Modeling and optimization of a rotational symmetric spherical triboelectric generator

Triboelectric nanogenerators (TENGs) are superb candidates to harvest low-frequency energy from water waves, wind, and ambient vibrations. They consist of triboelectrically-charged dielectric materials in relative motion and have been realized experimentally in several configurations and geometries. In this work, we provide a detailed mathematical analysis and fast computational method for designing spherical TENG devices to realize optimal performance. The method provides a self-consistent analysis to determine the charge distribution on spherical electrodes in compliance with the physical constraint of uniform potentials over the electrode surfaces. It is shown that the difference between the assumptions of a uniform potential vs. uniform charge density on electrodes for spherical TENG model parameters increases with the spatial dimensions of the electrodes relative to other characteristic dimensions of the TENG. For typical spherical TENGs the difference in harvested energy can be several percentages. A major benefit of the present model of a spherical TENG is its applicability to design large TENG network systems for which 3D methods, such as the finite element method, are computationally far too demanding.