Understanding hydrogen diffusion in between layers of 2D materials

In 2018, the group of Geim from Manchester performed very interesting experiments, in which hydrogen atoms were diffused and transported inside the interstitial space of layered materials, such as hexagonal boron nitride or MoS2, showing a good sieving of deuterium from protium. We later showed theoretically that indeed hydrogen atoms rather than ions are transported between the layers and reported their diffusion coefficients. We also showed that the transport is assisted by the layer shearing mode. In this work, we investigated the hydrogen diffusion between layers of different transition-metal dichalcogenides (TMDCs), where we studied the influence of possible stackings, stoichiometry, and exemplary twist angles between layers on the self-diffusion coefficient. The calculations were performed using well-tempered metadynamics simulations as implemented in CP2K package, which gives us access to the free energy surface. We found that TMDCs with Se or Mo atoms have lower free energy barriers than these with S or W. Furthermore, structural stackings of MoS2 (𝐻ℎℎ(2H), 𝑅ℎ𝑋 (3R), 𝑅ℎℎ, 𝐻ℎ𝑀, 𝐻ℎ𝑋) also result in different free energy barriers. These energy barriers affect strongly the self-diffusion coefficients, because they enter the diffusion equation as exponent.