Molecular dynamics simulation study of neon adsorption on single-walled carbon nanotubes

Physica E 43 (2010) 261–265

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Molecular dynamics simulation study of neon adsorption on single-walled carbon nanotubes Masumeh Foroutan n, 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 in fo

abstract

Article history: Received 15 June 2010 Received in revised form 15 July 2010 Accepted 24 July 2010 Available online 29 July 2010

Using molecular dynamics (MD) simulations, neon adsorption on an open-ended (10,10) single-walled carbon nanotube (SWCNT) was investigated at supercritical temperatures of neon, i.e. T¼ 50, 70, and 90 K. Adsorption isotherms, heat of adsorption, self-diffusion coefficients, activation energy, and structural properties of neon gas were computed and analyzed in detail. All adsorption isotherms are predicted to be of Langmuir shape type I at this range of temperature. The results show that temperature is in a direct correlation with adsorption capacity, i.e. increase in temperature causes lower adsorption of neon gas by SWCNT. All aforementioned quantities confirm this fact and are in good agreement with previous experimental and theoretical works. & 2010 Elsevier B.V. All rights reserved.

1. Introduction Carbon nanotubes (CNTs), since their first discovery in 1991 [1], have been found as promising materials due to their unique physical, optical, and mechanical properties [2]. The adsorption of various gases on CNTs is nowadays an extremely active research field of both experimental and theoretical approach due to their role as novel storage gas media. A large number of experimental studies have been carried out on the adsorption of diverse gases on various CNTs, single- or multiwalled, closed- or open-ended [3–8]. It has to be pointed out that the study of the adsorption behavior via experiments is difficult for such systems because microscopic properties of such systems are often hard to determine and many properties of fluids in these media become inaccessible to experimental measurements. Therefore molecular simulations can be considered as a good candidate for understanding and predicting the adsorption behavior of various gases on CNTs. Many molecular simulation studies have been performed so far to understand gas adsorption on CNTs, including adsorption of nitrogen and oxygen [9], xenon [10], krypton [10], methane [11], ethane [12], organic compounds [13], helium [14], hydrogen [15,16], and neon [17]. Physisorption of noble gases has been investigated using theoretical methods and experimental techniques extensively [6–8,10,14,17]. It has been found that opening the ends of the nanotube by chemical cutting increases both the kinetic rate and the saturation capacity of the nanotubes for rare gases [10,17]. Also, adsorption isotherms of several gases on various CNTs have been

investigated experimentally so far [3,6,7,18,19]. All obtained Langmuir adsorption isotherms are shown to be of type II at bulk adsorbate subcritical and of type I or IV at supercritical temperatures. The adsorption isotherms that have been predicted theoretically are of type I regardless of temperature, or in a few cases of type IV. Physically, prediction of type I isotherms is expected for bulk adsorbate at supercritical temperatures since multilayer adsorption is not likely to occur. However, at subcritical temperatures, multiple adsorption layers may form and wetting might occur, producing dissimilarities between theoretical predictions and experimental data (type II isotherm) [9]. Recently, there have been a few simulations examining the effect of external surface of a nanotube bundle on adsorption of hydrogen at supercritical temperatures [20] and adsorption of neon, argon, krypton, xenon, and methane at subcritical temperatures [21,22]. In the latter, the 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. In this paper, neon adsorption is investigated using MD simulations at several supercritical temperatures of neon (T¼50, 70, and 90 K) on a small finite isolated SWCNT with an external surface. Adsorption isotherms, heat of adsorption, activation energy, and structural and transport properties of such a system are investigated in detail and analyzed in a different way compared with previous similar works [10,17,22].

2. Method n

Corresponding author. Tel.: +98 21 61112896; fax: +98 21 66495291. E-mail address: [email protected] (M. Foroutan).

1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.07.020

We employed an empirical force field scheme using Tinker molecular modeling package (version 5.0) [23], similar to our

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recent paper in Ref. [24], to describe molecular interactions to allow large scale, long time MD simulations. Since it has been investigated that the chirality of the nanotubes has no significant effect on adsorption [15], and as the nanotubes prepared by carbon arc [25], and laser ablation [26] have predominantly an armchair architecture, we have selected an open-ended (10,10) SWCNT with diameter and length of 13.56 ˚ respectively. The nanotube is assumed to be flexible and 37 A, without exerting any constraint, within a periodic rectangular parallelepiped of 80.0  80.0  80.0 A˚ 3. 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 nanotube is truly isolated. The simulation boxes contain 100–1500 neon atoms, until the saturation condition is provided for. The saturation condition is defined as a condition in which all adsorption sites of CNT (adsorption capacity) are occupied by the first layer of fluid and increase in neon atoms (pressure) does not lead to more adsorption in this layer. Non-bonded van der Waals’ interactions were modeled by a Lennard–Jones potential with a cutoff distance of 10 A˚ as follows: "    # Uðrij Þ ¼ 4e

sij

12

rij



sij

6

3. Results and discussion

ð1Þ

rij

3.1. Adsorption isotherms

The values of sC–C (sNe–Ne) and eC–C (eNe–Ne) used in the simulations were, respectively, 3.40 (2.78) A˚ and 0.086 (0.069) kcal mol  1 [22,27]. Interatomic Lennard–Jones potentials were calculated according to the Lorentz–Berthelot mixing rule [28]:

sij ¼

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 canonical NVT ensemble; each MD trajectory is equilibrated during 100 ps and then propagated for another 200 ps, with a time step of 1 fs. The velocity form of Verlet algorithm method [28] and the Nose–Hoover thermostat algorithm [29] were used to integrate the equations of motion and temperature control, respectively. Starting from the external surface, attractive energy decreases with increase in distance from the nanotube. Sufficiently far from the nanotube, bulk gas behavior is found, as the gas atoms do not interact with the nanotube. Consequently, the number of adsorbed atoms is the total number of gas atoms in the simulation cell with the adsorbent as corrected by subtracting the number of gas atoms behaving as bulk gas. To do so, a cutoff distance from the center of the isolated nanotube is selected, within which the gas atoms are considered adsorbed.

ðsii þ sjj Þ 2

ð2Þ

eij ¼ ðeii ejj Þ1=2

In order to obtain adsorption isotherms, gravimetric storage capacity (absolute value adsorption per mass of adsorbent),rw , was calculated as follows [30]:

rw ¼

NNe mNe NNe mNe þ NC mC

ð8Þ

ð3Þ

Simulations involving flexible nanotubes also require the modeling of intramolecular forces. The relative potentials of these forces are approximated on the basis of the following equation (AMBER force field) [27]: Uintramolecular ¼ Ustretch þ Uangle þUdihedral

ð4Þ

Each contribution to Uintramolecular is further modeled according to Ustretch ¼ Kbond ðrr0 Þ2

ð5Þ

Uangle ¼ Kangle ðyy0 Þ2

ð6Þ

and Udihedral ¼ kdihedral :ð1þ cosðnjj0 ÞÞ

ð7Þ

Ustretch represents the force applied when the bond is stretched from its initial position r0 to the new position r; Uangle models the force exerted when the angle y between two bonds changes with respect to its initial angle y0 ; Udihedral describes the force that atoms separated by three covalent bonds exert when they are subjected to a torsion angle F; n is the periodicity of torsional motion; n¼ 2 term describes a rotation that is periodic by 1801. The values of these parameters for the flexible CNT are reported in Table 1. A snapshot of a possible initial configuration is shown in Fig. 1, consisting of 1500 neon atoms. The distance between neon atoms and SWCNT was chosen in a way so as to start the dynamics in a

Fig. 1. Snapshot of initial configuration of 1500 neon atoms around a (10,10) SWCNT (front view).

Table 1 Intramolecular forces (Eqs. (2)–(5)) parameters. kstretch

˚ r0 (A)

kangle (kcal mol  1 rad  2)

h0 (deg.)

kdihedral. (kcal mol  1)

n

U0 (deg.)

1.4

63

120

3.625

2

180

(kcal mol  1 A˚  2) CNT

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where NNe is the number of adsorbed Ne atoms and NC is the number of carbon atoms in the simulation box, and mNe and mC (g mol  1) are the corresponding molar masses, respectively. Keeping temperature, diameter, and length of SWCNT constant and varying pressure (number of neon atoms per simulation box), adsorption isotherms were obtained at supercritical temperatures of neon, i.e. T¼50, 70, and 90 K (see Fig. 2). The exo- and endoadsorption terms refer to the adsorption of neon on the external and internal surface of nanotube, respectively. Results reveal that gravimetric storage capacity of SWCNT (total, endo, and exo, according to Eq. (8)) increases with gas pressure, and on the other hand it decreases with increase in applied temperature, which confirms that again adsorption is a more favorable process at lower temperatures and high pressures. These observations are in good agreement with the experimental measurements for gas adsorption on SWCNTs [4,6] and previous theoretical works [9,10,30] and also the most recent work on neon adsorption [17]. The amount of neon adsorbed on the outer surface of SWCNT is more than that on inner side (see Fig. 2); this also has been observed previously in Refs. [10,17].

263

Fig. 3. Snapshots of neon adsorption on the internal and external surfaces of a (10,10) SWCNT at 50 K: (a) lateral and (b) front view.

Table 2 Heat of adsorption energies and self-diffusion coefficients of neon in (10,10) SWCNT at various temperatures.

Gravimetric storage capacity (g/g)

Temperatures (K) Adsorption energies (kcal mol  1) Self-diffusion coefficients (A˚ 2 ps  1)

Gravimetric storage capacity (g/g)

Pressure (MPa)

50  3.913 24.74

70  2.683 39.94

90  2.030 52.99

Langmuir shape isotherms are predicted to be of type I at supercritical temperatures (critical temperature of neon is 44.4 K), which is in good agreement with previous results [9,10,30]. These isotherms are indicative of enhanced solid–fluid interactions, implying that condensation is prohibited in small SWCNT. The result is consistent with previous reports [3,30], which indicate capillary condensation occurs when the pore is large enough to hold more than four layers of molecules. That is to say, in a pore with less than 2 layers of adsorption, capillary condensation is prohibited. Furthermore, at supercritical conditions, no capillary condensation is observed [9,30]. Fig. 3 shows snapshots of neon adsorption on the internal (endo) and external (exo) surface of nanotube at temperature of 50 K. 3.2. Heat of adsorption

Gravimetric storage capacity (g/g)

Pressure (MPa)

Pressure (MPa) Fig. 2. Adsorption isotherms of neon on (10,10) SWCNT at temperatures of: (a) 50 K, (b) 70 K, and (c) 90 K.

For computation of the heat of adsorption (adsorption energy) [15], the total energy for each MD run is obtained by timeaveraging the sum of energies in the entire simulation course and then utilized to define the heat of adsorption using.

DEadsorption ¼ Etube þ Ne Etube ENe

ð9Þ

where Etube and ENe are derived by running the system with nanotube (without neon atoms) and neon atoms (without nanotube) separately. The calculated values of heat of adsorption are given in Table 2 for saturation conditions. We assume that the highest average heat of adsorption represents the thermodynamically most favorable gas adsorption. It is noteworthy that increase in operating temperature decreases heat of adsorption. 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. This result is in agreement with the previous theoretical and experimental reports [15–17,31], which demonstrate that when the gas molecules are physisorbed on the nanotube surface, increase in operational temperature makes the adsorbed system unstable and therefore decreases heat of adsorption.

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Various methods are available to calculate self-diffusivity from the MD simulations. Here, we employed the Einstein relation [32], which relates the long-time limit of mean square displacement (MSD) of the particles to self-diffusivity, D, through 2

/9rðt þ DtÞrðtÞ9 S 1 limt-1 6 Dt

ð10Þ

The self-diffusion coefficients were evaluated from the limiting slope of the mean square displacement (MSD) curve with time (excluding both the initial, transient ballistic motion as well as the statistically noisy final region). The corresponding MSD plots are given in Fig. 4. It is obvious that with increase in temperature, the slope of MSD plots is increased accordingly, which results in higher values of self-diffusion coefficients. Therefore, temperature shows its significant role in adsorption systems in this section, in which, higher magnitudes of self-diffusion coefficient at higher temperatures cause considerable reduction in adsorption, i.e. lower value of rw (see Fig. 2) and subsequent decrease in heat of adsorption. The values of neon self-diffusion coefficients are also given in Table 2. However, a large diffusion coefficient is advantageous in this regard, as it assists in the loading and unloading of gas during the duty cycle of the material [32]. 3.4. Activation energy

1/T Fig. 5. Plot of ln D versus 1/T for diffusion process of neon at T¼50, 70, and 90 K.

gC-Ne (r)

D¼

Ln D

3.3. Self-diffusion coefficient

Using the Arrhenius equation [33] D ¼ D0 expðEa =RTÞ

ð11Þ

where Ea or activation energy is the potential barrier for translational motion of gas atoms. We can calculate the activation energy for the diffusion process of neon fluid. When ln D is plotted versus 1/T, calculated results show the characteristic Arrhenius behavior (linear behavior), suggesting that diffusion is an activated process as has been shown in Fig. 5. Indeed, we have estimated the potential barrier for translational motion of neon in such a system, which is equal to 0.17 kcal mol  1. 3.5. Radial distribution function In analyzing the structural characteristics of the adsorption systems, the radial distribution function (RDF), g(r), provides a better understanding of the quality of the adsorption process. This function is defined as the probability of finding neon atoms at distance r from the nanotube surface, relative to the probability expected for a completely random distribution at the same

r (Ǻ) Fig. 6. g(r) plots of carbon–neon for (10,10) SWCNT at 50, 70, and 90 K.

density of neon [16]. The corresponding g(r) plots at saturation conditions are given in Fig. 6. The sharp rise near 3 A˚ represents the distance of the closest approach of neon atoms to the SWCNT, demonstrating purely physisorption behavior. As deduced from the adsorption isotherms, heat of adsorption, and self-diffusion coefficients, once again the RDF plots emphasize that the lower the temperature applied, the more the neon adsorbed. This is in agreement with other experimental [19] and computational [11,16,17] works, which report monotonical increase in adsorption amount with decrease in temperature. This function approaches a value of unity in the limit of no correlation between investigated particles.

MSD (Å2)

4. Conclusion

Time (ps) Fig. 4. Mean square displacement for neon in (10,10) SWCNT at different temperatures.

In this work, we plotted the adsorption isotherms of neon adsorption on SWCNT; all of them are of Langmuir shape type I and agree well with previous experimental and theoretical works at supercritical temperatures. More properties of neon gas such as heat of adsorption, self-diffusion coefficient, and activation energy were computed compared with previous works. Results show that adsorption is a process that is very sensitive to applied temperature, i.e. increase in temperature results in lower adsorption; our results confirm this fact in a compatible way altogether. Previous works of Refs. [15,16] reveal that nanotube curvature may directly affect the SWCNT adsorbate atomistic potentials, which is not considered herein but will be the subject

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