage occupancy greater than one for small cages and less than four of the large cages, in order to minimise the level of cage and lattice deformation for hosting such a high number of guests. In this way, the overall energy of the full hydrate structure is lowered over time.
It is interesting that the small-cage D2 and H2 occupancies are almost identical at around 0.95 for both the nominal (i.e., initial) double- and triple-occupation of the large cages (cf. Figure 4). In this case, we see that there is less ‘leakage’ of the small-cavity H2 and D2 into the large cages than for (initial) single large-cage occupancies, for the essential equalisation of guest chemical potentials across the cage types in the most stable, lowest-energy systems. For the initial quadruple occupancy, with the cage distortion that this entails, there is occasional small-cage double occupation (i.e., circa 1.06, cf. Figure 4), which is energetically less preferred. Still, the large level of guest–guest repulsion in the large cages, especially at 240 K, leads to partial double-filling of small cages (for about 7½% of them at 240 K, for both H2 and D2).
A Markov chain is a sequence of trials in which the outcome of a successive trial depends only on the immediate predecessor. In a Markov chain, a new state will only be accepted if it is more favourable than the existing state. In the context of a simulation using an ensemble, this usually means that the new trial state is lower in energy. In the present study, one cage-hop travel is enumerated for Markov consideration if a guest molecule moves from one cage to a secondary cage. Each travel was labelled based on the starting and the secondary cage type, i.e., as Large-to-Large (LL), Large-to-Small (LS), Small-to-Large (SL), and Small-to-Small (SS) (cf. Figure 5).
The Markov model was calculated for all of the simulated systems at all of the temperatures. It was found that, in our system, LL travel dominates in inter-cage hopping. Each LL cage-hop transition represents a molecule passing through a hexagonal ring shared between each large cage. Keeping in mind the structure of a large cage in type II hydrate (51264), this means that each large cage has four ‘gates’ that are preferable for guest hopping, and twelve pentagonal portals with a much smaller priority and probability (Table 2).
The inter-cage hopping also depends upon the number of guest molecules present in the large cage, as well as their underlying (cage-hopping-dominated) [36] self-diffusivity. SL and LS showed almost the same probability in inter-cage hopping. The results of the inter cage hopping are illustrated in Figure 6, and the detailed tables are given in Tables S1 and S2 in the SI Section for H2 and D2, respectively. As discussed previously (Figure 4) in the systems with one or two occupancies, the cage radius is quite similar; therefore, lowering the number of molecules in the larger cages in the double-occupancy case will result in the lower flexibility of the cage structure, and serves to limit small-to-small (SS) cage-hop transitions in the case of higher-occupancy models. However, at a higher occupancy, the larger cage size (i.e., subject to cage deformation), owing to the larger number of guest molecules in the large cages, serves to rationalise the higher level of SL and LS migrations observed in Figure 6c,d.

4. Conclusions

The main aim of this article was to explore the inter-cage hopping of hydrogen molecules in the bulk structure of type II hydrate. Using classic molecular dynamics simulations, the effects of nominal (initial) large-cage composition and temperature on the number of inter-cage transitions and the dependence on cage occupancy were studied. In parallel, by the substitution of H2 molecules with D2 molecules, the behaviour of the heavier isotope was also investigated. The activation energy for the guest-molecule (inter-cage) diffusion was found to be the highest for the 1-occupancy model, whilst this number for the 2- and 3-occupancy was almost at the same level, but still lower than the 1-occupancy model. For the lattice-strained 4-occupancy system, this number was about two times lower than the 1-occupancy system, and almost 40% lower than the systems with 2- and 3-occupancy, owing to the larger amplitude of (thermally-activated) guest–guest collisions inducing H2 and D2 to ‘spill out’ of large cages and ingress partly into small ones.
The average occupancy for both the large and small cages for all of the systems showed the overall preference of the system to minimise the occupancy of small cages and overload the larger cages. It was found that, for the system starting with four guest molecules, the system allowed some of the small cages to have two guest molecules in order to decrease the average occupancy of the large cages to lower than that of the initial structure. Furthermore, by developing the Markov model, we confirmed the preference of hydrogen molecules to travel through the hexagonal ring, via large-to-large (LL) cage hopping, rather than the less-probable large-to-small (LS) or small-to-small (SS) transitions. The D2 molecules showed a statistically significant lower diffusion rate, while the diffusion activation energies for both cases were almost the same. Further studies, such as the one reported by Brumby et al. [50] on Gibbs-ensemble MC calculations to ascertain the right cage occupancies, would be ripe for future MSD and hopping/Markov analysis, along the lines of what we have performed here.

Supplementary Materials

The following are available online at https://www.mdpi.com/2076-3417/11/1/282/s1, Figure S1: Mean Square Displacement for Hydrogen in clathrate hydrate, Figure S2: Mean Square Displacement for Deuterium in clathrate hydrate, Figure S3: Averaged cage radius with respect to temperature, Figure S4: Simulation box pressure vs temperature, Table S1: Markov chain model for Hydrogen, Table S2: Markov chain model for Deuterium, Table S3: Diffusion constants for D2 with respect to temperature, Table S4: Diffusion constants for H2 with respect to temperature.

Author Contributions

Conceptualization, M.R.G. and Y.K.; methodology, M.R.G. and Y.K.; software, Y.K.; validation, M.R.G. and Y.K.; formal analysis, Y.K.; investigation, M.R.G., Y.K., A.D. and N.J.E.; writing—original draft preparation, M.R.G. and Y.K.; writing—review and editing, M.R.G., Y.K., A.D. and N.J.E.; supervision, M.R.G. and N.J.E.; project administration, N.J.E.; funding acquisition, M.R.G. and N.J.E. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Science Foundation Ireland (SFI 17/NSFC/5229) and Irish Research Council (GOIPD/2016/365).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

N.J.E. and Y.K. thank Science Foundation Ireland (SFI 17/NSFC/5229). M.R.G. thanks the Irish Research Council for a Government of Ireland postdoctoral fellowship (GOIPD/2016/365), whilst N.J.E. also thanks Science Foundation Ireland for funding under grant SFI 15/ERC-I3142. All authors thank Christian Burnham and Zdenek Futera for computational and technical assistance, as well as interesting and stimulating discussions.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Al-Juboori, O.; Sher, F.; Khalid, U.; Niazi, M.B.K.; Chen, G.Z. Electrochemical Production of Sustainable Hydrocarbon Fuels from CO2 Co-electrolysis in Eutectic Molten Melts. ACS Sustain. Chem. Eng. 2020, 8, 12877–12890. [Google Scholar] [CrossRef]
  2. Al-Juboori, O.; Sher, F.; Hazafa, A.; Khan, M.K.; Chen, G.Z. The effect of variable operating parameters for hydrocarbon fuel formation from CO2 by molten salts electrolysis. J. CO2 Util. 2020, 40, 101193. [Google Scholar] [CrossRef]
  3. Al-Shara, N.K.; Sher, F.; Yaqoob, A.; Chen, G.Z. Electrochemical investigation of novel reference electrode Ni/Ni(OH)2 in comparison with silver and platinum inert quasi-reference electrodes for electrolysis in eutectic molten hydroxide. Int. J. Hydrogen Energy 2019, 44, 27224–27236. [Google Scholar] [CrossRef]
  4. Al-Shara, N.K.; Sher, F.; Iqbal, S.Z.; Curnick, O.; Chen, G.Z. Design and optimization of electrochemical cell potential for hydrogen gas production. J. Energy Chem. 2020, 52, 421–427. [Google Scholar] [CrossRef]
  5. Al-Shara, N.K.; Sher, F.; Iqbal, S.Z.; Sajid, Z.; Chen, G.Z. Electrochemical study of different membrane materials for the fabrication of stable, reproducible and reusable reference electrode. J. Energy Chem. 2020, 49, 33–41. [Google Scholar] [CrossRef]
  6. Sher, F.; Al-Shara, N.K.; Iqbal, S.Z.; Jahan, Z.; Chen, G.Z. Enhancing hydrogen production from steam electrolysis in molten hydroxides via selection of non-precious metal electrodes. Int. J. Hydrogen Energy 2020, 45, 28260–28271. [Google Scholar] [CrossRef]
  7. Züttel, A. Hydrogen storage methods. Naturwissenschaften 2004, 91, 157–172. [Google Scholar] [CrossRef] [PubMed]
  8. Fichtner, M. Nanotechnological aspects in materials for hydrogen storage. Adv. Eng. Mater. 2005, 7, 443–455. [Google Scholar] [CrossRef]
  9. Mao, W.L.; Mao, H.; Goncharov, A.F.; Struzhkin, V.V.; Guo, Q.; Hu, J.; Shu, J.; Hemley, R.J.; Somayazulu, M.; Zhao, Y. Hydrogen Clusters in Clathrate Hydrate. Science 2002, 297, 2247–2249. [Google Scholar] [CrossRef]
  10. Humphry Davy, I. The Bakerian Lecture. On some of the combinations of oxymuriatic gas and oxygene, and on the chemical relations of these principles, to inflammable bodies. Philos. Trans. R. Soc. Lond. 1811, 101, 1–35. [Google Scholar] [CrossRef]
  11. Krishnan, Y.; Ghaani, M.R.; English, N.J. Electric-Field Control of Neon Uptake and Release to and from Clathrate Hydrates. J. Phys. Chem. C 2019. [Google Scholar] [CrossRef]
  12. Alavi, S.; Ripmeester, J.A. Hydrogen-gas migration through clathrate hydrate cages. Angew. Chem. Int. Ed. 2007, 46, 6102–6105. [Google Scholar] [CrossRef] [Green Version]
  13. Ma, R.; Zhong, H.; Liu, J.; Zhong, J.; Yan, Y.; Zhang, J.; Xu, J. Molecular insights into Cage Occupancy of hydrogen hydrate: A computational study. Processes 2019, 7, 699. [Google Scholar] [CrossRef] [Green Version]
  14. Ghaani, M.R.; English, N.J. Non-equilibrium molecular-dynamics study of electromagnetic-field-induced propane-hydrate dissociation. J. Chem. Phys. 2018, 149. [Google Scholar] [CrossRef]
  15. Ghaani, M.R.; Catti, M. Dehydrogenation properties of the LiNH2BH3/MgH2 and LiNH2BH3/LiBH4 bi-component hydride systems for hydrogen storage applications. Mater. Renew. Sustain. Energy 2018, 7, 1–6. [Google Scholar] [CrossRef] [Green Version]
  16. Hasegawa, T.; Brumby, P.E.; Yasuoka, K.; Sum, A.K. Mechanism for H 2 diffusion in sII hydrates by molecular dynamics simulations. J. Chem. Phys. 2020, 153, 054706. [Google Scholar] [CrossRef]
  17. English, N.J.; MacElroy, J.M.D. Perspectives on molecular simulation of clathrate hydrates: Progress, prospects and challenges. Chem. Eng. Sci. 2015, 121, 133–156. [Google Scholar] [CrossRef]
  18. Erfan-Niya, H.; Modarress, H.; Zaminpayma, E. Computational study on the structure II clathrate hydrate of methane and large guest molecules. J. Incl. Phenom. Macrocycl. Chem. 2011, 70, 227–239. [Google Scholar] [CrossRef]
  19. Loveday, J.S.; Nelmes, R.J. High-pressure gas hydrates. Phys. Chem. Chem. Phys. 2008, 10, 937–950. [Google Scholar] [CrossRef]
  20. Sloan, E.D., Jr.; Koh, C.A. Clathrate Hydrates of Natural Gases; CRC Press: Boca Raton, FL, USA, 2007. [Google Scholar]
  21. Falenty, A.; Hansen, T.C.; Kuhs, W.F. Formation and properties of ice XVI obtained by emptying a type sII clathrate hydrate. Nature 2014, 516, 231–233. [Google Scholar] [CrossRef]
  22. Gies, H.; Liebau, F.; Gerke, H. “Dodecasile”—Eine neue Reihe polytyper Einschlußverbindungen von SiO2. Angew. Chem. 2006, 94, 214–215. [Google Scholar] [CrossRef]
  23. Guloy, A.M.; Ramlau, R.; Tang, Z.; Schnelle, W.; Baitinger, M.; Grin, Y. A guest-free germanium clathrate. Nature 2006, 443, 320–323. [Google Scholar] [CrossRef] [PubMed]
  24. Gryko, J.; McMillan, P.F.; Marzke, R.F.; Ramachandran, G.K.; Patton, D.; Deb, S.K.; Sankey, O.F. Low-density framework form of crystalline silicon with a wide optical band gap. Phys. Rev. B Condens. Matter Mater. Phys. 2000, 62, R7707–R7710. [Google Scholar] [CrossRef]
  25. Alavi, S.; Ripmeester, J.A.; Klug, D.D. Molecular-dynamics study of structure II hydrogen clathrates. J. Chem. Phys. 2005, 123. [Google Scholar] [CrossRef]
  26. Essmann, U.; Perera, L.; Berkowitz, M.L.; Darden, T.; Lee, H.; Pedersen, L.G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577–8593. [Google Scholar] [CrossRef] [Green Version]
  27. Alavi, S.; Shin, K.; Ripmeester, J.A. Molecular dynamics simulations of hydrogen bonding in clathrate hydrates with ammonia and methanol guest molecules. J. Chem. Eng. Data 2015, 60, 389–397. [Google Scholar] [CrossRef] [Green Version]
  28. Nath Chakraborty, S.; Gelb, L.D. A Monte Carlo simulation study of methane clathrate hydrates confined in slit-shaped pores. J. Phys. Chem. B 2012, 116, 2183–2197. [Google Scholar] [CrossRef]
  29. Huang, Y.; Zhu, C.; Wang, L.; Cao, X.; Su, Y.; Jiang, X.; Meng, S.; Zhao, J.; Zeng, X.C. A new phase diagram of water under negative pressure: The rise of the lowest-density clathrate s-III. Sci. Adv. 2016, 2, e1501010. [Google Scholar] [CrossRef] [Green Version]
  30. Bekker, H.; Berendsen, H.J.C.; Van Drunen, R.; Spoel, D. Van Der Gromacs: A parallel computer for molecular dynamics simulations. Phys. Comput. 1993, 92, 252–256. [Google Scholar]
  31. Berendsen, H.J.C.; van der Spoel, D.; van Drunen, R. GROMACS: A message-passing parallel molecular dynamics implementation. Comput. Phys. Commun. 1995, 91, 43–56. [Google Scholar] [CrossRef]
  32. Lindahl, E.; Hess, B.; van der Spoel, D. GROMACS 3.0: A package for molecular simulation and trajectory analysis. J. Mol. Model. 2001, 7, 306–317. [Google Scholar] [CrossRef]
  33. Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A.E.; Berendsen, H.J.C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701–1718. [Google Scholar] [CrossRef] [PubMed]
  34. Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  35. Ghesquière, P.; Mineva, T.; Talbi, D.; Theulé, P.; Noble, J.A.; Chiavassa, T. Diffusion of molecules in the bulk of a low density amorphous ice from molecular dynamics simulations. Phys. Chem. Chem. Phys. 2015, 17, 11455–11468. [Google Scholar] [CrossRef] [Green Version]
  36. Cao, H.; English, N.J.; MacElroy, J.M.D. Diffusive hydrogen inter-cage migration in hydrogen and hydrogen-tetrahydrofuran clathrate hydrates. J. Chem. Phys. 2013, 138, 094507. [Google Scholar] [CrossRef]
  37. Burnham, C.J.; English, N.J. Free-energy calculations of the intercage hopping barriers of hydrogen molecules in clathrate hydrates. J. Phys. Chem. C 2016, 120, 16561–16567. [Google Scholar] [CrossRef]
  38. Lu, Q.; He, X.; Hu, W.; Chen, X.; Liu, J. Stability, Vibrations, and Diffusion of Hydrogen Gas in Clathrate Hydrates: Insights from Ab Initio Calculations on Condensed-Phase Crystalline Structures. J. Phys. Chem. C 2019, 123, 12052–12061. [Google Scholar] [CrossRef]
  39. Ferdows, M.; Ota, M. Molecular simulation study for CO2 clathrate hydrate. Chem. Eng. Technol. 2005, 28, 168–173. [Google Scholar] [CrossRef]
  40. Matsui, T.; Hirata, M.; Yagasaki, T.; Matsumoto, M.; Tanaka, H. Communication: Hypothetical ultralow-density ice polymorphs. J. Chem. Phys. 2017, 147. [Google Scholar] [CrossRef]
  41. Huang, Y.; Zhu, C.; Wang, L.; Zhao, J.; Zeng, X.C. Prediction of a new ice clathrate with record low density: A potential candidate as ice XIX in guest-free form. Chem. Phys. Lett. 2017, 671, 186–191. [Google Scholar] [CrossRef]
  42. Kosyakov, V.I.; Shestakov, V.A. On the possibility of the existence of a new ice phase under negative pressures. Dokl. Phys. Chem. 2001, 376, 49–51. [Google Scholar] [CrossRef]
  43. Liu, Y.; Huang, Y.; Zhu, C.; Li, H.; Zhao, J.; Wang, L.; Ojamäe, L.; Francisco, J.S.; Zeng, X.C. An ultralow-density porous ice with the largest internal cavity identified in the water phase diagram. Proc. Natl. Acad. Sci. USA 2019, 116, 12684–12691. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  44. Baia, J.; Angellb, C.A.; Zenga, X.C. Guest-free monolayer clathrate and its coexistence with two-dimensional high-density ice. Proc. Natl. Acad. Sci. USA 2010, 107, 5718–5722. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  45. Conde, M.M.; Vega, C.; Tribello, G.A.; Slater, B. The phase diagram of water at negative pressures: Virtual ices. J. Chem. Phys. 2009, 131. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  46. Desmedt, A.; Lechner, R.E.; Lassegues, J.-C.; Guillaume, F.; Cavagnat, D.; Grondin, J. Hydronium dynamics in the perchloric acid clathrate hydrate. Solid State Ionics 2013, 252, 19–25. [Google Scholar] [CrossRef]
  47. Desmedt, A.; Stallmach, F.; Lechner, R.E.; Cavagnat, D.; Lassègues, J.-C.; Guillaume, F.; Grondin, J.; Gonzalez, M.A. Proton dynamics in the perchloric acid clathrate hydrate HClO4⋅5.5H2O. J. Chem. Phys. 2004, 121, 11916–11926. [Google Scholar] [CrossRef] [PubMed]
  48. Desmedt, A.; Martin-Gondre, L.; Nguyen, T.T.; Pétuya, C.; Barandiaran, L.; Babot, O.; Toupance, T.; Grim, R.G.; Sum, A.K. Modifying the Flexibility of Water Cages by Co-Including Acidic Species within Clathrate Hydrate. J. Phys. Chem. C 2015, 119, 8904–8911. [Google Scholar] [CrossRef]
  49. Nguyen, T.T.; Pétuya, C.; Talaga, D.; Desmedt, A. Promoting the Insertion of Molecular Hydrogen in Tetrahydrofuran Hydrate With the Help of Acidic Additives. Front. Chem. 2020, 8. [Google Scholar] [CrossRef]
  50. Brumby, P.E.; Yuhara, D.; Hasegawa, T.; Wu, D.T.; Sum, A.K.; Yasuoka, K. Cage occupancies, lattice constants, and guest chemical potentials for structure II hydrogen clathrate hydrate from Gibbs ensemble Monte Carlo simulations. J. Chem. Phys. 2019, 150, 134503. [Google Scholar] [CrossRef]
Applsci 11 00282 g001 550
Figure 1. Schematic of a hydrogen/Deuterium hydrate in a bulk simulation box.
Figure 1. Schematic of a hydrogen/Deuterium hydrate in a bulk simulation box.
Applsci 11 00282 g001
Applsci 11 00282 g002 550
Figure 2. Diffusion coefficient for the different configurations at various temperature. (a) H2, (b) Arrhenius fitting for H2 (c) D2, and (d) Arrhenius fitting for D2. The area selected for the Arrhenius fitting is highlighted in yellow. The dashed lines present the fitted line for the Arrhenius equation.
Figure 2. Diffusion coefficient for the different configurations at various temperature. (a) H2, (b) Arrhenius fitting for H2 (c) D2, and (d) Arrhenius fitting for D2. The area selected for the Arrhenius fitting is highlighted in yellow. The dashed lines present the fitted line for the Arrhenius equation.
Applsci 11 00282 g002
Applsci 11 00282 g003 550
Figure 3. Averaged cage radius with respect to the temperature for (a) hydrogen (b) deuterium large cage occupancies, and (c,d) are for small cage occupancies for hydrogen and deuterium, respectively.
Figure 3. Averaged cage radius with respect to the temperature for (a) hydrogen (b) deuterium large cage occupancies, and (c,d) are for small cage occupancies for hydrogen and deuterium, respectively.
Applsci 11 00282 g003
Applsci 11 00282 g004 550
Figure 4. Cage occupancy averages vs temperature for large-cage occupancies (a) and small-cage occupancies (b) for hydrogen and deuterium.
Figure 4. Cage occupancy averages vs temperature for large-cage occupancies (a) and small-cage occupancies (b) for hydrogen and deuterium.
Applsci 11 00282 g004
Applsci 11 00282 g005 550
Figure 5. Schematic of a Markov model for internal cage hopping in clathrate hydrate. The diffusion between two large cages or between small cages is labelled as LL and SS, respectively. Diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled LS and SL, respectively.
Figure 5. Schematic of a Markov model for internal cage hopping in clathrate hydrate. The diffusion between two large cages or between small cages is labelled as LL and SS, respectively. Diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled LS and SL, respectively.
Applsci 11 00282 g005
Applsci 11 00282 g006 550
Figure 6. The inter-cage hopping with respect to the temperature. The results of the different systems—1-occupancy (a), 2-occupancy (b), 3-occupancy (c) and 4-occupancy (d)—for the model with H2 molecules as the guests are reported with solid colours, and hashed colours were used to present the results for the D2-containing model. The diffusion between two large cages or between small cages is labelled as LL and SS, respectively. The diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled as LS and SL, respectively.
Figure 6. The inter-cage hopping with respect to the temperature. The results of the different systems—1-occupancy (a), 2-occupancy (b), 3-occupancy (c) and 4-occupancy (d)—for the model with H2 molecules as the guests are reported with solid colours, and hashed colours were used to present the results for the D2-containing model. The diffusion between two large cages or between small cages is labelled as LL and SS, respectively. The diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled as LS and SL, respectively.
Applsci 11 00282 g006
Table
Table 1. Activation energy of hydrogen and deuterium for inter-cage diffusion.
Table 1. Activation energy of hydrogen and deuterium for inter-cage diffusion.
Applsci 11 00282 i001
ConfigurationActivation Energy (kJ/mol)
H2D2
1-Occupancy20.5 ± 0.620.9 ± 1.4
2-Occupancy14.7 ± 1.714.2 ± 4.3
3-Occupancy14.2 ± 0.315.0 ± 0.7
4-Occupancy9.8 ± 0.89.3 ± 0.7
Table
Table 2. Hydrate type II structural information and hopping-path possibilities. The diffusion between two large cages or between two small cages is labelled as LL and SS, respectively. Diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled as LS and SL, respectively.
Table 2. Hydrate type II structural information and hopping-path possibilities. The diffusion between two large cages or between two small cages is labelled as LL and SS, respectively. Diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled as LS and SL, respectively.
Cage TypeStructureTravel Possibility/CageCage Number/Unit CellTravel Possibility/Unit Cell
LLSL/LSSSLLSL/LSSS
Large51264412-814.28%42.85%42.85%
Small512-616
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Krishnan, Y.; Ghaani, M.R.; Desmedt, A.; English, N.J. Hydrogen Inter-Cage Hopping and Cage Occupancies inside Hydrogen Hydrate: Molecular-Dynamics Analysis. Appl. Sci. 2021, 11, 282. https://doi.org/10.3390/app11010282

AMA Style

Krishnan Y, Ghaani MR, Desmedt A, English NJ. Hydrogen Inter-Cage Hopping and Cage Occupancies inside Hydrogen Hydrate: Molecular-Dynamics Analysis. Applied Sciences. 2021; 11(1):282. https://doi.org/10.3390/app11010282

Chicago/Turabian Style

Krishnan, Yogeshwaran, Mohammad Reza Ghaani, Arnaud Desmedt, and Niall J. English. 2021. "Hydrogen Inter-Cage Hopping and Cage Occupancies inside Hydrogen Hydrate: Molecular-Dynamics Analysis" Applied Sciences 11, no. 1: 282. https://doi.org/10.3390/app11010282

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop