(405g) Multi-Scale Model of Electrochemical Double Layer Capacitors: Predicting Performance Limitations

Authors: 
Kroupa, M., Institute of Chemical Technology Prague
Kosek, J., University of Chemistry and Technology Prague
Mobile energy storage applications such as electric cars often require quick changes between the charging and discharging. For such operation mode, conventional batteries are not very suitable due to their internal resistance originating from Faradaic reactions. On the other hand, Electrochemical Double Layer Capacitors (EDLCs) store energy by the physical separation of charges on their large surface area. However, even for EDLCs, the utilizable capacitance is a function of the time-scale at which they are operated and this is strongly dependent on the construction and physical parameters of the device. The mathematical modeling is a useful for the identification of factors influencing the EDLC performance and the evaluation of their importance.
We simulated the dynamic behavior of an EDLC using a spatially resolved model based on the porous electrode theory. The established model of transport on the scale of one cell [1] was extended with an additional dimension describing the transport into the carbon particles, effectively separating the spatial scales of different pore sizes. The dynamic response of the model was obtained by simulating the most common electrochemical techniques: the Cyclic Voltammetry, Electrochemical Impedance Spectroscopy and Galvanostatic Cycling.
Our results show a large influence of the construction and physical parameters, such as the electrode thickness (Le), separator thickness (Ls) and electrolyte conductivity (κ) on the performance of EDLCs. In agreement with literature experimental data, the time constant (inverse of the frequency at which the capacitance drops to half of the maximum value) was an increasing function of Le and Ls and a decreasing function of κ. The effect of the potential dependence of capacitance (described by the Gouy-Chapman-Stern and Bikerman theories) was shown to be important only for cells that are close to a complete discharge. The main limitation was found to be on the scale of the whole cell (two electrodes and separator), while the transport into the particles became a limiting factor only if the particle size was unrealistically large. Using a simple RC circuit model, the results were generalized into a simplified relation allowing for a quick evaluation of performance for the design of new devices.
This work provides an insight into the performance limitation of EDLCs and identifies the critical parameters in this respect. The multi-scale approach that was developed in this work allows to compare the importance of phenomena occurring at pores of different size.

References
[1] Verbrugge, M. W.; Liu, P. Microstructural Analysis and Mathematical Modeling of Electric Double-Layer Supercapacitors. Journal of the Electrochemical Society 2005, 152, D79