Equivalent Circuit Paper

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

Develo r edouble lec

Jinhee Ka c, Xia Mechanical & rloo, Nb Electrical and , N2L c Chemical Eng rio, Cd Canadian Reg am Dr

a r t i c l

Article history:Received 25 SeReceived in reAccepted 3 NoAvailable onlin

Keywords:Electrical doubImpedance spEquivalent circPotential dependency of impedanceEquivalent series resistance

chem specapaciayer a, is s

obtactrolys (suc/elec

on the applied electrode potential is analyzed for two electrolytes during charging/discharging, and itscorrelation with the internal resistance (referred ESR) is studied.

2013 Elsevier Ltd. All rights reserved.

1. Introdu

Electricacapacitor, iapplicationand power much longeconditions, a battery anrecently beeteries or fuhave been iwhich constem reliabil[11,12]. Forobtain an acistics of EDLand design ifor EDLC mowithin a pomany attemistics of EDL

CorresponE-mail add

0013-4686/$ http://dx.doi.oction

l double layer capacitor (EDLC), named also as a super-s one of the emerging devices for energy storages, which has a potential to enable to robust both energydensities [15]. Compared to batteries, EDLCs exhibit ar operating life, a better adaptability to varying weatheran enhanced load balancing when used in parallel withd less environmental impacts. These EDLC devices haven used in power train systems in combination with bat-el cells for electric vehicles [610]. In addition, EDLCsnvestigated to develop a hybrid energy storage system,ists of both EDLCs and batteries for improving the sys-ity and efciency, in wind and solar power generation

these energy storage systems, it is very important tocurate model which describes the operation character-Cs, and subsequently to optimize the component sizesn different applications. Meanwhile, equivalent circuitsdeling are valuable to predict their dynamic behaviors

wer electronic circuit. For this purpose, there have beenpts in the literature to model the electrical character-Cs [1317]. In general, the equivalent circuit model of

ding author.resses: [email protected], [email protected] (J. Wen).

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-ed 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 simplied 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 [2326]. Therefore, for the

see front matter 2013 Elsevier Ltd. All rights reserved.rg/10.1016/j.electacta.2013.11.002pment of an equivalent circuit model fo layer capacitors (EDLCs) with distinct e

nga, John Wena,, Shesha H. Jayaramb, Aiping Yu Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Wate

Computer Engineering, University of Waterloo, 200 University Avenue West, Waterlooineering, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontaional Engineering Center, GM of Canada Ltd., General Motors Company, 1908 Colonel S

e i n f o

ptember 2013vised form 2 November 2013vember 2013e 14 November 2013

le layer capacitorectroscopyuit model

a b s t r a c t

An equivalent circuit model for electrolyzing the electrochemical impedanceon the Grahame theory, while these cand the ion adsorption at the double lupon its validation against the EIS datMeanwhile, experimental results arecarbon-based electrodes and two elemodel predicts the useful parametertrochemical reactions at the electrode/ locate /e lec tac ta

lectrochemicaltrolytes

aohui Wangd

2L 3G1, Ontrario, Canada3G1, Ontrario, Canadaanadaive, Oshawa, L1H 8P7, Ontario, Canada

ical double layer capacitors (EDLCs) is proposed through ana-troscopy (EIS) measurements. The model is developed basedtive or resistive behaviors in the presence of charge diffusioninterface and bulk media are investigated. This circuit model,uccessfully applied to characterize the practical EDLC devices.ined from different EDLC cells that consist of the activatedtes, namely, aqueous (H2SO4) and organic (Et4NBF4/PC). Theh as resistance and capacitance) which help interpret elec-trolyte interface. The quantitative dependence of impedance

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

development of an accurate circuit model, it is essential to rec-ognize the appropriate structure of the double layer and describekey electrochemical reactions at the electrode/electrolyte inter-face. This allows for a more accurate EDLC model which can bedeveloped ture and eleAccordinglyaccount theble layer baand preseninterfacial rpendent oncapacitanceever, depenand voltageEDLC devicdischarge) wreactions. TEDLC are ation and dporous elecby the volta[2830]. A prequires sufthe double-

Electrocful techniqanalysis ofor voltage. chemical inelements (Rtioned befoions transpthe physicastill obscurtype and vaphysical proions adsorpin interfaciequivalent on better ushould incluical reaction

This papcuit model ion transpoformation otical EDLC swith multiption and buobserved phthat this ciritive) behavcontributiopaper is orgfor the EDLchemical reare introdutures, specimeaningfultal data, thcells with twvoltammetrtheir specimeasuremecircuit. Fina

interpretations for each electrolytes properties are provided anddiscussed.

2. Circuit model development

iterachem-layeC str31], charventi. Thesed a

0rd

A

ere ty of, can

whithery an

the d theces orall nd th, the on. Ts.

2kTn

reforn be

qdV

ere nial drrge ont inon la34]. ered

1CH

+

urtheic aistinelm

P regs or a

formy, th

led natu

overver,

at thterists inoposf thebased on the true representation of its internal struc-ctrochemical properties of electrodes and electrolytes., the predictions of a circuit model should take into

electrochemical and kinetic characteristics of the dou-sed on theoretical descriptions of the EDLC structure,ts physics-based interpretations at the double-layeregion. Worthwhile to mention, an ideal EDLC is inde-

the working frequency or applied voltage when its and internal resistance are evaluated. In practice, how-dence of the capacitance and resistance on frequency

is commonly observed [27]. In addition, the practicales suffer from the charge leakage (dened as a self-hich results from potential-dependent charge transferhese deviations from the ideal capacitive behavior ofttributed mainly to ionic chemical/physical adsorp-iffusional impedance, incomplete polarization of thetrode, and Faradaic charge transfer resistance causedge differential across the electrode/electrolyte interfaceractical EDLC model should address these issues whilecient information on key electrochemical reactions atlayer interface.hemical impedance spectroscopy (EIS) is a very power-ue to characterize electrochemical phenomena in the

double layer capacitors under the charging currentFrom the evaluation of impedance data, the electro-terface behavior is often described by simple electrical, L, and C) in an equivalent circuit. However, as men-re, many details about the denition of electrolyteort, their electrochemical kinetics, and, in particular,l interpretation of equivalent circuits of an EDLC aree and unclear. This brings difculties in identifying thelues of these electrical elements. Moreover, multiplecesses occur simultaneously in the system, e.g. speciction into pore sites, diffusion phenomena taking placeal region and bulk electrolyte processes. An advancedcircuit should be therefore properly established basednderstanding of each of these physical processes, andde RC circuit branches to reect the key electrochem-s in EDLC devices.er aims to develop a more adequate equivalent cir-by considering these effects of the electrolyte on thertation (ionic diffusion and migration), adsorption layern the electrode surface, and bulk processes in prac-ystems. In this work, a new equivalent circuit modelle- RC elements (for accounting for diffusion, adsorp-lk media impedance, respectively) is proposed from theysical and electrochemical phenomena. It is expectedcuit model can be used to interpret resistive (or capac-iors of an EDLC device, and quantitatively to verify then of individual processes to devices performance. Thisanized as follows: First, several theoretical descriptionsC structures and models of both interfacial electro-actions and bulk media process in a real EDLC systemced. Then, based on the understanding of EDLC struc-ed impedance elements are built up and referred to

electrochemical processes. Thirdly, from experimen-e fundamental characteristics of carbon-based EDLCo kinds of electrolyte are analyzed by using the cyclicy and galvanostatic charge-discharge plots in terms ofc capacitances and internal resistances. Meanwhile, EISnts are used to acquire parameters of the equivalentlly, a more detailed view of EDLC characteristics and

In lhave sdoubleof EDLlayer [to the of controdesexpres

CH =

whmittivilayer, dFig. 1),

Anoby Guopart ofso thatinuenthe oveelds atheoryequatifollow

qd =(

TheCdiff, ca

Cdiff =

whpotentthe chaconstadiffusiStern [consid

1Cdl

=

In fof specthree douter HThe IH(cationto thequentltheoryby theity andMoreocessescharacelemenThe prment oture, a few theoretical treatments of EDLC structuresatically proposed to describe the properties of ther at electrode/electrolyte interfaces. The rst conceptuctures was introduced as the compact or Helmholtzwhere all counter-ions were assumed to be attractedged electrode surface. This model is analogous to thatonal dielectric capacitors with two metal planar elec-refore, the capacitance in Helmholtz model is simplys follows.

(1)

0, r are the free space permittivity and the relative per- the electrolyte, respectively. The distance of Helmholtz

be obtained from the radius of solvated ions (refer tole A is the surface area of the electrode.

theoretical description of the EDLC has been developedd Chapman [32,33], which is considering into the diffuseouble layer. This model treats the ions as point charges

ions movements in the electrolytes are driven by thef diffusion. This ions transportation in EDLC determinescapacitance. It is subjected to applied potential, thermale types of ions in the electrolyte. In the Guoy-Chapmandiffuse charge is determined by the Poisson-Boltzmannhis equation is given for a symmetrical electrolyte as

0)1/2

sinhe0V

2kT(2)

e, the specic capacitance according to the diffuse layer, evaluated as

=(

n0e202kT

)1/2cosh

e0V

2kT(3)

o is the number of ions in the bulk electrolyte, V is theop between the electrode and the bulk electrolyte, e0 isf the ion, k is the Boltzmann constant, is the dielectric

the electrolyte, and T is the temperature. And later, theyer model was combined with the Helmholtz model byIn that model, the overall capacitance in EDLC, Cdl, was

as a series of capacitance, CH and Cdiff,

1Cdiff

(4)

r developments, Graham [35] emphasised the presencedsorption of ions on the electrode surface, by modelingguished layers: the inner Helmholtz plane (IHP), theholtz plane (OHP) and the diffusion layer (see Fig. 1).ion is made of solvent molecules and/or adsorbed ionsnions in electrolytes) while the OHP region correspondsation of hydrated ions (solvated ions) layer. Subse-e diffusion layer develops outside the OHP. Grahamsto a better understanding of how EDLCs are affectedre of their electrolytes; such as ions size, polarizabil-all capacitance-dependency on the electrode potential.it is essential to clarify integral electrochemical pro-e double layer interface in order to present more realistictics of EDLC. Therefore, the theoretical treatment of all

this research will be discussed based on Graham model.ed circuit was followed by including initial develop-

relationships between electrical components, such as

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

electr

double-layecic adsorpinterfacial d

2.1. Electrointerface reg

As disculayer paramof electrodeness and nthe double-(CPE) reprethe CPE is pTable 1 listcomparisonburg elemeimpedance

2.1.1. HelmGraham

which is ctance (Cads)(Cdiff). The lexpressed bformation flayer whilegradient betrolytes ionresistance develop a cis a limited

s occThesFig. 1. Schematics of an electrochemical double layer and its

r capacitances combined with ions diffusion and spe-tion in both IHP and OHP, the presence of resistances at

proceslayer. ouble layer and bulk process in electrolyte.

chemical double-layer capacitance at the double layerion

ssed in the previous section, the measured double-eter is not an ideal capacitor because of the porosity

materials, inhomogeneous pores distribution, rough-on-linear current density. Due to non-ideal behavior,layer capacitor is replaced by a constant phase elementsentation and not a pure capacitor [36]. In many cases,laced in parallel with an interfacial resistor in a circuit.s the common circuit elements, their impedances, the

between a pure capacitor and CPE, resistor and War-nt (W). Each element is discussed with their concept ofrepresentation in EDLC circuit modeling.

holtz (CH) and diffusion (Cdiff) capacitances model presents the overall double layer capacitanceomposed of three contributions: adsorption capaci-, Helmholtz capacitance (CH) and diffusion capacitanceatter two capacitances can be connected in series andy Eq. (4). CH represents the compact Helmholtz layerrom solvated ions attracted electrostatically in the OHP

Cdiff results from the ions transportation, caused by atween the bulk and interfacial concentration of elec-. In fact, charge-transfer processes with the measurableconsume the electrolytes ions at the interface andoncentration gradient. In unsupported systems, there

supply of ions from the electrolyte and the diffusion

element (Wtance of bulis very impoin various afusion capacharge (conor low condfusion proccapacitancebe determinsurface area

2.1.2. AdsoIn Graha

in IHP regicic adsorpcapacitanceanother capcharge-trantance. Thereby Cads and ing in an eqfor an adsoritance is asdependent dened as:

Cads =(

q

Vode/electrolyte interface model.

urs in a bulk solution overlapping with the diffusione phenomena can be interpreted using the Warburg

) for the bounded diffusion layer in series with the resis-k solution (Rbulk) [37]. In EDLC, this diffusion capacitancertant factor to inuence the nal performance of EDLCspplications [38,39]. According to equation (3), the dif-citance is depending on the number of ions and theirductance) in electrolytes. When the frequency increasesuctive ions are used, the number of ions involved in dif-ess can be reduced, therefore resulting in a decrease of. Otherwise, various parallel diffusion mechanisms caned by changing the potential difference, the electrode

and the bulk solution concentration.

rption capacitance (Cads)mes theory, it was recognized that dehydrated ionson could reside on the electrode surface with spe-tion processes. This phenomenon results in adsorption, Cads. In a certain system, this Cads can be regarded asacitive element with some part of the electrochemicalsfer process. This phenomenon is called pseudocapaci-fore, the overall capacitance in EDLC can be representeda series combination with CH and Cdiff in parallel, result-uivalent circuit depicted in Fig. 2 (a). Generally speaking,bed species formed by charge transfer in IHP, the capac-sociated with a Faradaic charge (qF), and the charge ison the potential difference (V). This allows Cads to be

F)

(5)


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

jCA pure capacitorInversely liner dependency on frequencyC: capacitance, : frequency (s1)

ZCPE = 1Q (j) Constant phase element (CPE)Non-linear dependency on frequencyQ: CPE coefcient, : exponent (0 < < 1)

Warburg (W) ZW

= 1QW

j

coth[B

j] Bounded diffusion layer

QW: Warburg coefcientB is theoretically dened as follows;/D1/2

where, : Nernst diffusion layer thicknessD: diffusion coefcient

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

Therefore, it can be seen that Cads corresponds to the variationbetween the differential charge and voltage [40]. However, it isnecessary to differentiate with another pseudo-capacitance whichoriginates from Faradaic (oxidation/reduction reactions) processesdue to other sources such as metal oxide, conductive polymers orthe functional group. This pseudo-capacitance is different from theemployed here whose extent of faradaically delivered charges isa function of voltage, but a reversible process with the negligibleleakage current [41,42]. In terms of circuit congurations, whena pseudo-capacitance is involved, generally, there are a Faradaicleakage resistance in parallel with pseudo-capacitor. However, inan ideal EDLC system where there are no Faradaic processes frommetal oxide types of electrodes or conductive polymer, the leakageresistance in parallel with Cads may not be present or the magnitudeof leakage current may be negligible.

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 ofspecically 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 (SO42) in the aqueous electrolyte andFig. 2. Equivalent circuits modeling of (a) interfacial processes at the double layer, (b) considering bulk processes and (c) the complete circuit.


trolyte

Tetraethylaorganic elecing to the chis controlleddiffusion ofprinciple toto describethere is an wise, chargis polarisedis dependetemperatur

2.2.2. AdsorThe adso

specic adsmolecules) layer (Fig. 1trons directcurrent, butinterfacial ccan be reprcapacitor (Cpart of the of Cads withadsorption tion, such aor conductithe charge-a Faradaic pCads to preseelectrical dotherefore, t

Rint = Rct +

2.3. Bulk so

In manresponse msured totalimpedance bulk electrelectrochem

ed at formare nore, ses sC frenciesancel wiequerallel

Theserfacdevephyson ttancetanceublelyte.

HelW), ore, ttive eas dd ada)). TprocFig. 3. Cyclic voltammetry for organic and aqueous elec

mmonium (Et4N+) and Tetrauoroborate (BF4) in thetrolyte) in electrolytes and the electrode surface, lead-arge transfer phenomena. This charge transfer reaction

by the kinetics of the electrochemical reactions and the ions near the electrode surface. Hence, it is a common

connect Rct in parallel with double layer capacitance the interfacial leakage resistance at double layer. Ifelectron-transfer reaction, Rct becomes smaller, other-e-transfer resistance becomes very large and electrode

with poorly dened potential. Obviously this processnt on concentration of electrolytes, applied potential,e and surface structures of the electrode [43].

ption resistor (Rads)rption impedance depends on charges, associated withorption of charged species (dehydrated ions or solventin the inner Helmholtz as a portion of the adsorption). The adsorbed species typically do not exchange elec-ly with the electrode and do not produce a pure Faradaic

they change the surface charge density resulting in theurrent path [44]. The equivalent circuit in this systemesented by the combination of a resistor (Rads) with aads) in series. Here, the resistance, Rads, is an integralphysical phenomenon that gives rise to the formation

no charge transfer. Otherwise, as discussed before, theprocesses can be treated like most charge transfer reac-s pseudo-capacitance. In such systems with metal oxideve polymer electrodes, Rads is intimately associated with

observtime tothere Therefprocesling Afrequeimpedparallehigh frthe pa(Cbulk).the int

To of the based capacicapacipact doelectrotion oflayer (Therefcapacitance w(Rct) anFig. 2 (media transfer resistance (Rct) since Cads is corresponding torocess, resulting in a parallel combination of Rads withnt pseudo-capacitive effects. However, in this study, anuble layer with no pure Faradaic process is presented;

he total interfacial resistance (Rint) can be expressed as:

Rads (6)

lution impedance

y practical cases, the high-frequency impedanceust be carefully analyzed and separated from the mea-

impedance to identify the interfacial low-frequencycomponents. In a typical experimental situation, theolyte processes dominantly at high frequencies andical kinetics at the electrode-electrolyte interface is

whole frequfor EDLCs ithe total im

Z = RS +

where eThis equativalue for a

3. Experim

For the trodes, activs at the scan rate 20 mVs1.

lower frequencies. This is because there is not enough the double layer at the very high frequency, so thato effects from interfacial electrochemical reactions.the impedance analysis can treat bulk and interfacialeparately, on the basis of selective responses to samp-quencies. The bulk process is valid only at high AC, where the electric current must overcome the bulk. This may lead to the formation of a capacitance inth the bulk resistance. Hence, the expression for thency impedance from bulk solution can be modeled by

combination of bulk resistance (Rbulk) and capacitancee bulk impedance elements are placed in parallel withial impedance as shown in Fig. 2 (b).lop an accurate equivalent circuit, three major aspectsics of the EDLC have been taken into account. First,he theory of the interfacial layer in EDLC, the total

was approximated as a combination of three separates; adsorption layer (inner Helmholts layer), the com-

layer (outer Helmholtz layer) and diffusion layer in the More specically, it was represented by the combina-mholtz-layer capacitance (CH) in series with diffusionand adsorption capacitance (Cads) placed in parallel.he equivalent circuit of an EDLC was modeled by threelements. The second aspect is that the interfacial resis-ened by the combination of charge transfer resistancesorption resistance (Rads) in Helmholtz layer (Refer tohirdly, the circuit was modied by considering the bulkesses to present the impedance of the practical device in

ency range. As a result, the complete equivalent circuits given as in Fig. 2 (c) and the resulting expression forpedance of the cell becomes:

1ZCPEbulk

+ 1

Rbulk + ZW +[

1ZCPEH

+ 1Rint+ZCPEads]1

1

(7)

ach impedance (Z) for elements are dened in Table 1.on was employed to simulate the overall impedancecell at sufciently low frequencies.

ental

fabrication of EDLC-typed cells using porous elec-ated carbon (AB-520, MTI corp. USA) with high specic


Fig. 4. Cyclic vrespectively.

surface areaelectrode paste was proethylene (from Alfa in 90:5:5 m(NMP fromstainless sting activatea vacuum othe lm. Thin Table 2. Abuilt by assCelgard 240organic (Et4from Sigmaprepared. Apure Ar. Sintrolyte can during assethan 9% RH

The eleccal activateevaluated uing/discharoltammery at various scan rates, 5, 10 and 40 mVs1: (a) Organic (1 M Et4NBF4/PC) ele

(2000 m2g-1 as a powder) was used to produce activelms on a current collector. The activated carbon-basedrepared by mixing activated carbon (AC), polytetrauo-(PTFE from Aldrich) as a binding agent, and carbon blackAesar, surface area = 80 m2g-1) as a conductive agentass ratio using the solvent, N-Methyl-2-pyrrolidone

MTI corp.), and then this paste was cold-rolled on aeel (SST from Alfa Aesar) current collector. After coat-d carbon-based pastes, the electrode was placed intoven at 90 C for 12 h to remove moisture and solidifye specications for a single electrode are summarized

coin-typed cell with identical two-electrodes was thenembling each AC electrode, separated by a 25 m thick0 membrane. To compare different electrolytes, 1 MNBF4 from Alfa Aesar) salts in propylene carbonates (PC-Aldrich) and 1 M aqueous (H2SO4) electrolytes werell these cells were assembled in a glove box lled withce the chemical-electrical properties of the organic elec-be changed by water vapor, a special care was takenmbling to ensure the humidity in the glove box is less.trochemical properties of a coin-typed cell with identi-d carbon electrodes and two different electrolytes weresing cyclic voltammetery (CV) and galvanostatic charg-ging (CCD) measurements by a Gamry Reference 3000

Potentiostaperformed Inc.). All EISsoidal ampfrom 10 mHsurements on the typtance versutaking the rfrequenciesproposed eimaginary celement (caverted into

4. Results

4.1. Electrocharge-disc

Fig. 3 shmeasured ielectrolyte,and the ideresponse wctrolyte up to 2.4 V, (b) Aqueous (1 M H2SO4) electrolyte up to 0.8 V,

t. Electrochemical impedance spectroscopy (EIS) wason the same Potentiostat using EIS 300 software (Gamry

measurements were achieved by applying a low sinu-litude AC voltage of 4 mV on a cell at a frequency rangez to 100 kHz. To evaluate potential dependency, mea-

were performed at various xed DC voltages dependinge of electrolytes. Differential capacitance and resis-s frequency curves in Bode plots were obtained byeal components of the impedance at different operating. Through tting experimental EIS data with thequivalent circuit, the calculated values for real andomponents of the impedance were corrected for eachpacitors and resistors at frequency 10 mHz) and con-

total impedance of a cell using Eq. (7).

and discussion

chemical characteristics, cyclic voltammetry andharge plots

ow the cyclic voltammetry curves of coin-typed cellsn aqueous (1 M H2SO4) and organic (1 M Et4NBF4 / PC)

respectively. Since the two electrodes were identicalal activated carbon is non-Faradaic material, its currentas symmetrical and similar to an ideal EDLC. Although


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

AC lm thickness 0.15 mmDiameter 9/16 (14.28 mm)Area Total mass omass BET specic

aqueous eleat near 1 V shows thatto 2.7 V. Thsured fromorganic electively. In orreactions, fucarried out were maintistic of nonin both testsurface redthe electrod

The celldischarge teseries resisdrop at var[28,29,45]. measuremewere chargthe potentiresistance i

ESR = VI

where dischargingrent. The ovcalculated E(Fig. 5 (a)) (Fig. 5 (b)). Aas the charfor the orgbecause thethan organiESR values cClearly, theaffected by in capacitansignicant cimplies thaent on the pionic mobil

4.2. EIS ana

4.2.1. NyquFig. 6 pre

vated carbo1 M H2SO4 asection poinresistance otance in theSince two teelectrolyte,Therefore, t

ischarging processes at the constant current (30 C-rate) and the determi-f ohmic drops with different charging voltages for (a) Organic electrolyte,

vs. 2.4 V and (b) Aqueous electrolyte, up to 0.2 vs. 0.6 V, respectively.

yquist plots for cells in 1 M H2SO4 and 1 M Et4NBF4/PC electrolytes, respec-easurement was performed at the applied voltage of 5 mV, with the

cy range from 10 mHz to 100 kHz.

ower resistance. The semi-circle present at high frequenciesciated with the interfacial resistance between electrode and1.6 cm2

f an electrode 0.1713 g0.012g

surface area(activated carbon powder) 2000 (100) m2g1

ctrolyte shows some distortion from the ideal CV shapedue to the decomposition of the electrolyte, it clearly

the organic electrolyte did not have any distortion upe specic capacitance for a single electrode was mea-

CV measurements, which was about 108 Fg-1 in thetrolyte and 134 Fg-1 in the aqueous electrolyte, respec-der to clarify the absence of Faradaic processes of redoxrther CV measurements with different scan rates wereas described in Fig. 4. The parallelogram-like CV curvesained in various scan rates, which is a major character-Faradaic process in an EDLC. This result indicates that,ed cells, there was less pesudocapacitance caused byuction/oxidation or functional groups on the surface ofes.s were then subjected to the galvanostatic charge-st to evaluate their capacitive behaviors and equivalenttances (ESR or self-discharge) by measuring the IRious charging voltages, as suggested in the literatureFor this purpose, the data from charging/dischargingnts at constant current loads were analyzed. The cellsed from 0 V to different rated voltages to investigateal inuence on ESR. As a result, the measured seriess calculated as

(8)

V is the initial voltage (ohmic) drop at the beginning of process, and I is constant charging/discharging cur-erall internal resistance in a cell was represented by theSR values. As shown in Fig. 5, the organic electrolyteshows a higher voltage drop than aqueous electrolytelso, for the same electrolyte, the ohmic drop decreased

ging voltage increased. This difference is much largeranic electrolyte than the aqueous electrolyte. This is

aqueous electrolyte has a much higher conductancec electrolyte [46]. The corresponding ohmic drop andalculated according to Eq. (8) were collected in Table 3.

current response of the organic electrolyte is largelythe applied potential differential and shows an increasece and a decrease in ohmic drop with voltages. Less-hanges were observed in the aqueous electrolyte. Thist both capacitance and internal resistance are depend-roperties of the electrolyte, such as its conductance andity.

lysis of two electrolytes

ist plotssents the Nyquist plot for two cells with identical acti-n electrodes immersed in two different electrolytes:nd Et4NBF4 in propylene carbonate (PC). The rst inter-t on the real axis at the highest frequency shows a series

Fig. 5. Dnation oup to 1.2

Fig. 6. Ntively. Mfrequen

to the lis assof cells (RS) that generally originates from solution resis- electrolyte, separator and external circuit resistances.sted systems have the same components except for the

RS is mainly attributed to the resistance of electrolytes.he higher conductivity of the aqueous electrolyte leads

electrolyte.ous, displayat its interfa slope of 4sion pheno The organic electrolyte data, as compared to the aque-ed a larger semi-circle, indicating a higher resistanceacial layer. At medium frequencies, a straight line with5 appears and this impedance reects the ion diffu-mena in the porous structure. Subsequently, both cells


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

*This current value corresponds to 30 C-rate (1/30 hour) when discharging from the maximum voltage of 2.7 V for the organic electrolyte and 1.0 V for the aqueous electrolyte,respectively.

behave like a pure EDLC capacitor which is characterized by thevertical line at low frequencies.

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

capacitance as functions of the frequency. In Fig. 7 (a), three dis-tinguishable resistances, which are independent of frequency, existon both curves and can be correlated to individual resistive compo-nents (R) dened in Section 2. Specically, the resistance at the highfrequency range shows mainly the value of RS while the Faradaicleakage or charge transfer resistance from bulk electrolytes (Rbulk)appears at the medium frequency range between 10 Hz and 1 kHz.The low frequency range between 10 mHz and 1 Hz includes Rintcaused by interfacial processes, and represents the summation of

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 suf-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 insufcient ion transport, andthe major contribution changes to partial capacitance from bulkelectrolytes 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 aFig. 7. Bode polts of (a) the real impedance and (b) the real capacitance vs. the frequency for cells with aqueous and organic electrolytes.


Fig. 8. SimulaNyquist plots (

lower capathe greater occurs in bfusion (driv(driven by twas observin Fig. 7 (a))the organicclosely assoresults in a

4.3. Simulapotential de

The meapared withcircuit modmeasured (aqueous antal data cloand high frusing the mthe extractein Table 4. (Fig. 7), thea reasonablsimulation inant paramtested cellstics of ohmicapacitancein agreemeCads is arounrespectivelycapacitanceexhibits lowues of capacand ion radorganic eleclayer thicknous electrolwith the ththe lower cfusion impeelectrolytesto diffusion

easured (dots) and simulated (lines) EIS impedances for different applied with (a) Organic electrolyte, (b) Aqueous electrolyte, respectively. The

an enlarged view at high frequencies.

d 4.3 ) than one (2.1 ) of the aqueous electrolyte with a conductivity.rder to further characterize the resistance and capacitanceency on the applied voltage level, additional EIS measure-

was performed for voltage levels at 0.2 and 0.6 V on aqueouslytes, and at 1.2 and 2.4 V on organic electrolytes, respec-The applied voltages were respected to reect the relativeial differential at electrode-electrolyte interface. Fig. 9 showsquist plot for two electrolytes obtained at different voltage

At the low voltage with the decreased DC potential acrosserfacial double layer, the more right-shifted vertical line in

frequency region was shown and the larger semi-circle wasted, which means the overall resistance increases at doubleted (curves) impedances, Zreal and Zimag, in comparison with measureddots) for both aqueous and organic electrolytes.

citance throughout the entire frequency range, due toenergy barrier against its ion transport. This transportoth the bulk solution and diffusion layer as ionic dif-en by the concentration gradient) and ionic migrationhe electric eld). In this study the relevant impedanceed at the low frequency range from 1 Hz to 100 Hz (see, which conrms the diffusion dominant impedance for

electrolyte. Meanwhile, the ion transport impedance isciated with the double-layer formation process, whichless value of Cdl (see Fig. 7 (b)).

tions with an equivalent circuit and predictedpendency

sured EIS data from Nyquist and Bode plots were com- simulated parameters obtained from the equivalentel which is given in Fig. 2 (c). Fig. 8 describes thesymbols) and simulated (lines) impedance spectra ford organic electrolytes in Nyquist plots. The experimen-sely matches the model predicted data in both lowequency regions, which was unsuccessfully achievedodels shown in Fig. 2 (a). Using the equivalent circuit,d parameters for different electrolytes are summarizedIn comparison with measured data from Bode plots

simulated values for resistance and capacitance showe consistency with the measured ones. In addition, thisindicates that Rint can be considered as the most dom-eter in determining the operating ohmic resistance of. This means Rint can be used to study the characteris-c leakage current or internal resistance of EDLC cells. For

Fig. 9. Mvoltagesinsert is

(arounhigher

In odependmentselectrotively. potentthe Nylevels.the intthe lowpresen values, the model predicted, Cbulk of tens of microfarad,nt with experimental values. The summation of CH andd 640 mF in aqueous and 540 mF in organic electrolytes,. These values are close to the measured double layer, Cdl, shown in Fig. 7. Meanwhile, the organic electrolyteer CH and Cads compared to the aqueous one. These val-itance can be considered in terms of types of electrolyteius. According to equation (1), larger sized ions of thetrolyte possess lower Cads and CH because its Helmholtzess, d, of closest ions approach are larger than the aque-ytes one, leading to less capacitance. This result agreeseory and experiments reported by Grahame [35]. Also,onductivity of organic electrolytes exhibits higher dif-dance (ZW), which corresponds to the fact that organic

have the less ion movement and larger energy barrieral processes, resulting in the larger diffusion impedance

layer interfato larger leaacteristics oCCD measuESR. The difrequency wagreementswhile to nothe higher cthis effect ithe organicpotential chsimulation,equivalent in Tables 5able resistace. That is, the higher resistance at low potential causeskage current. This result was in agreement with char-f the current response from various applied voltages inrements, introducing the differences of ohmic drop orfferences in capacitance and resistance as function ofere described in Fig. 10, which again shows excellent

between measured and simulated data. It is worth-te that larger potential led to the lower resistance andapacitance over the whole frequency range. In addition,s more signicant in the organic electrolyte, indicating

electrolyte showed a larger dependency on the appliedange when compared to the aqueous electrolyte. For

the measured impedance spectra were tted by ancircuit and the simulated parameters are summarized

and 6. Similar to experimental EIS results, the notice-nce changes were observed. More details, compared to


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 Ssbulk 8.55E-01 8.69E-01Cbulk 16 17 FRbulk 2.67 2.45 ohmQW 3.16E-01 3.51E-01 Ss(1/2)B 4.85 3.15 s1/2

ZW 3.16 2.85 ohmQH 6.83E-01 4.78E-01 SsH 9.69E-01 8.97E-01CH 346 281 mFRint 1.93 0.279 ohmQads 1.61E-02 1.22E-01 Ssads 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 Ssbulk 7.94E-01 8.07E-01Cbulk 3.9 3.6 FRbulk 13.2 9.79 ohmQW 9.67E-02 8.33E-01 Ss(1/2)B 6.14 1.11 s1/2

ZW 10.34 1.2 ohmQH 9.59E-02 5.45E-02 SsH 4.56E-01 5.09E-01CH 121 25 mFRint 38 24.2 ohmQads 5.47E-02 3.05E-02 Ssads 8.58E-01 6.27E-01Cads 109 262 mF


Fig. 11. Impeddrop for differtrolyte, respec

other resistfacial resistincreased. Afer and kinHelmholtz electron train a smallewhile the adis reduced. reactions antial. Accordlayers, the tial as descconditions, to the overtrolytes, buseen in the (see Table 5more affectdeviation o

In ordeimpedance rent leakageobtained fromeasuremelated by simthe equivalthan other

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 between

deling and CCD measurement.

scuss

mauivalas dres on anSecoinfors. Throcesa. Ims of eing apacmpedllel ve btion f elet thee deonspoteful tly coEIS mo

4.4. Di

Twothe eqeling wstructudiffusilayer. ingful devicebulk pEIS datextentin formlayer cburg iin paraCads haadsorptivity oaccounthat thto demor the be usetypicalance from EIS modeling, ESR from the CCD measurement, and ohmicent applied voltages with (a) Organic electrolyte, (b) Aqeuous elec-tively.

ances (RS and Rbulk), it can be clearly seen that the inter-ance (Rint) is signicantly reduced when the potentials discussed before, Rint is associated with charge trans-etics of adsorbed ions in the formation of outer/innerlayers. Therefore, the higher potential leads to morensfer and ions adsorption at the interfacial layer, resultsr Rint. Also, the Helmholtz capacitance (CH) decreasessorption (Cads) increases, and the diffusion impedanceThis is mainly caused by the acceleration of adsorptiond diffusion rate caused by a larger differential poten-ing to the Gouy-Chapman model of diffusion doublecapacitance is proportional to the differential poten-ribed in equation (3). Consequently, at high potentialadsorption and diffusion capacitances contribute moreall capacitance. This tendency is similar for both elec-t it is seen in Table 6 that larger difference in ZW areorganic electrolyte when compared to the aqueous one), which means the diffusion of organic electrolyte ised by the potential differences resulting in the largerf ZW.r to validate the equivalent circuit model, thesecharacteristics were correlated with distributed cur-

or ESR in practical cells. In Fig. 11, the total impedancem the simulation is compared with the ESR from CCDnts. From equation (7), the total impedance was calcu-ulating each resistor and capacitor at 10 mHz. Althoughent resistance from EIS measurements is usually lower

measurement techniques [29], this value gives an

electrolyteselements pdensity andmainly dom

5. Conclus

This papinvestigatewith porouThe characnamely, aqstudied by athe impedathe validitythis new ciaqueous anmodel provoccurring wview of thetion, the EIproposed eEIS and CCthis circuitdependent

Acknowled

The autport of OnCanada (APof Canada (ion based on model prediction

jor considerations were made in the development ofent circuit model for an EDLC. First, the circuit mod-eveloped based on theoretical descriptions of ELDC

and effects of electrochemical reactions coupled withd adsorption phenomena in the electrochemical doublendly, this circuit was designed to provide the mean-mation on each physical process in practical EDLCe dominant resistive elements in both interfacial andses have been found by improving the tness to theportantly, the interfacial resistance (Rint) describes thelectron transfer reactions and kinetic of adsorbed ionsthe double layer. For capacitive elements, the doubleitance (Cdl) is represented by a combination of War-ance, W, and the compact Helmholtz capacitor, CH,with adsorption capacitor, Cads. The values of ZW andeen analyzed to understand the diffusion behavior andprocess which depends on the ions sizes and conduc-ctrolytes. Also, the bulk capacitance, Cbulk, takes into

bulk processes for a practical EDLC cell. It was foundned parameters in the proposed circuit are criticaltrate their characteristics, such as internal resistancential-dependency. Therefore, the proposed circuit cano characterize the EDLC-typed capacitors which aremposed of porous carbon-based electrodes with ionic. Furthermore, the simulated impedances of resistiverovides informative values to predict the energy/power

thermal behavior of EDLCs, because these factors areinated by internal resistances [47].

ion

er presents an improved equivalent circuit model to the electrochemical and dynamic behaviors of EDLCss carbon-based electrodes using different electrolytes.teristics of EDLC cells with two types of electrolytes,ueous 1 M H2SO4 and organic 1 M Et4NBF4/PC, werenalyzing CV and CCD measurements. At the same time,nce behaviors of these EDLCs were utilized to evaluate

of circuit modeling. The simulation results showed thatrcuit model was able to characterize EDLCs with bothd organic electrolytes. Moreover, the proposed circuitided a reasonable interpretation on physical processesithin the EDLC cell, through introducing a more clariedir electro-chemical and transport phenomena. In addi-S analysis on the potential dependency supported thelements in the model and the ESR correlation betweenD measurements was derived. It was suggested that

model is able to simulate sufciently the potential-characteristics of double layer capacitors.

gments

hors would like to acknowledge the nancial sup-tario Research Fund (ORF), Automotive PartnershipC), Natural Sciences and Engineering Research CouncilNSERC) and General Motors (GM).


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Development of an equivalent circuit model for electrochemical double layer capacitors (EDLCs) with distinct electrolytes1 Introduction2 Circuit model development2.1 Electrochemical double-layer capacitance at the double layer interface region2.1.1 Helmholtz (CH) and diffusion (Cdiff) capacitance2.1.2 Adsorption capacitance (Cads)

2.2 Resistance at double layer interface region (Rint)2.2.1 Charge transfer resistor (Rct)2.2.2 Adsorption resistor (Rads)

2.3 Bulk solution impedance

3 Experimental4 Results and discussion4.1 Electrochemical characteristics, cyclic voltammetry and charge-discharge plots4.2 EIS analysis of two electrolytes4.2.1 Nyquist plots4.2.2 Bode plots

4.3 Simulations with an equivalent circuit and predicted potential dependency4.4 Discussion based on model prediction

5 ConclusionAcknowledgmentsReferences

Equivalent Circuit Paper

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