Quantum dynamics of H2 in a carbon nanotube: Separation of time scales and resonance enhanced tunneling

Abstract

Quantum confinement effects are known to affect the behavior of molecules adsorbed in nanostructured materials. In order to study these effects on the transport of a single molecule through a nanotube, we present a quantum dynamics study on the diffusion of H 2 in a narrow (8,0) carbon nanotube in the low pressure limit. Transmission coefficients for the elementary step of the transport process are calculated using the flux correlation function approach and diffusion rates are obtained using the single hopping model. The different time scales associated with the motion in the confined coordinates and the motion along the nanotube's axis are utilized to develop an efficient and numerically exact approach, in which a diabatic basis describing the fast motion in the confined coordinate is employed. Furthermore, an adiabatic approximation separating the dynamics of confined and unbound coordinates is studied. The results obtained within the adiabatic approximation agree almost perfectly with the numerically exact ones. The approaches allow us to accurately study the system's dynamics on the picosecond time scale and resolve resonance structures present in the transmission coefficients. Resonance enhanced tunneling is found to be the dominant transport mechanism at low energies. Comparison with results obtained using transition state theory shows that tunneling significantly increases the diffusion rate at T < 120 K. Published by AIP Publishing. [http://dx

Helium Isotopes Quantum Sieving Through Graphtriyne Membranes

“…It would be then very interesting to see if the next member of the family, graphtetrayne, 37,38 recently synthesized and with an even larger nanopore, also show a similar quantum behavior at low energy and also to continue exploring the possibilities of this quantum effect. 22,55,56 On the one hand, (∆ x ∆ y ) −1/2 exp[iK • R] is the wave packet depending on the parallel coordinates, where ∆ x =14.691 Å and ∆ y =8.758 Å are the lengths of the unit cell. In this work, K = 0 to simulate a wave packet approaching to the membrane in the perpendicular direction.…”

Mini Review: Quantum Confinement of Atomic and Molecular Clusters in Carbon Nanotubes

“…Specially appealing in regards to the impact of quantum effects on the diffusion of H 2 and D 2 along carbon nanotubes is the experimental finding of reserved trends in their rates upon cooling (Nguyen et al, 2010), with the D 2 isotope becoming the faster inspite of its higher mass (Nguyen et al, 2010). The impact of quantum effects in confined H 2 and D 2 motion has been theoretically confirmed as well (Mondelo-Martell and Huarte-Larrañaga, 2016;Mondelo-Martell et al, 2017;Mondelo-Martell and Huarte-Larrañaga, 2021).…”

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“…Previous theoretical works [32][33][34][35][36] on the diffusion of hydrogen in nanoporous carbon, regardless of the specific potential energy surface employed, show that the interaction between the molecule and the nanostructure generates a potential energy profile that consists of collection of minima (adsorption sites) separated by maxima (diffusion barriers) along the nan-otube axis. Following previous studies 37 and given the shape of the potential energy, we have modelled the molecular diffusion process a set of uncorrelated jumps between neighbouring adsorptions sites 38,39 .…”

“…This effect has been claimed to result in an inverse kinetic isotope effect, namely, a faster diffusion of deuterium in nanoporous materials, compared with hydrogen [31][32][33] . However, these studies were based on semiclassical Transition State Theory simulations, which neglect the second quantum effect: resonant tunneling, which has been seen to enhance hydrogen transport properties in systems such as carbon nanotubes 34 . In this work we revisit the case of H2/D2 quantum sieving in single walled carbon nanotubes and provide accurate diffusion rates for for both molecules in the low pressure regime.…”

“…The results reported here evidence that by significantly extending the propagation time up to 20 picoseconds we are able to resolve quantum resonances below the diffusion barrier that change drastically the perspective of the previously published simulations. These much larger propagation times, required by the low corrugation of the potential energy profile along the nanotube axis, are achieved thanks to an adiabatic approach described in a previous work 34 .…”