1

Towards Understanding Surface Chemistry and Electrochemistry of La0.1Sr0.9TiO3-α

based Solid Oxide Fuel Cell Anodes

Vitaliy Yurkiv*(1,2), Guillaume Constantin (3,4), Aitor Hornes (1), Angela Gondolini

(5), Elisa Mercadelli (5), Alessandra Sanson (5), Laurent Dessemond (3,4), Rémi Costa

(1)

(1) German Aerospace Centre (DLR), Institute of Technical Thermodynamics,

Pfaffenwaldring 38-40, 70569 Stuttgart, Germany

(2) Institute of Thermodynamics and Thermal Engineering (ITW), Universität Stuttgart,

Pfaffenwaldring 6, 70550 Stuttgart, Germany

(3) Université Grenoble Alpes, Laboratoire d’Electrochimie et de Physico-Chimie des

Matériaux et des Interfaces, F-38000 Grenoble, France

(4) CNRS, Laboratoire d’Electrochimie et de Physico-Chimie des Matériaux et des Interfaces,

F-38000 Grenoble, France

(5) Institute of Science and Technology for Ceramics (ISTEC) of the National Research

Council (CNR), Via Granarolo 64, I-48018 Faenza (RA), Italy

*Corresponding author: E-mail: Vitaliy.Yurkiv@dlr.de, Phone: +49 (0) 711 6862-8044, Fax:

+49 (0) 711 6862-747

2

Keywords: Solid oxide fuel cell (SOFC), perovskite anode, impedance spectra, reaction

mechanism, elementary kinetic modeling

3

ABSTRACT

In the present contribution, we combine modeling and experimental study of electrochemical

hydrogen oxidation at an alternative perovskite based mixed-conducting SOFC anode. Com-

posite electrodes were produced by conventional wet ceramic processing (screen printing –

spraying) and sintering on YSZ electrolytes (La0.1Sr0.9TiO3-α-Ce1-xGdxO2-α | YSZ) with differ-

ent compositions and microstructure, and were electrochemically characterized using sym-

metrical button-cells configuration. An elementary kinetic model was developed and applied

to explore the performance of LST based SOFC anode. A detailed multi‐step heterogeneous

chemical and electrochemical reaction mechanism was established taking into account

transport of ions in all ionic phases, and gas transport in channel and porous media. It was

found that heterogeneous chemistry at LST surface has capacitive behavior that alters the im-

pedance spectra. In addition, surface charge-transfer reaction, which describes partial oxygen

ionization, caused impedance feature and is rate-limiting at high temperature. The gas

transport in the supply chamber (gas conversion) is significant only at moderate temperatures.

4

1. Introduction

Ni/YSZ composite materials have shown a tremendous success over the past years in ap-

plication as SOFC anodes. It is, however, well known that operation of those anodes upon

various fuels could cause different types of cell degradation [1]. Therefore, the replacement of

Ni cermet with alternative ceramic materials is essential for development of a long-term oper-

ating SOFC technology. One of the most promising candidates as alternative anode material is

perovskite ceramic oxides. In particular, SrTiO3 perovskite, partially substituted at A sites by

trivalent La3+ cations, possess high electronic conductivity, excellent mechanical robustness

and are resistant to many chemical poisons (e.g. carbon and sulfur) that affect conventional

Ni/YSZ cermet [2,3]. In addition, thermal expansion coefficient of lanthanum strontium titan-

ates perfectly matches the one of YSZ electrolyte. Although, LST materials are easily reduced

giving better electronic conductivity than their oxygen stoichiometric equivalents, they do not

exhibit good ionic conductivity. Therefore, LST is usually mixed with electrolyte materials

such as CGO or ScSZ.

In recent years, there was a tremendous increase of studies dedicated to the investigation

of LST-CGO|YSZ system. Most of them are however focused on structure determination

and/or mechanical stability of the materials [4–7], and therefore little is known about chemi-

cal and electrochemical mechanism of fuel oxidation. Périllat-Merceroz et al. [2] have inves-

tigated the properties of La0.33Sr0.67TiO3+δ and La0.23Ce0.1Sr0.67TiO3+δ anodes towards methane

reforming; concluding that ceria exsolution phenomena leads to a great enhancement of cata-

lytic activity. Similar conclusion has been made by Zhan et al. [8] who have investigated

La4Sr8Ti12O38-δ anodes in catalytic partial oxidation of methane. Other studies are focused

mainly on electrochemical testing of perovskite based SOFC anodes [9–11]. Nakamura et al.

[9] have shown based upon variety of impedance measurements that perovskite oxides an-

5

odes possess significant pseudocapacitances which is related to the variation of oxygen con-

tent. Miller et al. [10], on the other hand, have studied the effect of B-site doping on the struc-

ture and the electrochemical performance, and concluded that these anodes have very promis-

ing electrocatalytic activity, and therefore, the optimization of the microstructure may lead to

an improved anode performance.

The present work contributes to the understanding of the operating principles of perov-

skite based LST-CGO|YSZ SOFC anodes by implementing, parameterizing and validating a

quantitative reaction mechanism and a transport model, which is subsequently used to analyze

our own experimental electrochemical measurements. The present approach incorporates el-

ementary heterogeneous chemical and electrochemical charge-transfer reactions, multicom-

ponent porous-phase and channel-phase transport.

2. Button cell experiments

Figure 1 schematically depicts the experimental device together with the cell, used for the

modeling in the set-up used to record electrochemical impedance spectra and polarization

curves. The different symmetrical cells were produced by wet ceramic processing either by

suspension spraying or screen printing of different LST-CGO cermet anodes on YSZ pellets.

Cell fabrication

The different LST-CGO|YSZ symmetrical cells were produced by wet ceramic pro-

cessing and sintered in air at 1373 K for 5 hours using commercial powders (CerpoTech for

LST and Treibacher Industrie for CGO). The anode of the cell A was a 37 % porous compo-

site consisting of 50/50 vol-% La0.1Sr0.9TiO3 and Ce0.9Gd0.1O2-α with a thickness of 20 μm,

which was separated by a 1850 μm thicker YSZ electrolyte. The anode was deposited on both

6

sides of the YSZ pellets by suspension spraying method using an internal mixing nozzle cou-

pled with a 3D automated robot to spray an ethanol-based suspension.

The cell B was 15 μm thick 50/50 vol-% La0.1Sr0.9TiO3/Ce0.8Gd0.2O2-α 35 % porous anode

separated also by the same electrolyte as the cell A. The anode was fabricated by screen print-

ing: LST and CGO powders were mixed in terpineol with the proper amount of deflocculant,

pore former and binder to obtain a stable and homogeneous ink following the procedure re-

ported elsewhere [12]. The symmetrical cells were then successfully produced depositing the

ceramic ink onto each YSZ disc sides with an automatic screen printer. The SEM images of

the as obtained symmetrical cells A (a) and B (b) are shown in Fig. 2. Electrode porosity and

pore size were determined by the means of mercury porosimetry using Mercury Porosimeter

Pascal 140/240 set up (Thermo Fischer Scientific).

TPD/TPR measurements

Temperature-programmed desorption of H2O/O2 (TPD) and reduction (H2-TPR) experi-

ments on LST-CGO samples were performed under atmospheric flow conditions by means of

a dedicated device TPDRO 1100 (ThermoQuest). The reaction system, consisting of two con-

centric quartz reactors: the inner where material is placed and the outer to lead the reactive

gas into the former. The substrate temperature was measured using a type K thermocouple.

For the TPD experiments, samples were firstly outgassed at 673 K for 30 min using a stream

of dry He (20 mL·min‒1) in order to clean the sample surface of adsorbed byproducts, i.e. at-

mospheric H2O and/or CO2. Then, humidification of the samples took place by substitution of

the dry He flow with a wet He stream (5 mL·min‒1) achieved by means of a bubbler contain-

ing deionized water at room temperature for 1 h. After this, dry He was used again for purg-

ing the system for 30 min. H2-TPR experiments were carried out in the same device. In this

case, oxidized samples were pretreated at 773 K for 30 min using a pure oxygen flow (20

7

mL·min‒1) for cleaning their surface. Subsequently, a 5 vol-% H2 (Ar was used as inert) flow

was employed for the reaction.

Both experiments were carried out from room temperature up to 1273 K using a heating

ramp of 10 K·min‒1. Detailed description and results of TPD/TPR measurements will be re-

ported in our future work, since this paper focuses primarily on electrochemical testing and

modeling.

Cell electrochemical performance measurements

The electrochemical experiments were conducted in a furnace that maintains a required

uniform temperature ranging between 924 K and 1125 K. Impedance spectra measurements

were recorded for all temperatures with the voltage stimulus of 20 mV ranging between

5·10‒3 Hz and 2·104 Hz. Polarization curves were recorded in the same temperature range and

reported in terms of current density as a function of cell voltage.

All electrochemical measurements have been conducted with high flow rates of 50

mL·min‒1·cm‒2 using carefully controlled gas mixture of H2+3%H2O, thus, maintaining near-

ly uniform composition of the gasses along the investigated cell.

The more detailed description of experimental apparatus which was used for electro-

chemical characterization as well as methodology of measurements is given elsewhere [13].

Fine gold grid as current collector (680 mesh·cm‒2) were applied on both sides of the cells

prior to the electrochemical testing. Gold was chosen to avoid any catalytic contribution to the

oxidation of hydrogen. A mechanical pressure was applied on the grids to improve the electri-

cal contacts. The completed button cells have active diameter of app. 16 mm, which lead to an

active area of app. 2 cm2.

8

3. Modeling and simulation methodology

In this section, the models for detailed electrochemistry of mixed ionic/electronic con-

ducting electrodes and gas-phase transport in supply channel of the LST-CGO|YSZ button

symmetrical SOFC configuration are concisely described. The electrochemical models are

based on previously published electrochemical models [14,15] and consider the following

features:

• All chemical processes (thermal and electrochemical) are written as elementary reac-

tions. The rate of all processes are described by mass-action kinetic laws using mean-

field assumption [16].

• Charge-transfer is assumed to take place at the interface between at least two phases

(electrolyte/electrode and electrode/gas-phase).

• Reversibility of chemical processes is assured through thermodynamically consistent

properties for all participating species.

• Physically meaningful surface potential step and electric potentials rather than overpo-

tentials are used throughout the modeling.

3.1 Mixed conducting anode model

Since LST-CGO anode is a mixed ionic electronic conductor, we assumed that oxygen

oxidation proceeds via a bulk path in which oxygen first migrates from YSZ to the CGO

phase and then to LST surface. Subsequently, hydrogen is oxidized to water at the surface of

LST. Charge-transfer processes are driven by electric-potential difference at the interface be-

tween two or three adjacent phases. The electric properties of different phases are described

by a physically meaningful electric potential step instead of using an overpotential. Charge

transport and transfer depend upon spatial variation of potential within the electron conduct-

ing phase (e.g. LST) and ionic conducting phase (e.g. CGO in the anode and YSZ in the elec-

9

trolyte membrane). Thus, modeling of these processes severely depends upon the evaluation

of spatial variation in the electric potentials of each phase. In the current modeling frame-

work, the electric potential variation in the anode is governed by the following charge conser-

vation equation

( ) VV iiyy DLFLST2

LST

LSTCGO2

CGO

CGO +=

∂D∂

+

∂∂ φσ

τε

στε

, (1)

where, ɛ and τ represent porosity and tortuosity, respectively, of considered phase. σ ionic

conductivity of conducting phase which is temperature dependent [15]. The faradaic ( ViF ) and

double layer ( ViDL ) currents are calculated via Eqs. (2) and (3)

∑=CTR all

,VF ki

Vk szFAi , (2)

( )t

CAiV

∂D∂

=φint

DLVLST/CGODL

, (3)

where, z is number of electrons, F faradaic constant, VkA is the surface active area, kis , pro-

duction rate of reactions, VLST/CGOA is the interface area between LST and CGO phases and

intDLC is a double layer (DL) capacitance. The molar production rate for ith species resulting

from the Rth reaction is evaluated as

−= ∏∏

∈∈ r

j

f

j

Rj

vjr

Rj

vjfii ckckvs ´´´ , (4)

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here, iv is the stoichiometric coefficient, k is the reaction rate constant and c is the activity of

the participating species. The activity of the species is considered equal to the molar concen-

tration for gas-phase and to the surface coverage for the surface-adsorbed species. The for-

ward and reverse reaction rate constants are calculated according to following equations

−

−= ψβ

RTzF

RTEkk expexp

af0

ff , (5)

−−

D−= ψβ

RTzF

RTGkk R )1(expexp0

fr , (6)

where, ψ is equal to χ for surface charge transfer reaction and φD for interfacial CT reac-

tion. The electrostatic surface potential step χ is caused by the presence of the electrical DL

at LST surface, which is the difference between LST surface electrostatic potential and LST

bulk potential

surLST

bulkLST φφχ −= , (7)

where, surLSTφ is the electrostatic potential at the location of the adsorbed oxygen anions and

bulkLSTφ is the bulk LST electrostatic potential located just beyond the electrochemical double

layer. Since, we use mean field approximation, it is assumed that the oxygen anions are ho-

mogeneously distributed at the LST surface forming a simple plate capacitor, thus, χ is cal-

culated via

∑∈

−=mf,

zad

max |z|

Riiθχχ , (8)

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where, maxχ is the surface potential step for the fully covered with charge species surface and

is calculated by

surDL

LSTmax

||C

ezΓχ = , (9)

here, surDLC is the surface DL capacitance.

There are two types of electrical double layers which are characterized by two capaci-

tance values. The LST/gas-phase DL capacitance is assumed to be temperature-independent

and was determined by fitting the simulated impedance spectra to the electrochemical exper-

imental measurements. Based upon this fit, our model yields a DL capacitance of 79 F·m‒2

(farad per microscopic LST surface). Considering the fact that the surface DL represents the

so-called chemical capacitance, reflecting the variability of the oxygen stoichiometry on the

MIEC surface, the obtained value of 79 F·m‒2 is reasonable and stays in good agreement with

literature values of similar systems [14,17,18]. The LST-CGO interfacial DL capacitance is

assumed to be temperature-dependent. Based upon fit of impedance spectra, we obtain a value

of 2 F·m‒2 (farad per microscopic contact area between bulk LST and bulk CGO) at 1125 K.

3.2 Porous and channel phase gas transport

Reacting gas phase species transport through the porous phase of the anode is represented

by the coupled diffusive driven Stefan-Maxwell and pressure driven Darcy flux

( ) ∑∈

−=

∂∂

gSkeff

diffdiff

ij

ijjiig

DJXJX

yXc

, (10)

12

yp

μBcXJ g

ii ∂∂

=flow ,

(11)

with overall species conservation represented by the following equation

( ) ∑∈

+∂

∂−

∂∂

−=∂

∂

a

Vk

flowdiffg

Ski,k

iii sAy

Jy

JtXεc

. (12)

Details about the porous phase transport model, definition of the symbols and the computa-

tional implementation are given in Ref. [15].

In the SOFC button cell configuration used in the present study, gasses are supplied to the

anode via over-electrode gas supply volume represented by finite-gap stagnation point flow.

In this configuration, the gasses enter in the fuel chamber from an inlet perpendicular to the

anode surface; thus, stagnation surface is represented by the cell electrode. Although in stag-

nation flow reactors velocity distribution may be two-dimensional, we use one-dimensional

representation due to similarity reduction of the flow equations in the boundary layer region.

This makes computational simulation fast and it has the advantage of including the full cou-

pling of diffusion, convection and reactions. Figure 1 schematically illustrates flow conditions

of the present setup. The inlet provides a steady mass flow of gas species to the anode which

is different at the outlet due to species source or sink at the electrode surface. The species con-

tinuity equation is given by [19]

( ) ( )∑∈

+∂

∂−

∂

∂−=

∂∂

a

Vk

diff

Ski,k

iiyi sAy

Jy

YtY

ρυρ

, (13)

together with continuity and radial momentum equations

13

( )V

yty ρ

ρυρ 2−∂

∂−=

∂∂

, (14)

( ) ( )Λ−−

∂∂

∂∂

−∂

∂−=

∂∂ 2V

yV

yyV

tV y ρµ

ρυρ, (15)

The detailed explanation of the symbols and boundary conditions are given in [19].

3.3 Simulation methodology

Simulations were carried out using an in-house software package DENIS. All model

equations used in the present modeling and simulation work are thoroughly described else-

where [14,15]. Spatial derivatives are discretized using the finite-volume method and the re-

sulting differential-algebraic equation system is integrated using the semi-implicit extrapola-

tion solver LIMEX [20]. The absolute and relative solver tolerances during all calculations

were fixed at the values of 5·10–5 and 3·10–5, respectively. We solved both steady-state and

transient problems, which are required in order to model different phenomena, occurred dur-

ing SOFC characterization. Experimental electrochemical impedance spectra are simulated

using a potential step and current relaxation technique [21]. The impedance is obtained in the

frequency domain by a Fourier transformation of the resulting time-domain traces of current

and potential.

4. Chemistry and thermodynamics of LST-CGO phase

At room temperature, LST crystalized in the ABO3 cubic perovskite structure with the

lattice parameter of 0.39 nm, where titanium ions are six-fold coordinated by O2‒, whereas

each Sr2+ (or substituted La3+) ion is coordinated by twelve oxygen anions. The substitution of

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A site by La cations leads to the creation of oxygen rich defect regions [22]. However, after

heat treatment due to the anode preparation, variety of steps, kinks and distortions could be

created. The reactivity of all these surface morphological features differs, because some sites

can be more conductive to bonding adsorbed species than others (e.g. flat surface). Thus, the

attempt to model such surface at this high level of resolution is virtually impossible consider-

ing the current incomplete state of knowledge about atomic level structure and reactivity of

LST. For that reason, a relatively simple LST structure to model surface chemistry and elec-

trochemistry is adopted. The elementary cubic LST perovskite cell along the (111) plane has

5 atoms on the surface facing towards the gas phase. At this surface, only one oxygen atom of

the surface can create an oxygen vacancy or can absorb hydrogen atom to form an hydroxyl

group. Assuming that surface is clean and consists of such sites available to participate in

chemical reactions, this leads to surface site density of 6.7·1018 sites·m‒2 or 1.0·10‒5 mol·m‒2.

Figure 3 schematically illustrates the surface structure and adsorbed species of the LST mod-

eled in this study. The surface reaction chemistry uses two types of sites denoted as OLST and

LST. The first species (OLST) represents oxygen atom of the LST unit cell (the same as in the

bulk LST), whereas LST defines the surface oxygen vacancy. Both species have the same

position on the LST surface, so that they are located above the titanium atom. Since a free

strontium site (Sr) represents a surface level strontium atom, it could potentially be an adsorp-

tion site for the oxygen, thus species such as OSr and OHSr can certainly be present. Also, it

should be noted, that the position of the last surface oxygen (OSr) is quite different from the

position of the oxygen of LST bulk unit cell. Correspondingly, these two hydroxyl groups

have different chemical properties and therefore different thermodynamic and kinetic charac-

teristics.

The LST bulk density of 5.2 g·cm‒2 is taken from our own XRD measurements. The bulk

vacancy fraction is set by the doping level as 01.00V =X (corresponding to a concentration of

2·103 mol·m‒3) at atmospheric pressure in air and it does not depend on temperature.

15

Following the above described assumptions and definitions, we have developed hydrogen

oxidation mechanism over LST surface. The full mechanism, which includes heterogeneous

and electrochemical reactions, is listed in Table 3, and the thermodynamic data of all species

which form the basis for a thermodynamically consistent kinetic modeling is given in Table 2.

The mechanism contains four LST surface species (LST , −1LSTO , OLST and OHLST). The spe-

cies denoted as LST is taken as a reference species; therefore, enthalpy and entropy are set to

zero. In order to determine bulk oxygen standard-state chemical potential, which is directly

related to thermodynamic data of surface oxygen anions, the following procedure was per-

formed, the global oxygen reduction reaction 1/2O2 + ⋅⋅LST OV −2

LSTO at equilibrium, could

be described as follows

−

D−=

−

⋅⋅

⋅⋅

RTFE

RTG

Xp

XR 2expexp

1 0

V1/2O

V

LST O2

LST O , (16)

where, ⋅⋅LST OVX is the bulk oxygen vacancy fraction, p is the pressure, F faradaic constant, E is

the potential difference between anode and electrolyte, R is the universal gas constant and T is

the temperature. The Gibbs free energy ( 0GRD ) of the oxygen reduction reaction is described

as 0V

0,O

0O

0

LST O22O 2

1⋅⋅− −−=D µµµ gRG . Subsequently, by substituting this expression in Eq. 16, set-

ting thermodynamic data of oxygen vacancy to zero, and separating temperature dependent

and independent terms, the oxygen ion chemical potential can be expressed by the following

equation

16

−+−−+−=−

0

0

,2,2,22

1lnln

221

212 O

0O

0O

0O

V

V

XX

RpRsThFEggg

µ . (17)

Bearing in mind that chemical potential of the species is 000iii Tsh −=µ , the first two terms of

Eq. 17 could be assigned to the enthalpy of the oxygen species and expression in the brackets

corresponds to the entropy value. Thus, the derived enthalpy value of the oxygen anions is

0O2−h = ‒85.6 kJ·mol‒1 and entropy 0

O2−s = 139.1 J·K‒1·mol‒1. The enhancement of the LST sur-

face oxygen concentration may be reproduced by making enthalpy values of OLST slightly

lower than that of bulk, thus, a value of ‒89.1 kJ·mol‒1 was adopted. The latter value was also

determined to best reproduce the maintenance of sufficient oxygen concentration at LST sur-

face during electrochemical modeling. Using the above thermodynamic values as the basis,

temperature programmed desorption (TPD) measurements were modeled. Combining model-

ing and experimental study it was possible to derive, the reaction mechanism of hydrogen

oxidation on the surface of LST (Table 3). This includes three heterogeneous chemical reac-

tions (R1, R2 and R3). The adsorption of hydrogen gas (R1) from gas phase is assumed to be

dissociative with activation energy of 50 kJ·mol–1. The molecular water is not stable on the

surface and dissociates into two hydroxyl surface groups (R2). Water chemisorption occurs

by bonding a hydroxyl group of the water molecule to a cation site (OHSr) and transferring a

proton to a nearby oxygen atom (OHLST). As it is discussed above, the first hydroxyl group is

not stable and it is energetically favorable for the hydroxyl group to reposition over titanium

site, thus OHSr species is not stable and two equal hydroxyl groups are created in reaction R2.

Since the presence of additional oxygen at LST structure is favorable, the reaction R3 has a

significant energy barrier. This is also confirmed by TPD measurements. Figure 4 shows the

comparison between experimental (open dots) and simulation (line) TPD spectra. Fig. 4a rep-

resents water desorption which consists of two features at intermediate temperature (~500 K)

17

and at high temperature (~800 K). The intermediate temperature peak is assumed to originate

from physisorbed water and is not modeled. The high temperature water desorption is mod-

eled via reaction R2. Correspondingly, the high temperature oxygen desorption peak (Fig. 4b)

is evaluated using kinetic and thermodynamic parameters of the reaction R3. The intermediate

oxygen desorption peak (~600 K) originates from perovskite Ti4+ Ti3+ transition [23].

5. Electrochemical results

As it is described above, we use our own experimental measurements to explore perfor-

mance of alternative perovskite based anodes of the symmetrical SOFC. All experimental

data are compared to theoretically predicted results and further analyzed in order to evaluate

main performance limitation processes. Model geometrical and electrochemical parameters of

both cells A and B used in these simulations are summarized in Table 1. Geometrical parame-

ters of both cells together with specification of current collector mesh and gas supply volume

are taken from experiments. The microstructural parameters (i.e. surface specific area, porosi-

ty, etc.) and double layer characteristics of electrodes are evaluated by fitting them to electro-

chemical experimental measurements.

In this study, charge transfer reaction mechanism comprises partial oxygen ionization at LST

surface (reaction C2) followed by a complete oxidation with simultaneous incorporation into

CGO bulk (reaction C1). The mechanism is shown in Table 3 and corresponds to bulk path of

oxygen reduction/oxidation. The alternative scenario corresponding to surface path with the

active TPB is not considered here. Thermodynamic and kinetic data of these two charge-

transfer reactions are evaluated based upon electrochemical impedance measurements.

18

5.1 Electrochemical results: cell A

Fig. 5 shows the comparison between experimental and simulated electrochemical im-

pedance spectra (Bode plots) for various temperatures, at atmospheric pressure and open cir-

cuit potential. The corresponding Nyquist plots of the results shown in Fig. 5 are represented

in Fig. 6. For clarity reasons only two distinguished temperatures (924 K and 1125 K) are

shown. As it could be observed, there is a qualitative agreement between modeling and exper-

imental results concerning number of processes, magnitude of resistance and relaxation fre-

quencies over the complete investigated range of experimental conditions.

The electrochemical impedance spectra consist of several features. At high temperature

(1024 K – 1125 K), the spectra of the cell comprise a low-frequency feature with a maximum

between 0.7 Hz – 5 Hz and a high-frequency feature with a maximum in the kilohertz region

(~103 Hz). The low-frequency feature was assigned to charge-transfer at the anode surface.

The high-frequency part was attributed to electrochemical kinetics as well and in particular to

the resistance due to bulk charge-transfer reaction (reaction C1, Table 3). The further decrease

of temperature provokes appearance of an additional feature in the impedance spectra at lower

frequency. This feature could be already observed at temperature of 1024 K.

In order to further evaluate polarization characteristics of the LST-CGO|YSZ anodes, we

compare experimental and simulation results at different overpotentials. Figure 7 shows the

comparison between experimental and simulation results in H2-H2O system for different tem-

peratures and overpotentials in the form of Tafel plot (logarithm of current density as a func-

tion of overpotential). There are two distinguished regions in the Tafel plot, at the beginning

there is the significant increase of current density, which is followed up by relatively flat part.

At the beginning at OCV, the current density vanishes and due to the nature of Tafel plot its

value is not seen. At high overpotential, the simulation results show small deviation from ex-

19

perimental data, however, a good overall agreement indicates that chosen charge-transfer

chemistry is able to well represent the measurements.

5.1.1 Identification of physico-chemical processes

In order to identify all processes governing electrochemical behavior, we have performed

detailed impedance analysis using step by step model reduction. This is realized by systemati-

cally reducing the simulation results by electrochemistry and/or transport processes and as-

sessing the resulting impedance simulations. The comparison between full and a reduced

model is chosen at the temperature of 972 K, since at this temperature at least two processes

have similar resistance which makes it difficult to distinguish between them. The results of

model reduction study are shown in Fig. 8 as Bode (upper panel) and Nyquist (lower panel)

plots. The model was reduced in two steps by primarily assuming ideal gas supply over the

electrode surface and secondly setting the interfacial double layer capacitance to zero. When

gas transport in the gas supply chamber over the electrodes is assumed ideal (holding the gas

concentration at the outer boundary of the porous electrode constant to the gas chamber com-

position), no quantitative change in the impedance is observed. Thus, it can be concluded that

the gas supply to the electrode is sufficiently good and it does not cause any additional re-

sistance. As discussed above, there are two electrochemical double layers in the LST-CGO

anodes and they exist at two different interfaces (i.e. surface of LST and bulk LST/bulk

CGO). The first LST surface double layer is known as chemical capacitance and the second

interfacial double layer represents electrical capacitance. In order to evaluate the influence of

interfacial double layer, it can be set to zero which leads to disappearance of its corresponding

impedance feature, but its resistance will remain constant. This situation where interfacial

double layer capacitance is set to zero, is shown in Fig. 8 with dashed line. As can been seen,

the high frequency (HF) feature loses its capacitive properties, and therefore, apparently van-

20

ishes. Thus, the HF part was attributed to the resistance due to ion transfer reaction (reaction

C1, Table 3). The change in oxygen ion surface concentration provokes the formation of

chemical capacitance, and in the contrast to interfacial capacitance it cannot be set to zero.

Correspondingly, the surface charge-transport (reaction C2, Table 3) causes middle frequency

impedance feature. However, as can be seen in Fig. 8, there are still two contributions after

setting interfacial double layer to zero. This is further evaluated below. Also, it shall be noted

that electrolyte charge transport does not cause a whole ohmic resistance of 8 Ω·cm2, as de-

picted in Fig. 8b. Taking into account the thickness of electrolyte (925 μm), the model reveals

resistance due to oxygen ions transport of 5.1 Ω·cm2, which leads to leftover resistance of 2.9

Ω·cm2. The latter contribution to ohmic resistance was assigned to resistance due to contact-

ing and wires.

In order to further identify the middle and low frequency features, the following proce-

dure has been done. The hydrogen content has been systematically varied from 97 % down to

57 % with the partial pressure of H2O held fixed and being balanced by N2. This also provides

the more detailed understanding of the influence of different factors on fuel cell chemistry. As

shown in Fig. 9a, the decrease of hydrogen partial pressure leads to increase of both real and

imaginary parts of impedance at low frequency only. This indicates that surface chemistry has

capacitive behavior and plays a significant role in mixed conducting perovskite anodes. Thus,

the unchanged middle frequency feature can be assigned to surface charge-transfer reaction

C1. The other important characteristic of such anodes is the active surface area. Fig. 9b illus-

trates impedance simulation results varying this parameter. The results shown in Fig. 9b have

been obtained for initial fuel mixture (97 % H2, 3 % H2O) at the same temperature of 972 K.

While varying specific surface area both imaginary and real parts of impedance increase,

which directly reflects the strong dependency of surface charge-transfer and surface chemistry

on availability of active sites. This, again, indicates that surface heterogeneous reactions have

21

capacitive behavior and H2-H2O fuel is stored in the form of adsorbates at the surface of an-

ode, and it is represented by detailed surface chemistry.

5.2 Electrochemical results: cell B

The second set of data, which were modeled in the present work, describes the electro-

chemical results obtained based upon cell B. The cell parameters are listed in Table 1 and the

(electro-) chemical mechanism is kept the same as in the results described above (Tables 2

and 3).

Figure 10 illustrates the comparison between experimental and simulated impedance

spectra obtained for five different temperatures at OCV in the form of Bode plot. The Nyquist

plot of this data is shown in Fig. 11 and for clarity reason only two distinguished results for

temperature 1125 and 924 K are shown. We have obtained a qualitative agreement of the

model with experimental measurements over whole investigated range and similarly to the

previous results at least two distinguished processes could be observed. In addition, one more

impedance contribution at very low frequency (~0.01 Hz) and temperature of 924 K had ap-

peared.

In order to further identify the additional processes at very low frequency, the model re-

duction study similar to the one presented above has been done. First, we assumed ideal gas

supply over the electrodes, which lead to complete disappearance of the very low-frequency

peak, however, intermediate and high-frequency contributions remained unchanged (Fig. 12,

dashed line). This result clearly demonstrates that the low-frequency feature with a maximum

at ~0.01 Hz corresponds to resistance due to gas transport in the supply chamber. The further

reduction of the model, specifically, the setting interfacial double layer capacitance to zero,

provokes the vanishing of high frequency contribution, which corresponds to interfacial

22

charge-transfer (Fig. 12, dashed-dotted line). The remained resistance with the peak at fre-

quency of about 0.5 Hz is due to LST surface heterogeneous reactions as it was shown above.

The surface charge-transfer reaction C2 at this temperature is not visible, since it is over-

lapped by latter process.

It should be noted that all simulated curves were obtained based upon one single parame-

ters set. The main difference between cell A and cell B is the active surface area. In the case

of cell A, the active surface area reveals to be 1.1·105 m2/m3 and for cell B this area is reduced

to 4.6·104 m2/m3. This difference is mainly responsible for the increase of observable re-

sistance for cell B. Also, it should be noted that active surface area of both cells is relatively

small in comparison to conventional SOFC anodes, which greatly influences the overall sig-

nificant resistance of the cells. Such small active area could be caused by inhomogeneous

distribution of ionic conductor phase throughout LST anode, which correspondingly deter-

mines the availability of oxygen anions to heterogeneous surface reactions.

6. Summary and conclusions

We have performed the combined experimental and modeling study for evaluation of

LST-CGO|YSZ composite electrodes performance. Electrochemistry is modeled based on the

elementary kinetic description of (electro-)chemical reactions, and physically meaningful sur-

face potential and electric potential steps. Two types of double layers were taken into account,

that is, a surface DL and an interfacial DL. For the mass transport model, two scales were

taken into account: porous gas-phase diffusion in the electrode and gas-phase transport in the

gas supply chamber. The model was compared to electrochemical impedance measurements

that were carried out in a symmetrical button-cell experiment.

23

The detailed multistep (electro-)chemical mechanism has been derived and validated. It

was found that surface heterogeneous reactions provoke the appearances of impedance fea-

ture, i.e. it has capacitive behavior. In order to evaluate the influence of heterogeneous chem-

istry the thermodynamically consistent surface reaction mechanism has been derived. Two

steps oxygen charge-transfer mechanism was determined to best represent electrochemical

measurements of both cells. It should be noted, that there is certainly no guarantee of unique-

ness, however the derived mechanism delivers significant quantitative insight about the fun-

damental (electro-)chemical and transport processes responsible for cells behavior. However,

if more comprehensive electrochemical experiments will be available charge-transfer mecha-

nism over TPB might certainly be considered. Nevertheless, the built model based on elemen-

tary reaction pathways and surface potential step seems to provide a reasonable quantitative

representation of the measured polarization data over wide ranges of experimental conditions.

7. Acknowledgments

This work was funded by the European Union’s Seventh Framework Programme

(FP7/2007-2013) for the Fuel Cells and Hydrogen Joint Technology Initiative under grant

agreement n°303429. A.H. thanks the German Academic Exchange Service (DAAD) for a

DLR-DAAD (A/12/94095) grant under which his contribution to this work was done. V. Y.

acknowledges funding by the Initiative and Networking Fund of the Helmholtz Association.

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27

List of Tables

Table 1

Model parameters used for all simulations.

Table 2

Thermodynamic data (enthalpies and entropies) for surface and bulk species.

Table 3

Summary of the kinetics parameters for the LST-CGO|YSZ anode reactions. LST and CGO

surface site densities are 1.0·10–5 mol·m–2 and 1.1·10–5 mol·m–2, respectively. Symmetry fac-

tor of the charge-transfer reactions is set to 0.5. The parameters are: k0 pre-exponential factor,

Eact Arrhenius activation energy.

28

Parameter Value Reference

Symmetrical (half) cell A

Thickness of electrode, dLST-CGO 20 µm Experiment

Thickness of electrolyte, dYSZ 925 µm Experiment

Electrode area, Aelde 2 cm2 Experiment

Anode porosity, ε 0.37 Estimate

Anode tortuosity, τ 2 Estimate

Pore size, dP, c 1.0 µm Estimate

LST-CGO/gas surface specific area,

VCGO/GasLST−A

1.1·105 m2·m‒3 Fit

Surface site density, LSTΓ 1.0·10–5 mol·m–2 Estimate

Bulk density, LSTρ 5200 kg·m–3 Experiment

Ionic conductivity of anode bulk, anσ T/(1.4·107 K)· ( )TkBJ/ 65000e

S/m

Experiment and

[24,25]

LST-CGO surface specific area, VCGOLST−A 7.1·105 m2·m‒3 Fit

LST/gas phase DL capacitance, surDLC 79 F·m‒2 Fit

LST-CGO interfacial DL capacitance,

intDLC

2 F·m‒2 Fit

Symmetrical (half) cell B

29

Thickness of electrode, dLST-CGO 15 µm Experiment

Thickness of electrolyte, dYSZ 925 µm Experiment

Electrode area, Aelde 2 cm2 Experiment

Anode porosity, ε 0.35 Estimate

Anode tortuosity, τ 2 Estimate

Pore size, dP, c 0.5 µm Estimate

LST-CGO/gas surface specific area,

VCGO/GasLST−A

4.6·104 m2·m‒3 Fit

Surface site density, LSTΓ 1.0·10–5 mol·m–2 Estimate

Bulk density, LSTρ 5200 kg·m–3 Experiment

Ionic conductivity of anode bulk, anσ T/(1.4·107 K)· ( )TkBJ/ 78000e

S/m

Experiment and

[24,25]

LST-CGO surface specific area, VCGOLST−A 7.1·105 m2·m‒3 Fit

LST/gas phase DL capacitance, surDLC 79 F·m‒2 Fit

LST-CGO interfacial DL capacitance,

intDLC

1.1 F·m‒2 Fit

YSZ Electrolyte

Thickness, dYSZ 10 µm Experiment

Ionic conductivity of bulk YSZ, YSZσ T/(1.4·107K)· ( )TkBJ/ 90000e S/m [26,27]

Bulk density, YSZρ 6800 kg·m–3 [26,27]

30

Bulk vacancy/oxygen fraction 0.0401/0.9599 [26,27]

Current collector mesh

Thickness, dm 1.2·10‒4 m Experiment

Porosity, εm 0.4 Estimate

Tortuosity, τ m 2 Estimate

Pore size, dP, m 40 µm Experiment

Grid density 680 mesh·cm‒2 Experiment

Gas supply volume

Length, Dch 0.04 m Set up

Thickness, dch 1.0·10‒3 m Set up

Inflow velocity 50 mL·min‒1·cm‒2 Set up

Experimental conditions

Temperature, T 924 K – 1125 K Experiment

Pressure, p 1 atm Experiment

Gas Composition, X 97 % H2, 3 % H2O Experiment

31

Species, i hi (kJ·mol–1) si (J·K–1·mol–1) Ref.

LST-CGO phase

LST 0 0 reference species

OLST –89.1 139.1 TPD exp.

OHLST –199.0 0 TPD exp.

−1LSTO –114.0 139.1 Fit to electrochemical

results

×CGO OO –236.0 0 [26]

⋅⋅CGO OV 0 0 reference species

YSZ phase

×YSZ OO –236.0 0 [26]

⋅⋅YSZOV 0 0 reference species

32

No. Reaction k0 actE (kJ·mol–1) Ref.

LST-CGO phase R1 H2 + 2 OLST OHLST + OHLST 1.5·1014 cm2·mol–1·s–1 50.0 TPD

R2 H2O + OLST + �LST 2 OHLST 1.0·1018 cm2·mol–1·s–1 122.0 TPD

R3 OLST + OLST O2 + 2�LST 1.0·1022 cm2·mol–1·s–1 260.0 TPD

YSZ/CGO phase

R4 ×YSZ OO + ⋅⋅

CGO OV ×CGO OO + ⋅⋅

YSZOV 1.6·1022 cm2·mol–1·s–1 90.9 [28]

Charge-transfer reactions

C1 ×CGO OO + �LST

⋅⋅CGO OV + −1

LSTO + e‒ 4.9·1011 cm2·mol–1·s–1 129.0 Fit

C2 −1LSTO OLST + e‒

5.2·103 s–1 39.0 Fit

33

List of figures

Fig. 1. Schematic illustration of SOFC LST-CGO|YSZ symmetrical button cell together with

testing principles. Note that all structural details and scaling are exaggerated merely for illus-

tration purposes. See text for details.

Fig. 2. Scanning electron microscopy cross section image of the cell A (a) and cell B (b).

Fig. 3. Schematic illustration of structure of LST surface, bulk and chemical species that par-

ticipate in thermal and electrochemical reactions.

Fig. 4. Comparison between experimental and simulated TPD spectra of a LST-CGO|YSZ

anode exposed to H2O for 1 h at 973 K. a – corresponds to water TPD spectrum and b – cor-

responds to oxygen TPD spectrum.

Fig. 5. Comparison between experimental (open symbols) and simulated (solid lines)

electrochemical impedance spectra at different temperatures (Bode plots) for cell A.

Fig. 6. Comparison between experimental (open symbols) and simulated (solid lines) electro-

chemical impedance spectra for different temperatures. Nyquist plots of same data as Fig. 5.

Fig. 7. Comparison of polarization data between the model and experimental data of cell A.

Fig. 8. Comparison between impedance simulations using the full model (solid line) and a

reduced model assuming zero interfacial double layer capacitance (dashed line).

34

Fig. 9. Prediction of impedance spectra for different conditions and a constant temperature of

972 K. a) Nyquist plot representing variation of H2 content from 97 % 57 %; b) Nyquist plot

depicting variation of anode surface area.

Fig. 10. Comparison between experimental (open symbols) and simulated (solid lines)

electrochemical impedance spectra for different temperatures (Bode plots).

Fig. 11. Comparison between experimental (open symbols) and simulated (solid lines) elec-

trochemical impedance spectra for two temperatures (1125 K and 924 K). Nyquist plots of the

same data as Fig. 10.

Fig. 12. Comparison between impedance simulations using the full model (solid line), a re-

duced model assuming ideal gas channel transport (dashed line) and no interfacial double lay-

er capacitance (dashed-dotted line).

35

36

37

38

39

40

41

42