Electrochemical capacitors may be ideal energy storage devices for applications ranging from renewable energy storage to transportation. Electrochemical capacitors are characterized by high power density and cycle life, and can be classified based on the properties of their electrodes. Symmetric capacitors have two electrodes that exhibit the same behavior, while asymmetric capacitors have two electrodes that exhibit different behavior. A hybrid asymmetric capacitor is a device that has two electrodes that behave differently because of different processes occurring in them. In this paper, we present a mathematical model of hybrid asymmetric capacitors made up of a redox couple electrode and a double-layer electrode. We show that, because of the different behavior of each electrode, the hybrid asymmetric capacitor possesses higher energy and power density than the symmetric capacitor. Our model is generic and can be extended to any device so long as the properties of the electrodes are known. Electrochemical energy storage systems like electrochemical capacitors may be ideal to meet the needs of renewable energy storage and electric vehicles.1-3 Electrochemical capacitors are characterized by high power density and high cycle life. In the simplest terms, electrochemical capacitors store energy in the double layer at the interface of an electrically conductive material and the electrolyte. No faradaic reaction occurs. Double layer capacitance is low, usually between 10 and 40 μF cm −2 of electrode surface area. Therefore, high surface area materials are used (e.g., porous carbon electrodes) to significantly increase the capacitance of the device. 4 Because the voltage across a double layer is proportional to the charge stored, the voltage of a device decreases linearly with time during an entire constant-current discharge. In contrast, the voltage across a device where a faradaic reaction occurs across the electrode/electrolyte interface (i.e., a battery) is determined by the activity of the reactants and products. Therefore, its constant-current discharge curve is sigmoidal in shape, and hence the voltage is fairly constant over a significant portion of the discharge. Finally, pseudocapacitance is a term used to describe storage of charge via faradaic reactions where the activities of reactants and products are such that the discharge curve of a device more closely resembles a capacitor than it does a battery. Although pseudocapacitor response is much like a double-layer capacitor, they have considerably higher capacitance, and hence energy.Regardless of the type of device (i.e., double-layer capacitor or pseudocapacitor), the term "capacitor" is valid when the electrodes behave like a capacitor. Major efforts related to double-layer capacitors have focused on understanding the effect of electrode thickness and pore structure on the energy density and device capacity.
5-7Efforts toward developing pseudocapacitors have mostly focused on creating different electrode materials with most emphasis given to metal oxide...