Impedance Study on Estimating Electrochemical Mechanisms in

a Polymer Electrolyte Fuel Cell During Gradual Water

Accumulation

Samuel Cruz-Manzo1*, Ulises Cano-Castillo2, Paul Greenwood3

1School of Engineering, University of Lincoln, Lincolnshire, LN6 7TS, United Kingdom

2Instituto Nacional de Electricidad y Energias Limpias, Cuernavaca, Morelos, 62490, Mexico

3Abastecedora Electrica Tehuacan, Engineering Division, Tehuacan, Puebla, 75700, Mexico

[*]Corresponding author: s.cruz-manzo@hotmail.com

Abstract

In this study, the change of electrochemical parameters during the gradual water

accumulation of a polymer electrolyte fuel cell (PEFC) are estimated using electrochemical

impedance spectroscopy (EIS) measurements and an impedance model based on electrode

theory during a two-step oxygen reduction reaction (ORR). EIS measurements were carried

out in a 5 cm2 H2/O2 PEFC operated under a dead-ended configuration of the gas reactants

and during gradual accumulation of water. Kramers-Kronig evaluation demonstrated that the

EIS measurements comply with stability and linearity properties and the inductive loops

featured at low frequencies are attributed to electrochemical mechanisms within the PEFC

and not to instability during gradual water accumulation. The impedance model has been

reported in a previous study and simulates inductive loops at low frequencies which are

attributed to platinum oxide formation during the ORR. The estimated parameters obtained

from this EIS-modelling analysis can provide an insight into the decrease in PEFC

performance during flooding conditions. A further qualitative analysis considering the effect

of long-term water accumulation on the oxygen-reduction charge transfer resistance is

discussed. It is possible to have an insight into the physical mechanisms of the PEFC by

combining different experimental techniques and fundamental theory in a complimentary

manner.

Keywords: Dead-Ended Testing Configuration, Electrochemical Impedance Spectroscopy

(EIS), Oxygen Reduction Charge Transfer Resistance, Polymer Electrolyte Fuel Cell (PEFC),

Water Accumulation.

1 Introduction

Polymer electrolyte fuel cells (PEFCs) are promising candidates as a future source of power

for stationary, mobile and consumer electronic applications. The water management during

PEFC operation is a challenge to overcome as either a dehydration or a flooding (water

accumulation) condition reduces the performance of the PEFC and could yield irreversible

degradation mechanisms. Several approaches have been used to avoid gradual water

accumulation during PEFC operation such as high air stoichiometry at the cathode, hydrogen

recirculation at the anode, and water purge at the cathode. Electrochemical impedance

spectroscopy (EIS) is an in-situ experimental technique in which an ac signal is superimposed

onto the DC current or cell voltage. The resulting ac load opposition or impedance is

commonly represented in a Nyquist plot and can represent the response of the

electrochemical mechanisms of the PEFC at different frequencies. Studies in the literature

have been focused on the diagnosis and study of the PEFC during flooding conditions using

EIS [1-5]. An extensive literature review on flooding issues in PEFCs carried out by Li et al.

[6] attributes the reduction in PEFC performance to oxygen starvation and not to other

mechanisms such as the growth of platinum oxide which can have an irreversible impact in

the long-term PEFC operation under an excess of water accumulation. In a previous study

[7], the gradual flooding of a 5 cm2 H2/O2 PEFC was analysed through EIS measurements and

electrical circuits. A Randles circuit [8] and a transmission line circuit [9] were applied to the

EIS measurements to follow the change of the estimated parameters from the electrical

circuits during accumulation of water in the PEFC. However, neither the Randles circuit nor

the transmission line circuit could extract information from the EIS measurements with

positive imaginary components at low frequencies. EIS measurements with positive

imaginary components at low frequencies are known as inductive loops [10]. A literature

review on inductive loops of EIS measurements in PEFCs has been carried out by Pivac and

Barbir [11]. Inductive loops have been attributed to side reactions with intermediate species

[3,12], carbon monoxide poisoning [13], and water transport characteristics [14,15]. The

diameter of the impedance spectrum in the Nyquist plot has been related to the sum of charge

transfer resistance and mass transport resistance [8]. However, the estimation of the charge

transfer resistance and mass transport resistance from the diameter of the impedance

spectrum could be incorrect if EIS measurements with positive imaginary components are

present in the Nyquist plot. These measurements shrink or deform the end of the impedance

spectrum and make the interpretation of the electrochemical mechanisms of the PEFC

through a visual inspection of the Nyquist plot difficult [16]. The correct interpretation of the

electrochemical mechanisms within the PEFC can be achieved through an impedance model

derived from fundamental PEFC electrochemistry [17]. In this study, EIS measurements are

carried out during gradual water accumulation of a 5 cm2 H2/O2 PEFC operated under a dead-

ended configuration and are analysed using an impedance model [18] based on

electrochemical theory considering intermediate reactions during the oxygen reduction

reaction (ORR). The impedance model considers hydrogen peroxide and platinum oxide

formation during the ORR and has been validated within EIS measurements carried out in a

PEFC stack operated at optimal conditions (neither flooding nor drying conditions).

Furthermore, in this study, the change of parameters related to the charge transfer process

during the ORR, hydrogen peroxide and platinum oxide formation, and oxygen transport

mechanism are estimated through EIS measurements during gradual accumulation of water in

a 5 cm2 PEFC and also the impedance model reported in a previous study [18]. In addition,

based on the estimated electrochemical mechanisms during gradual water accumulation, a

qualitative analysis to study the effect of water accumulation and growth of platinum

oxidation on the charge transfer process during the ORR during long-term PEFC operation is

carried out. This impedance analysis could assist and provide boundary conditions to other

theoretical methodologies e.g. 1-D PEFC model [19] to study the effect of water

accumulation on electrochemical mechanisms across the thickness of the different layers

comprising the PEFC.

2 Experimental

2.1 Polarisation Curves

A 5 cm2 H2/O2 PEFC operated under a dead-ended configuration of both reactant gases was

considered for the EIS tests. The membrane electrode assembly (MEA) was constructed by

applying an electrocatalyst layer (~18 μm), onto a treated commercial membrane DuPont™

Nafion® 117. The PEFC was tested at room temperature. The gases supplied were dry and

the pressure of both gases was 103421 Pa. To demonstrate the reduction in performance of

the PEFC during gradual accumulation of water, polarisation (V-I) curves were constructed

in sequence by variation of the cell voltage and measurement of the current response, as

shown in figure 1. The sequence of the V-I curves started by purging the cathode side after

completing each polarisation curve until reproducibility of the V-I curves was achieved. Once

polarisation curves considering water purge can be repeated, thereafter two polarisation

curves without water purge were constructed in sequence, as shown in figure 1. More detailed

information about the construction of the polarisation curves and the purging process for the

PEFC operated under dead-ended conditions can be found in the previous study [7]. Curve A

represents a polarisation curve constructed with prior water purge. Curves B and C represent

polarisation curves constructed in sequence after completing curve A without purging. The

reduction in performance of the PEFC during accumulation of water is clearly demonstrated

in figure 1.

2.2 EIS Measurements

Strictly speaking, a dead-ended configuration will change the performance of the PEFC with

time, and EIS measurements carried out under this condition would not be consistent with the

frequency response of steady systems. The steady-state condition under a dead-ended

configuration could only endure during a limited frame of time and this steady-state lapse

will depend on operating conditions (current demand, pressure, temperature) and the structure

of the PEFC (MEA, gas channel, gas diffusion layer). Kramers-Kronig (K-K) transformations

can be a resourceful tool to evaluate EIS measurements carried out under a steady and linear

system [20,21]. Potentiostatic EIS measurements with a two-electrode configuration were

carried out in sequence at different cell voltage. The tests were performed using a Solartron

1287 electrochemical interface and a Solartron 1260 frequency response analyser. Water

purge was attained before carrying out the EIS measurements in sequence at different DC cell

voltage. The a.c. amplitude superimposed onto the DC cell voltage was 10 mV. The

frequency scan was considered from 100 kHz down to the frequency limit of 1 Hz to reduce

the experimental time and comply with (K-K) transformations. The dead-ended condition

allowed a simple test configuration without the need to implement a more sophisticated

experimental set-up to control the gas flow rate stoichiometry during the oscillating response

of the PEFC attributed to the a.c. perturbation. This is very important to consider for the

validation and application of the impedance model within EIS measurements and will be

discussed later. The polarisation curves shown in figure 1 demonstrate the reduction of PEFC

performance during water accumulation. However, the measured current during the

potentiostatic EIS measurements may not agree with the current measured in the polarisation

curves A, B, and C shown in figure 1 for a given cell voltage. This can be attributed to the

initial potentiostatic (cell voltage) condition considered between EIS and the V-I tests during

PEFC dead-ended conditions; for instance, the initial cell voltage considered for the sequence

of EIS measurements is 0.81 V as shown in figure 2 and for the sequence of V-I tests the

initial cell voltage considered is Open Circuit Voltage. Therefore, the amount of water

present in the PEFC under potentiostatic conditions may be different during EIS and V-I

tests. The difference in initial potentiostatic condition between EIS and V-I tests may change

the conductivity of the polymer electrolyte membrane (PEM) and catalyst layer (CL) at

different water concentration. The sequence of potentiostatic EIS measurements is shown in

figure 2. The total amount of time to complete the first EIS test was 54.8 s at 0.81 V and the

total sequence of EIS tests was completed in 756 s.

The EIS measurements shown in figure 3(a) correspond to the sequence of tests shown in

figure 2 from t=0 to t=331 s. The EIS measurements shown in figure 3(b) corresponds to the

sequence of tests from 332 to 595 s, as shown in figure 2. The EIS measurements shown in

figure 3(c) represent the tests carried out from 596 to 756 s. Low-water condition is related to

the set of measurements shown in figure 3(a). Medium-water condition has related to the

measurements shown in figure 3(b), and high-water condition to measurements shown in

figure 3(c). The EIS measurements present data with positive imaginary component Z’’ at

high frequencies. This is attributed to the inductance of the cables of the measurement system

[16]. The inductance of the cables was prominent in the EIS measurements at frequencies

higher than 8 kHz. The effect of the inductance of the cables on EIS measurements of PEFCs

masks the EIS measurements featuring a 45 degree straight-line at the high frequency region

attributed to the ionic resistance in the CLs [16]. The total Ohmic resistance of the PEFC has

been commonly represented where the imaginary component Z’’ of the EIS measurements

crosses the real axis Z’ of the Nyquist plot at high frequencies [22]. Figure 3(a) shows that

the Ohmic resistance represented in real component Z’ of the EIS measurements at 8 kHz

decreases with decreasing cell voltage. The decrease in Ohmic resistance is related to an

increase in water generation from the ORR and due to water accumulation attributed to the

dead-ended testing configuration. An increase in water concentration yields an increase in

ionic conductivity in the PEM and CLs. EIS measurements represented in figure 3(a)

demonstrates higher Ohmic resistance than the EIS measurements represented in figure 3(b)

and figure 3(c). It can also be shown that there is a small variation in Ohmic resistance in the

EIS measurements for medium-water and high-water conditions in figure 3(b) and figure 3(c)

respectively. It seems that the water accumulation in the PEFC during EIS measurements for

cases at medium-water and high-water conditions yields water saturation in the PEM. This

can be demonstrated in the small difference between Ohmic resistance between the EIS

measurements represented in figure 3(b) and figure 3(c) respectively. It is worth mentioning

that the Ohmic resistance also accounts for the ionic resistance in CLs and electron resistance

in gas diffusion layers (GDLs) and gas channels [22]. A reduction in the semicircle with

decreasing cell voltage is observed in the EIS measurements. The reduction in spectra with

decreasing cell voltage can mainly be attributed to an increase in the driving force for the

interfacial oxygen-reduction process [23]. The EIS measurements shown in figure 3 present

measurements with positive imaginary components Z’’ at low frequencies. As discussed

previously in the introduction, this feature also known as inductive loops has been attributed

to intermediate mechanisms or side reactions (e.g. hydrogen peroxide, platinum oxide) during

the ORR. The EIS measurements related to the inductive loop should converge at a real value

(imaginary component Z’’ equal to zero) as the frequency is reduced to zero. The value of

EIS measurements as frequency is reduced to zero is known as the DC polarisation resistance

and should be the same as the polarisation resistance calculated from the slope of the

polarisation curve at a defined current and voltage [24].

The PEFC operated under a dead-ended configuration of both reactant gases allowed the

gradual increase of the accumulation of water. It is possible to use a different experimental

strategy to increase the accumulation of water in the PEFC such as feeding reactant gases at

low stoichiometry. Maranzana et al. [25] reported that a bias between the DC polarisation

resistances calculated from the slope of the polarisation curve and from the low frequency

limit in EIS measurements is significant when testing a PEFC at low oxygen stoichiometry.

Similar results have been reported by Chandesris et al. [26]. This discrepancy between DC

polarisation resistance estimated from EIS and estimated from a polarisation curve is a

consequence of the amplification of oxygen concentration with increasing a.c. current

amplitude during the oscillating current response. Maranzana et al. [25] concluded that the

bias could be avoided by adapting the air flow rate to the oscillating current to keep the

oxygen stoichiometry constant in time when carrying out EIS. The oxygen stoichiometry

during EIS measurements carried out in a PEFC under dead-ended configuration is constant

in time S=1, and the oscillating oxygen concentration is in phase with the oscillating current.

Therefore, no difference between DC polarisation resistance from the polarisation curve and

from EIS is expected. This is a very important feature to consider for the application of the

impedance model within the EIS measurements. This will be demonstrated in the model

validation section. A K-K evaluation should also demonstrate whether or not the inductive

loops are related to electrochemical mechanisms of the PEFC.

2.3 Kramers-Kroing Analysis

The validity of EIS measurements of PEFCs have to be evaluated before an attempt is made

to interpret the electrochemical mechanisms represented in the complex-impedance plot using

equivalent electrical circuits or physics-based impedance models. This evaluation can be

carried out by data transformation (Z’ real component to Z’’ imaginary component and vice

versa) of EIS measurements using K-K relations. K-K relations are mathematical

transformations [20,21] that can be applied to electrochemical systems whose frequency

response is linear, causal and stable, such as the frequency response of a PEFC. Boukamp

[27] reported that it is possible to evaluate K-K by fitting the Voigt R-C model into EIS

measurements. If the EIS data cannot be well approximated by the Voigt model shown in

figure 4 containing a reasonable number of R-C pairs, therefore the data are not

transformable and do not represent the physical processes of the electrochemical system

studied.

An analysis of K-K to evaluate correctness of EIS measurements in the PEFC during gradual

water accumulation has been carrried out using ZView software (Scribner Associates Inc.).

The Voigt R-C model shown in figure 4 was constructed in ZView software considering four

R-C pairs. More details about the application of K-K in EIS measurements using ZView

software can be found elsewhere [28]. A disagreement between experimental and K-K

transformed data for frequencies higher than 2.5 kHz was present. The disagrament is

attributed to the inductive effect of the measurement cables (EIS measurements with positive

imaginary components) on the high frequency region of the impedance spectrum. As

previously mentioned the inductive effect of the cables deform the high frequency region of

the impedance spectrum between 2.5 kHz and 8 kHz . By considering only EIS

measurements from 2.5 kHz to 1 Hz during the K-K evaluation, it is possible to obtain a

correct data transformation, as shown in figure 5. EIS measurements with positive imaginary

components or inductive loops at low frequencies have been reported to represent

electrochemical processes in the PEFCs (e.g. intermediate reactions during the oxygen

reduction reaction) and have been reported to comply with K-K transformations [10]. Figure

5 also demonstrates that it is possible to achieve K-K transformation in EIS measurements of

the PEFC with positive imaginary components Z’’ at low frequencies. Therefore, the

inductive loops are related to electrochemical mechanisms and not to instability during

gradual water accumulation. The impedance model would allow the estimation of the

electrochemical mechanisms in the EIS measurements. It was not possible to obtain a

successful K-K transformation for the EIS measurements at cell voltage lower than 0.64

Volts and high-water conditions (Figure 3c). The increase in water accumulated and the water

produced during the ORR with increasing current yield instability during PEFC operation.

The instability during PEFC operation can be attributed to a poor water balance between

electroosmotic drag from anode to cathode and back-diffusion water mechanisms from

cathode to anode.

2.4 DC Polarisation Resistance

The resulting EIS measurements during gradual water accumulation in the PEFC featured

inductive loops at low frequencies. Inductive loops have not been experimentally validated at

a low frequency range (e.g. 1 μHz), because it is not practical to wait such a long time to

carry out EIS measurements under such a frequency range. An impedance model would

simulate EIS measurements at a low frequency e.g. 1 μHz to correlate the DC polarisation

resistance from EIS measurements and from the slope of the polarisation curve [9]. In

addition, an impedance model could give an insight into the phenomena which contribute to

the formation of the inductive loops and overall impedance spectrum during an excess of

water concentration in the PEFC. To estimate the DC polarisation resistance, polarisation

curves were constructed from the measured current during potentiostatic EIS measurements.

Figure 6 shows the estimation of the DC polarisation resistance from the slope of the

polarisation curve at 0.61 V constructed from potentiostatic EIS measurements (figure 3a) at

low-water conditions.

3 Results and Discussion

3.1 Impedance Model

It is well known that oxygen transport limitations in the GDL and cathode catalyst layer

(CCL) due to an increase in water concentration reduce the performance of the PEFC [6,29].

During increase in water concentration other mechanisms which could cause low

performance and degradation in the PEFC may arise e.g. platinum oxidation PtO [30] and

hydrogen peroxide formation H2O2 [10]. In a previous study [18], an impedance model

considering kinetics of intermediate reactions during the ORR was developed. The model

initially considered four-electron process during the ORR and the reaction for PtO formation

was considered as well. However, it was demonstrated that a better prediction of the

inductive loops at low frequency could be achieved by deriving an impedance model

considering two-step ORR for the formation of H2O2 and PtO. Further details about the

derivation of the impedance model can be found in the previous study [18]. The model

considered charge transfer mechanisms, double layer capacitance and oxygen transport

limitations during the ORR. In addition, the model considered hydrogen peroxide H2O2 and

platinum oxide PtO formation during the ORR which are commonly represented as inductive

loops at the lowest frequencies in EIS measurements [10]. The impedance model of the PEFC

is represented as:

ZFC ,CH 2O 2,PtO=Rohm+Za+Z cH 2 O2 , PtO (1)

where Rohm represents the total ohmic resistance of the PEM, bipolar plates, GDLs and CLs,

the second term on the right-hand side of Eq. (1) represents the anode impedance:

Za= Ra1+ j ω RaCa

(2)

Ra is the charge transfer resistance during the hydrogen oxidation reaction (HOR),Ca is the

double-layer capacitance, ω is the angular frequency and j is the imaginary component.

The cathodic side of the impedance model mainly considers the electrochemical mechanisms

that take place in the CCL, as the physical mechanisms within the adjacent layers have an

influence on the CCL performance. The third term on the right-hand side in Eq. (1) represents

the cathode impedance as:

Z c H2 O 2 ,PtO=[ 1

1RO2

+ZW+

1RH2 O2

+ A φH 2 O2+

1( τPtO j ω+1 ) RPtO

+Y ( j ω) P ] (3)

with

RO2=

(1−γeq , H 2O 2 ,ss ) (1−γeq , PtO, ss )i0 ,O 2

bO2exp (−bO 2

ηO 2 ,ss ) (1−γ H 2 O2 ,ss ) (1−γPtO ,ss ) (4)

A φH 2 O2= 1

(τ H 2 O2j ω+1) R φH 2 O2

(5)

τ PtO=L

RPtO= nF λ

iPt , f , ss+iPt ,b ,ss (6)

RO2 is the charge transfer resistance during the oxygen reduction process with i0 ,O2

as the

exchange current density, γ PtO is the fractional surface coverage of platinum oxide, γ H2 O2 is

the fractional surface coverage of hydrogen peroxide, and bO2 is the inverse Tafel slope; ZW is

the Warburg impedance to represent oxygen transport limitations in the frequency domain

from the GDL-CCL interface to the catalytic active sites [31] and is a function of oxygen

transport resistance RW and oxygen diffusion time constant TW; RH 2O 2 is the charge transfer

resistance during H2O2 formation; τ H 2 O2 is the time constant during H2O2 formation; R φH 2 O2 is

a resistance associated with H2O2 formation and is a function of charge transfer resistances

RO2 and RH 2O 2

, and Warburg impedance ZW ; τ PtO is the time constant during PtO formation;

RPtO is a resistance associated to PtO formation; Y and P are parameters related to a constant

phase element (CPE) to correct the nonhomogeneous distribution of charge in the CCL. A

detailed description and derivation of the parameters shown in Eq. (3) can be found in a

previous study [18]. Eq. (1) can be represented through an equivalent electrical circuit as

shown in figure 7. An inductor element Lc, connected in series with the total Ohmic

resistance and attributed to the inductance of the measurement system, has been considered to

reproduce the EIS measurements with positive imaginary components at high frequencies.

3.2 Model Application

Available software (e.g. ZView, ZMAN etc.) allows the construction of equivalent electrical

circuits and fitting with EIS measurements. In Eq. (1) there are some parameters that can be

estimated through a graphical interpretation of the complex plot and from theoretical relations

reported in the literature. The Ohmic resistance Rohm accounting for ohmic loses in the PEM,

GDL, and bipolar plate [32] can be estimated from the high frequency limit of the real part Z’

of the impedance spectrum. The charge transfer resistance RO2 for the oxygen-reduction

process can be estimated from the relation proposed by Ciureanu and Roberge [33] for the

double layer capacitance as:

CdlP = Y

( Rohm−1 +RO2

−1 )1−P (7)

and also as reported by Hsu [34]

Cdl=Y (2π f C )P−1 (8)

noting that fC is the characteristic frequency at which the negative imaginary part of the

impedance reaches its minimum value. In addition, the CCL oxygen diffusion time constant

TW in Eq. (1) can be fixed at 3 ms as reported by Springer et al. [35] for EIS spectra featuring

a single semicircle. This allows the reduction of the number of parameters to be fitted in the

measured EIS spectra. Eq. (1) is applied to the EIS measurements carried out in the PEFC

during gradual water accumulation. The parameter related to H2O2 formation A φH 2 O2 is an

analytical parameter and a frequency dependant parameter, therefore it cannot be represented

through conventional electrical components such as a resistor, inductor, and capacitor from

available software. First the equivalent circuit shown in figure 7 without the parameter

A φH 2 O2 related to H2O2 formation was constructed in ZView software and fitted to the EIS

measurements, as shown in figure 8. Also, as previously mentioned, parameters estimated

through a graphical interpretation of the complex plot and from theoretical relations reported

in the literature allowed the reduction of fitted parameters to the EIS measurements.

Thereafter, the analytical parameter A φH 2 O2 was implemented into the circuit shown in figure

8(a) as represented through the circuit shown in figure 7. The parameter A φH 2 O2 was fitted to

the EIS measurements using a Graphic User Interface (GUI) developed in Matlab and

considering the values of the parameters previously estimated through ZView software and

graphical interpretation. The use of the GUI to adjust parameters of an impedance model

within EIS measurements has been reported in a previous study [31]. The DC polarisation

resistance was calculated from the slope of the polarisation curve [24] shown in figure 6 and,

represented in EIS measurements as the frequency is reduced (black triangle), was taken as a

reference to simulate the inductive loop at low frequencies. The simulated frequency was

reduced to 1 μHz to converge the inductive loop with the DC polarisation resistance

represented by the black triangle. The DC polarisation resistance shown in figure 9 at the

frequency of 1 μHz corresponds to the DC polarisation resistance calculated from the

polarisation curve shown in figure 6.

The parameter Ra accounted for the charge transfer resistance during the HOR resulted in an

average value with an order of magnitude of 10-3 for all the EIS measurements. Therefore, in

this study the anode contribution in the EIS measurements is considered negligible assuming

no contaminants during the HOR such as carbon monoxide and assuming that reactant

transport losses are only attributable on the cathode side (no hydrogen starvation).

The least squares fitting method was used in order to find the best-fit between the simulated

data from the model shown in figure 7 and the measured data. A good quality fit is obtained

when the sum of the deviations squared (least square error) between the simulated and

measured impedance data has a minimum value. Orazem and Tribollet [36] reported in their

study that the Bode modulus and real part component of the impedance plots are relatively

insensitive to the quality of the fit of a model to impedance data. The imaginary component

of the impedance and Bode phase angle plots are modestly sensitive to fit quality. The sum of

the squared residuals for experimental and simulated impedance response (imaginary and real

data) was calculated. For example, the sum of squared residuals between experimental and

simulated imaginary components Z’’ resulted in a value < 0.02. The application of Eq. (1)

with EIS measurements has already been demonstrated in the previous study [18], where an

analysis of EIS measurements in an open-cathode H2/air PEFC stack was carried out. From

figure 9, it has been demonstrated that by combining different experimental techniques and

fundamental theory in a complimentary manner, it is possible to have an insight into the

mechanisms that yield a reduction in performance of the PEFC.

3.3 Analysis at Low-Water Accumulation

Figure 10 shows a comparison between experimental and simulated EIS at different cell

voltage considering low-water condition. The charge transfer resistanceRO2 during the

oxygen-reduction process and for the hydrogen peroxide formation RH 2O 2 decrease with

decreasing cell voltage or increasing current, as shown in Table 1. The charge transfer

resistance RH 2O 2for H2O2 formation is directly proportional to the charge transfer resistance

RO2 for the oxygen-reduction process, as it is considered that H2O2 formation is an

intermediate mechanism during the two-step ORR. An increase in oxygen transport

limitations during the ORR can arise from an excess of water concentration which hinders the

diffusion of reactants to reach the active sites in the CCL. Table 1 shows an increase in

oxygen transport resistance RW with decreasing cell voltage. The oxygen transport resistance

represents the opposition for the diffusion of oxygen from the CCL-GDL interface to the

active sites in the CCL. It has been reported that a second semicircle at low frequencies of the

Nyquist plot is attributable to oxygen transport limitations when EIS measurements are

carried out in a H2/air PEFC [8]. Figure 10 shows the semicircle that represents the charge

transfer during the ORR is overlapped with the semicircle representing oxygen transport

limitations. This overlapping effect is attributed to a low value of the oxygen diffusion time

constant TW [37].

The considered time constant to diffuse oxygen through the CCL expressed in the Warburg

impedance ZW from the cathode impedance Eq. (3), is defined by T W=δ2/ Deff where δ

represents the characteristic length scale of the diffusive process in the CCL, in which for this

specific case is considered to be the thickness of the CCL and Deff represents the effective

diffusion coefficient for oxygen transport in the CCL. Springer et al. [35] concluded that it is

not possible to visualize in the Nyquist plot the semicircle representing the charge transfer

effect and the semicircle representing oxygen transport effect in PEFC EIS measurements

with oxygen diffusion time constants of 10-4, 10-3, 10-2 orders of magnitude. A low value of

diffusion time constant TW when pure oxygen is supplied to the PEFC can be attributed to an

increase in the effective diffusion constant Deff for oxygen transport through the CCL. The

diffusivity of O2 diluted in N2 at 80 oC has been reported to be 2.8 x 10-5 m2 s-1, and the

oxygen diffusivity in He is 1.13 x 10-4 m2 s-1 under the same conditions [38]. So, when the

background gas in the cathode is switched to N2 from He, an increase in oxygen diffusion

time constant TW would be expected. Under H2/air PEFC condition the separation between

charge transfer resistance and oxygen transport resistance in EIS measurements is apparent

[39]. EIS measurements shown in figure 10 present inductive loops (positive imaginary

components at low frequencies). The impedance model simulates inductive loops considering

that both hydrogen peroxide formation and platinum oxide formation mechanisms are present

during the ORR. The resistance associated with platinum oxide formation RPtO decreases with

decreasing cell voltage, as shown in Table 1. As reported in the literature, an increase in

water concentration yields an increase of the rate of platinum oxide formation [30,40].

3.4 Analysis at Medium and Higher-Water Accumulation

A comparison between EIS measurements for the cases at low-water and medium-water

condition at the same cell voltage of 0.5 V is shown in figure 11(a). The Ohmic resistance

decreases for the case at medium-water condition compared with the case at low-water

condition which is attributed to an improvement of ionic conductivity through the PEM and

CL when increasing water accumulation. Table 1 shows a lower charge transfer resistance

RO2 for the oxygen reduction process for medium-water condition when comparing it with the

low-water condition at 0.5 V. The catalyst layer comprises Pt/C/ionomer agglomerates. Each

agglomerate is considered to be surrounded by a film of water. At high water concentration,

the film of water that surrounds the agglomerate increases and consequently improves

catalyst utilisation in the CL. This also yields an increase in H2O2 formation in the medium-

water condition at 0.5 V which is represented by a reduction in the charge transfer resistance

RH 2O 2 during H2O2 formation. The increase in water concentration at medium-water condition

at 0.5 V also yields an increase in oxygen transport resistance RW, with respect to the low-

water condition at 0.5 V as shown in Table 1. The reduction in charge transfer resistance

demonstrates that water accumulation has not reached a fully flooded condition in which all

the pores in the CCL are water-filled and the catalyst utilisation is reduced [41].

The rate of platinum oxidation is increased with increasing water concentration. This can be

observed through the reduction of the resistance RPtO accounting for Pt oxide formation for

medium-water condition compared with low-water condition at 0.5 V, as shown in Table 1.

The time constant τPtO for the platinum oxide formation is higher than the time constant TW for

oxygen diffusion to reach the active sites in the CCL. Figure 11(b) shows a comparison

between EIS measurements and simulated data for high-water condition at 0.64 V. The EIS

measurements at high-water condition presents the lowest resistance for platinum oxide

formation RPtO and the highest resistance for oxygen transport RW with respect to all the cases

for low-water and medium-water conditions, as shown in Table 1.

Although water concentration induces the formation of platinum oxide formation, the results

from Table 1, comparing the time constants for oxygen diffusion TW and platinum oxide

formation τPtO respectively, demonstrate that platinum oxide formation is a slow rate

mechanism compared to the oxygen transport mechanisms for the ORR and is commonly

represented at the lowest frequencies of EIS measurements. Reduction of catalytic active sites

attributed to platinum degradation mechanisms is apparent during long-term catalyst layer

operation [42]. The estimated time constant for platinum oxide formation with increasing

water concentration could justify the fact that a loss in catalyst utilisation attributed to

platinum oxide formation [42] is not reflected in the change of the charge transfer resistance

RO2 for the oxygen-reduction process from the EIS results.

3.5 Qualitative Analysis of Long-Term Water Accumulation

The relation between charge transfer resistance RO2 during the oxygen-reduction process and

platinum oxide formation resistance RPtO with increasing water accumulation should be

studied in detail through long-term PEFC operation and through the analysis of EIS

measurements at higher degrees of water accumulation. However, in this study EIS

measurements carried out at a higher degree of water accumulation resulted in scattered data.

The resulting scattered data demonstrated inconsistency with Kramers-Kronig analysis for

steady systems [43]. This can be attributed to an instability during PEFC operation due to a

poor water balance between electroosmotic and back diffusion water mechanisms. Therefore,

a qualitative analysis to study the effect of long-term water accumulation on the oxygen-

reduction charge transfer resistance is carried out.

3.5.1 Estimation of Water Accumulation

The amount of water accumulated during the sequence of potentiostatic measurements can be

estimated by calculating the amount of charge accumulated during the sequence of tests. One

sequence of potentiostatic tests defined as Ns=1 corresponds to the profile of measured

current shown in figure 12 from t = 0 to t = 756 s. Note that the current measured shown in

figure 12 corresponds to the sequence of defined cell voltage as shown in figure 2. The

amount of water accumulated can be calculated through the Faraday’s law:

g H2O=18 Q2F

(9)

where the constant 18 represents the number of grams of water in one mole of water, Q is the

accumulated charge in Coulombs (area under the curve) calculated from figure 12, and F is

the Faraday constant. The amount of water accumulated during the sequence of tests from

t=0 to t=756 s shown in figure 12 and calculated through Eq. (9) resulted in 2.33x10-3g.

3.5.2 Considerations for Long-Term CCL Performance Analysis

To analyse the long-term effect of water accumulation and platinum oxide formation on

charge transfer resistance during the ORR, the profile of potentiostatic tests shown in figure

12 is repeated 200 times, Ns=200. The following assumptions are considered for the long-

term water accumulation analysis:

Eikerling [41] defined an optimal wetting-state in the CCL for improving catalyst utilisation

when the primary pores are completely water-filled and the secondary pores for reactant

transport are water-free. The long-term CCL performance analysis in this study takes into

account the optimal wetting-state condition in which the water accumulation increases from a

low-water condition (primary pores are not water-filled) up to a wetting-state condition

(primary pores are completely water-filled) in the CCL during the sequence of tests Ns=1, 2,

…,200.

It is assumed that a control strategy in the water management of the PEFC system has been

implemented to maintain only wetting-state conditions and avoid fully flooded conditions in

which all the pores in the CCL are water-filled. Taking into account these assumptions an

increase of catalyst utilisation through the formation of new active sites (platinum/nafion-

water interface) is expected. In addition, it is assumed that gas concentration in the active

sites of the CCL is always present as the secondary pores for reactant transport are water-free.

The water adsorption and condensation in the CL as a function of vapour activity was

reported by Mashio et. al. [44]. The maximum water adsorption and condensation in the

primary pore of the CL was reported to be 300x10-3 mass of water per unit mass of carbon (gw

gc-1). Marquis and Coppens [45] reported the carbon density in the CL to be 21.5 g cm-3.

Considering the water adsoption reported by Mashio et. al. [44], the carbon density reported

by Marquis and Coopens [45] and the total volume of the CCL (thickness 18 μm, and active

area 5 cm2) as a first approximation, it is possible to estimate the amount of water required to

achieve a wetting-state in the CCL (only primary pores are completely water-filled). If the

amount of water required for a wetting-state is divided by the water accumulated and

calculated during the first sequence of potentiostatic tests 2.33 x 10-3 g at Ns=1; then, the

profile of potentistatic tests shown in figure 12 have to be repeated 25 times Ns=25 to

achieve a wetting-state in the CCL.

Considering the aforementioned assumptions, it is possible to define a relation for the water

concentration for a wetting-state in the CCL, number of sequence of tests, platinum oxide

resistance and charge transfer resistance RO2 as such:

RO2 , Ns=

RPtO , Ns

ln (1−γ H2 O2 , Ns)cH 2 O, Ns

cH 2 Omax , Ns=25

(10)

where the subscript Ns represents the sequence of test to consider from 1 to 200, RO2,Ns is the

charge transfer resistance during the oxygen-reduction process, RPtO,Ns is the platinum

oxidation resistance, ln (1−γH 2 O2 , Ns)=f (i ,b ,c H 2O ,Ns ) represents a nondimensional parameter

considering fractional surface coverage of hydrogen peroxide and kinetics of the ORR and

can be derived from the Butler-Volmer equation [12], and CH2O,Ns represents the water

concentration estimated after completing each sequence of tests Ns=1,2,3…200, CH2Omax,Ns=25

represents the water concentration at wetting-state in the CCL calculated from the

aforementioned assumptions when Ns=25. The ratio CH2O,Ns/ CH2Omax,Ns=25 is modelled as a first

order system in which the ratio between concentration increases from a minimum value and

becomes equal to 1 for N S ≥ 25.Note that Eq. (10) is analogous to the equation for charge

transfer resistance RO2 expressed in Eq. (4) with ln (1−γ H 2 O2 , Ns )=f (i ,b ,c H 2O ,Ns )relating

kinetics of the two-step ORR and fractional surface coverage of hydrogen peroxide, and

RPtO

c H2O ,Ns

c H 2Omax , Ns=25

= f (γ PtO, cH 2O) relating the fractional surface of platinum oxidation formation.

3.5.3 Effect of Long-Term Water Accumulation on CCL Performance

Figure 13 shows the considered decrease of platinum oxidation formation resistance RPtO

during the sequence of tests for Ns=1,2,3…200. The platinum oxidation resistance decreases

in a logarithmic manner based on the Tafel equation for electrode kinetic theory and the non-

linear response of the PEFC as water accumulation in the CCL increases. The first value of

the platinum oxidation resistance at Ns=1 reflects the last value of RPtO shown in Table 1,

1.8845 Ω. The considered nondimensional parameter ln (1−γ H 2 O2 , Ns )=f (i ,b ,c H 2O ,Ns ) related

to the fractional surface coverage of hydrogen peroxide and kinetics of the ORR also

decreases in a logarithmic manner following the theory of Tafel slope and the non-linear

response of the PEFC. The responses of the parameters shown in figure 13 are substituted

into Eq. (10) to estimate the charge transfer resistance RO2during accumulation of water. In

addition, the ratio CH2O,Ns/ CH2Omax,Ns=25 modelled as a first order system is considered in Eq.

(10).

The estimated transfer resistance RO2 during the ORR after each sequence of tests Ns=1,2,3…

200 calculated from Eq. (10) is shown in figure 14. It can be observed that the initial value of

the charge transfer resistance at Ns=1 corresponds to the last value of charge transfer

resistance RO2 from Table 1, 0.3425 Ω. There is a reduction of the charge transfer resistance

which can be related to the formation of active sites or new metal/solution interface for the

ORR as water concentration in the CCL increases. Thereafter, an increase in charge transfer

resistance is observed at NS>25. The increase in charge transfer resistance could be attributed

to the fact that the rate of platinum oxidation dominates over the ORR as there is a reduction

in the generation of more active sites in the CCL for the ORR when the wetting-state in the

CCL is achieved. The growth of platinum oxidation continues reducing CCL utilisation.

The increase of charge transfer resistance RO2 for Ns>25 as shown in figure 14 is related to

the slow rate of platinum oxidation formation as reported in the literature [42]. If the

sequence of tests is repeated for Ns=1000, Eq. (10) predicts that charge transfer resistance

will be higher than the one calculated after the first sequence of tests Ns=1 and would be

represented in Table 1 as: 0.3425 Ω for Ns=1 and 0.4858 Ω for Ns=1000.

Figure 15 shows that by considering the amount of water accumulation 2.33 x 10-3g in the

CCL calculated from figure 12 from t=0 to t=756 s at Ns=1 and increasing the CCL

geometric area, the maximum amount of water accumulated to achieve the wetting-state in

the CCL increases as well, Ns=25 for A=5 cm2 and Ns=38, 65, and 80 for A > 5 cm2;

therefore, the calculated charge transfer resistance RO2from Eq. (10) for A > 5 cm2 at Ns=1

increases, as shown in figure 15. This can be related to a reduction of the active sites

attributed to less metal/water interface at Ns=1 with increasing CCL geometric area.

Considering the case at Ns=80 which reflects the highest CCL geometric area shown in

figure 15, the value of the charge transfer resistance will be higher with 1.6966 Ω at Ns=1900

than the value 1.5792 Ω at Ns=1.

The long-term water accumulation condition may have a greater effect on high-power PEFC

stacks (kW) where high temperature improves water generation. Xu et al. [30] reported that

the rate of platinum oxidation increased significantly with increasing relative humidity in the

gases, and at high temperature both water and oxygen equally contribute to platinum

oxidation.

This EIS-modelling study could assist other experimental or theoretical methodologies for the

analysis of CCL degradation during platinum oxide formation and PEFC long-term operation.

A better experimental strategy to control the amount of water and to validate the effect of

high water accumulation on long-term PEFC performance through EIS measurements will be

developed in future work.

4 Conclusions

This study demonstrates that it is possible to attain an insight into the phenomenological

processes that yield low performance in the PEFC by combining the experimental EIS

technique with the fundamental electrochemical theory. A 5 cm2 H2/O2 PEFC was operated

under dead-ended configuration in both gases to reduce performance during an increase of

water accumulation. Potentiostatic EIS measurements were carried out at different degrees of

water accumulation in the PEFC. An impedance model reported in a previous study and

based on electrode theory during a two-step ORR was fitted to the resulting EIS

measurements. The dead-ended condition allowed a simple test configuration without the

need to implement a more sophisticated experimental set-up to validate and apply the

impedance model within EIS measurements. A graphical interpretation of the complex-

impedance plot and parameters and theoretical relations reported in the literature allowed the

reduction of parameters from the model to be fitted within EIS measurements. The

electrochemical parameters represented in the model and estimated from the EIS

measurements were compared at different cell voltage and with increasing water

accumulation. The results demonstrated that with increasing water accumulation, the short-

term reduction in PEFC performance is attributed to oxygen transport limitations. A

qualitative analysis demonstrated that platinum oxide formation could yield long-term CCL

degradation and reduction in PEFC performance. This EIS-modelling work could potentially

provide a valuable insight to correlate the amount of water accumulated with platinum oxide

formation in the CL. This impedance analysis could also assist and provide boundary

conditions (e.g. oxygen concentration at the CCL-GDL interface) to other theoretical

methodologies to study the effect of water accumulation on electrochemical mechanisms

across the thickness of the different layers (GDL, BP) comprising the PEFC.

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Figures.

Figure 1. Polarisation curves constructed during gradual accumulation of water. Curve A is constructed with prior water purge. Curves B and C are constructed in sequence after completing curve A without purging.

Figure 2. Sequence of potentiostatic EIS measurements.

Figure 3. EIS measurements at different water accumulation conditions, a) Low-water, b) medium-water, c) high-water.

Figure 4. Equivalent circuit (Voigt circuit) model for K-K transformation in EIS measurements.

Figure 5. K-K Analysis in ZView software using Voigt circuit.

Figure 6. DC polarisation resistance calculated from a polarisation curve constructed from potentiostatic EIS measurements (figure 3a) at low-water condition.

Figure 7. Equivalent electrical circuit considered for EIS analysis of PEFC during gradual water accumulation.

Figure 8. Fitting in ZView, a) circuit from figure 7 with no A φH 2 O2 term, b) fitting result for low-water condition (figure 3a) at 0.61 V.

Figure 9. Experimental and simulated spectrum for low-water condition (figure 3a) at 0.61 V.

Figure 10. Comparison between measured and simulated EIS spectra at different cell voltage and at low-water accumulation.

Figure 11. Comparison between experimental and simulated data with different degrees of water accumulated, a) Low-water (LW) and Medium-water (M-W), b) Medium-water (MW) and High-water (HW).

Figure 12. Current measured during potentiostatic measurements.

Figure 13. Parameters implemented into Eq. (10).

Figure 14. Estimated charge transfer resistance RO2during the ORR after long-term PEFC operation under water accumulation.

Figure 15. Effect of water concentration for wetting-state on charge transfer resistance.

Table 1. Parameters of Eq. (1) extracted from EIS measured data

Low-water accumulation Medium-water

accumulation

High-water

accumulation

Parameter 0.76 V 0.71 V 0.66 V 0.61 V 0.5 V 0.6 V 0.5 V 0.64 V

Rohm / Ω 0.253 0.24 0.228 0.213 0.19 0.117 0.111 0.118

RO2/ Ω 0.8324 0.6 0.42 0.3299 0.2056 0.292 0.1625 0.3425

Y / sP Ω-1 0.0048 0.0061 0.0041 0.0033 0.0014 0.0034 0.0022 0.0048

P dimensionless 0.8877 0.86 0.87 0.8836 0.9677 0.8977 0.9332 0.8532

RW / Ω 0.2449 0.32 0.36 0.4524 0.505 0.5336 0.6012 1.1612

TW / ms 3 3 3 3 3 3 3 3

RH 2O 2/ Ω 3.6165 2.08 1.64 1.1485 0.7373 0.943 0.4998 0.6198

RPtO / Ω 7.7526 6.2581 5.5381 4.6186 3.8639 4.1039 2.0445 1.8845

τ PtO / ms 40.1 20.2 20 20.1 40.2 41.1 21.9 21.9