Modelling of Supercapacitors: Factors Influencing Performance

Abstract

The utilizable capacitance of Electrochemical Double Layer Capacitors (EDLCs) is a function of the frequency at which they are operated and this is strongly dependent on the construction and physical parameters of the device. We simulate the dynamic behavior of an EDLC using a spatially resolved model based on the porous electrode theory. The model of Verbrugge and Liu (J. Electrochem. Soc. 152, D79 (2005)) was extended with a dimension describing the transport into the carbon particle pores. Our results show a large influence of the electrode thickness (L e ), separator thickness (L s ) and electrolyte conductivity (κ) on the performance of EDLCs. In agreement with experimental data, the time constant was an increasing function of L e and L s and a decreasing function of κ. The main limitation was found to be on the scale of the whole cell, while transport into the particles became a limiting factor only if the particle size was unrealistically large. 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 to consider for both systems engineers and material scientists. Electrochemical Double Layer Capacitors (EDLCs) store energy by the adsorption of ions from an electrolyte (resulting in its capacitive deionization), storing the ions in the electrochemical double layer of a charged electrode with a very large surface area. The high charge that can be stored gives rise to the name supercapacitors or ultracapacitors. The main advantages of EDLCs when compared to batteries are their ability to quickly release the stored energy, their high efficiency and their long cycle life. The amount of energy that can be stored is, however, not unlimited. The useable capacitance is dependent on the time scale of their operation and this causes the capacitance of EDLCs to be a function of frequency. As typical application of EDLCs requires them to supply or accept pulses of energy at frequencies ranging from 10 Hz to 0.1 Hz, 1 it is important that the full capacity can be utilized in this range. In order to improve the high-frequency behavior, it is necessary to understand the factors causing the limitation and to identify the critical ones.The key to the high capacitance of EDLCs is the high specific surface area (SSA) of their electrodes. This is achieved by using highly porous activated graphitic carbon materials.2 According to their size, the pores can be classified as micropores (<2 nm), mesopores (2 − 50 nm) or macropores (>50 nm).2 Pores of different sizes are connected in a highly complex hierarchical structure depending on the shape of carbon particles. A typical supercapacitor cell consists of two carbon electrodes with the porous separator in between and current collectors closing the cell from both sides.Experimentally, the frequency-dependent capacitance is commonly measured using either Cyclic Voltammetry (CV), Electrochemical I...

Charging Dynamics of Overlapping Double Layers in a Cylindrical Nanopore

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