WP4: Simulation and modeling

While the experimental results concerning the surface structure of the LMCats and their chemical characteristics are important inputs for the theoretical calculations, the outcome of computer simulations is crucial for understanding the catalytic properties of LMCats, growth mechanisms of 2DMs, and the optimisation of the growth process. At each step, the insights obtained from the results of the computer simulations will be important to choose the subsequent set of experiments on the LMCat set-up.

In addition, theoretical analyses over LMCats can shed light on several interesting conceptual questions in the field of catalysis. Even though it is commonly believed that the catalytic properties of a solid catalyst are limited to certain active centers on the crystalline surface, it is well established that in many cases catalytic activity extends beyond the melting point of the catalyst. Furthermore, solid catalysts often exhibit superior catalytic activity if they are made of nanoparticles. It has been speculated that one of the reasons is the "lattice flexibility" of nanoparticles. Surface atoms on nanoparticles are displaced more easily compared to catalysts with macroscopic sizes. During the chemical reaction, this can open up reaction pathways with lower energy barriers on the surface of nanoparticles. Theoretical studies of LMCats with a lattice flexibility higher than solid catalysts will be an ideal playground to assess the effect of lattice flexibility on catalytic activity in general and shed light on the origins of catalytic activity of liquid metal surfaces in specific.

Both the x-ray and Raman methods are averaging-ensemble techniques and will primarily yield signatures of predominant features within the sampled area. Independent, first-principles based theoretical simulations are thus an ideal complement. They can access individual elementary processes and local features, while their validity can continuously be checked against our experiments. The latter indispensably requires a multi-scale modeling approach that can span from electronic to mesoscopic length scales, to interpret the insights about the formation of surface phases/layering of LMCats, interactions among 2DMs and with surface capillary waves, provided by the x-ray/Raman experiments. At the atomistic level, on the other hand, important processes that need to be investigated and understood are the adsorption of precursors on the surface of LMCats, as well as their catalytic dissociation leading to the nucleation and initial growth of 2DM seeds. For the continued growth, mass transfer of reaction intermediates and 2DM flakes on the surface will then play an additional role.

The elementary processes at electronic and atomic scales will be studied using density functional theory (DFT) or its tight-binding version (DFTB). In particular the latter technique allows to access system sizes of the order of 100-1000s of atoms, and therewith the necessary system sizes to study the above described target processes. Even larger system sizes can be accessed with reactive force-field (reaxFF)-based simulations. A thorough benchmarking (and potential re-parametrization) of such more-approximate levels of theory against reference DFT data will correspondingly also be part of the theoretical investigations.

In particular DFTB (or reaxFF) will allow for extended ab initio molecular dynamics (MD) simulations to study the important temporal evolution of the liquid-catalyst surface. The auto-correlation function of this time-dependent information then automatically yields the vibrational signals to be compared to the Raman experiments, while the structural information can directly be compared to the SXRD measurements. Systematic comparisons of calculations on liquid and solid catalyst surfaces will hereby be a particularly valuable tool to disentangle the relevant effects introduced through the melting process. The structure of molten Cu catalyst underneath a 2DM flake, layering near the liquid surface, ordering, and its possible vertical and lateral extension away from the flakes are directly accessible to such simulations.

In the course of the project, the accumulating mechanistic insights will gradually be used to establish micro-kinetic models of the 2DM growth process. We will consider both lattice kinetic Monte Carlo (kMC) and rate-equation based formulations, to focus on either the detailed form or edge processes at a growing 2DM flake, or in a more coarse-grained perspective on the continued growth and interactions between 2DM flakes, respectively. The employed rate constants can be either directly computed or fit to experimental findings.