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Scandium and Titanium Containing Single-Walled Carbon Nanotubes for Hydrogen Storage: a Thermodynamic and First Principle Calculation

The generalized gradient approximation (GGA) to density functional theory (DFT) calculations indicate that the highly localized states derived from the defects of nitrogen doped carbon nanotube with divacancy (4ND-CNxNT) contribute to strong Sc and Ti bindings, which prevent metal aggregation. Comparison of the H2 adsorption capability of Sc over Ti-decorated 4ND-CNxNT shows that Ti cannot be used for reversible H2 storage due to its inherent high adsorption energy. The Sc/4ND-CNxNT possesses favorable adsorption and consecutive adsorption energy at the local-density approximation (LDA) and GGA level. Molecular dynamics (MD) study confirmed that the interaction between molecular hydrogen and 4ND-CNxNT decorated with scandium is indeed favorable. Simulations indicate that the total amount of adsorption is directly related to the operating temperature and pressure. The number of absorbed hydrogen molecules almost logarithmically increases as the pressure increases at a given temperature. The total excess adsorption of hydrogen on the (Sc/4ND)10-CNxNT arrays at 300 K is within the range set by the department of energy (DOE) with a value of at least 5.85 wt%.

Current echo political issues related to fossil-fuel energy resources have prompted broad interests in clean alternative energy. Biodiesel, solar energy, and wind farms are being pursued as supplements at commercially affordable scales. For automotive uses, hydrogen energy has been considered an ideal substitute for gasoline as it is recyclable and non-polluting. High-pressurized tank, liquefied form, or solid phase materials have been suggested and tested for hydrogen storage systems. Yet, none of the candidates suffices the requirements for commercial use in vehicles. Either the storage capacity or operating conditions are far short of the standard set by the Department of Energy (DOE) of the United States. Specific targets for automotive uses are summarized as gravimetric capacity of 5.5 wt% or higher for room temperature operations. Developing appropriate storage media is of the importance for practical application of hydrogen energy. Hydrogen has long been considered as a clean, abundant and efficient energy carrier.
The transition metals (TMs)-dispersed materials have been studied recently for large hydrogen storing capacity with respect to release temperature the TM-H 2 binding energy and ratio look very promising. However, the issue of structural stability and poor reversibility in TM dispersion has been a major concern as TM atoms tend to easily aggregate instead of being atomistically dispersed 10,12,13 . Strong metal cohesion is believed to be responsible for the aggregation. As a way to overcome such clustering, it was suggested to increase the binding strength between metal and dispersant materials (e.g., carbon based nanostructures) by introducing structural or chemical defects 10,11 . For example, nitrogen doping in graphitic materials was shown to improve dramatically the metal dispersion and hydrogen adsorption 11 . The 4ND defects in N-doped nanostructures enhance the reactivity and immobilization of TM 18,20 . To avoid the metal atoms forming cluster on the CNT, the metal species should meet the requirement that the binding energies are higher than their corresponding crystalline cohesive energies (E coh ) 20 . Among the 3d block TMs the Sc, Ti, V, Fe, Co and Ni show higher binding energies than their cohesive energies. However, only Scandium, Titanium and Vanadium qualify for efficient hydrogen storage at ambient conditions wherein the ideal adsorption energy should be at least 0.16 eV/H 2 for realizable reversible adsorption and desorption 20 with promising system-weight efficiency. The CNT with 4ND functionalized with Sc, Ti, and V are seen as an excellent hydrogen storage media with five, four, four H 2 adsorbed, respectively per metal as predicted by the famous 18-electron rule and they are lightweight.
Previous computations on hydrogen storage 16,17 identified that Sc, Ti, V are appropriate TM adsorbate for CNT surface addressing adsorption stability and increase in hydrogen storage capacity. In this paper, Nitrogen doped Carbon Nanotube with divacancy (4ND-CN x NT) as an effective medium for Sc and Ti atomic dispersion is elucidated in detail. Vanadium functionalized 4ND-CN x NT is currently being investigated and other metals aside from the 3d block TMs in which the results will be published elsewhere 20 . So which of the two TM candidates mentioned would be the best adsorbate for 4ND-CN x NT as hydrogen storage material with respect to stability and hydrogen storage capacity at ambient room temperature? Here we perform Density Functional Theory (DFT) calculations on the formation energy of the (4ND) n -CN x NT with n = 1 to 10 4ND deficiencies. A thorough comparison of the possibility that Sc and Ti decorated 4ND-CN x NT behave as an ideal H 2 -storage material was evaluated in detail. These was achieved by examining the binding energies as the number of H 2 molecules gradually increased from 1 to 5 for Sc, 1 to 4 for Ti. A model for the dispersion of the best metal atom to the 4ND 10 -CN x NT complexes with respect to the largest number of H 2 adsorption that is preferentially reversible was generated to fully simulate the adsorption scenario.
To gain additional insight into the microscopic details of the adsorption process, molecular modeling using central force fields is included in the manuscript to explain bulk properties of hydrogen storage and to provide adequate background information for theoretical and experimental practitioners. The condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) 21,22 force field was directly applied to system under study to explore the microscopic properties, dependence of molecular adsorption with respect to temperature and pressure. More specifically, the good agreement with experiment using COMPASS in simulating the adsorption of several molecules adsorbed on carbon warrants its use 22 . In the succeeding work illustrated below, the COMPASS force field determines the physisorbed state of H 2 on 4ND 10 -CN x NT metal complexes with respect to the largest number of H 2 adsorbed at temperatures starting from 77 K, the normal hydrogen adsorption process for the condition of liquid nitrogen at about 0.015 Gpa, to 400 K. The long-term objective is to aid in the development of accurate and reliable descriptions on the physical properties of molecular adsorption of H 2 on metal/4ND 10 -CN x NT surfaces that are capable of reversibly storing hydrogen at high densities within DOE specifications.

Computational
The 4ND-CN x NT was constructed as shown in Fig. 1(a). The DFT calculations are carried out by the Dmol3 code from Accelrys 21 . The generalized gradient-corrected Perdew-Burke-Ernzerhof (PBE/GGA) functional 23 , along with a double numerical basis set including p-polarization function (DNP), is applied for the geometry optimization and property calculations. Dispersion-corrected DFT (DFT-D) scheme is used to describe the van der Waals (vdW) interaction. DFT semi-core pseudo-potentials (DSPPs) were employed to efficiently treat the core electron of the Sc and Ti metals. The incorporation of DFT-D scheme further improves the accuracy in evaluating weak interactions wherein the geometry optimizations are carried out using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm with convergence threshold values specified as 1 × 10 −5 Ha for energies, 2 × 10 −3 Ha/Å for gradient and 5 × 10 −3 Å for displacement.
The Forcite algorithm is an iterative calculation available also from Accelrys 21 used for the molecular dynamics simulations in this paper. Due to its relatively low computational cost in comparison to DFT formalism, the COMPASS force field 22 was selected to study larger systems. The COMPASS by definition possesses two portions: one that deals with the valence terms and the other that addresses the nonbonded interaction terms, which represent most of the energetic contributions of a physisorbed H 2 molecule. The functional form for the nonbonded contributions includes a Lennard-Jones term and a Coulombic term which account for the vdW and the electrostatic interactions, respectively. The nonbonded energies were computed via Ewald summation wherein successful application in several investigations of carbon-based materials at the atomic scale is already established 24 . To achieve a reasonable three-dimensional model the optimized structure was redefined to create a supercell with a = b = 136.84 Å and c = 200.52 Å. During simulations, the calculate bonds tool monitors bonds, and automatically recalculates bonds if the position of the atoms changes. Typical NVT coupled to a NooséHover thermostat run time for all our simulations were 2.5 ns with time steps of 0.1 fs 25 . Different simulation temperatures from 77 up to 400 K were considered in order to determine the influence of temperature on the hydrogenation dynamics.

Results and Discussions
H 2 adsorption of Sc decorated 4ND-CN x NT. The atomic structure of the 4ND-CN x NT shows that the four nitrogen atoms within a unit cell have lone pairs of electrons that form highly localized acceptor like states near the Fermi level, as shown in Fig. 1(a). This acceptor like states led to a stronger binding of Sc atoms to the absorbent than pure CNT. The calculated charge transfer using population analysis shows that the charges transferred from Sc atom to CNT in this case carries a positive charge of 0.704 e. Partially cationic character of the Sc as shown in Fig. 1(b) is due to the charge transfer from metal to the (10, 0) 4ND-CN x NT and thus facilitating the adsorption of foreign molecules such as hydrogen gas 20 . It has been known that the charge transfer between TM atoms and ligands profoundly affect the H 2 binding property 11,26 . For example, the strong Sc binding to the 4ND-CN x NT leads to different characteristics of H 2 adsorption on 4ND-CN x NT from those on pure CNT. To study this issue in detail, the system is modified by incrementally attaching H 2 as one H 2 molecule is adsorbed on the TM/4ND-CN x NT system the H-H bond length is elongated. Figure 1(c) shows the structural variation from spin polarized calculations as a single H 2 molecule approaches Sc/4ND-CN x NT system. The energy first decreases slowly as the hydrogen gets closer to the nanotube and Sc atom. However, as the charge overlap gets large, the H 2 molecule is attracted towards the atom with a sudden decrease in the energy. For the Sc/4ND-CN x NT case, the optimized Sc-H and Sc-N distances are found to be 2.324 and 2.145 Å on the average, respectively. At this point, the H 2 molecule is still intact with a slightly increased H-H bond length from 0.752 Å of a free H 2 to 0.766 Å due to the charge transfer from the H 2 molecules to the Sc/4ND-CN x NT. The Sc/4ND-CN x NT has an initial adsorption of 0.279 eV/H 2 . The H 2 adsorption energies E ads in 4ND-CN x NT decorated by Sc was calculated by where E Sc/4ND-CNxNT+ nH 2 , E Sc/4ND-CNxNT and E nH 2 are the total energies of the Sc-decorated 4ND-CN x NT with n H 2 molecule, Sc-decorated 4ND-CN x NT and n H 2 molecule adsorbed, respectively. The calculated adsorption energies for n H 2 is summarized in Table S1 together with the other parameters for maximal n H 2 adsorption. The E ads in the Sc-4ND-CN x NT complex are larger than those in Sc + pure CNT complex [27][28][29][30] . Remarkably, it is also energetically favorable for the group to complex with additional hydrogen molecules as shown in Fig. 1(d-g) where the optimized structure, Surface Electrostatic Potential Map (SEP) and Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital (HOMO-LUMO) 31 variation is displayed as the succeeding four molecules approach the Sc atom attached to its first hydrogen, respectively. Just like the first adsorption, the succeeding four hydrogen molecules are in intact but with a rather elongated bond length of 0.758, 0.757, 0.755, 0.755 Å. For the complete structural parameters please refer to Figure S1. This 5% increase is rather a reminiscent of the elongated H-H bonds complexes first synthesized by Kubas 32,33  where E Sc/4ND-CNxNT+ nH 2 and E Sc/4ND-CNxNT+ (n−1)H 2 are the total energies of Sc-decorated 4ND-CN x NT with n and n − 1 H 2 molecules, respectively. E H 2 is the energy of a hydrogen molecule adsorbed as defined previously. The energy required for successive additions of H 2 molecules was evaluated using Eq. (2). Physically, it is used to evaluate the reversibility of storing H 2 molecules from n to n − 1 H 2 . Correspondingly, the calculated ΔE based on GGA-PBE calculations are summarized in Table S1 with the entire ΔE larger than 0.166 eV/H 2 , our simulations confirm that the maximum adsorption numbers of H 2 molecules can reach five for Sc as stipulated earlier.
Moreover, as shown in Fig. 1(c), the featured HOMO of the first H 2 molecule with the adsorbent indicates strong chemical adsorption between the first H 2 molecule and Sc atom where the adsorbed H 2 remain molecular.
H 2 adsorption of Ti decorated 4ND-CN x NT. Figure 2( Fig. 2(e). The energy gained by the fourth adsorption for Ti, 0.162 (0.211 with vdW incorporated) eV/H 2 , is slightly smaller than for the other cases but is still substantial as summarized in Table S1 along with the succeeding three hydrogen molecules as they approach the Ti atom attached to its first hydrogen. For the three succeeding H 2 attached to Ti the bond length is also elongated (0.799, 0.786, 0.767 Å). For the complete structural parameters please refer to Figure S2. The Kubas interaction is dominated by σ-donation from the H 2 to the metal, but is more balanced between σ-donation and π-back-donation for the Ti analogues. This behavior can be traced to a lowering in energy of the metal 3d orbitals. Several attempts to add a 5 th hydrogen molecule at a variety of positions failed for Titanium, suggesting a limit of 4H 2 per Ti. The final-optimized structures shown need not be the global minimum. Among many different isomers tried, a very symmetric configuration was found. In contrast, the E ads of Ti with the first H 2 at 0.608 eV is well above the threshold while the succeeding ΔE of the second to the forth H 2 is quite low which impedes storage reversibility of H 2 molecules compared to Sc/4ND-CN x NT system. The relationship between E ads and ΔE can now be established as seen clearly in Table S1 and S2 for example if we take the average of ΔE 1 and ΔE 2 (0.608 and 0.056 eV) it yields the E ads (0.332 eV) for the two H 2 bonded to the Ti/4ND-CN x NT. If we take the average of ΔE 1 , ΔE 2 and ΔE 3 (0.608, 0.056 and 0.105 eV) it yields the E ads (0.256 eV) for the three H 2 bonded to the Ti/4ND-CN x NT and so on. Therefore E ads is equal to the average of ΔE n 's for n H 2 bonded to the Ti/4ND-CN x NT. One of the major obstacles to the widespread adoption of hydrogen as a fuel is the lack of a way to store hydrogen with sufficient gravimetric and volumetric densities to be economically practical. An appealing approach for solving this problem is the development of materials that are capable of reversibly storing hydrogen at high densities. Ti/4ND-CN x NT store hydrogen too strongly due to the strong interaction between hydrogen and Ti metal, hindering the extraction of hydrogen under practical operating conditions. It can be noted though that the adsorption energies, E ads, are still within the right range for room temperature storage for both Sc a Ti. For the number of H 2 to be adsorbed on each metal atom, it is similar to that in Sc/Ti − pure CNT or other Sc/Ti-dispersed graphitic materials, such as graphene or nanoribbons (for example, five H 2 /Sc and four H 2 /Ti) [27][28][29][30][31][32] . Based from previous discussions, Sc is the transition metal of choice in designing advance composite material for reversible hydrogen adsorption and desorption with promising system-weight efficiency evaluated at room temperature. While many technical issues remain to be resolved, this study will show that Sc-dispersed CNTs have great potentials for hydrogen storages. H 2 Loading of (Sc/4ND) n -CN x NT. Assuming a substitutional doping through a chemical process 2 2 n x 6 12 The formation energy of a single 4ND defect is calculated to be about 3.20 eV (endothermic) using the formula, where E(4ND) n -CN x NT is the total energy of the (10, 0) 4ND-CN x NT with n porphyrin defects. The u C is the chemical potential of C obtained from the pure CNT with 120 carbons and u N is the chemical potential of N obtained from the nitrogen gas. Processes that are more realistic may be necessary for calculating the true formation energy, our estimation for n = 1 to 10 is regarded to be within the usual synthesis conditions. It is worth noting that the formation energy for a maximum of ten vacancies is 30.89 eV. A linear regression model expressed in the form of E f (n) = 3.149n + 0.458 can fit the formation energy (E f ) vs. n porphyrin defects data with r 2 = 0.996. The physical and chemical structure of the synthesized highly nitrogen-enriched graphitic carbon was investigated experimentally by powder X-ray diffraction, scanning and transmission electron microscopy, selected area electron diffraction, energy dispersive spectroscopy, elemental analysis, Fourier transform infrared spectroscopy, X-ray photoemission spectroscopy, and electron energy loss spectroscopy and theoretically by using DFT formalisms [24][25][26][27][28][29][30][31][32][33][34][35][36] . The analysis confirmed that the product has a highly crystalline nitrogen-enriched graphitic structure with a carbon-to-nitrogen ratio of 1:1.12 corresponding to a maximum of n = 10 defects. The Sc functionalized CN x NT with n = 1 to 10 4ND defects was further studied. The (Sc/4ND) 10 -CN x NT system can be visualized by isolating a single Sc functionalized nanotube from the array shown in Fig. 3. The adsorption of H 2 molecules with the isolated (Sc/4ND) 10 -CN x NT system possess favorable binding energy as seen in Table S2 as plotted in Fig. 4(a). The binding energy is considerably greater than the cohesive energy of bulk Sc metal 20 preventing unnecessary clustering and agglomeration. As H 2 was placed on each Sc atom, the starting configuration for each geometry optimization was taken by attaching one to five H 2 around each n Sc atoms above the n 4ND defects, wherein the hydrogen atoms attached all remained molecular with an average bond length of around 0.755 Å. The average hydrogen adsorption energy for a (Sc/4ND) 10 -CN x NT complex with fifty H 2 is 0.166 eV/H 2 calculated using GGA-PBE functional. Therefore the H 2 storage capacity may be predicted to be at least well above 5.8 wt%, for (Sc/4ND) 10 -CN x NT with 5H 2 attached per Sc. In addition, a consecutive adsorption energy computation suggests an ideal reversible hydrogen adsorption and desorption energy range of 0.16 to 0.42 eV/H 2 as shown in Fig. 4(b). It is astonishingly achieved at the GGA level with a ΔE Ave value between 0.193 to 0.244 eV/H 2 . A Calculation using LDA-PWC was also carried out and the average hydrogen adsorption energy along with the consecutive adsorption energy is in good agreement within the requirement of hydrogen storage at room temperature. As mentioned earlier Fig. 3 shows the (Sc/4ND) 10 -CN x NT array. Representative snapshots of the adsorption process in correspondence to the time history of potential energy, pressure and number of adsorption molecules are shown in Fig. 4(c-e). Here, the normal hydrogen adsorption process for the condition of liquid nitrogen temperature at 77 K and about 0.015 GPa is shown in Fig. 4(c-f) in blue. The hydrogen molecules rapidly intruded the surface of the (Sc/4ND) 10 -CN x NT assembly as shown in Figs 3(a) and 4(c-e). Here, the profile of the potential energy curve can be accounted for due to the sudden decrease of van der Waals interaction. The pressure change for 77 K was recorded in Fig. 4(d) versus simulation time in nanoseconds for the final configuration in Fig. 3(a). The amount of hydrogen attached to the scandium-nanotube assembly has reached 7.84 wt%. Interestingly, at 300 K the COMPASS prediction agrees well with the GGA predicted value at 5.85 wt% (Fig. 3(d)). The variations of bond lengths which is the defined to be the difference between the current length of the bond and its equilibrium value as time elapses is further analyzed. The variation of the Sc-N, C-C and H-H molecules bond length at room temperature is oscillating between 0.1 and −0.1 Å. Indicating that the entire complex is stable at room temperature. The suggested temperature for H 2 delivery by the DOE is in the range of 233-393 K. Hence MD simulations for the maximum number of H 2 molecules adsorbed on the surface were performed upto 400 K. It is worth noting that at 233 K the adsorb hydrogen is 7.02 wt% which is also above the DOE target. However, the (Sc/4ND) 10 -CN x NT arrays poorly adsorbs hydrogen at a temperature near 393 K as depicted in Fig. 3(e). This is because the hydrogen molecules have enough kinetic energy to overcome the adsorption potential of the system with temperature greater than 400 K in the range of pressure that were studied. The number of absorbed hydrogen molecules almost logarithmically increases as the pressure increases at a given temperature as seen in Fig. 4(f). The results reach the gravimetric density of DOE target, which means that the adsorption storage of hydrogen on (Sc/4ND) 10 -CN x NT has practical importance.

Conclusion
The electronic properties of single-walled carbon nanotubes in the presence of 4ND defect and Sc/Ti impurities were studied using DFT. The 4ND defects in single-wall carbon nanotubes caused an enhanced chemical functionalization of Sc/Ti species suggesting a considerable reduction of clustering of metal atoms over the metal decorated nanotube. Strong binding of hydrogen molecule to the composite material Sc or Ti/4ND-CN x CNT was observed. The binding energy of Ti exceeded the threshold for storage reversibility of H 2 molecules. The interaction of hydrogen molecule to the composite material was further investigated by attaching 50H 2 around the (Sc/4ND) 10 -CN x CNT. It turns out that the system is capable of reversibly storing hydrogen at high densities calculated based on LDA and GGA level. Also, Molecular Dynamics simulation shows that the total excess adsorption of hydrogen on the (Sc/4ND) 10 -CN x NT arrays is stable with a value of 5.85 wt%. The number of absorbed hydrogen molecules almost logarithmically increases as the pressure increases at a given temperature as predicted using central force fields. Sc/4ND-CN x CNT complex holds promise for the design of lightweight reversible adsorption system for H 2 storage preferentially at room temperature.