Quasi-electrostatic three-dimensional charge model for contact-separation triboelectric nanogenerator

Triboelectric nanogenerators (TENGs) are at the forefront of energy harvesting and self-powered sensors, while further improvements in TENGs' development and utilization essentially depend on the theoretical models. To understand the intrinsic mechanism of TENGs, a formal physical framework of TENGs was introduced based on Maxwell's equations. Triboelectric charges would be produced on the dielectric layer surface after contact triboelectrification. As concerned about any transient, the electric field originating from the arbitrary fixed position over the finite charged plane would not change, constituting the electrostatic field. Since TENGs maintain lowfrequency movement, they enter a quasi-electrostatic state. Under this state, the electric field would change along with the distance from the charged plane. Herein, a quasi-electrostatic three-dimensional (QETD) charge model was constructed to refine the theoretical modeling of TENGs. Finite element modeling (FEM) simulations were first provided to reveal the distribution of polarization vector (Pz), electric potential (phi), electric field (Ez) and electric displacement (Dz). Furthermore, an optimized theoretical framework for contact-separation TENGs was established, and it was validated by different driving and structural variables. Besides, the intrinsic displacement current of TENGs was linked with the conduction current to deduce the output capability. Compared with previous works, this QETD model shows the most consistent trend with experimental results, providing accurate predicts for distinct TENGs' performance.