Transmission Line Circuit and Equation for an Electrolyte-Filled Pore of Finite Length

I discuss the strong link between the transmission line (TL) equation and the TL circuit model for the charging of an electrolyte-filled pore of finite length. In particular, I show how Robin and Neumann boundary conditions to the TL equation, proposed by others on physical grounds, also emerge in the TL circuit subject to a stepwise potential. The pore relaxes with a timescale tau, an expression for which consistently follows from the TL circuit, TL equation, and from the pore's known impedance. An approximation to tau explains the numerically determined relaxation time of the stack-electrode model of Lian et al. [Phys. Rev. Lett. 124, 076001 (2020)].

Automated summary

This study discusses the strong connection between the transmission line equation and the transmission line circuit model in the charging process of an electrolyte-filled pore. It shows how boundary conditions such as Robin and Neumann emerge in the TL circuit, and explains the relaxation time τ consistently across the TL circuit, TL equation, and known impedance of the pore. An approximation of τ clarifies the relaxation time determined numerically in the stack-electrode model by Lian et al.