Casimir force and its effects on pull-in instability modelled using molecular dynamics simulations: Modeling Casimir forces in MD Simulation

Abstract

We present a new methodology to incorporate the Casimir forces within the molecular dynamics (MD) framework. At atomistic scales, the potential energy between two particles arising due to the Casimir effect can be represented as U(r ij) = C/r 7. Incorporating the Casimir effect in MD simulations requires the knowledge of C, a problem hitherto unsolved. We overcome this by equating the total potential energy contributions due to each atomistic pair with the potential energy of continuum scale interacting bodies having similar geometries. After having identified the functional form of C, standard MD simulations are augmented with the potential energy contribution due to pairwise Casimir interactions. The developed framework is used to study effects of the Casimir force on the pull-in instability of rectangular and hollow cylindrical shaped deformable electrodes separated by a small distance from a fixed substrate electrode. Our MD results for pull-instability qualitatively agree with the previously reported analytical results but are quantitatively different. The effect of using longer-ranged Casimir forces in a constant temperature environment on the pull-in behaviour has also been studied.