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Sealing off a carbon nanotube with a self-assembled aqueous valve for the storage of hydrogen in GPa pressure

The end section of a carbon nanotube, cut by acid treatment, contains hydrophillic oxygen groups. Water molecules can self-assemble around these groups to seal off a carbon nanotube and form an"aqueous valve". Molecular dynamics simulations on single-wall (12,12) and (15,15) tubes with dangling carboxyl groups show that the formation of aqueous valves can be achieved both in the absence of and in the presence of high pressure hydrogen. Furthermore, significant diffusion barriers through aqueous valves are identified. It indicates that such valves could hold hydrogen inside the tube with GPa pressure. Releasing hydrogen is easily achieved by melting the"aqueous valve". Such a design provides a recyclable and non- destructive way to store hydrogen in GPa pressure. Under the storage conditions dictated by sealing off the container in liquid water, the hydrogen density inside the container is higher than that for solid hydrogen, which promises excellent weight storage efficiency.

As cylinders formed by rolling up robust graphenes, carbon nanotubes enclose much empty spaces. Foreign particles, including both ions and molecules, can be inserted into these tubes, to form quasi-1D structures with interesting physical and chemical properties. [1][2][3] Inserting hydrogen molecules into carbon nanotubes can be easily achieved, due to their small size. But for hydrogen, it is the compressibility, rather than the structure, that is the most interesting, [4][5][6][7][8][9] since H 2 has a weak van der Waals potential and is highly compressible all the way up to and above GPa pressure (tens of thousands of bars). [10,11] The mechanical strength of a carbon nanotube could stand pressure up to 40 GPa, as measured by experiment. [12] Therefore, compressing hydrogen to GPa pressure, which is two orders of magnitude higher than the pressure in a typical gas tank, would be ideal for the storage of hydrogen, provided a suitable nano-scale valve could be made. [4][5][6]9] Such a valve should block hydrogen inside carbon nanotubes, and control the filling and release of hydrogen in a recyclable and non-destructive way, which is a challenge in both design and implementation.
Attempts have been made to design such a nano valve. Our groups have suggested a design modeled after the "ball check valve", composed of a C 60 molecule enclosed by a halfspherical carbon nanotube cap. Molecular dynamics (MD) simulations indicated that the position of C 60 could be switched between "open" and "close" states, as the external pressure was varied. [4,6] Vakhrushev and Suyetin suggested that a positively charged endohedral complex K + @C 60 could be used as the blocker for the storage of hydrogen and methane, which could then be controlled by the application of electric field. [9,13] Transition metal particles are often attached to the end of carbon nanotubes during the growth process, and asymmetric permeability of hydrogen through metal layers could also offer opportunities in designing a nano valve. [14] However, turning such elaborate designs into actual structures at the molecular level would be quite challenging. In this paper, we present a new design based on readily made structures that could be easily implemented.
Our starting point is the common structural feature of a carbon nanotube, typically consisted of two parts: a cylindrical tube body, which nowadays could be made into considerable length with little defects, and two end sections, where the caps are usually cut off by acid treatment and the dangling bonds are typically saturated by oxygen containing groups, such as carboxyl(-COOH), carbonyl (-C=O) or hydroxy groups(-OH). [15,16] As curved graphene sheet, the tube wall contains no polar groups, and would prefer to bind non-polar molecules such as hydrogen. In contrast, the oxygen containing groups at the end sections are polar, and would prefer to bind with water molecules through hydrogen bonds.
Our design for the valve is to seal the open end section by exposure to water molecules.
Around oxygen containing hydrophilic groups, water molecules should automatically aggregate to form an "aqueous valve", hold together by hydrogen bonds. There must be a barrier for the diffusion of hydrogen through an aqueous valve. Filling hydrogen into the tube would require the growth of an aqueous valve in the presence of hydrogen under high pressure, while the diffusion barrier should lock the hydrogen inside after the withdrawal of external pressure. Experimental implementation of such a valve is straightforward, as it depends on the self-assembly of water molecules around the hydrophilic groups. Furthermore, nor is it difficult to modify these groups so that their structures and hydrophilic propensities could be adjusted. The crucial questions are therefore to examine the growth of the aqueous valve and to understand the mechanism and barrier for hydrogen diffusion through such a valve at various pressures.
Although the energy of one hydrogen bond between two water molecules is only around 5 kcal/mol, it has been demonstrated by experiments that hydrogen molecules squeezed into ice under GPa pressure remained locked inside ice lattice when the external pressure was withdrawn. [17,18] Even at GPa pressure, the hydrogen bonded ice lattice could stand up to the the van der Waals repulsion exerted by hydrogen molecules. The relative weakness of the hydrogen bonds, compared to typical chemical bonds, is actually a big advantage when it comes to the release of hydrogen through an aqueous valve. Moderate heating above the melting point easily disrupts the hydrogen bonds and opens the valves. Furthermore, such heating does not damage the dangling groups, and aqueous valves can be formed again upon exposure to water at lower temperatures.
For this study, a molecular model is built as shown in Figure 1a. Two types of singled walled carbon nanotubes, with an index of (12,12) or (15,15) respectively, are studied. Each tube is capped at one end and functionalized by carboxyl groups (-COOH) on the other end.
Aggregation of water molecules around the carboxyl groups is readily observed in the following simulation. Initially, a chunk of regular ice of Ih lattice, containing 640 water molecules, is placed 8Å below the carboxyl groups, as shown in Figure 1b. During an MD simulation of 10 ns at 220 K, the ice chunk is melted and the water molecules are self-assembled around the hydrophilic carboxyl groups. The temperature is then gradually lowered from 220 K to 77 K over 1 ns, and an amorphous structure of water aggregates is formed at the end section, as shown in Figure 1c, which blocks the entrance into the tube and could potentially be an aqueous valve. Such a self-assembly process is facilitated when water is in its liquid state, and the simulation temperature of 220 K is above the melting point of water as described by the SPC/E potential, which is around 215 K. [19] It is known from the phase diagram of ice [20] that its melting point changes little with pressure. The triple point for ice V, ice VI, and liquid water is identified at 0.63 GPa and 273 K. It means that in experiment hydrogen gas could be pressed to 0.63 GPa just above 273 K to fill open nanotube containers, and exposure to water, which is in liquid state under such conditions, could then induce self-assembly around the end section to seal off these containers. Such a scheme could also work at higher pressure, to ∼1 GPa, when the temperature is raised to ∼ 300 K, according to the experimental phase diagram.
For such a filling process, one must ask whether the formation of an aqueous valve is affected by the presence of hydrogen under high pressure. To simulate it, two artificial plates are introduced outside the tube, as shown in Figure 2a. Space between the two plates are filled by hydrogen molecules. By placing the bottom plate at different positions, the pressure of hydrogen could be raised to GPa range. Again, a chunk of ice is placed below the carboxyl groups, leaving the end section open for the filling of hydrogen inside the tube.
In the beginning step, water molecules in the ice chunk are artificially frozen in their positions, as hydrogen molecules are introduced between the plates at 250 K, which diffuse not only into the tube but also into the lattice of the fixed ice chunk, eventually reaching an equilibrium pressure of 0.6 GPa in 300 ps. Then the frozen water molecules are set free, and the temperature is raised to 270 K, so that the ice chunk is melted and the self-assembly of water molecules around the hydrophilic carboxyl groups is started. After 300 ps, an aqueous valve is again formed. The system is then cooled down to 77 K in 500 ps, and the process produces the same kind of aqueous valve as shown in Figure 1, obtained in the absence of hydrogen. Careful examination of the structure shows that no hydrogen molecule is left inside the water aggregate. The result is not surprising because the non-polar and hydrophobic hydrogen molecules do not mix with the polar water molecules, and with their weak van der Waals potentials, hydrogen molecules can easily move out of the way of the aggregating water molecules. Finally, the two plates and the hydrogen molecules outside the sealed container are withdrawn, as in Figure 2b, and the system is equilibrated at 77 K for 300 ps. The aqueous valve is stable and no leakage of hydrogen molecules from inside the tube, which is at 0.6 GPa, is observed during the simulation.
While the above simulations prove that the container could be sealed off, with and without the presence of high pressure hydrogen, the robustness of such an aqueous valve must be further examined by calculating the diffusion barriers. A number of calculations are carried out in which a hydrogen molecule is forced to move through an aqueous valve by constraining the z coordinate of one particular hydrogen molecule, with z axis being the axial direction of the carbon nanotube. Typically, this hydrogen molecule would move close to the tube wall and find a path near the wall. As there is no hydrogen bond between the tube wall and water molecules, such a diffusion path produces less structural disruption. Figure 3a is a typical potential energy curve along the diffusion path, when the internal pressure inside the tube and the external pressure outside the tube are both at zero. The z coordinate is chosen so that the averaged z coordinate for the C=O oxygen atoms in the -COOH groups around the end section is zero. In other words, z = 0 could be treated as an approximate dividing line, so that a hydrogen molecule is inside the container at positive z and outside the container at negative z values. The energy at z =10Å (inside the tube) is ∼ 0.1 eV lower than the energy at z =-20Å (outside the tube), since a hydrogen molecule inside the tube has more favorable van der Waals interactions with carbon atoms on the tube wall and other hydrogen molecules than its interaction with water molecules at an interstitial site of ice.

Shown in
There are many barriers and wells connecting these two points along the potential energy curve. Starting from z =10Å, when the hydrogen moves into the aqueous valve, it passes through two interstitial sites, seen as two energy minima (around z =1 and z = 4Å respectively), and hits a barrier of 1.0 eV centered near z =0, where the carboxyl groups are located. Inside the tube, the diffusing hydrogen passes through the space between water and the nanotube wall. Near the end of the tube, the hydrogen molecule must squeezes through the spaces around the carboxyl groups covalently bonded to the nanotube, which accounts for the big barrier. The energy difference between the top of this peak and the position inside the tube is defined as the release barrier. Afterwards, the hydrogen moves into the outer part of the aqueous valve, which is mainly amorphous ice. There are several barriers in this region, which are more or less comparable to the diffusion barrier in Ih ice (∼0.3 eV), although it could bump into a larger barrier too (e.g. at -12Å), which is due to the disorder in the ice structure. There are of course many possible trajectories, and shown in  Table 1.  Figure 3b and 3c. When both P ext and P int are at zero, the RDF around the -COOH groups at the end section and the RDF in the amorphous ice outside the container are almost identical, with a sharp peak around 2.64Å and a broad feature centered just above 4Å. When the internal pressure P int is increased to 1 GPa and the external pressure maintained at 0, the broad feature centered around 4Å is maintained with its center slightly shifted to shorter distance for the RDF around the -COOH groups.
For the ice outside the tube, the RDF is little changed. In other words, there is only slight structural tightening around the -COOH groups and little effect on the ice outside of the tube, when P int is raised to 1 GPa, as the effect of the internal pressure is restricted by the tube wall and the valve.
The release barriers for the (15,15)-COOH valve are also calculated, as listed in Table   1, and the values are typically lower than the corresponding values for the (12,12)-COOH valve. More significant changes in the release barrier are also observed when the pressure is varied. With P ext kept at zero, there is still a substantial barrier above 0.6 eV for the release of hydrogen, when P int is at 0 or 1 GPa. However, when P int is raised further to 2.0 GPa, the barrier drops to around 0.3 eV, which is comparable to the calculated diffusion barrier in ice. It indicates the difficulty for the (15,15) The weak structural link in our model aqueous valve is the hydrogen bonds that hold the water aggregate to the carboxyl groups. The energy for such a typical hydrogen bond is only 5 kcal/mol, and at high internal pressure, the force exerted on the valve may be strong enough to break collectively these hydrogen bonds and push the water aggregate out of the tube. The threshold pressure can be evaluated by molecular dynamics simulations.
Hydrogen molecules are added consecutively inside a sealed container step by step. At each step, the configuration is first optimized at 0 K, and then the temperature is gradually raised to 77 K and equilibrated for 100 ps. The threshold pressure is found to be 3.0 GPa for (12,12)-COOH and 2.6 GPa for (15,15)-COOH respectively, when the aqueous valve is pushed out during the equilibration step The storage pressure envisioned for aqueous valves is between 0.6 GPa around 273 K and 1.0 GPa around 300 K, for which the mechanical stability is not a concern. These two pressures are determined by the phase diagram of water. To seal off the valve, water should be in liquid state to facilitate its self-assembly around the tube ends. Using the equation of state measured by Mills and co-workers, [21] the molar volume of hydrogen is 17.1693 cm 3 at 0.6 GPa and 273 K, and 14.6072 cm 3 at 1.0 GPa and 300 K, both being more favorable than even the molar volume around 23 cm 3 for solid hydrogen at 4.2 K. [10] The weight storage efficiency varies with the tube diameter. With the carbon atoms on the tube surface, the efficiency is higher for tubes with larger diameters since they have larger volume to surface ratios. For a long tube, the weight of the aqueous valve adds only a very small overhead and could be ignored, and the H/C mass ratio α can be estimated by the weight of hydrogen contained in the volume of a tube segment and the weight of carbon on the tube wall (see supporting information), which is for an (n,0) tube, and for an (n,n) tube. In the above formula, d CC is the C-C distance on a carbon nanotube, taken to be 1.42Å, ρ is the hydrogen mass density in a.m.u/Å 3 , and d CH is the shortest distance between the surface of a spherical hydrogen molecule and a carbon atom on a carbon nanotube for the calculation of available storage volume, which is taken as 1.6Å based on previous studies. [22] At 0.6 GPa and 273 K, the calculated weight efficiency, which is plotted in Figure 4, reaches 5% at a tube diameter of 2.0 nm and 8% at 3.0 nm. At 1 GPa and 300 K, the weight efficiency reaches 5% at 1.8 nm, and close to 10% around 3.0 nm.
In principle, an aqueous valve could be built for larger tubes by extending the -COOH For water molecules, SPC/E model is employed. A hydrogen molecule is treated as spherical and the interactions between two hydrogen molecules are modeled by the Silvera-Goldman potential. [10,27] The interaction between hydrogen and water molecules is L-J potential. [28] Our calculated barriers for type-sII clathrate are in good agreement with the previously reported values. [29] Within Ih ice, the diffusion barrier of a hydrogen molecule is found to be 0.3 eV along a/b direction and 0.2 eV along c direction, which is also reproduced by simulations using the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) program. [30] The interactions between carbon atoms are modeled by the second-generation reactive empirical bond order potential. [31] The van der Waals interaction between a hydrogen molecule and a carbon atom is described by the recently fitted potential by some of us, which reproduces the high level ab initio results over a wide range of attractive and repulsive regions. [32] The cutoff for all unbonded interactions is set to 60Å. For different types of atoms, the L-J potential is calculated by the Lorentz-Berthlot combination rules.
Four carbon atoms on the carbon nanotube are fixed to prevent unnecessary movement of the tube during all the simulations.