Asymptotic analysis on charging dynamics for stack-electrode model of supercapacitors
arXiv:2212.02214 · doi:10.1098/rspa.2023.0044
Abstract
Supercapacitors are promising electrochemical energy storage devices due to their prominent performance in rapid charging/discharging rates, long cycle life, stability, etc. Experimental measurement and theoretical prediction on charging timescale for supercapacitors often have large difference. This work develops a matched asymptotic expansion method to derive the charging dynamics of supercapacitors with porous electrodes, in which the supercapacitors are described by the stack-electrode model. Coupling leading-order solutions between every two stacks by continuity of ionic concentration and fluxes leads to an ODE system, which is a generalized equivalent circuit model for zeta potentials, with the potential-dependent nonlinear capacitance and resistance determined by physical parameters of electrolytes, e.g., specific counterion valences for asymmetric electrolytes. Linearized stability analysis on the ODE system after projection is developed to theoretically characterize the charging timescale. The derived asymptotic solutions are numerically verified. Further numerical investigations on the biexponential charging timescales demonstrate that the proposed generalized equivalent circuit model, as well as companion linearized stability analysis, can faithfully capture the charging dynamics of symmetric/asymmetric electrolytes in supercapacitors with porous electrodes.
arXiv comment26 pages, 6 figures
References in corpus (11)
- Double layer in ionic liquids: Overscreening vs. crowding
- Diffuse-Charge Dynamics in Electrochemical Systems
- Molecular understanding of charge storage and charging dynamics in supercapacitors with MOF electrodes and ionic liquid electrolytes
- Accelerating charging dynamics in sub-nanometer pores
- Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes
- Charge fluctuations in nano-scale capacitors
- A Blessing and a Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging
- Charging Dynamics of Electrical Double Layers Inside a Cylindrical Pore: Predicting the Effects of Arbitrary Pore Size
- Capacitance of the Double Layer Formed at the Metal/Ionic-Conductor Interface: How Large Can It Be?
- Transmission line circuit and equation for an electrolyte-filled pore of finite length
- Lattice Boltzmann Electrokinetics simulation of nanocapacitors