A coarse-grained model for mechanical behavior of phosphorene sheets.

The popularity of phosphorene (known as monolayer black phosphorus) in electronic devices relies on not only its superior electrical properties, but also its mechanical stability beyond the nanoscale. However, the mechanical performance of phosphorene beyond the nanoscale remains poorly explored owing to the spatiotemporal limitation of experimental observations, first-principles calculations, and atomistic simulations. To overcome this limitation, here a coarse-grained molecular dynamics (CG-MD) model is developed via a strain energy conservation approach to offer a new computational tool for the investigation of the mechanical properties of phosphorene beyond the nanoscale. The mechanical properties of a single phosphorene sheet are first characterized by all-atom molecular dynamics (AA-MD) simulations, followed by a force-field parameter optimization of the CG-MD model by matching these mechanical properties from AA-MD simulations. The intrinsic out-of-plane puckered feature is conserved in our CG-MD model, rendering mechanical anisotropy and heterogeneity in both the in-plane and out-of-plane directions preserved. The results indicate that our coarse-grained model is able to accurately capture the anisotropic in-plane mechanical performance of phosphorene and quantitatively reproduce Young's modulus, ultimate strength, and fracture strain under various environmental temperatures. Our CG-MD model can also capture the anisotropic out-of-plane bending stiffness of phosphorene. We demonstrate the applicability of our model in capturing the fracture toughness of phosphorene in both the armchair and zigzag directions by comparison with the results from AA-MD simulations. This CG-MD model proposed here offers greater capability to perform mechanical mesoscale simulations for phosphorene-based systems, allowing for a deeper understanding of the mechanical properties of phosphorene beyond the nanoscale, and the potential transferability of the developed force-field can help design hybrid phosphorene devices and structures.