Simulation of hydrogen species diffusion and transport between and through layers of 2D materials

Recent experiments by Geim’s group have demonstrated transport and separation of hydrogen isotopes through the van der Waals gap in hexagonal boron nitride (h-BN) and molybdenum disulfide (MoS2) bulk layered materials. The experiments could not distinguish whether the transported particles are protons (H+) or protium (H) atoms. In one of our recent works, we reported theoretical studies, which indicate that protium atoms, rather than protons, are transported through the gap.[1] First-principles calculations combined with well-tempered metadynamics simulations at finite temperature reveal that for h-BN and MoS2, the diffusion mechanism of both protons and protium (H) atoms involves a hopping process between adjacent layers. This process is assisted by low-energy phonon shear modes. The extracted diffusion coefficient of protium matches the experiment, while for protons, it is several orders of magnitude smaller. This indicates that H atoms are responsible for the experimental observations. These results allow for a comprehensive interpretation of experimental results on the transport of H isotopes through van der Waals gaps and can help identify other materials for hydrogen isotope separation applications.
In more recent investigations, we focus on H atom diffusion between layers of transition-metal dichalcogenides (TMDCs), such as MoS2, where we investigate the impact of transition metal atom, chalcogen atom, stacking order, and moiré pattern on the diffusion coefficients. We want to learn whether the free energy barriers are lowered (resulting in higher diffusion coefficients) and whether the moiré patterns can enforce directional transport.
We use well-tempered metadynamics simulations in our studies as implemented in the cp2k code. Our approach to H atom diffusion can be extended to investigations of other species, such as Eu(III)-species diffusion in clay mineral layered materials.
[1] Y. An, A. Kuc, P. Petkov, M. Lozada-Hidalgo, T. Heine, Small 1901722 (2019) 1-7.