The vibration of nanosprings affected by van der Waals interactions

The vibration of tightly helical nanosprings affected by van der Waals (vdW) interactions is investigated based on continuum modelling. Explicit solutions are derived to clarify the influence of initial pitch, stiffness and the number of nanosprings on the period, frequency and amplitude of the vibration. Unlike classic linear/nonlinear springs, the waveform of the vibration is always asymmetric for tightly helical nanosprings due to the asymmetry of vdW attraction and repulsion. The at most three equilibrium positions for the nanosprings strongly depend on the deformation due to competition between the vdW interactions and the elastic energy of the nanosprings. This study provides physical insights into the origin of the novel dynamic properties of such nanosprings.