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Charging and Discharging Electrochemical Supercapacitors in the Presence of Both Parallel Leakage Process and Electrochemical De

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Charging and Discharging Electrochemical Supercapacitors in the Presence of Both Parallel Leakage Process and Electrochemical De Electrochimica Acta 90 (2013) 542–549 Contents lists available at SciVerse ScienceDirect Electrochimica Acta jou rnal homepage: www.elsevier.com/locate/electacta Charging and discharging electrochemical supercapacitors in the presence of both parallel leakage process and electrochemical decomposition of solvent a a,∗ a a a b Shuai Ban , Jiujun Zhang , Lei Zhang , Ken Tsay , Datong Song , Xinfu Zou a National Research Council of Canada, Vancouver, BC, Canada V6T 1W5 b Department of Applied Mathematics, University of Western Ontario, London, ON, Canada N6A 5B7 a r t i c l e i n f o a b s t r a c t Article history: Simple models for electrochemical supercapacitors are developed to describe the charge–discharge Received 5 November 2012 behaviors in the presence of both voltage-independent parallel leakage process and electrochemical Received in revised form decomposition of solvent. The models are validated by experimental data collected using a symmetric 14 December 2012 two-electrode test cell with carbon powder as the electrode layer material and stainless steel as the Accepted 15 December 2012 current collector. Available online 22 December 2012 © 2013 Published by Elsevier Ltd. Keywords: Electrochemical supercapacitor Charge and discharge Parallel leakage Self-discharging Solvent decomposition 1. Introduction and ionic liquid solutions which have wider electrode potential windows [4,7–9]. From the energy density equation mentioned Electrochemical supercapacitors (ESs) are considered important above, it is obvious that increasing cell voltage to enhance energy energy efficiency devices for rapid energy storage and deliv- density is more effective than increasing the specific capacitance ery. Among the advantages of ESs are high power density, long because the voltage is squared in the formula. However, if the cell lifecycle, high efficiency, wide range of operating temperatures, voltage is too high, the electrochemical decomposition of solvent environmental friendliness, and safety. ESs also serves as a bridg- may occur due to the limited electrode material stability and/or ing function for the power/energy gap of traditional dielectric solvent’s thermodynamic decomposition windows. This solvent capacitors. These characteristics have made ESs very competitive electrochemical decomposition could produce gaseous products, for applications in electric hybrid vehicles, digital communication leading to the pressure build-up inside the cell, causing safety devices such as mobile phones, digital cameras, electrical tools, concerns, and self-discharge [10–17]. Another challenge of super- pulse laser technique, uninterruptible power supplies, and storage capacitors is the parallel leakages, causing a fast self-discharge, of the energy generated by solar cells [1–3]. Unfortunately, there reducing the shelf-life. The main contributors to the parallel leak- are still some challenges, such as low energy density, high cost, and ages of the supercapacitors can be summarized into four processes high self-discharge rate, which have limited wider applications of [7]: (1) Faradaic reaction of electrolyte impurities; (2) parasitic ESs [3,4]. redox reactions involving impurities (oxygen groups and metals); In order to increase energy density, according to the energy den- (3) non-uniformity of charge acceptance along the surface of elec- 2 sity expression E = 1/2CV , where E is the ES’s energy density, C is trode material pores; and (4) possible short-circuit of the anode and the specific capacitance, and V is the cell voltage, respectively, two cathode from improperly sealed bipolar electrodes. Due to these major approaches have been taken. One is to increase the specific parallel leakages, the shelf-life could be significantly reduced when capacitance (C) of the electrode material [3–6], and the other is to compared to those of electrochemical batteries [7]. increase the cell voltage (V) using solvents such as non-aqueous To better understand the effects of parallel leakage process and/or electrochemical decomposition of solvent on supercapa- citors’ performance, some experimental and theoretical studies ∗ have been carried out to investigate the charge and discharge Corresponding author at: 4250 Wesbrook Mall, Vancouver, B.C. V6T 1W5, behaviors [18–23]. Since the parallel leakage process and the sol- Canada. Tel.: +1 604 221 3087; fax: +1 604 221 3001. E-mail address: [email protected] (J. Zhang). vent decomposition are mainly related to the electrochemical 0013-4686/$ – see front matter © 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.electacta.2012.12.056 S. Ban et al. / Electrochimica Acta 90 (2013) 542–549 543 Nomenclature o Vn standard electrode potentials for negative electrode Symbol, Meaning reaction (V) ˛ electron transfer coefficient in the rate determining n Vp positive electrode potential of the solvent electro- step of negative electrode reaction chemical decomposition (V) o ˛ electron transfer coefficient in the rate determining p Vp standard electrode potentials for positive electrode step of positive electrode reaction reaction (V) b Tafel slope of the negative electrode reaction n Vsc supercapacitor voltage (V) b Tafel slope of the positive electrode reaction max p Vsc designed charging voltage of the supercapacitor (V) −2 o C capacitance (F cm ) V sc maximum supercapacitor voltage (V) −2 Cdl double-layer capacitance (F cm ) −1 Cm specific capacitance (F g ) −3 Cs mole concentration of the solvent (mol cm ) processes occurring inside the supercapacitor cells, describing the o o o o o V = Vp − Vn − bp ln ip − bn ln (in) charge and discharge behaviors by electrochemical parameters, e− electron −2 such as equivalent series resistance, capacitance, and several elec- E energy density (Wh cm ) trode kinetic constants, seems more appropriate, in particular for (Em)max maximum energy density of the supercapacitor −1 electrochemical decomposition of the solvent. (Wh kg ) −1 In this paper, for fundamental understanding of supercapacitor F Faraday’s constant (96,487 C mol ) charging and discharging behaviors, through experiment validation iF current density induced by the solvent electrochem- −2 we present some simple mathematical models incorporating the ical decomposition (A cm ) voltage-independent parallel leakage process and electrochemical in current density of the negative electrode reaction −2 decomposition to describe the supercapacitor charge and dis- (A cm ) charge behaviors. Using these models, the experiment data could ip current density of the positive electrode reaction −2 be simulated to obtain the desired values of parameters such as (A cm ) specific capacitance and equivalent series resistance from which isc charging or discharging current density of the −2 both the energy and power density can be calculated. The sim- supercapacitor (A cm ) ulated parameter values related to both parallel leakages and Icell constant current density for charging or discharging −2 solvent decomposition could be used to predict supercapacitor’s the supercapacitor (A cm ) self-discharge and shelf-life, performance/efficiency losses, as well kn reaction constant of the negative electrode reaction −1 as the limiting workable cell voltage of the supercapacitors. There- (cm s ) fore, the proposed models are useful in evaluating and diagnosing kp reaction constant of the positive electrode reaction −1 supercapacitor cells. We hope these simple models could be used as (cm s ) a tool for understanding the charging–discharging behavior of the m mass of the electrode material (g) supercapacitors. Furthermore, we believe that these models could n˛n electron transfer number in the rate determining also be useful in obtaining the essential parameters of the supercap- step of negative electrode reaction acitors such as equivalent series resistance and capacitance based n˛p electron transfer number in the rate determining on the recorded curves of charging–discharging. step of positive electrode reaction nn overall electron transfer number in the negative 2. Experimental electrode reaction np overall electron transfer number in the positive 2.1. Electrode layer preparation electrode reaction pn product of the negative electrode reaction For electrode layer materials, Carbon black BP2000 (Cabot Cor- pp product of the positive electrode reaction poration), conducting carbon Super C45 (from TIMCAL), and 60 wt% (Pm)max maximum power density of the supercapacitor −1 Polytetrafluoroethylene (PTFE)-water dispersion (Aldrich) were (W kg ) −1 −1 used as received without further modification. R universal gas constant (8.314 J K mol ) For electrode layer preparation, the procedure has been Resr equivalent series resistance of the supercapacitor 2 described in our previous publication [3], and is repeated as below. ( cm ) 2 Carbon and conducting carbon powders were first mixed with a Rlk equivalent leakage resistance ( cm ) Vortex Mixer (Thermo Scientific) for 30 min to form a uniformly- S reactant of the solvent mixed powder, which was then transferred into a beaker containing t time (s) both PTFE binder and ethanol solution under constant stirring to tfd time needed for a supercapacitor being fully dis- form a suspension. After the solvent was evaporated at high tem- charged (s) perature, the paste formed was collected on a glass slide. This paste T temperature (K) was manipulated by repeatedly folding and pressing using a spatula Ts time needed when the supercapacitor voltage goes until a sufficient mechanical strength was achieved. Then this paste down
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