The flexodynamic effect on nanoscale flexoelectric energy harvesting: a computational approach

Nanoscale flexoelectric energy harvesting is one of the most practical and tantalizing applications of flexoelectricity. Since flexoelectricity scales with sample's size, the energy conversion efficiency of a flexoelectric energy harvester is believed to be high at the nanometer scale. However, at such small length scale, only considering the static bulk flexoelectric effect is not sufficient. Previous works usually neglect the flexodynamic effect, a coupling between the polarization and the accelerated motion of the material, whose strength increases with the vibration frequency of the system. In this work, we examine the impact of the flexodynamic effect on the performance of a nanoscale flexoelectric energy harvester based on a general flexoelectric formulation. Through numerical simulations, we find that, when the cantilever beam's thickness reduces to several nanometers, the flexodynamic effect could be comparable to the static flexoelectric effect due to the sharp increase of its natural frequencies. This effect is negative to the flexoelectric energy harvesting. The simulation results show that the flexodyanmic effect can lead to 50% drop of a 10 nm thickness flexoelectric beam's conversion efficiency. In this work, we also give a possible solution to the problem. Properly adjusting the nanobeam's aspect ratio can effectively reduce the natural frequency and consequently diminish the negative impact of the dynamic flexoelectric effect without sacrificing the conversion efficiency.