Energy Optimization of a Mirror-Symmetric Spherical Triboelectric Nanogenerator

A general theoretical analysis of a 3D generic TENG structure is presented. Using a dimensionless formulation, it is demonstrated that the optimal TENG geometry does not depend on the frequency of the moving dielectric but the external ohmic impedance for maximum power output is inversely proportional to the frequency. It is also found that the energy is proportional to the cube of the size of the TENG, the square of the triboelectric charge density sigma(T), and the angular frequency omega of the moving dielectric. In the case of a spherical TENG where the moving dielectric is a sphere and the electrodes are spherical caps on a larger sphere three dimensionless parameters that determine the harvested energy are identified: the ratio between the radii of the two spheres r<^> = r/R, the polar angle theta of the two spherical caps formed by the electrodes, and Z<^> = Z epsilon R omega, where Z is the external impedance, R is the radius of the large sphere, epsilon is the permittivity of the system, and omega is the angular frequency of the moving sphere. Under the crude assumption of constant charge density on the electrodes, the optimal parameters can be easily calculated. It is found that theta = 1.1 rad, r<^>= 0.67, and Z<^>= 0.18.