High-order calculation of triboelectric charge density using a transition matrix element in a triboelectric nanogenerator system

Abstract

The second-order calculation for triboelectric charge density (σtribo) between a metal and polymer is performed analytically based on the molecular-ion-state model. The transition matrix element |MAB | is approximately calculated for two cases where the distance between metal and polymer is very small (d<<1) and the electronic energy is near the Fermi energy level (EF) because electron transfer between metal and polymer is dominant at this level. The σtribo approaches zero-order approximation as d approaches zero. Thus, although d is very small (d<<1), its effect as a second-order approximation, such as dielectric constant and dielectric thickness, is shown here.