Adsorption simulation of open-ended single-walled carbon nanotubes for various gases

In order to study the adsorption capacity of open-ended single-walled carbon nanotubes for various gases, the grand canonical Monte Carlo method is used to simulate the adsorption capacities of methane, nitrogen, water, carbon dioxide, and carbon monoxide in different types of open-ended single-walled carbon nanotubes at temperatures of 273.15 K and 298.15 K and pressures of 1 Pa–101.325 kPa. Gas adsorption isotherms under various conditions were obtained. The effects of temperature and diameter of open-ended single-walled carbon nanotubes on gas adsorption capacity were discussed. The results showed that the open-ended single-walled carbon nanotubes had a certain adsorption capacity for five kinds of gases under low pressure conditions. For a given temperature, as the diameter of the tube increased, the adsorption capacities of various gases were enhanced. Each gas exhibited different growth gradients; specifically, the growth gradients of methane and nitrogen were relatively small, while the growth grad...


I. INTRODUCTION
It has been 28 years since the first carbon nanotubes (CNTs) were discovered. 1 CNTs are formed by rolled graphite sheets, of which the inner diameter starts from 7 nm up to several nm and has a length of 10-100 μm. The single-walled carbon nanotubes (SWCNTs) are formed by only one single graphite layer. At present, researchers pay much attention to SWCNTs because of their electronic and remarkable physico-chemical properties. [2][3][4][5][6][7][8][9] SWCNTs are attractive materials for adsorption-related applications, such as the use of nanotubes for developing sensors of pollutant gases, [10][11][12][13][14] storage of alternative fuels, [15][16][17] membranes, [18][19][20][21][22] and removal of hazardous pollutants from gas streams, 23 for which the study on the characteristics of their adsorption properties are significant.
This research is mainly on adsorption sites, adsorption capacities of various gases, and the influence of different structural arrays of carbon nanotube bundles on external surface adsorption. However, little emphasis has been given to the adsorption on open-ended SWCNTs. CO and other gases generated by spontaneous combustion of coal seams in goafs of coal mines or the working face seriously threaten the life safety of underground workers. Although gas concentration monitoring sensors are arranged on the roadway, the CO concentration overrun problem cannot be processed well in time.
In this article, a series of molecular simulations of various gas adsorption capacities inside the tubes of open-ended SWCNTs were carried out, and the results were analyzed. The various gas

A. The model of open-ended SWCNTs and adsorbates
Open-ended SWCNTs with three different diameters are shown in Fig. 1. The molecular structures of adsorbates are shown in Fig. 2. The open-ended SWCNT diameter d, which is defined as the internuclear distance between diametrically opposed carbon atoms on the external surface of a nanotube, and the length L define the geometry of the model. The parameters of the supercell we have established are shown in Table I. The supercell is composed of three unit cells.

B. Simulations
The grand canonical (constant chemical potential, volume, and temperature) Monte Carlo method was used to simulate the adsorption of gases (CH 4 , N 2 , H 2 O, CO 2 , and CO) in SWCNTs at 273.15 K and 289.15 K. In the study, CH 4 38 and N 2 39 used the TraPPE model, H 2 O adopted the extended simple point charge (SPC-E) model, 40 CO 2 adopted the EPM2 [EPM2 is obtained by rescaling the potential parameters of the elementary physical model (EPM)] model, 41 and the Lennard-Jones (LJ) parameters of linear molecules of CO was calculated by Bohn. 42 It was assumed that the SWCNTs and each fluid molecule were rigid and remained electrically neutral during the simulations. CH 4 and N 2 are non-polar molecules. Although CO is a polar molecule, due to the feedback π bond, the polarity of the molecule is very weak and can be negligible. Therefore, the interaction of these three molecules with the combined atoms of SWCNTs did not require consideration of the long-range charge Coulomb force, and only the short-range van der Waals force was needed to be considered. For them, the interaction between the carbon atoms of nanotubes and each adsorbate molecule is modeled using the LJ potential, expressed as where r is the intermolecular distance. CO 2 and H 2 O are polar molecules that carry a charge; hence, the effect of the long-range charge Coulomb force needs to be considered when interacting with carbon atoms of nanotubes. The LJ potential is expressed as  where qi and qj are the atomic charge, ε 0 is the dielectric constant, εi/kB is the well depths, kB is the Boltzmann constant, and σi is the collision diameters. The parameters are listed in Table I. Cross-terms are obtained using the standard Lorenz-Berthelot combining rules, represented by the following equations: This potential is applicable to gas adsorption inside the tube of SWCNTs. Periodic boundary conditions were employed in the calculation of adsorbate interactions beyond the simulation cell. The Lennard-Jones potential parameters are listed in Table II.
The construction and optimization of open-ended SWCNTs and adsorbent molecules were completed by the Forcite module of the Materials Studio software. Simulations were performed by the Sorption module, of which the calculation process was based on the GCMC method. In the simulation, both the van der Waals and It was impossible to take the forces between all molecules into account during calculation. At the same time, in order to reduce the calculation time, a truncation radius was introduced (that is, the interaction between molecules mainly comes from truncation within the radius; hence, the force outside the range was small and could be ignored). The truncation radius of the vdW force in this paper was half of the minimum side length of the supercell (equal to 0.5a). The summation method of the van der Waals force was atom based, and that of the electrostatic force was Ewald based, of which the accuracy was 0.001 kcal/mol. For the purpose of making the simulation results more credible, the equilibrium steps and production steps were set to one million and two million, respectively, and the adsorption isotherm of each gas was simulated three times. Finally, the average value was taken as the adsorption amount. The parameter settings in GCMC simulations were listed in Table III, and all of them had been verified in the literature. 43 , the tubes may be regarded as supermicropore (7 < d < 20 Å) 45 with strongly enhanced interaction potentials, resulting in type I shape isotherms in each case. The interstitial space available to the adsorptive molecules was enhanced with the increase in d, which in turn resulted in an increase in the adsorption amount.
The growth gradient is calculated by   (9,9) is studied in the literature. 47 We find that the densities of CH 4 , CO 2 , and CO, shown in Table VI, are of an order of magnitude smaller than that in the literature. 47 This is because in the simulation, the gas is only adsorbed on the tube of open-ended SWCNTs, and gas adsorption does not occur outside the tube. At the same time, the unit cell established is a hexagonal structure, leaving free space at the corners. This free volume participates in the calculation of the densities, so the densities we obtained are smaller than the true values. The computational model in the literature 48 is SWCNT (10,10). Comparing it with the adsorption amount of H 2 O we obtained from the simulation, the relative errors are 23%, 27.33%, and 23%, respectively. Through this analysis, we can make sure that the established model and simulation are correct.  (6,6) and SWCNT (7,7) are similar, and that of SWCNT (8,8) is the greatest at 101.325 kPa due to its largest tube volume.   (7,7) and SWCNT (8,8) are nearly zero due to their adsorption potential not being stronger enough to adsorb CO 2 molecules, which indicates that the adsorption potential in the tube of open-ended SWCNT (6,6) is the strongest. Furthermore, the adsorption amount of open-ended SWCNT (8,8) is about twice that of open-ended SWCNT (6,6) and SWCNT (7,7).  For open-ended SWCNT (6,6), no matter what the temperature is, 273.15 K or 298.15 K, the maximum adsorption amounts of H 2 O, CO 2 , and CO are the same, and the adsorption amounts of CH 4 and N 2 are very close. At 273.15 K, the adsorption amounts of gases on average are slightly larger than those at 298.15 K. After analysis, we can conclude that temperature is not the main effect on the adsorption amount of open-ended SWCNT (6,6) with the diameter of 8.14 Å. Due to hydrogen bonds between H 2 O molecules, it is easier to interact with the adsorption potential in the tube of openended SWCNTs, resulting in the amount of H 2 O adsorbed on the tube of SWCNT (6,6)  of open-ended SWCNTs is not affected by temperature and remains equal.

B. Effect of the pore diameter of open-ended SWCNTs on adsorption capacity
In the simulations, we researched on the adsorption sites of CH 4 , N 2 , H 2 O, and CO 2 in the tubes of open-ended SWCNT (6,6) and SWCNT (7,7), as shown in Fig. 6, which indicates that gas adsorption takes place primarily inside the tube of open-ended SWCNTs under the given simulation conditions. However, the adsorption sites of CO are not all inside the tube of open-ended SWCNT (8,8). A few of the CO molecules are adsorbed on the external surface of open-ended SWCNT (8,8), and most of the CO molecules exist in the tube of open-ended SWCNT (8,8). This is related to the size of the CO molecule. The volume of the simulation box, which is made of three vectors, OA, OB, and OC, is 2577.47 The diameter of the oxygen atom is 1.32 Å, which is smaller than the diameter of the carbon atom. Combined with the adsorption form of CO shown in Fig. 7, the distance of available space is 5.965 − 1.82 = 4.145 > 3.76 Å (van der Waals radius), so the residual volume in the simulation box can provide adsorption space for CO.