Effect of Tubular Chiralities and Diameters of Single Carbon Nanotubes on Gas Sensing Behavior : A DFT Analysis

Using density functional theory, the adsorption of CO, CO2, NO and CO2 gas molecules on different chiralities and diameters of single carbon nanotubes is investigated in terms of energetic, electronic properties and surface reactivity. We found that the adsorption of CO and CO2 gas molecules is dependent on the chiralities and diameters of CNTs and it is vice versa for NO and NO2 gas molecules. Also, the electronic character of CNTs is not affected by the adsorption of CO and CO2 gas molecules while it is strongly affected by NO and NO2 gas molecules. In addition, it is found that the dipole moments of zig-zag CNTs are always higher than the arm-chair CNTs. Therefore, we conclude that the zig-zag carbon nanotubes are more preferred as gas sensors than the arm-chair carbon nanotubes, especially for detecting NO and NO2 gas molecules.


Introduction
Monitoring of combustible gas alarms, gas leak detection, and environmental pollution is of great concern in public security.Advances in nanotechnology give great promise for achieving new sensing materials.Since the discovery of carbon nanotubes in 1991, the single-walled carbon nanotubes (SWCNTs) have been intensively investigated as nanoscale gas sensors because of their great surface areas to bulk ratio and their abilities to mod-ulate electrical properties upon adsorption of various kinds of gas molecules [1]- [17].The emission of carbon and nitrogen oxides (CO, CO 2 , NO and NO 2 ) results from the combustion of fossil fuels, contributing to both smog and acid precipitation, and affecting both terrestrial and aquatic ecosystems [18].Although many efforts have been made to use catalysts to reduce the amount of carbon or nitrogen oxides in the air [19]- [25], an efficient method of sensing and removing carbon and nitrogen oxides is still required.
Because carbon and nitrogen oxides are the most dangerous air pollutants, toxic and global warming gases, our work is concentrated on investigating the effect of tubular chiralities and diameters of single carbon nanotubes on gas sensing behavior for CO, CO 2 , NO and NO 2 gas molecules, applying the first principle calculations.

Computational Methods
All calculations were performed with the density functional theory as implemented within G03W package [26]- [29], using B3LYP exchange-functional and applying basis set 6 -31g (d,p).Pure carbon nanotubes ( ) The obtained diameters [30] and the adsorption energies of gas molecules on CNTs (E ads ) [31] are calculated from the following relations: ( ) where n and m are integral numbers, the composition of chiral vector.

Adsorption of CO, CO2, NO and NO2 Gas Molecules on CNTs
We have adsorbed CO and CO 2 gas molecules vertically on different three positions of ( ) 5, 0 , ( ) 9, 0 , ( ) and ( ) 6, 6 CNTs: above a carbon atom (carbon site), above a bond between two carbon atoms (bond site) and above a center of a hexagon ring (vacant site).The calculated adsorption energies of CO and CO 2 gas molecules   Also, we have adsorbed NO and NO 2 gas molecules vertically on different three positions of ( ) 5, 0 , ( ) 9, 0 , ( ) 5,5 and ( ) 6, 6 CNTs: above a carbon site, above a bond site and above a vacant site.The calculated adsorption energies of NO and NO 2 gas molecules are listed in Table 3.It is found that the best adsorption energies of NO gas molecule are on the ( ) 9, 0 CNT above a bond site, then above a carbon site and after that above a vacant site with adsorption energies of −1.65 eV, −1.55 eV and −1.34 eV, respectively.However, for NO 2 gas molecule is found to be above the bond site on ( ) 9, 0 CNT with adsorption energy of −1.75 eV.Also, it is noticed that the vacant site is always preferred for NO 2 gas adsorption on all the studied CNTs except for ( ) 9, 0 CNT.Therefore, one can conclude that all CNTs can be used as gas sensors for NO and NO 2 gas molecules.
From Table 2, Table 3, one can investigate the effect of the chiralities and the diameters on the CNT gas sensors behavior.It is clear that the adsorption of CO and CO 2 gas molecules is dependent on the chiralities and the diameters of CNTs.The adsorption of CO and CO 2 gas molecules is enhanced with increasing the diameter of the zig-zag CNTs.However, the adsorption of NO and NO 2 gas molecules is independent on the chiralities and the diameters of CNTs.

Energy Gaps of Adsorbed CO, CO2, NO and NO2 Gas Molecules on CNTs
From Table 4, it is clear that the adsorption of CO and CO 2 gas molecules on CNTs does not affect the elec-   tronic character of the CNTs.Also, the band gaps of pristine CNTs and the adsorbed CO and CO 2 gas molecules on CNTs are so close.
From Table 5, the adsorption of NO and NO 2 gas molecules on CNTs is strongly affected the electronic character of the ( ) 9, 0 and ( ) 5, 0 CNTs.However, there is not any change of the electronic character for ( ) and ( ) 6, 6 CNTs.The band gap of pristine ( ) 5, 0 CNT is increased from 0.70 eV to 1.61 eV and to 1.37 eV when NO and NO 2 gas molecules are adsorbed on it, respectively.Also, The band gap of pristine ( ) 9, 0 CNT is increased from 0.25 eV to 1.34 eV and to 1.25 eV when NO and NO 2 gas molecules are adsorbed on it, respectively.One can conclude that the electronic character of ( ) 5, 0 , ( ) 9, 0 , ( ) 5,5 and ( ) 6, 6 CNTs is not affected by the adsorption of CO and CO 2 gas molecules.The adsorption of NO and NO 2 gas molecules on CNTs is only strongly affected the electronic character of the ( ) 9, 0 and ( ) 5, 0 CNTs, however the ( )

HOMO-LUMO Orbitals of Adsorbing CO, CO2, NO and NO2 Gas Molecules on CNTs
Our calculated band gaps show that the adsorption of CO and CO 2 gas molecules on CNTs is not affected the band gaps of the pristine CNTs, however the adsorption of NO and NO 2 gas molecules is strongly affected the band gaps.To explain that the molecular orbitals of adsorbing CO, CO 2 , NO and NO 2 gas molecules on ( ) Comparing the HOMO-LUMO energies of the pristine CNTs with ones after the adsorption of CO and CO 2 gas molecules, it is clear that the energy values are so close.Also, it is noticed that there is not any contribution from the gas molecules at the molecular orbitals and the electron density of HOMO and LUMO is distributed over all the carbon atoms of CNTs except for ( ) 9, 0 CNT is located at the terminals of the tube, see Figure 2. Comparing the HOMO-LUMO energies of the pristine CNTs with ones after the adsorption of NO and NO 2 gas molecules, it is clear that the energy values are so close in case of ( ) 5,5 and ( ) 6, 6 CNTs and are quite far in case of ( ) 5, 0 and ( ) 9, 0 CNTs.The HOMO energy levels in case of ( ) 5, 0 and ( ) 9, 0 CNTs after adsorbing NO and NO 2 gas molecular are getting deep (lower) in energy however the LUMO energy levels are getting higher in energy.Results in increasing the band gap from 0.70 eV to 1.81 eV in Table 4.The calculated energy gaps (E g ) of CO and CO 2 above a carbon site, a bond site and a vacant site of pristine ( )   case of ( ) 5, 0 CNT and from 0.25 eV to 1.34 eV in case of ( ) 9, 0 CNT.Also, it is noticed that there is representation from the NO gas molecule at LUMO of ( ) 9, 0 and ( ) 6, 6 CNTs, see Figure 3.

The Reactivity of CNT Surfaces before and after Adsorbing Gas Molecules
Our calculated band gaps and molecular orbitals show that the adsorption of CO and CO 2 gas molecules on CNTs is not affected neither the band gaps nor the molecular orbitals of the pristine CNTs but the adsorption of NO and NO 2 gas molecules is strongly affected both of the band gaps and the molecular orbitals of ( ) 5, 0 and ( ) 9, 0 CNTs.To clear that the reactivity of CNT surfaces before and after adsorbing CO, CO 2 , NO and 2 gas molecules on ( ) 5, 0 , ( ) 9, 0 , ( ) 5,5 and ( ) 6, 6 CNTs are studied, see Table 6, Table 7.The surface reactivity of the pristine CNTs is calculated and is listed in Table 6.The dipole moments of pristine ( ) 5, 0 , ( ) 9, 0 , ( ) and ( ) 6, 6 CNTs are found to be 0.54 Debye, 0.20 Debye 0.00 Debye and 0.00 Debye, respectively.Comparing the dipole moments of the pristine CNTs with ones that are adsorbed the CO and CO 2 gas molecules, it is clear that the dipole moment values are so close in case of the adsorption of the CO gas molecule but they are higher in case of the adsorption of the CO 2 gas molecule, see Table 6.Also, it is noticed that the highest dipole moments after the adsorption of the CO 2 gas molecule are 0.74 Debye (when CO 2 is adsorbed above the bond site of ( ) 9, 0 CNT) and 0.77 Debye (when CO 2 is adsorbed above the vacant site of ( ) 6,6 CNTs.Energies of HOMO and LUMO are listed above their molecular orbitals and are given by eV.
Table 6.The calculated dipole moments of pristine and after adsorbing CO and CO 2 gas molecules above a carbon site, a bond site and a vacant site of ( ) 5,0 , ( ) 9,0 , ( ) 5,5 and ( ) 6,6 CNTs.All dipole moments are given by Debye.spectively.Comparing the dipole moments of the pristine CNTs with ones that are adsorbed the NO and NO 2 gas molecules, it is found that the dipole moments are getting higher.When the NO and NO 2 gas molecules are adsorbed on the vacant sites of CNTs, their dipole moments are either quite close to or are lower than the dipole moments of pristine CNTs, except in case of adsorbing NO 2 on ( ) 5, 0 CNT, the dipole moment is increased.Also, all the calculated dipole moments of adsorbing NO and NO 2 gas molecules on the carbon sites of CNTs  are increased, except in case of adsorbing NO 2 on ( ) 5, 0 CNT, the dipole moment is decreased.In case of adsorbing NO and NO 2 gas molecules on the bond sites of CNTs the dipole moments are also increased, except in case of adsorbing NO 2 on ( ) 9, 0 CNT is decreased, see Table 7.
From Table 6, Table 7, it is clear that the dipole moments of zig-zag ( ) 5, 0 and ( )

Conclusion
The gas sensing behavior of CNTs, considering a range of different nanotube diameters and chiralities, as well as different adsorption sites is reported.The adsorption of CO, CO 2 , NO, and NO 2 gas molecules on the ( ) 5, 0 , ( ) 9, 0 , ( ) 5,5 and ( ) 6, 6 CNTs are studied using B3LYP/6-31 g(d, p).Three different adsorption sites (above a carbon site, a bond site and a vacant site) are applied on CNTs.It is found that the adsorption of CO and CO 2 gas molecules is dependent on the chiralities and the diameters of CNTs and it is enhanced with increasing the diameter of the zig-zag CNTs.However, the adsorption of NO and NO 2 gas molecules is independent on the chiralities and the diameters of CNTs.Also, the electronic character of ( ) 5, 0 , ( ) 9, 0 , ( ) 5,5 and ( ) 6, 6 CNTs is not affected by the adsorption of CO and CO 2 gas molecules.While, the adsorption of NO and NO 2 gas molecules on CNTs is only strongly affected by the electronic character of the ( ) 9, 0 and ( ) 5, 0 CNTs but the ( ) 5,5 and ( ) 6, 6 CNTs are not affected at all.It is found that the dipole moments of zig-zag ( ) 5, 0 and ( ) 9, 0 CNTs are always higher than the arm-chair ( ) 5,5 and ( ) 6, 6 CNTs.Also, it is noticed that the dipole moment of adsorbing NO gas molecule on the bond site of ( ) 5, 0 CNT is increased by ten times compared with the dipole moment of pristine ( ) 5, 0 CNT.Therefore, these findings prove that the zig-zag carbon nanotubes are better than the arm-chair carbon nanotubes as gas sensors, especially for NO and NO 2 gas molecules.

Table 2 .
It is found that the best position and adsorption energy for CO gas molecule is above the bond site on ( )

Table 1 .
The configuration structures and diameters of the studied CNTs.

Table 3 .
The calculated adsorption energies (E ads ) of NO and NO 2 above a carbon site, a bond site and a vacant site of pris-
6, 6 CNTs are investigated, see Figure 2, Figure 3.The band gaps of the pristine CNTs are calculated and are listed in

Table 5 .
The calculated energy gaps (E g ) of NO and NO 2 above a carbon site, a bond site and a vacant site of pristine ( )

Table 7 .
The calculated dipole moments of pristine and after adsorbing NO and NO 2 gas molecules above a carbon site, a bond site and a vacant site of ( )