Homogenization of carbon-nanotube brush electrodes

Abstract

Carbon nanotube brushes (carbon nanotubes attached to a current collector) have been proposed for nanoscale electrodes. While the detailed molecular scale physics is important in its own right, often a more useful scale to examine electrode performances is the micro and meso scale continuum. The detailed structure of microscale material parameters results from statistical mechanics and will not be discussed here, rather we focus on the micro scale homogenization to the meso scale wherein material parameters result from a micro scale “cell” problem for a periodic lattice. We apply a matched asymptotic formulation to obtain the meso scale field equations and material parameters. The finite element method (FEM) and finite volume method (FVM) are employed to solve the micro scale cell problem and the mesoscale field equations, respectively. Numerical results are presented for the electrical potential field and concentration of cations and anions. For a test case, it is observed that a doubling of the electrode area can create a ten-fold increase in the potential which has interesting implications for electrode design.