Journal of Power Sources 186 (2009) 216–223 Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour Mathematical functions for optimisation of conducting polymer/activated carbon asymmetric supercapacitors Graeme A. Snook 1 , Gregory J. Wilson ∗ , Anthony G. Pandolfo CSIRO Energy Technology, Box 312, Clayton, Vic. 3169, Australia article info Article history: Received 23 April 2008 Received in revised form 5 August 2008 Accepted 5 September 2008 Available online 2 October 2008 Keywords: Electrochemical double-layer capacitor Ultracapacitor Asymmetric supercapacitor Hybrid supercapacitor Electrically conducting polymer abstract Equations routinely used to describe the properties of conventional symmetric electrochemical double- layer capacitors (EDLCs) are expanded to develop straightforward mathematical functions that can effectively describe the performance characteristics of asymmetric supercapacitors based on electrically conducting polymer and activated carbon (ECP–AC) electrodes. Formulae are developed to describe cell parameters (based on total active material mass) such as maximum specific capacitance (Fg -1 ), max- imum specific energy (Wh kg -1 ), and optimum electrode mass ratios that can be used for maximising the specific energy of asymmetric cells. The electrode mass ratios are found to have a significant impact on the swing voltages across the positive and negative electrodes. Illustrative EDLC and ECP–AC devices are explored and employed to verify the derived equations that serve to predict essential parameters of both symmetric and asymmetric systems, irrespective of electrolyte ion concentration, solvent or species and independent of voltage. The utility of the equations is demonstrated by predicting cell parameters for a number of theoretical asymmetric ECP–AC systems and used to correlate experimentally obtained parameters. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Ultracapacitor, or supercapacitor, is a generic term given to a versatile class of energy storage devices that rely on the physical adsorption of ions at an electrode|electrolyte interface to form an electric double-layer; hence the more specific term of electrochem- ical double-layer capacitor (EDLC) [1]. The most highly developed commercial form of a supercapacitor is the symmetric carbon EDLC, which consists of two identical porous electrodes separated by an ion-permeable separator and electrolyte. These devices are char- acterised by rapid charge and discharge capabilities, high specific power, good stability, and a lifetime of greater than 500 000 deep charge–discharge cycles. Traditionally, porous activated carbon (AC) is utilised as the active electrode material in these devices due to its high porosity (electrolyte accessibility), good conductivity, low cost, and high sur- face area. A wide range of activated carbons, with BET surface areas of up to ∼3000 m 2 g -1 , has been evaluated in supercapacitors [2–4], and whilst higher capacitances are theoretically achievable for this material [1,5], in practice, the upper limit for the measured capac- itance of activated carbon (on a single electrode basis) is generally ∗ Corresponding author. Tel.: +61 395458632; fax: +61 395628919. E-mail address: Greg.Wilson@csiro.au (G.J. Wilson). 1 Current address: CSIRO Minerals, Box 312, Clayton South, Vic. 3169, Australia. around ∼130 F g -1 in non-aqueous electrolytes, and ∼200 F g -1 in aqueous electrolytes [6,7]. The energy stored by a supercapacitor is given by E = 1 2 CV 2 (1) where C is the capacitance and V is the voltage. Therefore, to improve the amount of energy stored in a supercapacitor that is already operating at V max , an increase in the gravimetric capaci- tance of the electrodes and/or a decrease in volume is necessary. The total (cell) capacitance, CT, of a symmetric EDLC, with two porous electrodes in series, is given by 1 C T = 1 C 1 + 1 C 2 (2) where C 1 and C 2 refer to the double-layer capacitance at each individual electrode. For identical capacitance electrodes, there- fore, the total cell capacitance equals half the individual electrode capacitance, i.e., C T =½C 1 . One method to overcome the limitation identified by the above relationship, and also to increase the energy of the cell, is to substitute one of the porous electrodes with a very high capacitance material to form an ‘asymmetric cell’. Thus, for example, if C 2 ≫ C 1 , then 1/C T ≈ 1/C 1 and so C T ≈ C 1 . That is, the asymmetric cell now has almost twice the capacitance of a compa- rable symmetric cell in which both the electrodes utilise the same porous carbon. 0378-7753/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2008.09.085