Neutral Gases Adsorption With Hydrogen on Silicon Nanotubes : A Fuel Cell

In the present study, adsorption of helium, neon, argon and binary mixtures of one of them with hydrogen on (5, 5) armchair silicon nanotube at Temperatures of 50, 100 and 150K and Pressures of 1, 5, 7, 10 and 15MPa were studied. For each binary mixture three different mole fractions of hydrogen were examined. Canonical Monte Carlo simulation by ab-initio calculation was employed for studding the adsorption of above gases on single-walled silicon nanotubes (SW-Si-NTs). The interaction energy of gases with the surfaces of the single Si-NTs obtained from quantum mechanics calculations was fitted to an exact potential functions used for simulating the system. Lennard-Jones potential was used for gas-gas and Morse potential was used for gas-silicon nanotubes interaction. The work was carried out at several temperatures and pressures by using Canonical-Monte-Carlo or CMC simulation in order for studding the effect of temperature and pressure on gas adsorption. The adsorption results showed that by increasing the pressure and decreasing the temperature, the amount of adsorption increases. It was concluded that among the rare gases discussed helium was lowest impact on hydrogen adsorption in a mixture of helium and hydrogen.


INTROdUCTION
Duo to environmental issues current researches are concentrated on new clean fuels, many studies have been focused on conversion of conventional fossil fuels to hydrogen because of lower pollutant emissions while hydrogen burning.
Last decade, a few efforts have been focused on the hydrogen adsorption capacities of carbon nanotubes duo to their peculiar electronic and mechanical properties and potentials applications of the hydrogen for fuel 12 cell vehicles [22][23][24][25][26][27] .However, many of those efforts has been failed for reaching the gravimetric 22 densities proposed via the U.S. Department of Energies (6.5 Wt %).Apparently, the designing of a novel material and a modified of porous material significantly increases the adsorption capacities of hydrogen [28][29][30] .
In a contrast of Carbon-based and Siliconbased nanomaterials 27 , in the terms of their Physico-Chemical properties 25 , is deeply 26 rooted in attributes of the elements and its disparate atomic properties.Generally, Si differs from the C in five points as follows: (1)-lower electronegativity; (2)-kinetically more reactivity; (3) -larger atomic-radius 26 , and consequently larger orbitals; (4)-smaller energies differences between both S and the P orbitals, and consequently a lower hybridization 26 energies; and (5)-the availabilities of energetically 30 lowlying "d" orbitals and the abilities for expanding its coordination spheres 31 .Those properties of Si and their apparently contrast with C, make Si chemistry and its material so interesting 32 and worthy to study 33 .
One of the main factors that impact the chemicals and physicals proper ties of Si in comparison with those of carbons are the larger atomic sizes of Si that has longer Si-Si =2.35Å bonds 34 in size and weaker bonds with the bond energies of 222,Kj/mol, comparing to carbon-carbon bonds equal 1.54Å including bond energy= 345.6Kj/mol 33 .
Further more, the poor p-p overlapping for Si, Si-Si = 2.16Å with bond energies equal 327Kj/mol are much weaker than the carbon-carbon bonds (1.34Å) with bond energies equal 602Kj/mol 34 .This disparity leads to a existence 35 of varieties in the organic chemistry and nonmaterial like graphite carbon, fullerenes and carbon Nano tubes, whereas 36 exist only a few number of stable molecules including Si=Si p bonding 2 .In the cases of Nano-tubes contrasting with the CNTs, the analogous Si-NTs based on rolled up graphene like sheet seems to be relatively not easily synthesized 34 , but its existence on a basis of various experimental or theoretical investigation has been reported.
Eberl and Schmidt first have demonstrated the possibilities of the rolling up for a thin Si films [30][31][32] .Moreover to this, Yang has been reported a novel synthesis of the large diameters around e"50 nm Si-NTs using the chemical vapour deposition methods while using the transmission-electronmicroscopy or TEM techniques 33 in 2002.After that, Lee 35 published a paper related on the growth of pure silicon Nano -tubes using molecular beam epitaxial 35 on the porous alumina without any catalysts 34 .Tang published two works which has been reported the growth of silicon Nano-tubes including a smaller diameter around 13 nm using silicon oxide via hydrothermal synthesis 35,36 .
To our knowledge, the most interesting results on the synthesis and characterization 35 of a thin and presumably single-walled silicon Nano-tubes provided by De Crescenzi, through experimental studies 37,38 The successful synthesises of silicon nanotubes caused to a wide investigations for assessing the suitability of silicon Nano-tubes bundles 37 as a candidate material for adsorbing efficiently H 2 .On the aforementioned comparison, between carbon and silicon, silicon has lot electrons in the outer shells, which leads to a higher polarizabilities and stronger dispersion 36 forces.Correspondingly, the silicon Nanotubes may show a large and stronger van-der-Waals attraction 36 for hydrogen rather than Carbon Nano-tubes.Therefore, it has been reported a multiscale theoretical method for investigating adsorption of instance gases in the silicon Nano-tubes arrays 36 .
The rest of those papers are organized as follows [36][37][38] .(1)-the binding energies between adsorbent and adsorbate obtained from ab-initio calculations were fitted for a propering potential function 36 .So the result was applied as an input 36 in the canonical Monte-Carlo simulation for evaluateing capacities of adsorption of instance gases on SiNT at different pressures, temperatures and mole fractions of mixture.The amount of H 2 adsorption in pure and mixture forms on SiNt were also compared to each other.

Methods and Calculations
Computational methods are well placed to a multiscale theoretical approach that combines the first-principle calculation for obtaining the binding energies between instance gases and the SiNt and Canonical-Monte-Carlo (CMC) simulation 39 for obtaining the weight percentage of pure rare gases and H2 in a mixture of each one of rare gases that might be stored in pure SiNt arrays at different thermodynamic conditions.
The first principles quantum chemical calculations applied for investigating of the nature in the gases interactions with the single (5, 5) SiNt were accomplished in a DFT system using the package Gaussian03 40 .Duo to its relatively small diameter, the cylinder cluster model of Si 70 H 20 was selected for SiNT (5, 5) that appears nanotube properties in the lowest possible of length.In the first step, the geometries of the model were optimized.
In all of the calculations, the gases molecules and their nearest six Si atoms have been treated with a 6-311++G** basis set, whereas the next atoms were treated with commonly used 4-21G basis set, carried out by the MP1PW91 41 exchangecorrelation function, which can be provided a more exact dispersion forces rather than B3LYP 42,43 .On nanotube surface, there are several adsorption sites, depending on the position and orientation of gas molecules: the molecule can be located in the above of Si atoms, the bridge of Si-Si bonds and the centre of silicon hexagon or hollow 44 .All those cases have been occurred into account for adsorption of all gases in the Si-NTs surfaces.The results have shown among different adsorption position, the hollow 44 sites with the H-H bond vertical on the tube surfaces are the most favourable adsorption mode for the outside SiNT wall (see figure 1).This phenomenon has already been observed for adsorption of hydrogen on CNT 30 and SiNT 45 surface.The orientation (horizontal or vertical) of gas molecules only considered for hydrogen molecule because the noble gas molecules were described as spherically symmetric.
An efficient way to implement the results obtains from first-principle calculation in the CMC simulation 45 , which is an accurate-potential-function to bridge both kinds of calculation.
In this work, the ab-initio potential energies results of the gases with SiNt were fitted for a number of usual system 'functions', and it has been found that the Morse-potential 46 in eq. 1 is the best selection.The parameters in the Morse-potential 46 have been obtained according to the fitted binding energies for the molecules in the surfaces which are as close as possible of determining by the firstprinciple calculations described formerly.It is worth mentioning that the Morse-potential has been used successfully to fit interaction potential computed by the 1 th principle calculations in the previous works [46][47][48][49] .
The interactions between the fluid molecules and the surfaces of the nanotubes were fitted to the Morse-potential, and the form is expressed as follows:  Where r i is the distance between fluid molecule and the tubes surfaces (Å).The values of the constant D, g and r e for gas adsorption outside the nanotube are given in the Table 1.
As previously mention, we used a CMC-simulation to study the adsorptions of the gases on the (5, 5) SWSiNT.The intermolecular interaction was modelled by the typical 12 -6 Lennard-Jones pair potential: Where, {ε ff and 5 ff} are the energies and the length parameter in the Lenard Jones potentials, and {r} denoted the centre-towards-centre distances.The subscriptions of {ff} stand for interaction between two section fluid molecules and {φ/ LJ } represent the full Lenard Jones potentials.
Cross parameters of the unlike pair i and j particles were obtained using the Lorentz-Berthelot mixing rules: All the interaction potential parameters are given in Table 2 [50][51] .Details of the method can be found elsewhere 52,53 .
The Monte-Carlo simulation is based on the probabilistic phenomenon and concepts.In these methods a system composed of N interacting atoms which are given a set of initial coordinates and orientations.The evolutions of these initial configurations are then generated by successive random displacements of the atoms.The ensemble averages, of the physical quantities f of function of N particles coordinates, such as the potential energies, are then obtained as an unweighted average over the resulting set of configurations 54 .Typically between 10 6 -10 5 configurations are generated.In the Monte Carlo approach, no time scales are involved, and the orders in which configurations occur have no particular significance.In most practical applications, the objectives have been estimated Canonical ensemble 54 averages, representing the systems composed of fixed number of particles 54 , N, confined to a fixed volume, V and at a fixed pre-set temperature, T 54 .
In this work, an armchair type SW-Si-NTs (5, 5) with highly symmetrical structures, with 200 atoms and diameter of 37 Å was selected in our systems.The simulation box used are around 100.00 Å × 100.00 Å × 45.00 Å) contained one SW-Si-NTs.The cut off radius was 2.5 times the collision diameter.The number of the gases molecules in the simulation box (a box with 100.0 Å × 100.00 Å × 45.00 Å dimensions) can be easily calculated at the special temperatures and pressures using virial equation of state 54 .
Periodic boundaries conditions were applied in all three dimensions 54 .For each state point, C-M-C simulation consisted of 5×10 7 configurations that 2×10 7 steps were to guarantee equilibration and 3×10 7 steps were to sample the desired thermodynamic properties 54 .
Furthermore, for obtaining adsorption isotherms, the common parameters were calculated as follows.Gravimetric storage capacities, ρ w , were calculated as follows too: Where N Si and N gas are the number of Si atoms and gas molecules in our simulation box, and m gas and m Si are the related molar masses, respectively.

RESULTS ANd dISCUSSIONS
Adsorption of pure He, Ne and Ar on (5, 5) SiNT.The adsorption behaviours of rare gases on (5,5) SiNT, according to eq. ( 3), are evaluated at one subcritical (50K) and two supercritical (100 and 150K) and pressure ranging between 1 to 15Mpa.The simulation results are exhabited in fig. 1.
All the adsorption isotherms for He, Ne and Ar were characterized by type I (Langmuir shape).The intrinsic properties of type I isotherms are that adsorptions are limited to a completion of the single monolayer of adsorbate at the adsorbent surfaces.Type I isotherms (parabolic behaviour) are visible for the adsorption of gases on microporous [55][56][57] solids whose sizes (pore) are not much larger than the molecular diameters of the adsorbate which complete filling of those narrow pores 55 .Moreover, adsorption isotherms imply that condensation is prohibited 55 .Capillary condensation observes when the pores have diameters larger than approximately 2 nm at adequately 55 low temperature.It is notable that with a diameter less than 2 nm, no condensations are occurred because the system becomes onedimensional 56 , as for SW-CN-Ts.Those explanations are proved with the experimental result for Neon adsorption 57 and molecular simulation results for Helium, Xenon and Argon mixture 59 .
The adsorption isotherms of Helium, Neon and Argon are plotted in figures 1a and 1b as function of pressure at 50K (figure1a) and temperature at 1Mpa (figure 1b).Three He, Ne and Ar adsorption isotherms exhibit similar behaviours.Comparing the amount of He, Ne and Ar adsorbed, it can be seen in figure 1 that the amount of Ar adsorbed is more than that of Ne and the amount of Ne adsorbed is more than that of He at the pressure and temperature range specified 55 .These are duo to the fact that the gases molecules can varies considerably in the sizes, physical properties, structures and electric properties (dipole and quadruple moments).Hence, Ar has stronger interaction and greater adsorption capacity on SiNTs than Ne that is more than He, under identical conditions.

Adsorption of H 2 in mixture with rare gases on (5, 5) SiNT
It is well known that hydrogens are the most promising alternative fuels because of their cleanness and high energies density 60,61 .Although it is a gas with critical temperature {33.19K} 62 , above this temperature hydrogen cannot be liquefied and is unsafe for storage and transported  . In ths work, we consider hydrogen in binary mixture with each rare gas (He, Ne and Ar) as a solution for safer storage of hydrogen as well as overall the substitution of hydrogen for other flues as fuel cell vehicles.
As we all know, the temperature, pressure and bulk composition play an important role in the adsorption process.For all considered binary mixtures, the gravimetric storage capacities of hydrogens in three mole fraction (x H = 0.3, 0.5 and 0.7) are illustrated in figure 2, 3 and 4. To investigate the adsorption behaviour at different pressure and temperature, temperature and pressure were set at 50K (figure 2a, 3a and 4a) and 1Mpa (figure 2b, 3b and 4b) respectively.As we can observe, the variation patterns of H 2 adsorption with pressure and temperature is similar to pure He, Ne and Ar adsorption.It is obvious, these calculation indicates that the amount of storage capacity of hydrogen in x H = 0.7 is higher than other mole fractions.The   2-4.In addition, it can be shown in the figure 2a that the greatest gravimetric adsorption amount of hydrogen is in x H = 0.7 and x He = 0.3 mixture, duo to the interaction manner of fluid molecules together and fluid molecules with Si-NTs.
Comparison of H 2 /He mixture and pure H 2 adsorptions on (5, 5) SiNT Fig. 5 depicts a gravimetric storages capacities for pure hydrogen and 1/3 hydrogen/ helium mixtures on the (5, 5) Si-N-Ts as a function of pressure at 50K.As it can be seen from this figure, both isotherms of adsorption are characterized by Langmuir shape, and there is no observation of capillary condensation.Obviously, amount of pure hydrogen adsorption is larger than hydrogen/helium mixture adsorption due to difference between fluid -fluid interaction in mixture and pure condition.In other words, in mixture level of simulation hydrogen molecules not only interact with other hydrogen molecules but have interaction with helium molecule and the number of hydrogen molecules captured by helium molecules.Consequently, hydrogen molecules have lower interaction with SiNT in the mixture level.
In this part, despite the lower amount of stored hydrogen in x H = 0.7 and x He = 0.3 mixture, this system is safer than that of pure hydrogen as a system for storage hydrogen in its applications as fuel cell vehicles.

CONCLUSIONS
For investigating the effect of pressure, temperature and bulk composition in the adsorption behavior of hydrogens, helium, argon and neon, 5 pressures in the range from 1 -15 Mpa, three temperatures (50, 100 and 150K) and three mole fraction (0.3, 0.5 and 0.7) in mixture condition were considered.In all studies, the adsorption capacity for adsorption of pure helium, argon, and neon, mixture of each instance rare gases with hydrogen at different mole fractions and pure hydrogen are increasing functions of pressure and decreasing functions of temperatures.
As an amazing result from this research, in x H = 0.7 and x He = 0.3 mixture, despite comparatively larger amount of stored hydrogen in pure hydrogen condition on (5, 5) Si-NTs, this system is safer, i.e. duo to use rare gases, dangerous of explosion in bulk storage of hydrogen decrease in its application as fuel cell vehicles and amount of gravimetric storage capacity in this condition is approximately close the pure hydrogen adsorption.

Fig. 1 :Fig. 2 :
Fig. 1: Asorption isotherms of He, Ne and Ar as function of pressure and temprature, (a) adsorption istherms of He, Ne and Ar in variuos pressure at 50K, (b) adsorption isotherms of He, Ne and Ar in variuos temprature at 1Mpa.(a) (b)

Fig. 5 :
Fig. 5: Comparison of stored hydrogen between x H =0.7 and x He =0.3 mixture and pure hydrogen conditions on (5,5)SiNT in various pressure at 50K.