Abstract
The potential energy curve for the adsorption of a hydrogen molecule by a truncated hollow sphere consisting of carbon atoms was evaluated by using the Lennard–Jones function for the pair interaction between a carbon atom and a hydrogen molecule. The sphere surface was regarded as a continuum with a uniform density identical to that of a graphite layer. The lower limit of the potential was found to be −200 meV when the sphere had a radius of 3.4 Å and no opening. By increasing the radius of the opening to 2.9 Å, the energy barrier for an incoming molecule disappeared and the lower limit increased to −150 meV, which is three times as deep as that observed for a graphite surface. The Langmuir isotherm for the truncated sphere of this size was evaluated based on the eigenvalues of the potential curve. We found that the pressure yielding a half occupancy was <50 bar at a temperature below 250 K. This indicates that a carbon pore with this shape and size can store a hydrogen molecule under mild conditions.
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Appendix: List of symbols
Appendix: List of symbols
Symbols | Description |
---|---|
\(\epsilon_{{{\text{C}}{\text{-}}{\text{H}}_{2} }}\) | Lennard–Jones potential depth between C and H2 |
\(\epsilon_{n}\) | The nth eigenvalue of the potential energy curve for the H2 adsorption |
θ | Azimuthal angle of the surface of the truncated carbon sphere |
θ a | Azimuthal angle of the opening edge on the truncated carbon sphere |
θ(p, T) | Occupancy of the H2 adsorption site given by the Langmuir isotherm |
ρ s | Surface density of the carbon sheet |
\(\sigma_{{{\text{C}}{\text{-}}{\text{H}}_{2} }}\) | Lennard–Jones distance parameter between C and H2 |
a | Opening radius of the truncated carbon sphere |
d | Radius of the truncated carbon sphere or the distance between H2 and an infinite single carbon sheet |
d e | Equilibrium radius of the closed carbon sphere for the H2 adsorption |
d g | Gravimetric H2 density of the substrate |
dσ | Surface element of the carbon surface |
d sg | Equilibrium distance between H2 and an infinite single carbon sheet |
d v | Volumetric H2 density of the substrate |
D | Potential depth of the H2 adsorption by the closed carbon sphere |
\(\overline{{N_{0} }} (T)\) | Lower limit of the number density of the H2 adsorption sites |
\(\overline{{N_{\text{site}} }}\) | Number density of the H2 adsorption sites |
\(\overline{{N_{{{\text{H}}_{2} }}^{\text{ads}} }} (p, T)\) | Number density of adsorbed H2 molecules in the substrate |
\(\overline{{N_{{{\text{H}}_{2} }}^{\text{gas}} }} \left( {p, T} \right)\) | Number density of gaseous H2 molecules |
p 0(T) | Half-occupancy pressure of the Langmuir isotherm for the H2 adsorption |
\(p_{ \hbox{max} } (T)\) | Pressure at which the substrate has the same H2 density as the gas |
r | Distance between C and H2 |
z | Position of the H2 molecule adsorbed by the truncated carbon sphere |
z ads(T) | Molecular partition function of the adsorbed H2 molecule |
z gas(T) | Molecular partition function of the gaseous H2 molecule per unit volume |
\(V_{\text{LJ}} \left( r \right)\) | Lennard–Jones potential |
W | Integral form of the H2 adsorption energy |
\(W_{\text{sg}} \left( d \right)\) | H2 adsorption energy by an infinite single carbon sheet |
W(z, d, a) | H2 adsorption energy by the truncated carbon sphere |
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Ishikawa, S., Yamabe, T. The potential energy curve and Langmuir isotherm of hydrogen adsorption by a truncated carbon sphere. Appl. Phys. A 119, 1365–1372 (2015). https://doi.org/10.1007/s00339-015-9107-2
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DOI: https://doi.org/10.1007/s00339-015-9107-2