Simulation study of hydrogen storage in single walled carbon nanotubes

Simulation study of hydrogen storage in single walled carbon nanotubes

International Journal of Hydrogen Energy 26 (2001) 691–696 Simulation study of hydrogen storage in single walled ca...

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International Journal of Hydrogen Energy 26 (2001) 691–696

Simulation study of hydrogen storage in single walled carbon nanotubes Chong Gua , Guang-Hua Gaoa; ∗ , Yang-Xin Yua , Zong-Qiang Maob a Department

b Institute

of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China of Nuclear Energy Technology, Tsinghua University, Beijing 100084, People’s Republic of China

Abstract Hydrogen storage in single-walled carbon nanotubes (SWNTs) is studied by grand canonical Monte Carlo (GCMC) simulation. Hydrogen–hydrogen and hydrogen–carbon interactions are both modeled with Lennard–Jones potential. Hydrogen– carbon interactions are integrated over the whole nanotube to get molecule–tube interactions. Three adsorption isotherms of di3erent diameters at 293:15 K, one adsorption isostatics at 2:66 MPa with radius of 0:587 nm, the amount of adsorption as a function of van der Waals (VDW) distance of nanotubes with the three diameters at 3 MPa (where the VDW distance is deuences of pressures, temperatures, the diameters and VDW distances of SWNTs on adsorption are discussed. ? 2001 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved. Keywords: Single-walled carbon nanotubes; Computer simulation; Adsorption; Hydrogen storage

1. Introduction Hydrogen is one of the renewable and environmentally friendly energy sources. One of the most promising uses of hydrogen is to be the material of fuel cells for applications such as power generation and transportation. In a typical fuel cell, hydrogen and oxygen react to generate electricity, heat and water. There are now several technical challenges to the wide-spread use of hydrogen in fuel cell powered vehicles, the most important of which is lack of safe and eDcient ways of hydrogen storage. Four main technologies for hydrogen storage are currently used, which are compressed gas, liquefaction, metal hydrides and physisorption. Targets for gravimetric (6:2 wt%) and volumetric (65%) densities for storage and transportation were recently standardized in the Department of Energy US as a “DOE Hydrogen Plan” [1].

∗ Corresponding author. Tel.: +86-10-62782558; fax: +8610-62770304. E-mail address: [email protected] (G.-H. Gao).

Several research groups have focused on experimental studies of hydrogen adsorption on graphitic sorbents, which include activated carbons [2], carbon nanotubes [3,4] and graphitic nano
0360-3199/01/$ 20.00 ? 2001 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 3 1 9 9 ( 0 1 ) 0 0 0 0 5 - 2


C. Gu et al. / International Journal of Hydrogen Energy 26 (2001) 691–696

regarded the parameters of solid–>uid potential adjustable, then he drew a conclusion that even triple the solid–>uid potential at the optimum tube conuence of VDW distance and the tube size on the adsorption, we assumed that the radius can vary continuously and we got di3erent results with Rzepka [14], this is because the two studies were based on di3erent assumptions. To make a more comprehensive work, the in>uence of temperature as well as pressure on the adsorption is also studied. The study is carried out by using a grand canonical Monte Carlo program (GCMC). And the simulation results can be used to optimize the pore geometry for hydrogen storage at a given pressure and temperature. 2. Potential models In this work, hydrogen molecules and carbon atoms are both treated as structureless spherical particles. Both hydrogen–hydrogen and hydrogen–carbon interactions result from Lennard–Jones potential located at the mass center of the particles. For a pair of particles i and j separated by the distance r, the interaction between them is given by:    ij 12  ij 6 ij (r) = 4ij ; (1) − r r where i and j denote hydrogen or carbon particles. =k and  are the energy and size potential parameters, which are 36:7 K and 0:296 nm for hydrogen, and 28:2 K and 0:335 nm for carbon, respectively. Hydrogen–carbon interactions are calculated by Lorentz–Berthelot rules through the parameters listed above. It is unnecessary in this work to use quantum correction like Johnson [10], who considered situations below 20 K. Temperatures in our work are higher than 100 K, where quantum e3ect becomes negligible. Moreover, the goal of this work is to
Fig. 1. The reduced potential (V ∗ = V=) as a function of distance between the hydrogen molecule and the nearest point on the nanotube.

tions between individual carbon atoms and the hydrogen molecules:  ij (|ri − rj |); (2) V (r) = j

where ri is the position of hydrogen moleculer, rj is that of a carbon atom and ij (r) is the pair potential between hydrogen molecules and carbon atoms, while the sum is over all of the tube’s atoms. Assuming that the atoms of the solid are distributed continuously up and on a sequence of parallel surfaces that form the pore wall, then the interaction potential of the >uid molecule with one of these surfaces of area A and number density is given by [17].     HC 12  HC 6 V (r) = d v(r) = 4HC d ; − r r A A (3) where =38 nm−2 ; HC and HC are Lennard–Jones parameters of hydrogen and carbon interactions. Integrating over the whole nanotube, the following expression can be obtained:   21 HC 10 2 V (r; R) = 3 HC HC M11 (x) 32 R −




 M5 (x) ;


where r is the distance between the adatom and the nearest point on the cylinder. R is the radius of the nanotube and x=r=R is the ratio of distance to radius. is the same surface number density as above. Here the following integrals are used.   1 Mn (x) = d’ : (5) (1 + x2 − 2x cos ’)n=2 0 Simpson integration is used to get the
C. Gu et al. / International Journal of Hydrogen Energy 26 (2001) 691–696


For simplicity of programming, the following expression was adopted to represent the results of the integration:  10   4  4    V (R; r)= = A +B +C R10 R4 R3  +D

4 R2


4 R


where A; B; C; D and E are constants dependent on the radius R of the nanotubes and can be determined from the numerical integration and results.

Fig. 2. The chemical potential as a function of pressure at 293:15 K.

3. Simulation method First, Widom test particle method [18] in an NVT ensemble is used to determine the relation between chemical potentials and the bulk pressures. The simulation is started with face centered cubic (FCC) structure, which involves 500 hydrogen molecules. One million conuid–>uid interaction is set to 53 and cuto3 of >uid–solid interaction is set to 5fs , where 3 and fs are the LJ size parameters of the >uid–>uid and the >uid–solid interaction, respectively. Beyond this distance, the Lennard–Jones potential is smaller than 2 × 10−4 3 and 2 × 10−4 fs . 4.5 million con
Fig. 3. One of the con
potential exactly. Through the curve in Fig. 2, the analytic expression of chemical potential can be obtained, which is ∗ = −56:317 + 7:95 ln(P ∗ )


where, ∗ = =; P ∗ = P3 =; ∗ and P ∗ are the reduced chemical potential and the reduced pressure used in the program, respectively. One of the con

C. Gu et al. / International Journal of Hydrogen Energy 26 (2001) 691–696

Fig. 4. The adsorption isotherms for hydrogen in carbon nanotubes of various radii at 293:15 K.

We have calculated the adsorption isotherms of three di3erent radii 0.352, 0.587, and 0:9785 nm, in which the VDW distances (i.e. the distance between the walls of the nearest neighbor tubes in the bundle [9]) between tubes are
Fig. 5. The amount of adsorption as a function of the VDW distances.

range of pressures. Tube with radius of 0:9785 nm takes a bit less volume density than tube with radius of 0:587 nm. All the results obtained here are in agreement with the results of Rzepka et al. [14], which show that there is a sharp maximum in the volumetric storage capacity for a pore size of about d = 0:7 nm. In this particular case, one hydrogen molecule
C. Gu et al. / International Journal of Hydrogen Energy 26 (2001) 691–696

of 0:352 nm; Fig. 5b is for the radius of 0:587 nm; and Fig. 5c is for the tube of 0:9785 nm. The gravimetric density resembles with the volumetric one in the trend of the whole range, so only the volumetric density is shown. In Fig. 5, both the amounts inside and outside the nanotubes are displayed, respectively. It is shown that the number of particles inside the tube increases with the radii of the nanotubes. However, number of particles outside the tube di3ers little between di3erent nanotubes. To each given radius, it is not surprising that number of particles outside the tube varies with the VDW distances. However, in spite of that the space inside the tube does not change, numbers of particles there are not

Fig. 6. The amount of adsorption as a function of the nanotube radius.

Fig. 7. The adsorption isostatics at 2:65953 MPa.


C. Gu et al. / International Journal of Hydrogen Energy 26 (2001) 691–696

function of temperature. Fig. 6b shows the excess adsorption percentage as a function of temperature. In both uenced by the e3ective surface area and volume. The packing geometry of SWNTs plays an important role in hydrogen adsorption. Work on optimizing the packing geometry in tube arrays at di3erent temperatures must be done further. And we have to stress that our simulation results depended on our choice of intermolecular potentials between hydrogen molecules and carbon atoms, but such potentials seem to be a reasonable estimate of these molecular interactions. More accurate models are being studied in the future.

Acknowledgements We acknowledge the National Science and Technology Department through Hydrogen Energy Grant, No. 2000026400 and Tsinghua University Fundamental Study Fund. We also thank Professor T. Nitta for providing useful materials and Professor G.Y. Chen for giving helpful discussions.

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