Valence-force model and nanomechanics of single-layer phosphorene

In order to understand the relation of strain and material properties, both a microscopic model connecting a given strain to the displacement of atoms, and a macroscopic model relating applied stress to induced strain, are required. Starting from a valence-force model for black phosphorous [Kaneta et al., Solid State Communications, 1982, 44, 613] we use recent experimental and computational results to obtain an improved set of valence-force parameters for phosphorene. From the model we calculate the phonon dispersion and the elastic properties of single-layer phosphorene. Finally, we use these results to derive a complete continuum model, including the bending rigidities, valid for long-wavelength deformations of phosphorene. This continuum model is then used to study the properties of pressurized suspended phosphorene sheets.