Quantum Filtering of Hydrogen Isotopes through Graphene

TL;DR

This work addresses hydrogen isotope separation by exploiting quantum filtering through a monolayer graphene barrier. It develops a continuum Lennard-Jones–based potential for isotope–graphene interactions, computes classical trajectories, and evaluates three quantum-tunneling schemes—delta-function, rectangular barrier, and WKB—to obtain isotope transmission probabilities; it also analyzes quantum adsorption via Fermi’s golden rule. The results show that tunneling probabilities are extremely small but the H/D ratio is highly sensitive to the model, with ratios spanning from a few (delta) to as large as $10^{60}$ (rectangular) and $10^{50}$ (WKB), while deuterium exhibits a higher sticking propensity by about a factor of $5.7$. This combination of selective tunneling and adsorption suggests that consecutive graphene layers could serve as a low-energy, high-separation-factor avenue for enriching deuterium, albeit within the limits of the approximations made (e.g., near-surface breakdown, neglect of zero-point energy and long-range charge-transfer effects). Overall, the study provides a robust theoretical foundation for graphene-based quantum sieving of hydrogen isotopes with potentially significant practical impact for energy and nuclear applications.

Abstract

Driven by the growing demand in the energy, medical, and industrial sectors, we investigate a hydrogen isotope separation technique that offers both a high separation factor and economic feasibility. Our findings reveal that filtering isotopes through two-dimensional graphene layers provides an exceptionally efficient quantum-mechanical method for isotope separation. Using a recently developed analytical pairwise potential between hydrogen isotopes and carbon atoms in graphene, we examine the classical trajectories of isotopes near the graphene layer, as well as the quantum-mechanical tunneling properties of isotopes through the graphene layer. Using various quantum-mechanical methods, we calculate both the isotope tunneling probabilities and the quantum-mechanical isotope sticking probabilities. Our study shows that quantum filtering through graphene layers can be an effective technique for enriching deuterium by separating it from protium.

Figures (11)

• Figure 1: Schematic view of the graphene sheet at $z = 0$. Notice the Cartesian coordinate system where the $x$-axis and $y$-axis are lying in the infinite graphene layer. The hydrogen isotope atom is migrating from a point where the Cartesian coordinate $(x,y,z)$ with $z > 0$ is located above the graphene plane. Notice $b = \sqrt{3} a$, the distance between the centers of two hexagons in the honeycomb lattice is set as our unit of length.
• Figure 2: The variation of the interaction potential energy for an H-isotope at a distance $a$ above the graphene surface along the $x$-axis.
• Figure 3: The variation of the interaction potential energy for an H-isotope at a distance of $a$ above the graphene surface along the $y$-axis.
• Figure 4: Contour plots showing the variation of the interaction potential energy for H-isotopes at a distance of $1.1a$ above the graphene surface on the $xy$-plane. The color gradient, ranging from black to white, indicates an increase in the magnitude of the potential.
• Figure 5: The variation of the interaction potential energy for isotopes along the $z$-axis. The figure shows both the attractive part at large $z$ and the repulsive part at small $z$ for the H-isotope (black) and D-isotope (gray).