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

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. The difference between P and PS, and how PS enters into the governing equations of triboelectric nanogenerator is considered. A 3D mathematical-physical model for the sliding mode freestanding TENGs is established to confirm the relationship between free charge distribution and dynamics of output power. The mathematical-physical models of TENGs in rectangular coordinates, cylindrical coordinates, and spherical coordinates are summarized. image