## 2 Energy Storage, Materials, and Construction of Electrochemical Capacitors  
Electrochemical capacitors (ECC) are devices that store electrical energy [2] by capacitive (charge separation) mechanisms and require electrochemical phenomena to function. As shown in Figure 1, the charge is stored in the nanopores of a microporous material that form the electrodes of the device. The construction of the electrochemical capacitor is similar to that of a battery, but they use different materials in the electrodes. Most of the electrochemical capacitors commercially available use microporous activated carbon in both electrodes, and are termed electric double-layer capacitors (EDLCs). These devices are considered ideal ECCs in that by storing the electrical charge in the double layer, they can attain very high power capability (>5 kW/kg) and extremely long cycle life (>1 million deep discharge cycles). However, at present, EDLCs have energy densities of only 3-5 Wh/kg. This low energy density limits the applications for which the EDLCs can compete with batteries. Recent research [1,3,4] on EECs has focused on significantly improving their energy density. This can be done by increasing the specific capacitance (F/g) of the electrode materials and the rated (maximum) voltage of the cell for both EDLCs and other types of electrochemical capacitors. Based on the weight of the active material in the electrodes, the energy density of an EDLC is given by:  
\[(\mathrm{Wh/kg})_{\mathrm{act.mat.}}=1/8\;(\mathrm{F/g})\;(\mathrm{V_{r}}^{2} -\mathrm{V_{min}}^{2})/3.6 \tag{1}\]  
The resistance R of any EEC is difficult to calculate as it depends on the ionic conductivity of the electrolyte, the thickness and porosity of the electrodes, the electronic conductivity of the carbon and the contact resistance between the carbon particles and the current collector. The maximum power from a ECC can be calculated from \(\mathrm{V_{r}}^{2}/4\mathrm{R}\), and its pulse power capability (W/kg) can be calculated [2] using:  
\[\mathrm{Pulse\ power}\;(\mathrm{W})=9/16\;(1-\mathrm{n_{eff}})\;\mathrm{V_{r}}^{ 2}/\mathrm{R} \tag{2}\]  
\[(\mathrm{W/kg})_{\mathrm{pulse}}=3/2\;(1-\mathrm{n_{eff}})(\mathrm{Wh/kg/RC}) \;(3600) \tag{3}\]  
where RC is the time constant of the SC and n\({}_{\mathrm{eff}}\) is the efficiency of the pulse. The pulse power capability is proportional to the energy density and RC of the device. Many researchers use \(\mathrm{V_{r}}^{2}/4\mathrm{R}\) to rate the power capability of their devices, but the pulse power capability is a more realistic estimate for most applications. In many cases, an  
Figure 1: Schematic of an electric double-layer capacitor. efficiency of 95% is used to calculate the power capability. Both capacitance and resistance can be determined from charge/discharge tests of devices. Hybrid supercapacitors (HSC) are being developed [1; 2; 3; 4] to increase the energy density. As shown in Figure 2, \"hybrid\" indicates that one of the electrodes is like those in an EDLC, and one is like an electrode in a battery. The energy stored in an HSC is dominated by the voltage of the battery-like electrode and the capacitance of the carbon electrode [1; 2]. \[\mathrm{E_{HSC,act\;mat}}=\frac{1}{2}\;(\mathrm{F/g})_{\mathrm{carb}}\;W_{ \mathrm{carb}}\;[\mathrm{V_{max}}^{2}-(\mathrm{V_{max}}-\Delta\mathrm{V_{carb} })^{2}]\;\mathrm{where}\;\Delta\mathrm{V_{carb}}=\mathrm{V_{max}}/2 \tag{4}\]  
\[\mathrm{E_{HSC,act\;mat}}=3/8\;(\mathrm{F/g})_{\mathrm{carb}}\;W_{\mathrm{carb} }\;\mathrm{V_{max}}^{2} \tag{5}\]  
The energy density of the HSC will be higher than that of EDLC devices using the same carbons and electrolyte, because the cell voltage will be higher and the carbon is used more efficiently. The resistance R of the HSC tends to be significantly higher than that of the EDLC because of the resistance of the battery-like electrode. As a result, the RC time constant of HSCs is higher, and the power density is lower than EDLCs. The same formula can be used to calculate the pulse power capacity of both HSCs and EDLCs.