A machine-learned molecular dynamics modeling of the spontaneous rolling-up and assembly of MoS₂ monolayers designed with vacancy defects

Mono-sulfur vacancy (V_S) and di-sulfur vacancy (V_S2) are two types of point defects commonly observed in chemically grown MoS₂ monolayers. These defects can provide opportunities to tune the physical and chemical properties of such two-dimensional materials. In this study, we model the spontaneous curling of free-standing MoS₂ monolayers engineered with V_S and V_S2 defects using molecular dynamics (MD) driven by a neural network potential (NNP). The NNP is trained on Density Functional Theory (DFT) calculations and shows an excellent agreement on the prediction of structural and vibrational properties while retaining a linear scaling with the system size. We first use the cluster expansion (CE) method to identify the ground state crystal structures at the different S vacancy concentrations. The NNP is then used to run large-scale MD simulations of MoS₂ sheets of various sizes for the vacancy concentrations of interest. The curling process is found to be mainly dominated by the vacancy concentration, having either V_S or V_S2 defects and the tailored MoS₂ sheet size. It is also found that when the dimension is larger than an upper threshold, the two free ends can sew up forming one-dimensional MoS₂ single/multilayer nanotubes.