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Adsorption behavior of ternary mixtures of noble gases inside single-walled carbon nanotube bundles
Chemical Physics Letters 497 (2010) 213–217
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Adsorption behavior of ternary mixtures of noble gases inside single-walled carbon nanotube bundles Masumeh Foroutan *, Amir Taghavi Nasrabadi Department of Physical Chemistry, School of Chemistry, College of Science, University of Tehran, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 26 June 2010 In final form 15 August 2010 Available online 18 August 2010
a b s t r a c t In order to study the gas-storage and gas-filtering capability of carbon nanotube (CNT) bundles simultaneously, we considered the adsorption behavior of a ternary mixture of noble gases, including Argon (Ar), Krypton (Kr), and Xenon (Xe), i.e., Ar–Kr–Xe mixture, on (10, 10) single-walled carbon nanotube (SWCNT) bundles. Molecular dynamics (MD) simulations at different temperatures of (75, 100, 150, 200, 250, and 300) K were performed, and adsorption energies, self-diffusion coefficients, activation energies, and radial distribution functions (RDFs) were computed to analyze the thermodynamics, transport and structural properties of the adsorption systems. It is observed that the SWCNT bundles have larger contents of heavier noble gases compared to the lighter ones. This interesting behavior of SWCNT bundles makes them proper candidates for gas-storage and gas molecular-sieving processes. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Discovery of CNTs [1] has opened a new field of research in diverse fields of science, especially nanoscience and nanotechnology. One of the main reasons of this occurrence is the unique physical, optical, and mechanical properties [2] of these promising nanostructures. The adsorption of gases on CNTs and their applicability is still an extremely active research field as their well-defined structures with hollow nanosize interiors suggest their potential use as sorbents for gas adsorption. The internal and external adsorption sites of the curved nanotubes enhance surface proximity for adsorbates and hence influence the extent of adsorption and separation. A large number of studies have been carried out thus far on the adsorption of diverse gases on various CNTs, single- or multiwalled, closed- or open-ended [3–6]. Among the different methods employed to study this topic, computer simulation experiments are playing an increasingly important role, because many properties of fluids in porous media become inaccessible to experimental measurements when the characteristic dimensions of the confining medium approaches molecular scale. Physisorption of noble gases on CNTs are investigated using theoretical methods and experimental techniques extensively, including adsorption of helium [7], neon [8], argon [9], krypton [10] and xenon [6,10]; because the inertness of the noble gases typically excludes the possibility of chemical and polar interactions with the surface and exclusively results in physical absorption only. * Corresponding author. Fax: +98 21 66495291. E-mail address: [email protected] (M. Foroutan). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.08.022
Adsorptive separation of particular gaseous mixtures is a viable industrial process, where one component can be selectively adsorbed on a suitable adsorbent relative to the other components. Most of the studies on adsorptive separation are based on carbon sorbents, in which CNTs are now considered as promising candidates for gas separation applications due to not only their stable thermodynamic and mechanical properties but also their uniform porosity distribution and easily controllable pore size. However, less studied is the competitive adsorption of a gas mixture on CNTs. Grand canonical Monte Carlo (MC) simulations of the adsorption of a binary Lennard–Jones gas mixture into a SWCNT revealed that the larger species is preferentially adsorbed rather than smaller ones [11]. From vibrational spectroscopy and simulation of the adsorption of a carbon tetrafluoride–xenon mixture on the internal and external surfaces of opened SWCNTs, it was found that xenon preferentially displaces internally adsorbed carbon tetrafluoride at high coverages [12]. The adsorption of a nitrogen oxides–sulfur dioxide–carbon dioxide mixture in the presence of oxygen on CNTs showed that the uptake of nitrogen oxides is much higher than that of sulfur dioxide and carbon dioxide and indicated that CNTs are a very good and reversible sorbents for the removal of nitrogen oxides at room temperature [13]. Path integral MC simulations were used to explore the adsorption of hydrogen isotope mixtures on CNTs, and the results suggest that CNTs can act as highly effective quantum sieves to separate hydrogen isotopes [14]. Grand canonical MC simulations [15] showed the separation of binary gas mixture of carbon monoxide–hydrogen in the presence of SWCNTs. Another work of Grand canonical MC simulations provided possible usage of SWCNTs bundles as an efficient storage and separation device of hydrogen–methane
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mixtures at room temperature [16]. Furthermore, previous simulation studies on nitrogen–oxygen mixture (representing air) separation using CNTs [17–19] have shown that oxygen is selectively adsorbed rather than nitrogen, which will be of high importance in industrial applications. All the previous works show that the selectivity in gas adsorbates is controlled by a number of factors: the adsorbate–adsorbate interactions for like and unlike molecules including the strength of adsorbate–adsorbent interactions, as well as geometric considerations such as pore width and the size and shape of the adsorptive species and ambient conditions, i.e., temperature and pressure. The objective of the present work is to study the adsorption and separation of ternary mixtures of noble gases on (10, 10) SWCNT bundles at different temperatures using MD simulations in order to estimate the gas-storage and gas-filtering capability of CNTs simultaneously. 2. Methods We employed an empirical force field scheme using Tinker molecular modeling package (version 5.0) [20,21], to describe molecular interactions to allow large scale, long-time MD simulations. Experiments have shown that CNTs form bundles of nearly uniform and finite diameter [22,23], and the open-ended kinds of them are obtained after heat treatment in the presence of O2 and CO2 [24]. It was found that opening the ends of the nanotube by chemical cutting increases both the kinetic rate and the saturation capacity of the nanotubes for noble gases [25]. Thus, we have not considered isolated as grown CNTs but rather bundles of open-ended nanotubes. Moreover, It has been demonstrated that the chirality of nanotubes has no significant effect on the gas adsorption [26], and the nanotubes prepared by carbon arc [22] and laser ablation [23] have predominantly an armchair architecture. There have been a few simulations examining the effect of the external surface of a nanotube bundle on the adsorption of the adsorption of neon, argon, krypton, xenon, methane, and nitrogen–oxygen at subcritical temperatures [17,27], the obtained adsorption isotherms were predicted to be of type II, consistent with experiment. This suggests that, to correctly predict adsorption on a finite-sized nanotube bundle, the external surface must be taken into account. Regarding the above statements, a (10, 10) finite-sized nanotube bundle is considered in this work. The finite isolated bundle is assumed to be composed of seven hexagonal SWCNTs, all of the same chirality (10, 10) and fixed length (30.0 Å), and unaffected by adsorption of the gas within a periodic rectangular parallelepiped of 80 80 60 Å. All the simulation boxes contain 1200 gas atoms. The lengths in the x, y, and z directions are sufficiently large to eliminate the nearest neighbor interactions with periodic images, ensuring that the finite bundle is truly isolated and external surface condition is provided. The van der Waals gap (i.e., the distance between the walls of the nearest neighbor tubes in the bundle) is set as a constant 3.0 Å. The nanotube bundles are kept rigid and only the motion of the gas atoms (internal and relative to the SWCNT bundle) is considered during the simulations. A ternary mixture of noble gases is considered in this Letter, including Ar–Kr–Xe with the constant atomic ratio of 400:400:400 per simulation box. The intermolecular interactions are calculated using a wellknown Lennard–Jones potential:
"
Uðrij Þ ¼ 4e
rij rij
12
rij r ij
6 # ð1Þ
A cutoff radius of 10.0 Å is applied to the nonbonding interactions. The Lennard–Jones parameters are listed in Table 1 [28].
Table 1 Lennard–Jones parameters for the intermolecular interactions. Interaction C–C Ar–Ar Kr–Kr Xe–Xe
e
r
(kcal/mol)
(Å)
0.0700 0.2339 0.3170 0.4330
3.5500 3.4010 3.6240 3.9350
Interatomic Lennard–Jones potentials were calculated according to the Lorentz–Berthelot mixing rule [29]:
rij ¼
rii þ rjj
ð2Þ
2
eij ¼ ðeii ejj Þ
1=2
ð3Þ
The distance between gas atoms and SWCNT was chosen in a way to start the dynamics in a situation where the gas atoms were not sitting right on the Lennard–Jones minimum but still within its attractive range. Starting from this initial configuration, the MD simulations are performed within the NPT ensemble; each MD trajectory is equilibrated during 500 ps and then propagated for another 1 ns, with a time step of 1 fs. The velocity form of Verlet algorithm method [29] was used to integrate the equations of motion and temperature controls of 75, 100, 150, 200, 250, and 300 K was provided by the Nose–Hoover thermostat algorithm [30]. The simulations were performed under moderate pressure of 1 atm using Berendsen barostat [29]. 3. Results and discussion 3.1. Adsorption energy The dynamic behavior of the gas molecules can be illustrated by tracking the adsorption energy of the SWCNT bundle–gas molecules. The adsorption energy is estimated from the difference between the potential energy of the composite (bundle + gas) and the potential energies for the gas atoms and the corresponding SWCNT bundle as follows [26]:
DEadsorption ¼ Ebundleþgas Ebundle Egas
ð4Þ
where Ebundle+gas is the total potential energy of the system, Ebundle is the energy of the SWCNT bundle without the gas mixture, and Egas is the energy of the gas mixture without the nanotube bundle. In other words, the adsorption energy can be calculated as the difference between the minimum energy and the energy at an infinite separation of the SWCNT bundle and the gas mixture. The calculated amounts of adsorption energy are provided in Table 2. As the results show, increasing the operating temperature decreases the adsorption energy. This is fundamentally consistent with the fact that higher temperatures give the adsorbates more kinetic energy and this, in turn, results in less chance of being adsorbed and subsequent low adsorption energy. This result is in agreement with the previous works on gas adsorption [26,31] which demonstrate that, when the gas molecules are physisorbed on the nanotube surface, increasing the operational temperature makes the adsorbed system unstable and therefore decreases the adsorption energy. Thus, we assume that the highest average of Table 2 Adsorption energies of simulated systems at different temperatures. Temperature (K) Adsorption energy (kcal/mol)
75
100
150
200
250
300
1.25
1.11
0.951
0.949
0.938
0.931
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adsorption energy represents the thermodynamically most favorable gas adsorption process.
the heavier ones, thus, lighter noble gases have higher mobility, as shown in Table 3.
3.2. Self-diffusion coefficient
3.4. Radial distribution function
The self-diffusion coefficients were evaluated from the limiting slope of the mean square displacement (MSD) curve with time. There are three regimes in the MSD of the diffusant: a ballistic regime for short time scales, followed by a subdiffusive regime, and finally a Fickian diffusive regime in which the MSDs are proportional to time (linear behavior). The Einstein relation [32] was employed to obtain self-diffusion coefficients of noble gases in this region, which relates the long-time limit of MSD of the gas atoms to the self-diffusivity, D, through
In analyzing the structural characteristics of the adsorption systems, g(r), provides a better understanding of the quality of the adsorption process. This function is defined as the probability of finding gas atoms at distance r from the nanotube surface, relative to the probability expected for a completely random distribution at the same density of gas [31]. Figure 1 represents the RDF plots of Ar–Kr–Xe mixture adsorption on a (10, 10) SWCNT bundle at different temperatures. The two sharp rises (near 5 and 10 Å) represent the distance of closest approach of gas atoms to the SWCNT bundle, demonstrating purely physisorption behavior. The shape of RDF profiles is a characteristic indication of physisorption phenomenon. This function approaches a value of unity in the limit of no correlation. As deduced from the adsorption energies and self-diffusion coefficients, once again, the RDF plots emphasize that the lower the temperature applied, the more the gas is adsorbed, as the heights of peaks are reduced versus temperature increase. This is in agreement with the other experimental [34] and computational [19,31] works which report monotonical increase in adsorption amount while decreasing the temperature.
D E 2 jrðt þ DtÞ rðtÞj 1 D ¼ lim 6 t!1 Dt
ð5Þ
The self-diffusion coefficients of each noble gas at different temperatures were calculated individually. The results are given in Table 3. As expected, the self-diffusion coefficients increase with increasing temperature, as occurs in a bulk gas or fluid [32]. It is evident that when the temperature is increased, the corresponding kinetic energy increases, which results in higher translational mobility of adsorbates. The increasing trend in self-diffusion coefficients versus temperature is completely contrary to the adsorption energy behavior versus temperature. These two behaviors cooperates together, because the larger amounts of self-diffusion coefficients at higher temperatures give rise to considerable reduction in gas adsorption, and subsequent decrease in adsorption energy. Another considerable phenomenon which is observed for all temperatures is that the lighter atoms have the higher values of self-diffusion coefficients and vice versa. Indeed, it originates from their corresponding atomic mass, such that, at a fixed temperature and subsequent kinetic energy, heavier atoms have lower translational mobility compared to their lighter species. 3.3. Activation energy We can calculate the activation energy for the diffusion process of ternary mixture components using the Arrhenius equation [33],
D ¼ D0 expðEa =RTÞ
ð6Þ
Activation energy is defined as the potential barrier for translational motion of gas atoms inside nanotube bundles. When Ln D is plotted versus 1/T, calculated results show the characteristic Arrhenius behavior (linear behavior), suggesting that diffusion is an activated process. Activation energies of 1.06, 1.07, and 1.20 (kcal/mol) were computed for Ar, Kr, and Xe in gas mixture, respectively. It is observed that the lighter atoms have the lower values of activation energy compared to heavier ones, so the diffusion process is a more facilitated process for lighter noble gases rather than Table 3 Self-diffusion coefficients (Å2/ps) of Ar–Kr–Xe mixture components inside a (10, 10) SWCNT bundle at different temperatures. Temperature (K)
Ar
Kr
Xe
75 100 150 200 250 300
0.194 0.863 13.4 20.0 25.2 30.2
0.0596 0.185 1.78 8.07 13.5 16.7
0.0414 0.0631 0.278 1.10 5.96 7.49
3.5. Separation of ternary mixture components In this section we focus on the separation of components of ternary mixture, i.e., Ar, Kr, and Xe, using their corresponding RDF plots. As shown in Figure 1a, where the temperature is 75 K, the peaks of Ar, Kr and Xe are nearly the same and no separation among them is observed, while at 100 K (Fig. 1b), the peaks are separated slightly from each other, such that the Xe peak places on top, then Kr and Ar. At temperature of 150 K, these peaks are separated markedly. This profile shows obviously that the amount of adsorption of noble gases differs at this temperature, where Xe is adsorbed most, then Kr and finally Ar. This behavior is observed and enhanced for higher temperatures, so that; we can imagine a gradual separation of gaseous mixture components with increasing temperature. At temperature of 300 K (Fig. 1f), the separation distance between these peaks reaches to its most egregious difference, which implies on the most separative behavior of gaseous mixture components. So, along with the increase of temperature from 75 to 300 K, the separation increases to a maximum. In general, we can conclude that in a ternary mixture of noble gases, the heavier atoms are more adsorbed in a selective manner by CNT rather than the lighter ones, and replace them at higher temperatures. Figure 2 shows the snapshot of adsorption of Ar–Kr–Xe mixture on a (10, 10) SWCNT bundle at temperature of 300 K. The green, white, and pink balls represent the Ar, Kr, and Xe atoms, respectively. The selective adsorption of ternary mixture of noble gases can be interpreted by the adsorbate–adsorbent interactions. As Table 1 shows, the van der Waals interaction of noble gases with CNT follows this arrangement: Xe > Kr > Ar, so in general, in a ternary mixture of them, the heavier noble gas has the stronger interaction with SWCNT under identical conditions, which results in its more adsorption and subsequent separation. Such an approach will be useful for design and usage of CNTs as gas-filtering or molecularsieving systems, where one component is expected to separate and collected from bulk gas. 3.6. Distribution of noble gases inside SWCNT A deeper insight of the adsorption process, understanding how and where the gas molecules are physisorbed will certainly be of
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a6
b6
C-Ar C-Kr
5
C-Ar C-Kr
5
C-Xe
C-Xe
4
g (r)
g (r)
4 3
3
2
2
1
1
0
0
5
10
15
20
25
30
0
35
0
5
10
Distance (Å)
c
15
20
25
30
6
C-Ar
d
C-Kr
5
6
C-Ar C-Kr
5
C-Xe
C-Xe
4
g (r)
g (r)
4 3
3
2
2
1
1
0
0
5
10
15
20
25
30
0
35
0
5
10
15
20
25
30
35
Distance (Å)
Distance (Å)
e
35
Distance (Å)
5
f
C-Ar
4
4.5
C-Kr
4
C-Xe
3.5
C-Ar C-Kr C-Xe
3
g (r)
g (r)
3 2
2.5 2 1.5 1
1
0.5 0
0
5
10
15
20
25
30
35
Distance (Å)
0
0
5
10
15
20
25
30
35
Distance (Å)
Figure 1. RDF plots of Ar–Kr–Xe mixture adsorption on a (10, 10) SWCNT bundle at temperatures of (a) 75 K, (b) 100 K, (c) 150 K, (d) 200 K, (e) 250 K, and (f) 300 K.
aid in the design of materials with a larger gas-storage or gas-filtering capacity. However, it is important to emphasize that gas adsorption is a highly dynamic and chaotic phenomenon [26]. As such, gas atoms do not reside at a specific site permanently and, even when physisorbed in the nanotube, the gas atoms move actively in the bundle. Thus, it must be kept in mind that, although we refer to adsorption sites, these are not static fixed geometries with an absolute minimum energy. Therefore, we have inspected the positions occupied by the adsorbed gas atoms in the SWCNT bundles once the stationary state is achieved. To do this, we assume that the system has reached (dynamic) equilibrium at the end of the last MD simulation and consider the distribution of the adsorbed gas atoms as the equilibrium
one. Figure 3 shows the last snapshot of Ar–Kr–Xe adsorption on a (10, 10) SWCNT bundle at temperature of 75 K. Two main adsorption sites can be found, first, gas atoms are adsorbed inside the nanotubes (interior space of tubes) distributed rather uniformly, as a coaxial cylinder. A second adsorption site is observed on the external surface of nanotube bundle, while, no adsorption was observed in the interstitial threefold pores between the tubes forming the bundle. As Figure 3 shows, one may think that some gas atoms have been adsorbed in the interstitial threefold pores, but in fact, these atoms have been adsorbed on upper side of CNTs (external adsorption). Whether or not a gas can adsorb into the interstitial channels in a real nanotube bundle is of considerable interest, which is related
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4. Conclusions Adsorption and separation of ternary mixture of noble gases including Ar, Kr, and Xe on (10, 10) SWCNT bundles was simulated by extensive equilibrium MD. Adsorption energies, self-diffusion coefficients, activation energies, and RDFs were calculated to address the thermodynamics, transport and structural properties of adsorption process. The simulation results of exposing Ar–Kr–Xe mixture on (10, 10) SWCNT bundles at temperatures of (75, 100, 150, 200, 250 and 300) K, show that amount of adsorption is strongly influenced by the applied temperature. On the other hand, RDF plots show obviously that separation of ternary gaseous mixture is occurred, where the heavier noble gases are adsorbed more than the lighter ones in a selective manner by SWCNT bundles. It is seen that the increasing the applied temperature results in more separation. These findings provide us a possible application of CNTs as efficient nanomaterials for separation and storage of gas mixtures. References Figure 2. Snapshot of adsorption of Ar–Kr–Xe mixture on a (10, 10) SWCNT bundle at T = 300 K.
Figure 3. Adsorption sites of Ar–Kr–Xe mixture inside (10, 10) SWCNT bundle at T = 75 K.
to the potential use of nanotubes as a gas-storage medium. Experimental studies were usually performed at rather low pressures for the adsorption of xenon, neon, and methane on closed-ended SWCNT bundles [35]. They concluded that the interstitial channels were not accessible to any of these three gases. This experimental conclusion is consistent with our simulation results on the finite bundle at low pressures (1 atm), in which gas atoms are not adsorbed into the interstitial channels. However, it can be suggested that the interstitial channels may be occupied at high pressures.
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Adsorption behavior of ternary mixtures of noble gases inside single-walled carbon nanotube bundles Masumeh Foroutan *, Amir Taghavi Nasrabadi Department of Physical Chemistry, School of Chemistry, College of Science, University of Tehran, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 26 June 2010 In final form 15 August 2010 Available online 18 August 2010
a b s t r a c t In order to study the gas-storage and gas-filtering capability of carbon nanotube (CNT) bundles simultaneously, we considered the adsorption behavior of a ternary mixture of noble gases, including Argon (Ar), Krypton (Kr), and Xenon (Xe), i.e., Ar–Kr–Xe mixture, on (10, 10) single-walled carbon nanotube (SWCNT) bundles. Molecular dynamics (MD) simulations at different temperatures of (75, 100, 150, 200, 250, and 300) K were performed, and adsorption energies, self-diffusion coefficients, activation energies, and radial distribution functions (RDFs) were computed to analyze the thermodynamics, transport and structural properties of the adsorption systems. It is observed that the SWCNT bundles have larger contents of heavier noble gases compared to the lighter ones. This interesting behavior of SWCNT bundles makes them proper candidates for gas-storage and gas molecular-sieving processes. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Discovery of CNTs [1] has opened a new field of research in diverse fields of science, especially nanoscience and nanotechnology. One of the main reasons of this occurrence is the unique physical, optical, and mechanical properties [2] of these promising nanostructures. The adsorption of gases on CNTs and their applicability is still an extremely active research field as their well-defined structures with hollow nanosize interiors suggest their potential use as sorbents for gas adsorption. The internal and external adsorption sites of the curved nanotubes enhance surface proximity for adsorbates and hence influence the extent of adsorption and separation. A large number of studies have been carried out thus far on the adsorption of diverse gases on various CNTs, single- or multiwalled, closed- or open-ended [3–6]. Among the different methods employed to study this topic, computer simulation experiments are playing an increasingly important role, because many properties of fluids in porous media become inaccessible to experimental measurements when the characteristic dimensions of the confining medium approaches molecular scale. Physisorption of noble gases on CNTs are investigated using theoretical methods and experimental techniques extensively, including adsorption of helium [7], neon [8], argon [9], krypton [10] and xenon [6,10]; because the inertness of the noble gases typically excludes the possibility of chemical and polar interactions with the surface and exclusively results in physical absorption only. * Corresponding author. Fax: +98 21 66495291. E-mail address: [email protected] (M. Foroutan). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.08.022
Adsorptive separation of particular gaseous mixtures is a viable industrial process, where one component can be selectively adsorbed on a suitable adsorbent relative to the other components. Most of the studies on adsorptive separation are based on carbon sorbents, in which CNTs are now considered as promising candidates for gas separation applications due to not only their stable thermodynamic and mechanical properties but also their uniform porosity distribution and easily controllable pore size. However, less studied is the competitive adsorption of a gas mixture on CNTs. Grand canonical Monte Carlo (MC) simulations of the adsorption of a binary Lennard–Jones gas mixture into a SWCNT revealed that the larger species is preferentially adsorbed rather than smaller ones [11]. From vibrational spectroscopy and simulation of the adsorption of a carbon tetrafluoride–xenon mixture on the internal and external surfaces of opened SWCNTs, it was found that xenon preferentially displaces internally adsorbed carbon tetrafluoride at high coverages [12]. The adsorption of a nitrogen oxides–sulfur dioxide–carbon dioxide mixture in the presence of oxygen on CNTs showed that the uptake of nitrogen oxides is much higher than that of sulfur dioxide and carbon dioxide and indicated that CNTs are a very good and reversible sorbents for the removal of nitrogen oxides at room temperature [13]. Path integral MC simulations were used to explore the adsorption of hydrogen isotope mixtures on CNTs, and the results suggest that CNTs can act as highly effective quantum sieves to separate hydrogen isotopes [14]. Grand canonical MC simulations [15] showed the separation of binary gas mixture of carbon monoxide–hydrogen in the presence of SWCNTs. Another work of Grand canonical MC simulations provided possible usage of SWCNTs bundles as an efficient storage and separation device of hydrogen–methane
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mixtures at room temperature [16]. Furthermore, previous simulation studies on nitrogen–oxygen mixture (representing air) separation using CNTs [17–19] have shown that oxygen is selectively adsorbed rather than nitrogen, which will be of high importance in industrial applications. All the previous works show that the selectivity in gas adsorbates is controlled by a number of factors: the adsorbate–adsorbate interactions for like and unlike molecules including the strength of adsorbate–adsorbent interactions, as well as geometric considerations such as pore width and the size and shape of the adsorptive species and ambient conditions, i.e., temperature and pressure. The objective of the present work is to study the adsorption and separation of ternary mixtures of noble gases on (10, 10) SWCNT bundles at different temperatures using MD simulations in order to estimate the gas-storage and gas-filtering capability of CNTs simultaneously. 2. Methods We employed an empirical force field scheme using Tinker molecular modeling package (version 5.0) [20,21], to describe molecular interactions to allow large scale, long-time MD simulations. Experiments have shown that CNTs form bundles of nearly uniform and finite diameter [22,23], and the open-ended kinds of them are obtained after heat treatment in the presence of O2 and CO2 [24]. It was found that opening the ends of the nanotube by chemical cutting increases both the kinetic rate and the saturation capacity of the nanotubes for noble gases [25]. Thus, we have not considered isolated as grown CNTs but rather bundles of open-ended nanotubes. Moreover, It has been demonstrated that the chirality of nanotubes has no significant effect on the gas adsorption [26], and the nanotubes prepared by carbon arc [22] and laser ablation [23] have predominantly an armchair architecture. There have been a few simulations examining the effect of the external surface of a nanotube bundle on the adsorption of the adsorption of neon, argon, krypton, xenon, methane, and nitrogen–oxygen at subcritical temperatures [17,27], the obtained adsorption isotherms were predicted to be of type II, consistent with experiment. This suggests that, to correctly predict adsorption on a finite-sized nanotube bundle, the external surface must be taken into account. Regarding the above statements, a (10, 10) finite-sized nanotube bundle is considered in this work. The finite isolated bundle is assumed to be composed of seven hexagonal SWCNTs, all of the same chirality (10, 10) and fixed length (30.0 Å), and unaffected by adsorption of the gas within a periodic rectangular parallelepiped of 80 80 60 Å. All the simulation boxes contain 1200 gas atoms. The lengths in the x, y, and z directions are sufficiently large to eliminate the nearest neighbor interactions with periodic images, ensuring that the finite bundle is truly isolated and external surface condition is provided. The van der Waals gap (i.e., the distance between the walls of the nearest neighbor tubes in the bundle) is set as a constant 3.0 Å. The nanotube bundles are kept rigid and only the motion of the gas atoms (internal and relative to the SWCNT bundle) is considered during the simulations. A ternary mixture of noble gases is considered in this Letter, including Ar–Kr–Xe with the constant atomic ratio of 400:400:400 per simulation box. The intermolecular interactions are calculated using a wellknown Lennard–Jones potential:
"
Uðrij Þ ¼ 4e
rij rij
12
rij r ij
6 # ð1Þ
A cutoff radius of 10.0 Å is applied to the nonbonding interactions. The Lennard–Jones parameters are listed in Table 1 [28].
Table 1 Lennard–Jones parameters for the intermolecular interactions. Interaction C–C Ar–Ar Kr–Kr Xe–Xe
e
r
(kcal/mol)
(Å)
0.0700 0.2339 0.3170 0.4330
3.5500 3.4010 3.6240 3.9350
Interatomic Lennard–Jones potentials were calculated according to the Lorentz–Berthelot mixing rule [29]:
rij ¼
rii þ rjj
ð2Þ
2
eij ¼ ðeii ejj Þ
1=2
ð3Þ
The distance between gas atoms and SWCNT was chosen in a way to start the dynamics in a situation where the gas atoms were not sitting right on the Lennard–Jones minimum but still within its attractive range. Starting from this initial configuration, the MD simulations are performed within the NPT ensemble; each MD trajectory is equilibrated during 500 ps and then propagated for another 1 ns, with a time step of 1 fs. The velocity form of Verlet algorithm method [29] was used to integrate the equations of motion and temperature controls of 75, 100, 150, 200, 250, and 300 K was provided by the Nose–Hoover thermostat algorithm [30]. The simulations were performed under moderate pressure of 1 atm using Berendsen barostat [29]. 3. Results and discussion 3.1. Adsorption energy The dynamic behavior of the gas molecules can be illustrated by tracking the adsorption energy of the SWCNT bundle–gas molecules. The adsorption energy is estimated from the difference between the potential energy of the composite (bundle + gas) and the potential energies for the gas atoms and the corresponding SWCNT bundle as follows [26]:
DEadsorption ¼ Ebundleþgas Ebundle Egas
ð4Þ
where Ebundle+gas is the total potential energy of the system, Ebundle is the energy of the SWCNT bundle without the gas mixture, and Egas is the energy of the gas mixture without the nanotube bundle. In other words, the adsorption energy can be calculated as the difference between the minimum energy and the energy at an infinite separation of the SWCNT bundle and the gas mixture. The calculated amounts of adsorption energy are provided in Table 2. As the results show, increasing the operating temperature decreases the adsorption energy. This is fundamentally consistent with the fact that higher temperatures give the adsorbates more kinetic energy and this, in turn, results in less chance of being adsorbed and subsequent low adsorption energy. This result is in agreement with the previous works on gas adsorption [26,31] which demonstrate that, when the gas molecules are physisorbed on the nanotube surface, increasing the operational temperature makes the adsorbed system unstable and therefore decreases the adsorption energy. Thus, we assume that the highest average of Table 2 Adsorption energies of simulated systems at different temperatures. Temperature (K) Adsorption energy (kcal/mol)
75
100
150
200
250
300
1.25
1.11
0.951
0.949
0.938
0.931
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215
adsorption energy represents the thermodynamically most favorable gas adsorption process.
the heavier ones, thus, lighter noble gases have higher mobility, as shown in Table 3.
3.2. Self-diffusion coefficient
3.4. Radial distribution function
The self-diffusion coefficients were evaluated from the limiting slope of the mean square displacement (MSD) curve with time. There are three regimes in the MSD of the diffusant: a ballistic regime for short time scales, followed by a subdiffusive regime, and finally a Fickian diffusive regime in which the MSDs are proportional to time (linear behavior). The Einstein relation [32] was employed to obtain self-diffusion coefficients of noble gases in this region, which relates the long-time limit of MSD of the gas atoms to the self-diffusivity, D, through
In analyzing the structural characteristics of the adsorption systems, g(r), provides a better understanding of the quality of the adsorption process. This function is defined as the probability of finding gas atoms at distance r from the nanotube surface, relative to the probability expected for a completely random distribution at the same density of gas [31]. Figure 1 represents the RDF plots of Ar–Kr–Xe mixture adsorption on a (10, 10) SWCNT bundle at different temperatures. The two sharp rises (near 5 and 10 Å) represent the distance of closest approach of gas atoms to the SWCNT bundle, demonstrating purely physisorption behavior. The shape of RDF profiles is a characteristic indication of physisorption phenomenon. This function approaches a value of unity in the limit of no correlation. As deduced from the adsorption energies and self-diffusion coefficients, once again, the RDF plots emphasize that the lower the temperature applied, the more the gas is adsorbed, as the heights of peaks are reduced versus temperature increase. This is in agreement with the other experimental [34] and computational [19,31] works which report monotonical increase in adsorption amount while decreasing the temperature.
D E 2 jrðt þ DtÞ rðtÞj 1 D ¼ lim 6 t!1 Dt
ð5Þ
The self-diffusion coefficients of each noble gas at different temperatures were calculated individually. The results are given in Table 3. As expected, the self-diffusion coefficients increase with increasing temperature, as occurs in a bulk gas or fluid [32]. It is evident that when the temperature is increased, the corresponding kinetic energy increases, which results in higher translational mobility of adsorbates. The increasing trend in self-diffusion coefficients versus temperature is completely contrary to the adsorption energy behavior versus temperature. These two behaviors cooperates together, because the larger amounts of self-diffusion coefficients at higher temperatures give rise to considerable reduction in gas adsorption, and subsequent decrease in adsorption energy. Another considerable phenomenon which is observed for all temperatures is that the lighter atoms have the higher values of self-diffusion coefficients and vice versa. Indeed, it originates from their corresponding atomic mass, such that, at a fixed temperature and subsequent kinetic energy, heavier atoms have lower translational mobility compared to their lighter species. 3.3. Activation energy We can calculate the activation energy for the diffusion process of ternary mixture components using the Arrhenius equation [33],
D ¼ D0 expðEa =RTÞ
ð6Þ
Activation energy is defined as the potential barrier for translational motion of gas atoms inside nanotube bundles. When Ln D is plotted versus 1/T, calculated results show the characteristic Arrhenius behavior (linear behavior), suggesting that diffusion is an activated process. Activation energies of 1.06, 1.07, and 1.20 (kcal/mol) were computed for Ar, Kr, and Xe in gas mixture, respectively. It is observed that the lighter atoms have the lower values of activation energy compared to heavier ones, so the diffusion process is a more facilitated process for lighter noble gases rather than Table 3 Self-diffusion coefficients (Å2/ps) of Ar–Kr–Xe mixture components inside a (10, 10) SWCNT bundle at different temperatures. Temperature (K)
Ar
Kr
Xe
75 100 150 200 250 300
0.194 0.863 13.4 20.0 25.2 30.2
0.0596 0.185 1.78 8.07 13.5 16.7
0.0414 0.0631 0.278 1.10 5.96 7.49
3.5. Separation of ternary mixture components In this section we focus on the separation of components of ternary mixture, i.e., Ar, Kr, and Xe, using their corresponding RDF plots. As shown in Figure 1a, where the temperature is 75 K, the peaks of Ar, Kr and Xe are nearly the same and no separation among them is observed, while at 100 K (Fig. 1b), the peaks are separated slightly from each other, such that the Xe peak places on top, then Kr and Ar. At temperature of 150 K, these peaks are separated markedly. This profile shows obviously that the amount of adsorption of noble gases differs at this temperature, where Xe is adsorbed most, then Kr and finally Ar. This behavior is observed and enhanced for higher temperatures, so that; we can imagine a gradual separation of gaseous mixture components with increasing temperature. At temperature of 300 K (Fig. 1f), the separation distance between these peaks reaches to its most egregious difference, which implies on the most separative behavior of gaseous mixture components. So, along with the increase of temperature from 75 to 300 K, the separation increases to a maximum. In general, we can conclude that in a ternary mixture of noble gases, the heavier atoms are more adsorbed in a selective manner by CNT rather than the lighter ones, and replace them at higher temperatures. Figure 2 shows the snapshot of adsorption of Ar–Kr–Xe mixture on a (10, 10) SWCNT bundle at temperature of 300 K. The green, white, and pink balls represent the Ar, Kr, and Xe atoms, respectively. The selective adsorption of ternary mixture of noble gases can be interpreted by the adsorbate–adsorbent interactions. As Table 1 shows, the van der Waals interaction of noble gases with CNT follows this arrangement: Xe > Kr > Ar, so in general, in a ternary mixture of them, the heavier noble gas has the stronger interaction with SWCNT under identical conditions, which results in its more adsorption and subsequent separation. Such an approach will be useful for design and usage of CNTs as gas-filtering or molecularsieving systems, where one component is expected to separate and collected from bulk gas. 3.6. Distribution of noble gases inside SWCNT A deeper insight of the adsorption process, understanding how and where the gas molecules are physisorbed will certainly be of
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a6
b6
C-Ar C-Kr
5
C-Ar C-Kr
5
C-Xe
C-Xe
4
g (r)
g (r)
4 3
3
2
2
1
1
0
0
5
10
15
20
25
30
0
35
0
5
10
Distance (Å)
c
15
20
25
30
6
C-Ar
d
C-Kr
5
6
C-Ar C-Kr
5
C-Xe
C-Xe
4
g (r)
g (r)
4 3
3
2
2
1
1
0
0
5
10
15
20
25
30
0
35
0
5
10
15
20
25
30
35
Distance (Å)
Distance (Å)
e
35
Distance (Å)
5
f
C-Ar
4
4.5
C-Kr
4
C-Xe
3.5
C-Ar C-Kr C-Xe
3
g (r)
g (r)
3 2
2.5 2 1.5 1
1
0.5 0
0
5
10
15
20
25
30
35
Distance (Å)
0
0
5
10
15
20
25
30
35
Distance (Å)
Figure 1. RDF plots of Ar–Kr–Xe mixture adsorption on a (10, 10) SWCNT bundle at temperatures of (a) 75 K, (b) 100 K, (c) 150 K, (d) 200 K, (e) 250 K, and (f) 300 K.
aid in the design of materials with a larger gas-storage or gas-filtering capacity. However, it is important to emphasize that gas adsorption is a highly dynamic and chaotic phenomenon [26]. As such, gas atoms do not reside at a specific site permanently and, even when physisorbed in the nanotube, the gas atoms move actively in the bundle. Thus, it must be kept in mind that, although we refer to adsorption sites, these are not static fixed geometries with an absolute minimum energy. Therefore, we have inspected the positions occupied by the adsorbed gas atoms in the SWCNT bundles once the stationary state is achieved. To do this, we assume that the system has reached (dynamic) equilibrium at the end of the last MD simulation and consider the distribution of the adsorbed gas atoms as the equilibrium
one. Figure 3 shows the last snapshot of Ar–Kr–Xe adsorption on a (10, 10) SWCNT bundle at temperature of 75 K. Two main adsorption sites can be found, first, gas atoms are adsorbed inside the nanotubes (interior space of tubes) distributed rather uniformly, as a coaxial cylinder. A second adsorption site is observed on the external surface of nanotube bundle, while, no adsorption was observed in the interstitial threefold pores between the tubes forming the bundle. As Figure 3 shows, one may think that some gas atoms have been adsorbed in the interstitial threefold pores, but in fact, these atoms have been adsorbed on upper side of CNTs (external adsorption). Whether or not a gas can adsorb into the interstitial channels in a real nanotube bundle is of considerable interest, which is related
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4. Conclusions Adsorption and separation of ternary mixture of noble gases including Ar, Kr, and Xe on (10, 10) SWCNT bundles was simulated by extensive equilibrium MD. Adsorption energies, self-diffusion coefficients, activation energies, and RDFs were calculated to address the thermodynamics, transport and structural properties of adsorption process. The simulation results of exposing Ar–Kr–Xe mixture on (10, 10) SWCNT bundles at temperatures of (75, 100, 150, 200, 250 and 300) K, show that amount of adsorption is strongly influenced by the applied temperature. On the other hand, RDF plots show obviously that separation of ternary gaseous mixture is occurred, where the heavier noble gases are adsorbed more than the lighter ones in a selective manner by SWCNT bundles. It is seen that the increasing the applied temperature results in more separation. These findings provide us a possible application of CNTs as efficient nanomaterials for separation and storage of gas mixtures. References Figure 2. Snapshot of adsorption of Ar–Kr–Xe mixture on a (10, 10) SWCNT bundle at T = 300 K.
Figure 3. Adsorption sites of Ar–Kr–Xe mixture inside (10, 10) SWCNT bundle at T = 75 K.
to the potential use of nanotubes as a gas-storage medium. Experimental studies were usually performed at rather low pressures for the adsorption of xenon, neon, and methane on closed-ended SWCNT bundles [35]. They concluded that the interstitial channels were not accessible to any of these three gases. This experimental conclusion is consistent with our simulation results on the finite bundle at low pressures (1 atm), in which gas atoms are not adsorbed into the interstitial channels. However, it can be suggested that the interstitial channels may be occupied at high pressures.
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