Graphane -- material for hydrogen storage, breathers and kinks

TL;DR

This paper models hydrogen atom dynamics on graphane using the Frenkel-Kontorova and Sine-Gordon models, revealing kink and breather excitations that could impact hydrogen storage properties.

Contribution

It introduces a novel application of the Frenkel-Kontorova and Sine-Gordon models to study hydrogen atom excitations in graphane, including kink and breather solutions.

Findings

Identification of three distinct hydrogen atom motion cases.

Existence of kink solutions with localized velocity in the lattice.

Presence of breather solutions indicating localized oscillations.

Abstract

In this paper we study the graphane. The Frenkel-Kontorova model on hexagonal lattice was used. We studied the case of one H atom above the C atom in the plane of graphane (we used the approximation of the hexagonal lattice in the plane). Continuous limit of the Lagrange-Euler equations is found from the Hamiltonian for $H$ atoms motion, they enabled us to study kink and breather excitations of $H$ atoms in the $H$ plane above the $C$ plane. We have found that there are three cases in the one $H$ atom motion The case $1$, when the $H$ atom is at the position which is below the position at which it is desorbed. Then the motion of this $H$ atom at time $t_{h}$ is described. The case $2$, when the $H$ atom is at the position of the suppressed atom $H$ in the direction to the $C$ (nearer) atom. This $H$ atom will be desorbed from the graphane going through the minimum of the potential energy and then through the point of desorption. Its motion of at time $t_{h}$ is described. The case $3$, when the $H$ atom is near the position of small oscillations near the potential energy minimum. The position of the atom $H$ at the time $t_{0}$ is the position to which the atom $H$ was excited with external force. The lattice of $H$ atoms in graphane may be excited as described by the kink solution of the Sine-Gordon equation. The kink has its velocity $U$, $ U^{2} < 1$, and in time $T$ and in $X^{'}$ coordinate direction localization. The Sine-Gordon equation has the breather solution in the $X^{'}$ direction. There $\omega$ is the frequency of the breather, $T_{0}$ and $X^{'}_{0}$ are in time $T$ and in $X^{'}$ direction localization.