Theoretical study on the output of contact-separation triboelectric nanogenerators with arbitrary charging and grounding conditions

Highlights: • The output of contact-separation nanogenerators is derived for arbitrary charging and grounding conditions. • The schematic of applying the universal formulas to derive the open-circuit voltage are proposed. • The validity of the formulas is verified by its consistency with the simulated results of finite element method. • The influence of charging and grounding conditions on open-circuit voltage is investigated analytically and numerically. Nanogenerators of contact-separation mode have been studied comprehensively both from the theoretical perspective and for practical applications. Compared with the in-situ charging through contact electrification during each cycle of operation, pre-charging has shown its advantages and benefits of less wear, longer lifetime, high stability, improved output power, good controllability and repeatability. In this work, universal formulas are derived for the output of contact-separation mode triboelectric nanogenerators (TENG), which is applicable to arbitrary charging conditions including the triboelectrification, pre-charging, and even those with unbalanced charges on the two counterparts of dielectric layers. The formula is also validated and appropriate to various grounding conditions of the two conductive terminals. A systematic study is conducted on various combinations of device configurations, charging conditions and grounding settings to compare the results derived from the universal formula proposed in this work with that of previous work as well as the simulated results based on finite element modeling. The applicability of the universal formula is verified by the simulated results and it also consists with the conventional formula for TENGs under specific settings. The universal formula proposed in this work can operate as not only a convenient tool to derive the output of contact-separation TENGs with known charging and grounding conditions, but also a guidance for the fabrication and experiment of contact-separation TENGs to improve its output performance with a given configuration of device.