Quantifying Output Power and Dynamic Charge Distribution in Sliding Mode Freestanding Triboelectric Nanogenerator

Abstract

The general concept of dielectric polarization density (P) is a macroscopic description of the underlying microscopic structure in the presence of an external electric field and polarized materials itself. A time‐dependent polarization PS induced by a non‐electric field also exists in practice due to the mechanically driven relative motion of media owing to the effects of contact electrification or piezoelectricity. In this work, the starting point is to consider the difference between P and PS, and how PS enters into the governing equations, since it describes the dielectric polarization density without an applied electric field, finally modifying the constitutive relations, Faraday's law, and Maxwell's equations. On this background, a 3D mathematical‐physical model for the sliding mode freestanding triboelectric nanogenerators (TENGs) is established that is taken as an example to confirm the relationship of free charge distribution and dynamics of output power. What needs to be emphasized is that the method of segmented uniform charge distribution is effective and the physical basis for modeling construction and analysis. Finally, we summarized the mathematical‐physical models of TENGs in rectangular coordinates, cylindrical coordinates, and spherical coordinates, building a bridge to reveal the underlying principle behind the microscopic polarization and energy conversion.

Momentum Transfer in Triboelectric Nanogenerators

“…Thus, the total electric field distributed at the overlapping regions of the two dielectric is insignificant, a fact which was demonstrated in Refs. [ [3,11,12] ] Besides, although the triboelectric charges are created uniformly at the nonoverlapping regions of the dielectrics, the generated corresponding electric field can be shielded by the free charges that are induced at the nonoverlapping regions of the electrodes. Even so, one can still observe a high electric field from the nonoverlapping regions.…”

“…As mentioned above, since the TENG is usually operated at low frequency, the generated magnetic induction is extremely weak and can be ignored. Using our proposed mathematical model, [3,[10][11][12][13][14][15] the electric potential 𝜑(x, y, z), time-varying electric field E(x, y, z), and the relevant electric field components [E x (x, y, z), E y (x, y, z), E z (x, y, z)] have been obtained (see Section S1, Supporting Information). It is found by Equation (S4c, Supporting Information) that the z-component of the electric field along the symmetry axis E z (L/2, L/2, z) is [10] :…”

“…[1,2] A series of theoretical models of TENGs such as the equivalent circuit model [3][4][5][6] and the distancedependent electric field model [7][8][9] has been developed to investigate the basic working principles of TENGs. Recently, a universal time-and spatial-dependent mathematical model with varying geometric configurations in Cartesian, [10][11][12][13] cylindrical [14,15] and spherical [16] coordinate systems are presented, which can be utilized to characterize the time-varying electric field, electric polarization, electric displacement vector, and the displacement current. This is because the basic laws of electromagnetism relating various scalar and vector quantities hold irrespective of the coordinate system.…”

U-Shaped Tube Based Liquid–Solid Triboelectric Nanogenerator for Harvesting Unutilized Compressed Air Energy

“…The U-shaped tube is equipped with symmetrical and staggered copper foil electrodes at both ends. The UFC-TENG is a sliding mode freestanding triboelectric nanogenerator [33] based on the triboelectric effect [34]. With the relative movement of contact separation between the frictional layers of the liquid inside the tube and the tube wall, electrons continuously transfer between the electrodes.…”