Transmission line circuit and equation for an electrolyte-filled pore of finite length

Abstract

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), arXiv:1911.09924].

arXiv comment5 pages, 3 figures

References in corpus (4)

• A Blessing and a Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging
• Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation
• Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes
• Relation between charging times and storage properties of nanoporous supercapacitors

Cited by in corpus (5)

• Charging Dynamics of Electrical Double Layers Inside a Cylindrical Pore: Predicting the Effects of Arbitrary Pore Size
• Equivalent circuit and continuum modeling of the impedance of electrolyte-filled pores
• Resonantly-driven nanopores can serve as nanopumps
• Convection can enhance the capacitive charging of porous electrodes
• Asymptotic analysis on charging dynamics for stack-electrode model of supercapacitors