Development of an equivalent circuit model for ...chemeng.uwaterloo.ca/zchen/publications/documents/1-s2.0-S... · or in parallel [18,19]. This model structure is useful to provide

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Electrochimica Acta 115 (2014) 587– 598

Contents lists available at ScienceDirect

Electrochimica Acta

jo u r n al hom ep age: www.elsev ier .com/ locate /e lec tac ta

evelopment of an equivalent circuit model for electrochemicalouble layer capacitors (EDLCs) with distinct electrolytes

inhee Kanga, John Wena,∗, Shesha H. Jayaramb, Aiping Yuc, Xiaohui Wangd

Mechanical & Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontrario, CanadaElectrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontrario, CanadaChemical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontario, CanadaCanadian Regional Engineering Center, GM of Canada Ltd., General Motors Company, 1908 Colonel Sam Drive, Oshawa, L1H 8P7, Ontario, Canada

r t i c l e i n f o

rticle history:eceived 25 September 2013eceived in revised form 2 November 2013ccepted 3 November 2013vailable online 14 November 2013

a b s t r a c t

An equivalent circuit model for electrochemical double layer capacitors (EDLCs) is proposed through ana-lyzing the electrochemical impedance spectroscopy (EIS) measurements. The model is developed basedon the Grahame theory, while these capacitive or resistive behaviors in the presence of charge diffusionand the ion adsorption at the double layer interface and bulk media are investigated. This circuit model,upon its validation against the EIS data, is successfully applied to characterize the practical EDLC devices.

eywords:lectrical double layer capacitormpedance spectroscopyquivalent circuit modelotential dependency of impedancequivalent series resistance

Meanwhile, experimental results are obtained from different EDLC cells that consist of the activatedcarbon-based electrodes and two electrolytes, namely, aqueous (H2SO4) and organic (Et4NBF4/PC). Themodel predicts the useful parameters (such as resistance and capacitance) which help interpret elec-trochemical reactions at the electrode/electrolyte interface. The quantitative dependence of impedanceon the applied electrode potential is analyzed for two electrolytes during charging/discharging, and itscorrelation with the internal resistance (referred ESR) is studied.

. Introduction

Electrical double layer capacitor (EDLC), named also as a super-apacitor, is one of the emerging devices for energy storagepplications, which has a potential to enable to robust both energynd power densities [1–5]. Compared to batteries, EDLCs exhibit auch longer operating life, a better adaptability to varying weather

onditions, an enhanced load balancing when used in parallel with battery and less environmental impacts. These EDLC devices haveecently been used in power train systems in combination with bat-eries or fuel cells for electric vehicles [6–10]. In addition, EDLCsave been investigated to develop a hybrid energy storage system,hich consists of both EDLCs and batteries for improving the sys-

em reliability and efficiency, in wind and solar power generation11,12]. For these energy storage systems, it is very important tobtain an accurate model which describes the operation character-stics of EDLCs, and subsequently to optimize the component sizesnd design in different applications. Meanwhile, equivalent circuitsor EDLC modeling are valuable to predict their dynamic behaviors

ithin a power electronic circuit. For this purpose, there have beenany attempts in the literature to model the electrical character-

stics of EDLCs [13–17]. In general, the equivalent circuit model of

∗ Corresponding author.E-mail addresses: [email protected], [email protected] (J. Wen).

013-4686/$ – see front matter © 2013 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.electacta.2013.11.002

© 2013 Elsevier Ltd. All rights reserved.

an ELDC is composed of one or more pure capacitors (C) coupledwith their equivalent resistances (R) which are arranged in seriesor in parallel [18,19]. This model structure is useful to provide thequantitative information on parameter variations with ease inter-pretation and simple simulation. For example, the voltage-currentcharacteristics of an EDLC with charge transfer can be representedby the combination of ohmic resistors (RS) and charge transferresistors (Rct), while the electrochemical double-layer capacitance(Cdl) can be modeled simply with one or two parallel-connectedcapacitors [20,21]. However, limitations exist when these simpli-fied equivalent circuit models, developed mainly to describe theelectro-chemical processes occurring at the interfacial layer, wereused to explain the observed resistive and capacitive behaviorsof practical EDLCs during experiments. As a result, the simulationresults of these simplified circuit models deviated from experimen-tal measurements in a practical device across its frequency range,especially at low frequencies. Worthwhile to mention, a recentmodel applied the multiple RC branches to account for the distri-bution of pores with a particular geometric structures for porouselectrodes [22]. That model was still unable to qualitatively predictthe kinetic properties of electrolytes and effective electrochemicalprocesses at the double-layer interfaces.

In principle, EDLCs utilize the large surface area of porouscarbon-based electrodes and store electrochemical or electrostaticenergy by polarizing charges at the interface between an ionicelectrolyte and an electrode surface [23–26]. Therefore, for the

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88 J. Kang et al. / Electrochim

evelopment of an accurate circuit model, it is essential to rec-gnize the appropriate structure of the double layer and describeey electrochemical reactions at the electrode/electrolyte inter-ace. This allows for a more accurate EDLC model which can beeveloped based on the true representation of its internal struc-ure and electrochemical properties of electrodes and electrolytes.ccordingly, the predictions of a circuit model should take intoccount the electrochemical and kinetic characteristics of the dou-le layer based on theoretical descriptions of the EDLC structure,nd presents physics-based interpretations at the double-layernterfacial region. Worthwhile to mention, an ideal EDLC is inde-endent on the working frequency or applied voltage when itsapacitance and internal resistance are evaluated. In practice, how-ver, dependence of the capacitance and resistance on frequencynd voltage is commonly observed [27]. In addition, the practicalDLC devices suffer from the charge leakage (defined as a self-ischarge) which results from potential-dependent charge transfereactions. These deviations from the ideal capacitive behavior ofDLC are attributed mainly to ionic chemical/physical adsorp-ion and diffusional impedance, incomplete polarization of theorous electrode, and Faradaic charge transfer resistance causedy the voltage differential across the electrode/electrolyte interface28–30]. A practical EDLC model should address these issues whileequires sufficient information on key electrochemical reactions athe double-layer interface.

Electrochemical impedance spectroscopy (EIS) is a very power-ul technique to characterize electrochemical phenomena in thenalysis of double layer capacitors under the charging currentr voltage. From the evaluation of impedance data, the electro-hemical interface behavior is often described by simple electricallements (R, L, and C) in an equivalent circuit. However, as men-ioned before, many details about the definition of electrolyteons’ transport, their electrochemical kinetics, and, in particular,he physical interpretation of equivalent circuits of an EDLC aretill obscure and unclear. This brings difficulties in identifying theype and values of these electrical elements. Moreover, multiplehysical processes occur simultaneously in the system, e.g. specific

on’s adsorption into pore sites, diffusion phenomena taking placen interfacial region and bulk electrolyte processes. An advancedquivalent circuit should be therefore properly established basedn better understanding of each of these physical processes, andhould include RC circuit branches to reflect the key electrochem-cal reactions in EDLC devices.

This paper aims to develop a more adequate equivalent cir-uit model by considering these effects of the electrolyte on theon transportation (ionic diffusion and migration), adsorption layerormation on the electrode surface, and bulk processes in prac-ical EDLC systems. In this work, a new equivalent circuit modelith multiple- RC elements (for accounting for diffusion, adsorp-

ion and bulk media impedance, respectively) is proposed from thebserved physical and electrochemical phenomena. It is expectedhat this circuit model can be used to interpret resistive (or capac-tive) behaviors of an EDLC device, and quantitatively to verify theontribution of individual processes to device’s performance. Thisaper is organized as follows: First, several theoretical descriptionsor the EDLC structures and models of both interfacial electro-hemical reactions and bulk media process in a real EDLC systemre introduced. Then, based on the understanding of EDLC struc-ures, specified impedance elements are built up and referred to

eaningful electrochemical processes. Thirdly, from experimen-al data, the fundamental characteristics of carbon-based EDLCells with two kinds of electrolyte are analyzed by using the cyclic

oltammetry and galvanostatic charge-discharge plots in terms ofheir specific capacitances and internal resistances. Meanwhile, EIS

easurements are used to acquire parameters of the equivalentircuit. Finally, a more detailed view of EDLC characteristics and

ta 115 (2014) 587– 598

interpretations for each electrolyte’s properties are provided anddiscussed.

2. Circuit model development

In literature, a few theoretical treatments of EDLC structureshave schematically proposed to describe the properties of thedouble-layer at electrode/electrolyte interfaces. The first conceptof EDLC structures was introduced as the compact or Helmholtzlayer [31], where all counter-ions were assumed to be attractedto the charged electrode surface. This model is analogous to thatof conventional dielectric capacitors with two metal planar elec-trodes. Therefore, the capacitance in Helmholtz model is simplyexpressed as follows.

CH = ε0εr

dA (1)

where ε0, εr are the free space permittivity and the relative per-mittivity of the electrolyte, respectively. The distance of Helmholtzlayer, d, can be obtained from the radius of solvated ions (refer toFig. 1), while A is the surface area of the electrode.

Another theoretical description of the EDLC has been developedby Guoy and Chapman [32,33], which is considering into the diffusepart of the double layer. This model treats the ions as point chargesso that the ions’ movements in the electrolytes are driven by theinfluences of diffusion. This ions transportation in EDLC determinesthe overall capacitance. It is subjected to applied potential, thermalfields and the types of ions in the electrolyte. In the Guoy-Chapmantheory, the diffuse charge is determined by the Poisson-Boltzmannequation. This equation is given for a symmetrical electrolyte asfollows.

qd =(

2kTn0ε

�

)1/2

sinhe0V

2kT(2)

Therefore, the specific capacitance according to the diffuse layer,Cdiff, can be evaluated as

Cdiff = ∂qd

∂V=

(n0εe2

02�kT

)1/2

coshe0V

2kT(3)

where no is the number of ions in the bulk electrolyte, V is thepotential drop between the electrode and the bulk electrolyte, e0 isthe charge of the ion, k is the Boltzmann constant, ε is the dielectricconstant in the electrolyte, and T is the temperature. And later, thediffusion layer model was combined with the Helmholtz model byStern [34]. In that model, the overall capacitance in EDLC, Cdl, wasconsidered as a series of capacitance, CH and Cdiff,

1Cdl

= 1CH

+ 1Cdiff

(4)

In further developments, Graham [35] emphasised the presenceof specific adsorption of ions on the electrode surface, by modelingthree distinguished layers: the inner Helmholtz plane (IHP), theouter Helmholtz plane (OHP) and the diffusion layer (see Fig. 1).The IHP region is made of solvent molecules and/or adsorbed ions(cations or anions in electrolytes) while the OHP region correspondsto the formation of hydrated ions (solvated ions) layer. Subse-quently, the diffusion layer develops outside the OHP. Graham’stheory led to a better understanding of how EDLCs are affectedby the nature of their electrolytes; such as ions size, polarizabil-ity and overall capacitance-dependency on the electrode potential.Moreover, it is essential to clarify integral electrochemical pro-cesses at the double layer interface in order to present more realistic

characteristics of EDLC. Therefore, the theoretical treatment of allelements in this research will be discussed based on Graham model.The proposed circuit was followed by including initial develop-ment of the relationships between electrical components, such as

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J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598 589

e laye

dci

2i

lont(tTcbi

2

wt(eflgtrdi

Fig. 1. Schematics of an electrochemical doubl

ouble-layer capacitances combined with ions diffusion and spe-ific adsorption in both IHP and OHP, the presence of resistances atnterfacial double layer and bulk process in electrolyte.

.1. Electrochemical double-layer capacitance at the double layernterface region

As discussed in the previous section, the measured double-ayer parameter is not an ideal capacitor because of the porosityf electrode materials, inhomogeneous pores distribution, rough-ess and non-linear current density. Due to non-ideal behavior,he double-layer capacitor is replaced by a constant phase elementCPE) representation and not a pure capacitor [36]. In many cases,he CPE is placed in parallel with an interfacial resistor in a circuit.able 1 lists the common circuit elements, their impedances, theomparison between a pure capacitor and CPE, resistor and War-urg element (W). Each element is discussed with their concept of

mpedance representation in EDLC circuit modeling.

.1.1. Helmholtz (CH) and diffusion (Cdiff) capacitanceGraham’s model presents the overall double layer capacitance

hich is composed of three contributions: adsorption capaci-ance (Cads), Helmholtz capacitance (CH) and diffusion capacitanceCdiff). The latter two capacitances can be connected in series andxpressed by Eq. (4). CH represents the compact Helmholtz layerormation from solvated ions attracted electrostatically in the OHPayer while Cdiff results from the ions transportation, caused by aradient between the bulk and interfacial concentration of elec-

rolyte’s ion. In fact, charge-transfer processes with the measurableesistance consume the electrolyte’s ions at the interface andevelop a concentration gradient. In unsupported systems, there

s a limited supply of ions from the electrolyte and the diffusion

r and its electrode/electrolyte interface model.

process occurs in a bulk solution overlapping with the diffusionlayer. These phenomena can be interpreted using the Warburgelement (W) for the bounded diffusion layer in series with the resis-tance of bulk solution (Rbulk) [37]. In EDLC, this diffusion capacitanceis very important factor to influence the final performance of EDLCsin various applications [38,39]. According to equation (3), the dif-fusion capacitance is depending on the number of ions and theircharge (conductance) in electrolytes. When the frequency increasesor low conductive ions are used, the number of ions involved in dif-fusion process can be reduced, therefore resulting in a decrease ofcapacitance. Otherwise, various parallel diffusion mechanisms canbe determined by changing the potential difference, the electrodesurface area and the bulk solution concentration.

2.1.2. Adsorption capacitance (Cads)In Grahame’s theory, it was recognized that dehydrated ions

in IHP region could reside on the electrode surface with spe-cific adsorption processes. This phenomenon results in adsorptioncapacitance, Cads. In a certain system, this Cads can be regarded asanother capacitive element with some part of the electrochemicalcharge-transfer process. This phenomenon is called pseudocapaci-tance. Therefore, the overall capacitance in EDLC can be representedby Cads and a series combination with CH and Cdiff in parallel, result-ing in an equivalent circuit depicted in Fig. 2 (a). Generally speaking,for an adsorbed species formed by charge transfer in IHP, the capac-itance is associated with a Faradaic charge (qF), and the charge isdependent on the potential difference (V). This allows Cads to bedefined as:

Cads =(

∂qF

∂V

)(5)

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590 J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598

Table 1Circuit elements used in the model and mathmatical equation for each impedance.

Equivalent element Impedance Note

Resistor (R) ZR=R Independent on frequencyCapacitor (C) Z = 1

jωCA pure capacitorInversely liner dependency on frequencyC: capacitance, �: frequency (s−1)

ZCPE = 1Q (jω)˛ Constant phase element (CPE)

Non-linear dependency on frequencyQ: CPE coefficient, ˛: exponent (0 < � < 1)

Warburg (W) Z∗W

= 1QW

√jω

coth[B√

jω] Bounded diffusion layer

QW: Warburg coefficientB is theoretically defined as follows;ı/D1/2

where, ı: Nernst diffusion layer thickness

*

bnodtealalamro

Parameters used for fitting this element: QW in Simens-s1/2 and B in s1/2.

Therefore, it can be seen that Cads corresponds to the variationetween the differential charge and voltage [40]. However, it isecessary to differentiate with another pseudo-capacitance whichriginates from Faradaic (oxidation/reduction reactions) processesue to other sources such as metal oxide, conductive polymers orhe functional group. This pseudo-capacitance is different from themployed here whose extent of faradaically delivered charges is

function of voltage, but a reversible process with the negligibleeakage current [41,42]. In terms of circuit configurations, when

pseudo-capacitance is involved, generally, there are a Faradaiceakage resistance in parallel with pseudo-capacitor. However, in

n ideal EDLC system where there are no Faradaic processes frometal oxide types of electrodes or conductive polymer, the leakage

esistance in parallel with Cads may not be present or the magnitudef leakage current may be negligible.

Fig. 2. Equivalent circuits modeling of (a) interfacial processes at the doub

D: diffusion coefficient

2.2. Resistance at double layer interface region (Rint)

At the double layer interface, the electrochemical reaction isusually composed of charge transfer, adsorption and mass trans-port. Therefore, the interfacial resistance is associated with (1)a charge-transfer resistance (Rct) where the electrode/electrolyteinterface is not polarised in an ideal manner. This leads to cur-rent leakage, and (2) an adsorption resistance (Rads) representingthe impedance to the formation of Cads resulting from kinetics ofspecifically adsorbed ions at interfacial layer.

2.2.1. Charge transfer resistor (Rct)The charge-transfer resistance, Rct, is mainly related to the gra-

dients of potentials between the electroactive species (in this study,hydrogen (H+) and sulfate (SO4

2−) in the aqueous electrolyte and

le layer, (b) considering bulk processes and (c) the complete circuit.

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J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598 591

aqueo

Toiidpttwiit

2

smltciccpoatotaCet

R

2

rsibe

Fig. 3. Cyclic voltammetry for organic and

etraethylammonium (Et4N+) and Tetrafluoroborate (BF4−) in the

rganic electrolyte) in electrolytes and the electrode surface, lead-ng to the charge transfer phenomena. This charge transfer reactions controlled by the kinetics of the electrochemical reactions and theiffusion of ions near the electrode surface. Hence, it is a commonrinciple to connect Rct in parallel with double layer capacitanceo describe the interfacial leakage resistance at double layer. Ifhere is an electron-transfer reaction, Rct becomes smaller, other-ise, charge-transfer resistance becomes very large and electrode

s polarised with poorly defined potential. Obviously this processs dependent on concentration of electrolytes, applied potential,emperature and surface structures of the electrode [43].

.2.2. Adsorption resistor (Rads)The adsorption impedance depends on charges, associated with

pecific adsorption of charged species (dehydrated ions or solventolecules) in the inner Helmholtz as a portion of the adsorption

ayer (Fig. 1). The adsorbed species typically do not exchange elec-rons directly with the electrode and do not produce a pure Faradaicurrent, but they change the surface charge density resulting in thenterfacial current path [44]. The equivalent circuit in this systeman be represented by the combination of a resistor (Rads) with aapacitor (Cads) in series. Here, the resistance, Rads, is an integralart of the physical phenomenon that gives rise to the formationf Cads with no charge transfer. Otherwise, as discussed before, thedsorption processes can be treated like most charge transfer reac-ion, such as pseudo-capacitance. In such systems with metal oxider conductive polymer electrodes, Rads is intimately associated withhe charge-transfer resistance (Rct) since Cads is corresponding to

Faradaic process, resulting in a parallel combination of Rads withads to present pseudo-capacitive effects. However, in this study, anlectrical double layer with no pure Faradaic process is presented;herefore, the total interfacial resistance (Rint) can be expressed as:

int = Rct + Rads (6)

.3. Bulk solution impedance

In many practical cases, the high-frequency impedanceesponse must be carefully analyzed and separated from the mea-

ured total impedance to identify the interfacial low-frequencympedance components. In a typical experimental situation, theulk electrolyte processes dominantly at high frequencies andlectrochemical kinetics at the electrode-electrolyte interface is

us electrolytes at the scan rate 20 mVs−1.

observed at lower frequencies. This is because there is not enoughtime to form the double layer at the very high frequency, so thatthere are no effects from interfacial electrochemical reactions.Therefore, the impedance analysis can treat bulk and interfacialprocesses separately, on the basis of selective responses to samp-ling AC frequencies. The bulk process is valid only at high ACfrequencies, where the electric current must overcome the bulkimpedance. This may lead to the formation of a capacitance inparallel with the bulk resistance. Hence, the expression for thehigh frequency impedance from bulk solution can be modeled bythe parallel combination of bulk resistance (Rbulk) and capacitance(Cbulk). These bulk impedance elements are placed in parallel withthe interfacial impedance as shown in Fig. 2 (b).

To develop an accurate equivalent circuit, three major aspectsof the physics of the EDLC have been taken into account. First,based on the theory of the interfacial layer in EDLC, the totalcapacitance was approximated as a combination of three separatecapacitances; adsorption layer (inner Helmholts layer), the com-pact double layer (outer Helmholtz layer) and diffusion layer in theelectrolyte. More specifically, it was represented by the combina-tion of Helmholtz-layer capacitance (CH) in series with diffusionlayer (W), and adsorption capacitance (Cads) placed in parallel.Therefore, the equivalent circuit of an EDLC was modeled by threecapacitive elements. The second aspect is that the interfacial resis-tance was defined by the combination of charge transfer resistance(Rct) and adsorption resistance (Rads) in Helmholtz layer (Refer toFig. 2 (a)). Thirdly, the circuit was modified by considering the bulkmedia processes to present the impedance of the practical device inwhole frequency range. As a result, the complete equivalent circuitfor EDLCs is given as in Fig. 2 (c) and the resulting expression forthe total impedance of the cell becomes:

Z = RS +

⎢⎢⎢⎢⎣ 1ZCPEbulk

+ 1

Rbulk + ZW +[

1ZCPEH

+ 1Rint+ZCPEads

]−1

⎥⎥⎥⎥⎦−1

(7)

where each impedance (Z) for elements are defined in Table 1.This equation was employed to simulate the overall impedancevalue for a cell at sufficiently low frequencies.

3. Experimental

For the fabrication of EDLC-typed cells using porous elec-trodes, activated carbon (AB-520, MTI corp. USA) with high specific

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592 J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598

F M Etr

sepr(i(siatibCofpptdt

cei

ig. 4. Cyclic voltammery at various scan rates, 5, 10 and 40 mVs−1: (a) Organic (1espectively.

urface area (2000 m2g-1 as a powder) was used to produce activelectrode films on a current collector. The activated carbon-basedaste was prepared by mixing activated carbon (AC), polytetrafluo-oethylene (PTFE from Aldrich) as a binding agent, and carbon blackfrom Alfa Aesar, surface area = 80 m2g-1) as a conductive agentn 90:5:5 mass ratio using the solvent, N-Methyl-2-pyrrolidoneNMP from MTI corp.), and then this paste was cold-rolled on atainless steel (SST from Alfa Aesar) current collector. After coat-ng activated carbon-based pastes, the electrode was placed into

vacuum oven at 90 ◦C for 12 h to remove moisture and solidifyhe film. The specifications for a single electrode are summarizedn Table 2. A coin-typed cell with identical two-electrodes was thenuilt by assembling each AC electrode, separated by a 25 �m thickelgard 2400 membrane. To compare different electrolytes, 1 Mrganic (Et4NBF4 from Alfa Aesar) salts in propylene carbonates (PCrom Sigma-Aldrich) and 1 M aqueous (H2SO4) electrolytes wererepared. All these cells were assembled in a glove box filled withure Ar. Since the chemical-electrical properties of the organic elec-rolyte can be changed by water vapor, a special care was takenuring assembling to ensure the humidity in the glove box is lesshan 9% RH.

The electrochemical properties of a coin-typed cell with identi-al activated carbon electrodes and two different electrolytes werevaluated using cyclic voltammetery (CV) and galvanostatic charg-ng/discharging (CCD) measurements by a Gamry Reference 3000

4NBF4/PC) electrolyte up to 2.4 V, (b) Aqueous (1 M H2SO4) electrolyte up to 0.8 V,

Potentiostat. Electrochemical impedance spectroscopy (EIS) wasperformed on the same Potentiostat using EIS 300 software (GamryInc.). All EIS measurements were achieved by applying a low sinu-soidal amplitude AC voltage of 4 mV on a cell at a frequency rangefrom 10 mHz to 100 kHz. To evaluate potential dependency, mea-surements were performed at various fixed DC voltages dependingon the type of electrolytes. Differential capacitance and resis-tance versus frequency curves in Bode plots were obtained bytaking the real components of the impedance at different operatingfrequencies. Through fitting experimental EIS data with theproposed equivalent circuit, the calculated values for real andimaginary components of the impedance were corrected for eachelement (capacitors and resistors at frequency 10 mHz) and con-verted into total impedance of a cell using Eq. (7).

4. Results and discussion

4.1. Electrochemical characteristics, cyclic voltammetry andcharge-discharge plots

Fig. 3 show the cyclic voltammetry curves of coin-typed cells

measured in aqueous (1 M H2SO4) and organic (1 M Et4NBF4 / PC)electrolyte, respectively. Since the two electrodes were identicaland the ideal activated carbon is non-Faradaic material, its currentresponse was symmetrical and similar to an ideal EDLC. Although

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J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598 593

Table 2Typical specifications for a single electrode made of activated carbon.

AC film thickness 0.15 mmDiameter 9/16” (14.28 mm)Area 1.6 cm2

Total mass of an electrode 0.1713 g

aastsotrcwiist

dsd[mwtr

E

drc((afbtECaisiei

4

4

v1srtSeT

Fig. 5. Discharging processes at the constant current (30 C-rate) and the determi-nation of ohmic drops with different charging voltages for (a) Organic electrolyte,up to 1.2 vs. 2.4 V and (b) Aqueous electrolyte, up to 0.2 vs. 0.6 V, respectively.

mass 0.012gBET specific surface area(activated carbon powder) 2000 (±100) m2g−1

queous electrolyte shows some distortion from the ideal CV shapet near 1 V due to the decomposition of the electrolyte, it clearlyhows that the organic electrolyte did not have any distortion upo 2.7 V. The specific capacitance for a single electrode was mea-ured from CV measurements, which was about 108 Fg-1 in therganic electrolyte and 134 Fg-1 in the aqueous electrolyte, respec-ively. In order to clarify the absence of Faradaic processes of redoxeactions, further CV measurements with different scan rates werearried out as described in Fig. 4. The parallelogram-like CV curvesere maintained in various scan rates, which is a major character-

stic of non–Faradaic process in an EDLC. This result indicates that,n both tested cells, there was less pesudocapacitance caused byurface reduction/oxidation or functional groups on the surface ofhe electrodes.

The cells were then subjected to the galvanostatic charge-ischarge test to evaluate their capacitive behaviors and equivalenteries resistances (ESR or self-discharge) by measuring the IRrop at various charging voltages, as suggested in the literature28,29,45]. For this purpose, the data from charging/discharging

easurements at constant current loads were analyzed. The cellsere charged from 0 V to different rated voltages to investigate

he potential influence on ESR. As a result, the measured seriesesistance is calculated as

SR = �V

�I(8)

where �V is the initial voltage (ohmic) drop at the beginning ofischarging process, and �I is constant charging/discharging cur-ent. The overall internal resistance in a cell was represented by thealculated ESR values. As shown in Fig. 5, the organic electrolyteFig. 5 (a)) shows a higher voltage drop than aqueous electrolyteFig. 5 (b)). Also, for the same electrolyte, the ohmic drop decreaseds the charging voltage increased. This difference is much largeror the organic electrolyte than the aqueous electrolyte. This isecause the aqueous electrolyte has a much higher conductancehan organic electrolyte [46]. The corresponding ohmic drop andSR values calculated according to Eq. (8) were collected in Table 3.learly, the current response of the organic electrolyte is largelyffected by the applied potential differential and shows an increasen capacitance and a decrease in ohmic drop with voltages. Less-ignificant changes were observed in the aqueous electrolyte. Thismplies that both capacitance and internal resistance are depend-nt on the properties of the electrolyte, such as its conductance andonic mobility.

.2. EIS analysis of two electrolytes

.2.1. Nyquist plotsFig. 6 presents the Nyquist plot for two cells with identical acti-

ated carbon electrodes immersed in two different electrolytes: M H2SO4 and Et4NBF4 in propylene carbonate (PC). The first inter-ection point on the real axis at the highest frequency shows a seriesesistance of cells (RS) that generally originates from solution resis-

ance in the electrolyte, separator and external circuit resistances.ince two tested systems have the same components except for thelectrolyte, RS is mainly attributed to the resistance of electrolytes.herefore, the higher conductivity of the aqueous electrolyte leads

Fig. 6. Nyquist plots for cells in 1 M H2SO4 and 1 M Et4NBF4/PC electrolytes, respec-tively. Measurement was performed at the applied voltage of 5 mV, with thefrequency range from 10 mHz to 100 kHz.

to the lower resistance. The semi-circle present at high frequenciesis associated with the interfacial resistance between electrode andelectrolyte. The organic electrolyte data, as compared to the aque-

ous, displayed a larger semi-circle, indicating a higher resistanceat its interfacial layer. At medium frequencies, a straight line witha slope of 45◦ appears and this impedance reflects the ion diffu-sion phenomena in the porous structure. Subsequently, both cells

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594 J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598

Table 3Measured values of ohmic drop and ESR from the charging/discharging cycle at the constant current (30 C-rate) for two electrolytes.

Electrolytes Constant current* (mA) Vmin Vmax Capacitance during discharging (mF) Ohmic drop (�V) ESR (˝)

Organic (1M Et4NBF4/PC) 6.8 0 1.2 281 0.315 26.20 2.4 325 0.206 17.1

Aquous (1M H2SO4) 2.3 0 0.2 514 0.022 4.820 0.6 545 0.02 4.34

* maximr

bv

4

ctonflaTc

This current value corresponds to 30 C-rate (1/30 hour) when discharging from the

espectively.

ehave like a pure EDLC capacitor which is characterized by theertical line at low frequencies.

.2.2. Bode plotsThe Bode plots shown in Fig. 7 describe the resistance and

apacitance as functions of the frequency. In Fig. 7 (a), three dis-inguishable resistances, which are independent of frequency, existn both curves and can be correlated to individual resistive compo-ents (R) defined in Section 2. Specifically, the resistance at the high

requency range shows mainly the value of RS while the Faradaic

eakage or charge transfer resistance from bulk electrolytes (Rbulk)ppears at the medium frequency range between 10 Hz and 1 kHz.he low frequency range between 10 mHz and 1 Hz includes Rintaused by interfacial processes, and represents the summation of

Fig. 7. Bode polts of (a) the real impedance and (b) the real capacitance

um voltage of 2.7 V for the organic electrolyte and 1.0 V for the aqueous electrolyte,

RS, Rbulk and Rint. On the other hand, Fig. 7 (b) demonstrates thefrequency dependence of the capacitance. The capacitance reachesits maximum at the low frequency because the ions have suffi-cient time to reach to the pores and then form the double layeron the electrode surface. The value of capacitance at the lowestfrequency hence represents the overall capacitance at the dou-ble layer interface (Cdl). The rated capacitance is around 670 mFfor aqueous H2SO4 electrolyte and 470 mF for organic Et4NBF4/PCelectrolyte at 10 mHz, respectively. As the frequency increases, thecontribution of Cdl decreases due to insufficient ion transport, and

the major contribution changes to partial capacitance from bulkelectrolyte’s process (Cbulk) measured as above 14 to 5 �F at 5 kHzfor both electrolytes, respectively. Compared to the aqueous elec-trolyte, the organic electrolyte exhibits a larger resistance and a

vs. the frequency for cells with aqueous and organic electrolytes.

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J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598 595

FN

ltof(witcr

4p

pcmatauti(asittciCrceuaolowtfet

simulation, the measured impedance spectra were fitted by an

ig. 8. Simulated (curves) impedances, Zreal and Zimag, in comparison with measuredyquist plots (dots) for both aqueous and organic electrolytes.

ower capacitance throughout the entire frequency range, due tohe greater energy barrier against its ion transport. This transportccurs in both the bulk solution and diffusion layer as ionic dif-usion (driven by the concentration gradient) and ionic migrationdriven by the electric field). In this study the relevant impedanceas observed at the low frequency range from 1 Hz to 100 Hz (see

n Fig. 7 (a)), which confirms the diffusion dominant impedance forhe organic electrolyte. Meanwhile, the ion transport impedance islosely associated with the double-layer formation process, whichesults in a less value of Cdl (see Fig. 7 (b)).

.3. Simulations with an equivalent circuit and predictedotential dependency

The measured EIS data from Nyquist and Bode plots were com-ared with simulated parameters obtained from the equivalentircuit model which is given in Fig. 2 (c). Fig. 8 describes theeasured (symbols) and simulated (lines) impedance spectra for

queous and organic electrolytes in Nyquist plots. The experimen-al data closely matches the model predicted data in both lownd high frequency regions, which was unsuccessfully achievedsing the models shown in Fig. 2 (a). Using the equivalent circuit,he extracted parameters for different electrolytes are summarizedn Table 4. In comparison with measured data from Bode plotsFig. 7), the simulated values for resistance and capacitance show

reasonable consistency with the measured ones. In addition, thisimulation indicates that Rint can be considered as the most dom-nant parameter in determining the operating ohmic resistance ofested cells. This means Rint can be used to study the characteris-ics of ohmic leakage current or internal resistance of EDLC cells. Forapacitance values, the model predicted, Cbulk of tens of microfarad,n agreement with experimental values. The summation of CH andads is around 640 mF in aqueous and 540 mF in organic electrolytes,espectively. These values are close to the measured double layerapacitance, Cdl, shown in Fig. 7. Meanwhile, the organic electrolytexhibits lower CH and Cads compared to the aqueous one. These val-es of capacitance can be considered in terms of types of electrolytend ion radius. According to equation (1), larger sized ions of therganic electrolyte possess lower Cads and CH because its Helmholtzayer thickness, d, of closest ion’s approach are larger than the aque-us electrolyte’s one, leading to less capacitance. This result agreesith the theory and experiments reported by Grahame [35]. Also,

he lower conductivity of organic electrolytes exhibits higher dif-

usion impedance (ZW), which corresponds to the fact that organiclectrolytes have the less ion movement and larger energy barriero diffusional processes, resulting in the larger diffusion impedance

Fig. 9. Measured (dots) and simulated (lines) EIS impedances for different appliedvoltages with (a) Organic electrolyte, (b) Aqueous electrolyte, respectively. Theinsert is an enlarged view at high frequencies.

(around 4.3 �) than one (2.1 �) of the aqueous electrolyte with ahigher conductivity.

In order to further characterize the resistance and capacitancedependency on the applied voltage level, additional EIS measure-ments was performed for voltage levels at 0.2 and 0.6 V on aqueouselectrolytes, and at 1.2 and 2.4 V on organic electrolytes, respec-tively. The applied voltages were respected to reflect the relativepotential differential at electrode-electrolyte interface. Fig. 9 showsthe Nyquist plot for two electrolytes obtained at different voltagelevels. At the low voltage with the decreased DC potential acrossthe interfacial double layer, the more right-shifted vertical line inthe low frequency region was shown and the larger semi-circle waspresented, which means the overall resistance increases at doublelayer interface. That is, the higher resistance at low potential causesto larger leakage current. This result was in agreement with char-acteristics of the current response from various applied voltages inCCD measurements, introducing the differences of ohmic drop orESR. The differences in capacitance and resistance as function offrequency were described in Fig. 10, which again shows excellentagreements between measured and simulated data. It is worth-while to note that larger potential led to the lower resistance andthe higher capacitance over the whole frequency range. In addition,this effect is more significant in the organic electrolyte, indicatingthe organic electrolyte showed a larger dependency on the appliedpotential change when compared to the aqueous electrolyte. For

equivalent circuit and the simulated parameters are summarizedin Tables 5 and 6. Similar to experimental EIS results, the notice-able resistance changes were observed. More details, compared to

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596 J. Kang et al. / Electrochimica Acta 115 (2014) 587– 598

Table 4Equivalent circuit parameters (Capacitance and Resistance) obtained from the simulation for two electrolytes.

Impedance values Aqueous (1M H2SO4) Organic (1M Et4NBF4/PC) Unit

Simulated Measured Simulated Measured

Rs 0.184 0.2 1.306 1.2 ohmRbulk 1.512 1.6 7.508 6.9 ohmRint 5.899 6.7 10.2 7.1 ohmZW 2.131 - 4.272 - ohmCbulk 15 14 6 4.6 �FCH 340 - 248 - mFCads 302 - 262 - mFCdl 642 610 510 470 mF

Fig. 10. Measured (dots) and simulated (lines) capacitances and resistances for different applied voltages with (a) Organic electrolyte, (b) Aqueous electrolyte, respectively.

Table 5Calculated parameters (Capacitance and Resistance) obtained from the simulationwith different applied voltages for the aqueous electrolyte (1M H2SO4).

Simulated impedance values 0.2 V 0.6 V Unit

Rs 3.08E-01 2.85E-01 ohmQbulk 9.51E-05 8.73E-05 S·s˛

˛bulk 8.55E-01 8.69E-01Cbulk 16 17 �FRbulk 2.67 2.45 ohmQW 3.16E-01 3.51E-01 S·s(1/2)

B 4.85 3.15 s1/2

ZW 3.16 2.85 ohmQH 6.83E-01 4.78E-01 S·s˛

˛H 9.69E-01 8.97E-01CH 346 281 mFRint 1.93 0.279 ohmQads 1.61E-02 1.22E-01 S·s˛

˛ads 4.79E-01 5.35E-01Cads 224 315 mF

Table 6Calculated parameters (Capacitance and Resistance) obtained from the simulationwith different applied voltages for the organic electrolyte (1 M Et4NBF4/PC).

Simulated impedance values 1.2 V 2.4 V Unit

Rs 2.05 1.63 ohmQbulk 4.55E-05 3.79E-05 S·s˛

˛bulk 7.94E-01 8.07E-01Cbulk 3.9 3.6 �FRbulk 13.2 9.79 ohmQW 9.67E-02 8.33E-01 S·s(1/2)

B 6.14 1.11 s1/2

ZW 10.34 1.2 ohmQH 9.59E-02 5.45E-02 S·s˛

˛H 4.56E-01 5.09E-01CH 121 25 mFRint 38 24.2 ohmQads 5.47E-02 3.05E-02 S·s˛

˛ads 8.58E-01 6.27E-01Cads 109 262 mF

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J. Kang et al. / Electrochimica Ac

Fig. 11. Impedance from EIS modeling, ESR from the CCD measurement, and ohmicdt

ofifHeiwirtltctts(md

iromltt

The authors would like to acknowledge the financial sup-

rop for different applied voltages with (a) Organic electrolyte, (b) Aqeuous elec-rolyte, respectively.

ther resistances (RS and Rbulk), it can be clearly seen that the inter-acial resistance (Rint) is significantly reduced when the potentialncreased. As discussed before, Rint is associated with charge trans-er and kinetics of adsorbed ions in the formation of outer/innerelmholtz layers. Therefore, the higher potential leads to morelectron transfer and ions adsorption at the interfacial layer, resultsn a smaller Rint. Also, the Helmholtz capacitance (CH) decreases

hile the adsorption (Cads) increases, and the diffusion impedances reduced. This is mainly caused by the acceleration of adsorptioneactions and diffusion rate caused by a larger differential poten-ial. According to the Gouy-Chapman model of diffusion doubleayers, the capacitance is proportional to the differential poten-ial as described in equation (3). Consequently, at high potentialonditions, adsorption and diffusion capacitances contribute moreo the overall capacitance. This tendency is similar for both elec-rolytes, but it is seen in Table 6 that larger difference in ZW areeen in the organic electrolyte when compared to the aqueous onesee Table 5), which means the diffusion of organic electrolyte is

ore affected by the potential differences resulting in the largereviation of ZW.

In order to validate the equivalent circuit model, thesempedance characteristics were correlated with distributed cur-ent leakage or ESR in practical cells. In Fig. 11, the total impedancebtained from the simulation is compared with the ESR from CCDeasurements. From equation (7), the total impedance was calcu-

ated by simulating each resistor and capacitor at 10 mHz. Althoughhe equivalent resistance from EIS measurements is usually lowerhan other measurement techniques [29], this value gives an

ta 115 (2014) 587– 598 597

informative indication of internal resistance for EDLC devices. Note,the value from modeling is not exactly same as the experimentalESR, but the similar potential dependency has been shown betweenEIS modeling and CCD measurement.

4.4. Discussion based on model prediction

Two major considerations were made in the development ofthe equivalent circuit model for an EDLC. First, the circuit mod-eling was developed based on theoretical descriptions of ELDCstructures and effects of electrochemical reactions coupled withdiffusion and adsorption phenomena in the electrochemical doublelayer. Secondly, this circuit was designed to provide the mean-ingful information on each physical process in practical EDLCdevices. The dominant resistive elements in both interfacial andbulk processes have been found by improving the fitness to theEIS data. Importantly, the interfacial resistance (Rint) describes theextents of electron transfer reactions and kinetic of adsorbed ionsin forming the double layer. For capacitive elements, the doublelayer capacitance (Cdl) is represented by a combination of War-burg impedance, W, and the compact Helmholtz capacitor, CH,in parallel with adsorption capacitor, Cads. The values of ZW andCads have been analyzed to understand the diffusion behavior andadsorption process which depends on the ions sizes and conduc-tivity of electrolytes. Also, the bulk capacitance, Cbulk, takes intoaccount the bulk processes for a practical EDLC cell. It was foundthat the defined parameters in the proposed circuit are criticalto demonstrate their characteristics, such as internal resistanceor the potential-dependency. Therefore, the proposed circuit canbe useful to characterize the EDLC-typed capacitors which aretypically composed of porous carbon-based electrodes with ionicelectrolytes. Furthermore, the simulated impedances of resistiveelements provides informative values to predict the energy/powerdensity and thermal behavior of EDLCs, because these factors aremainly dominated by internal resistances [47].

5. Conclusion

This paper presents an improved equivalent circuit model toinvestigate the electrochemical and dynamic behaviors of EDLCswith porous carbon-based electrodes using different electrolytes.The characteristics of EDLC cells with two types of electrolytes,namely, aqueous 1 M H2SO4 and organic 1 M Et4NBF4/PC, werestudied by analyzing CV and CCD measurements. At the same time,the impedance behaviors of these EDLCs were utilized to evaluatethe validity of circuit modeling. The simulation results showed thatthis new circuit model was able to characterize EDLCs with bothaqueous and organic electrolytes. Moreover, the proposed circuitmodel provided a reasonable interpretation on physical processesoccurring within the EDLC cell, through introducing a more clarifiedview of their electro-chemical and transport phenomena. In addi-tion, the EIS analysis on the potential dependency supported theproposed elements in the model and the ESR correlation betweenEIS and CCD measurements was derived. It was suggested thatthis circuit model is able to simulate sufficiently the potential-dependent characteristics of double layer capacitors.

Acknowledgments

port of Ontario Research Fund (ORF), Automotive PartnershipCanada (APC), Natural Sciences and Engineering Research Councilof Canada (NSERC) and General Motors (GM).

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