Theoretical study on the oscillatory triboelectric charge density in a contact-mode triboelectric nanogenerator

We have analytically derived an oscillatory triboelectric charge density σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sigma$\end{document}, induced by triboelectrification in a contact-mode triboelectric nanogenerator. We assumed that charge is conserved when σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sigma$\end{document} reaches equilibrium state over time. A form of cycling operates between charges induced on the metal electrode and those on the dielectric surface, resulting in σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sigma$\end{document} oscillations over time in a contact-mode triboelectric nanogenerator.