Discussion on a Percolating Conducting Network ... - ACS Publications

Jun 26, 2014 - A three-dimensional percolation network is achieved in the LSCF/GDC composite, while a two-dimensional percolation network is observed ...
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Discussion on a Percolating Conducting Network of a Composite Thin-Film Electrode (≤1 μm) for Micro-Solid Oxide Fuel Cell Application Guillaume Muller,†,‡,§ Armelle Ringuedé,*,∥ and Christel Laberty-Robert*,†,‡,§ †

Laboratoire de Chimie de La Matière Condensée de Paris, UMR7574, UPMC Univ Paris 06, Sorbonne Universités, 11 Place Marcellin Berthelot, 75231 Paris, France ‡ Laboratoire de Chimie de La Matière Condensée de Paris, UMR7574, Collège de France, 11 Place Marcellin Berthelot, 75231 Paris, France § Laboratoire de Chimie de La Matière Condensée de Paris, UMR7574, Centre National de la Recherche Scientifique (CNRS), 11 Place Marcellin Berthelot, 75231 Paris, France ∥ PSL Research University-Chimie Paristech-CNRS, Institut de Recherche de Chimie Paris, 75005, Paris, France S Supporting Information *

ABSTRACT: Ni/Gd0.1Ce0.9O2−δ (Ni/GDC) and La0.6Sr0.4Fe0.8Co0.2O3−δ/Gd0.1Ce0.9O2−δ (LSCF/GDC) porous thin-film electrodes with thicknesses between 120 and 500 nm were synthesized through templated sol−gel chemistry coupled with the dip-coating process and heat treatment. The thin films consist of two interpenetrated networks made of pores and inorganic materials. The porous structure was composed of multi-scale pores with dimensions ranging from macro- to nanosize and with an oriented columnar structure. The dimension of the percolation network is discussed as a function of the chemical nature of the percolating components and the particle/thickness ratio. A three-dimensional percolation network is achieved in the LSCF/GDC composite, while a twodimensional percolation network is observed for the Ni/GDC composite. This difference is related to the microstructure of the composite thin film. An anisotropic columnar structure is observed for Ni/GDC, while an isotropic structure is achieved for LSCF/GDC.

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INTRODUCTION Porous composite electrodes are commonly used in energy transformation or storage applications. Their electrochemical performances strongly depend upon their microstructure (thickness, particle size, and pore size) that defined the dimension of the percolation network.1−7 In solid oxide fuel cell (SOFC) electrodes, the porous composite electrode is made of an insulating pore network and an electron-ionconducting network. The electrochemical reactions of both hydrogen oxidation and oxygen reduction occur at the triplephase boundary (TPB); the TPB is the area where the three phases necessary for electrochemical reactions meet: oxide-ionconducting phase, electron-conducting phase, and gas phase.3,7,8 A good fuel cell maximizes the TPB area, allowing for the reaction to occur in more sites, thus maximizing current flow. The TPB area can be tuned using a composite electrode made of both electronic and ionic conductors. The concentration of the electronic conductor phase thus has a relevant role in extending the TPB area and then changing the electrical behavior of the composite from a pure ionic conductor to a metallic conductor. This evolution occurs when the concentration of the electronic conductor phase © 2014 American Chemical Society

reaches a threshold point corresponding to the formation of a percolation conductive network. In 1940, Brunauer et al. introduced the idea of an interpenetrate network through the theory of gas adsorption.9 Then, the original theory of percolation was developed as a mathematical probability problem by Broadbent and Hammersley in 1957.10 In 1973, Kirkpatrick published an extension of the theory to analyze conduction and transport properties of inhomogeneous real systems.11 Multiple models are proposed to describe the electrical conductivity of a heterogeneous binary media conductor−insulator.12 The first experimental results were reported on a graphite sheet with random holes.13 Since then, a percolation theory has been developed, discussed, and extended to a wide range of materials and phenomena over the past few years, and the fundamental mathematics are wellunderstood.14−18 Application to electrical conductivity in simple and composite phases has been reviewed in detail by several authors.19−26 Experimental results based on electrical Received: January 16, 2014 Revised: June 17, 2014 Published: June 26, 2014 8889

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and acetone. The deposition was performed under ambient temperature and atmosphere. During evaporation of the solvent, the system co-assembles to form an inorganic−organic composite film. Upon heating at 700 °C for 10 h in air, the composite develops pore−solid architecture with nanocrystalline walls. A multi-layer deposit was made to increase the film thickness with a stabilization step of each layer at 200 °C between two dip coatings. For convenience, Ni50/50GDC corresponds to 50/50 vol % of the Ni/GDC porous thin film and LSCF50/50GDC corresponds to 50/50 vol % of the LSCF/GDC porous thin film. Characterizations. The microstructure and the film thickness of the films obtained after different heat treatments (under an oxidizing or a reducing atmosphere) were observed by field emission gun scanning electron microscopy (FE-SEM, Hitachi SU-70). Ellipsometry measurements [environmental ellipsometry porosimetry (EEP)] were performed on an ultraviolet−visible (UV−vis) variable-angle spectroscopic ellipsometer (VASE) from Woollam. Measurements were fitted between 500 and 1000 nm. Adsorption− desorption isotherms were performed with toluene or water as a function of the pore size. The data were analyzed using the WVase32 software and the different isotherms by the IIC pore contraction model and a modification of the Kelvin equation, as detailed elsewhere.47 Impedance spectroscopy measurements were carried out under a flux of 10% H2/Ar with a flow rate of 3 L h−1 in a temperature range of 350−500 °C for anode thin films (Ni/GDC) and in air between 400 and 700 °C for cathode thin films (LSCF/GDC). A frequencyresponse analyzer, PGStat20 Autolab Ecochemie BV from 1 MHz to 1 Hz, using 11 points per frequency decade, is used. The linearity of the system was checked by modifying the alternating current (AC) amplitude from 50 to 350 mV before any in situ measurement. The electrical properties were obtained using an in-plane configuration measurement. In fact, specific two Pt electrodes of roughly 200 nm thick, 1 cm length, and 1 mm width were sputtered onto the mesoporous films. The distance between the two stripes was 7 mm (see Figure S5 of the Supporting Information). Prior to measurement, to stabilize the microstructure of the current collector, the mesoporous films with Pt stripes were heated at 700 °C for 5 h. The electrical contact on the sample was ensured through two gold wires (0.25 mm in diameter), which were applied with low pressure (spring system) onto the Pt stripes. The gas flows were controlled through mass flow controllers (Brooks Instrument 4800 Series). In Figure 1 is reported, after the reduction step at different temperatures and Ni concentrations, the typical impedance diagrams of the mesoporous thin film. Regardless of the reduction temperature and reduction time, the thin-film contribution is described by one semi-circle in these conditions. The total resistance of the thin film was attributed to the diameter of the semi-circle (Figure 1). From this resistance and using eq 1, we have calculated at various temperatures and reduction times the total in-plane conductivity of the thin films

measurement and modeling approaches, including the percolation theory or computer simulation techniques, are often used for describing the relations that exist between the microstructure and the electrical properties.2−6,27−33 Several authors demonstrated that the microstructure of the porous electrodes strongly influences their electrochemical performances.1−3,5,28 For example, the use of a composite electrode made of electronic and ionic conducting particles in a SOFC allows for increasing the number of active sites.2,7,34,35 Further, the use of a fine-grained microstructure increases the number of three-phase boundaries (TPBs) per unit volume.36,37 Typically, nanoscale grain sizes are expected to produce larger TPB length per unit volume of electrode.32,34,38 Controlling the pore architecture of the electrode, i.e., pore size and distribution, constitutes an interesting parameter for modifying the electrical percolation threshold.4,39,40 These have been demonstrated with various types of pore formers used during the electrode synthesis.6,30,41,42 The relationship between the pore size and its geometry and the pore percolation threshold are often discussed through modeling approaches.27,37,38 This paper reports the influence of the electrode composition and the geometry of the porous network on the electrical percolation for the electrode developed in view of micro-solid oxide fuel cell (μ-SOFC) devices. Two types of porous composite electrodes, Ni/Gd0.1Ce0.9O2−δ (Ni/GDC) and La0.6Sr0.4Fe0.8Co0.2O3−δ/Gd0.1Ce0.9O2−δ (LSCF/GDC) were then studied. The synthesis and characterization of these porous composite electrodes were studied in our previous works.42−45 Those works were mainly dedicated to the electrical characterization by impedance spectroscopy of a composite thin-film three-dimensional (3D) nanoarchitecture based on GDC. The objectives were to define the best compromise in terms of composition and microstructure to reach the best electrical conductivity for μ-SOFC application. In this study, the main purpose was different and focused on the understanding of the behavior of electrical data of these composite electrodes using the percolation theory. The discussion of the data will be performed by considering several aspects, such as the percolation threshold and the dimensionality of these porous composite electrode types.

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EXPERIMENTAL SECTION

Chemical. Lanthanum(III) acetate hydrate (Aldrich, 99.9%), strontium(II) chloride (Aldrich, 99.9%), cobalt(II) acetate tetrahydrate (Aldrich, 99.9%), iron(III) nitrate nonahydrate (Aldrich, 99.9%), nickel(II) chloride hexahydrate (Aldrich, 99.999%), cerium(III) chloride heptahydrate (Aldrich, 99.999%), gadolinium(III) chloride hexahydrate (Aldrich, 99.999%), ethylalcohol, and tetrahydrofuran (THF) were used as received. Polystyrene (40 000)−block−poly(ethylene oxide) (45 000) (PS-b-PEO) is noted PS40−PEO45 (Polymer Sources, Inc.). Preparation of Porous Thin Films. The synthesis was described in details elsewhere, and here, we reported the main steps.42−46 Briefly, a solution containing precursor powders, ethanol, and water was stirred for 1 h to allow for the dissolution. Separately, the block copolymer poly(styrene-b-ethylene oxide) was dissolved in THF. The block copolymer solution was added to the precursor solution. The final solution was stirred for 24 h for homogenization. Table S1 of the Supporting Information shows the chemical composition of the solutions used to synthesize Ni/GDC and LSCF/GDC thin films. An evaporation-induced self-assembly approach is used to produce the porous thin films. The electrode thin films were deposited by dip coating onto Si/SiO2 or Al2O3 substrates with a withdrawal speed of 3−6 mm s−1. Previously, alumina and Si/SiO2 substrates were treated in nitric acid to clean the surface and, afterward, washed with ethanol

σ=

1 d R eL

(1)

where R is the total in-plane resistance, d is the distance between the two electrodes, L is the length of the Pt electrodes, and e represents the thickness of the film. Two-dimensional grazing incidence small-angle X-ray scattering (2D-GISAXS) measurements were performed with a Rigaku S-max 3000 equipped with a 2D Gabriel detector placed behind 1480 nm of the thin film. The measurements were performed with an incident angle of 0.2° for 2 h. The 2D-GISAXS analysis was performed according to the procedure described elsewhere.48,49

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RESULTS AND DISCUSSION Microstructure. The electrode thin films were synthesized via the dip-coating process of a sol−gel solution, followed by a heat treatment at high temperatures in air. The description of the synthesis procedure was reported elsewhere.42−45 Thermal treatment is used to initiate hydrolysis and condensation 8890

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Figure 2. FE-SEM surface and cross-section images of (a and b) LSCF30/70GDC and (c and d) NiO30/70GDC porous thin films heated at 700 °C in air and (e and f) Ni30/70GDC porous thin films after reduction at 400 °C for 40 h under 10% H2/Ar. All films are 250 nm thick.

Figure 1. Nyquist impedance plots of 250 nm thick mesoporous thin films calcined at 700 °C in air. (a) For Ni30/70GDC, the effect of the working temperature on the Nyquist plots in 10% H2/Ar (3 L h−1): (1) 500 °C, (2) 450 °C and (3) 400 °C. (b and c) At T = 400 °C, the effect on the composition on the Nyquist plots in 10% H2/Ar (3 L h−1): (1) GDC, (2) Ni30/70GDC, (3) Ni40/60GDC, (4) Ni50/ 50GDC, and (5) Ni70/30GDC. Logarithms of frequency are indicated in the figure.

reactions, to decompose the PS-b-PEO template, and to induce the crystallization of both GDC and LSCF or NiO oxides. The pore size in the film is controlled by the nature of the block copolymer, the solvent used in the sol−gel chemistry, and the final heat treatment.50,51 Their distribution mainly depends upon the processing parameters (temperature and humidity) of dip coating.50,51 The final heat treatment is very important because it influences the particle size, their crystallinity, and the pore size. Typical FE-SEM micrographs are reported in Figure 2 for LSCF/GDC (panels a and b of Figure 2) and Ni/GDC (panels c−f of Figure 2) thin films deposited onto a dense Al2O3 substrate. The porous Ni/GDC cermet thin film is obtained through the reduction of NiO to metallic Ni. This reduction step occurs usually during the first heating of the fuel cell under the operating conditions. The reduction of NiO to Ni modifies the microstructure of the composite and then the porous network (panels b and c of Figure 2). This is related to the modification of the Ni particle diameter compared to the NiO particle diameter (see Table S2 of the Supporting Information).52 The porosity of the thin films was then evaluated by environmental ellipsometry−porosimetry, and the results are reported in Figure 3. Previous papers describe the technique developed for estimating the LSCF/GDC44 and Ni(O)/GDC42 pore volumes. Briefly, the solvent adsorption−desorption isotherms exhibit type IV sorption behavior with H1- or H4type hysteresis loops, characteristic of mesopores47,53 (see Figure S1 of the Supporting Information). From the adsorption

Figure 3. Porosity (vol %) as a function of the volume fraction of Ni or LSCF in 250 nm thick composite Ni/GDC or LSCF/GDC thin films.

and desorption branches, the porous volumes were estimated (see Figure S1 of the Supporting Information). An increase of the porous volume is observed with the Ni content for the Ni/ GDC composite, while the overall electrode volume decreases for the LSCF/GDC composite when increasing the LSCF content. This modification in the pore volume is due to different mechanisms. The increase of the porous volume for Ni/GDC is mainly related to the change in the particle size during the reduction of NiO to Ni52 and a reorganization of the particles, as seen in Figure 2. Ni particles have a tendency to 8891

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correlation distance (center−center column distance) are 34 ± 6 and 37 ± 9 nm, respectively.49 These values are consistent with the observations made by scanning electron microscopy (Figure 4a), where pores with a diameter of ∼40 nm and a center−center pore distance of 50 nm are measured. The diffuse ellipsoidal ring is attributed to deviations from a perfect mesostructural orientation and also from packing defects of the mesopores. Percolation. For integrating these thin films as electrodes in μ-SOFC, the cermet anodes or the composite cathodes must be electronically conductive as well as porous. To do so, three percolating interpenetrated phases need to be achieved: ionic, electronic, and pores. The electrode conductivity with different compositions and microstructures was measured by impedance spectroscopy. The percolation threshold will be then discussed according to the electrical data. The evolution of σ as a function of the Ni content has been studied following different reducing treatment temperatures: 400, 450, and 500 °C in 10:90 H2/N2. A strong increase of the conductivity from 10 to 104 S/m is observed as a function of the nickel content regardless of the reduction treatment temperature (Figure 5a). This rapid change occurs in a range from 30 to 40 vol % of Ni into the Ni/GDC cermet. Reporting conductivity variation as a function of these reduction temperatures in the Arrhenius plot allows for the calculation of the associated activation energy for different nickel contents (see Figure 5b). Additional measurements at a fourth temperature of 350 °C were also reported in this figure. The activation energy changes with the nickel content in the film. For a high nickel content, the value is close to the value observed for the electronic conductor, while for a low nickel content, the value corresponds to the ionic conductor, GDC. We note drastic changes of the activation energy values for Ni content superior to 30 vol %, corresponding to the change of the cermet conductivity. For LSCF/GDC mesoporous films, the conductivity value in air varies with the LSCF content. First, a decrease of the conductivity value up to 50 vol % of LSCF is observed regardless of the operating temperature between 400 and 700 °C. This is attributed to the difference in ionic conductivity between GDC (2 × 10−1 S/m at 500 °C) and LSCF (1 × 10−2 S/m at 500 °C). Then, the conductivity increases by close to 4 orders of magnitude from 10−3 to 10 S/m when LSCF varies from 50 to 80 vol %, at 400 °C. This increase in conductivity is related to the percolation of the LSCF phase in the electrode volume. The activation energy was estimated from the Arrhenius plot, and the values gradually evolve from 0.6 to 0.03 eV, thus from ionic to mainly electronic conductivity. The latter differ from the Ni/GDC composite because the electronic conductivity of LSCF is lower than those observed for metallic Ni. These studies demonstrate that the percolation threshold depends upon the nature and microstructure of the electrode (pores, particle size, thickness, and chemistry of the component in the composite). The electrical percolation threshold is achieved for film with a minimum of 30 to 40 vol % of Ni in Ni/GDC films and with a minimum of 50 vol % of LSCF for LSCF/GDC films. Note that the difference of the value of the percolation threshold for the two composites is related to the difference in the particle size because the thicknesses of these composite films are comparable. In Table S2 of the Supporting Information, the mean particle sizes of LSCF, GDC, and Ni estimated from high-resolution transmission electron micros-

agglomerate. For LSCF/GDC, the decrease of the pore volume is related to a densification of the film because of the delayed LSCF crystallization (Tcrystallization = 700 °C) versus the decomposition of the block copolymer (T = 200 °C). The pore collapse increases with the LSCF content in the film, as supported by FE-SEM images (see Figure S1 of the Supporting Information). The mesostructure of the porous thin films was further analyzed by 2D-GISAXS. The experimental setup (see Figure S6 of the Supporting Information) allows for studying of the organization of the pores in the film and their geometry. For these experiments, Si/SiO2 substrates were covered with a 150 nm thick NiO/GDC electrode layer (Figure 4a). Figure 4b

Figure 4. (a) FE-SEM image of NiO50/50GDC porous thin-film cross-section calcined at 700 °C with a heating rate of 1 °C min−1 for 1 h in air. (b) 2D-GISAXS patterns of a mesostructured NiO/GDC thin film recorded with an angle of incidence b = 0.2°. (c) Scheme of the oriented porous network. (d) Scheme of the 2D percolating metallic phase (in red).

shows 2D-GISAXS data, which demonstrate the orientation of the pore in the NiO/GDC thin films. The distinct deformed diffraction spots in the z direction are assigned to two columnar structures perpendicular to the substrate and homogeneously distributed (i.e., two columns are separated by a constant distance). This organization was already reported48 and corresponds to an arrangement of pores in hexagonal p6m structure. The average diameter of the columns and their 8892

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Figure 5. Evolution of the total conductivity as a function of Ni or LSCF content at various temperatures for 250 nm thick composite (a) Ni/GDC and (c) LSCF/GDC films. Arrhenius plots of the conductivity as a function of the temperature for (b) Ni/GDC and (d) LSCF/GDC composite thin films.

Table 1. Values of the Critical Exponent t, Coordination Number z, and Percolation Threshold in the Model Sites pc (vol %) Depending upon the Nature of the Network and Its Dimensionality According to Equation 211,55

copy (HR-TEM) images have been reported. The particle size for Ni is higher than the particle size for LSCF, 10 and 6 nm, respectively. This means that percolation of Ni will occur for a lower volume percentage than LSCF. Nevertheless, the values of the percolation threshold are in agreement with the values reported in the literature, ∼30 vol % of Ni54 and ∼50 vol % of LSCF3 in GDC-based composite films. Percolation Network Dimension. Because the electrical conductivity of Ni is superior to the electrical conductivity observed for GDC, the conductivity of the Ni/GDC thin film can be represented as a function of the volume fraction p by eq 2 according to the percolation theory for dense film for p > pc ,

σ = σi(p − pc )t

dimension

network

pc (vol %)

z

2D

triangular cubic kagome honeycomb face-centered cubic hexagonal close-packed simple cubic diamond

50 59 65 70 20 24 31 43

6 4 4 3 12 8 6 4

3D

(2)

where pc is the critical volume fraction called the percolation threshold, σi represents the conductivity of Ni or LSCF, and t is the critical exponent of the model, depending upon the topology of the system. t takes different values depending upon the topology of the porous network. Kirkpatrick11 and Scher and Zallen55 defined the values for the critical exponents according to the dimension of the percolation network. The results are summarized in Table 1. t is equal to 1 for conductive channels, while t is comprised between 1 and 1.3 for a 2D network (sheets, platelets, etc.). Finally, t is close to 2 for a 3D network. In the present study, films are porous; thus, the conductivity values must be corrected by the film porosity. The film porosity was estimated from the environmental ellipsometry−porosim-

t 1−1.3

1.7−2.2

etry analysis. To do so, the following eq 3 has been used, where the pore volumes and the dimension of the conductivity network are taken into account:56 σ=

⎛ 2 1 ⎞⎟ σfp/⎜1 − por − ⎝ 3 dim ⎠

(3)

where σfp is the electrical conductivity of the porous composite film, por is the volume fraction of the porous film, and dim is the dimension of the conduction network. Considering that the film thickness is 10 times greater than the particle size, we consider that the conductivity occurs in a 3D network. The conductivity values used in eq 2 were those corrected by the porosity according to eq 3. The variation of σ as a function 8893

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Figure 6. Evolution of the total conductivity as a function of the (a) Ni content for Ni/GDC thin films and (b) LSCF content for LSCF/GDC thin films. Log−log plots of the total conductivity as a function of (p − pc) for 250 nm thick (c) LSCF50/50GDC thin films and (d) Ni50/50GDC thin films.

of Ni or LSCF volume content is reported in panels a and b of Figure 6 for different dimensions of the conduction network. For p > pc, σ increases with the Ni or LSCF content, while for p < pc, the behavior is different for the two composites. For Ni/ GDC, the conductivity is constant, while for LSCF/GDC, σ decreases with the LSCF content. These changes in conductivity allow for the determination of the minimum content of Ni or LSCF for achieving either the Ni percolation network or the LSCF percolation network. Percolation is achieved for 31 vol % of Ni in Ni/GDC. This value is in the range of 30−40 vol % of Ni determined from electrical measurement. For LSCF/GDC (see panels a and b of Figure 6), the percolation network is achieved for 48 vol % in LSCF according to this mathematical model. The value is comparable to the value obtained from the electrical measurement and is higher than the value expected for dense LSCF/GDC films (∼30 vol % of LSCF).3 Nevertheless, this behavior has already been observed by Dusastre et al.3 on a thick, porous LSCF/ GDC composite electrode. It has been shown that the value for achieving percolation of an electrical network increases with the porous volume. The log σ as a function of (p − pc) has been plotted for Ni/GDC and LSCF/GDC, and the results are reported in panels c and d of Figure 6, respectively. From these data, the t value was estimated. It describes the dimension of the conduction network. t is equal to 2 for the LSCF/GDC composite thin film, corresponding to a 3D percolated network. t can take both values (t = 1 or 2) in the case of the Ni/GDC composite thin film, depending upon the dimension of the conduction network, dim, taken into account for the estimation of the porous film conductivity (eq 3). t is equal to 1 corresponds to a 2D network for the Ni network (dim = 3), while t is equal to 2 is attributed to a 3D network for the Ni network (dim = 2). These results highlight a discrepancy between the value estimated from eq 2 with and without the correction from eq 3. Nevertheless, this discordance is generally

observed for anisotropic conduction networks. This anisotropy can be explained by conduction pathways along the z direction, i.e., perpendicular to the substrate. This affects the dimension of the percolation network, and it changes from a 3D network to a 2D network. This behavior is in agreement with the microstructural characterization on porous NiO/GDC films. We demonstrated that pores are connected to a direction perpendicular to the film substrate. Accordingly, Ni particles are connected in z direction, which form a 2D network (see Figure 4d). The electron pathway occurs through this oriented inorganic wall. This oriented microstructure is interesting in SOFC application. The porous columnar structure with a diameter of ∼40 nm allows for efficient gas diffusion, and the smallest pores between the column increase the tortuosity of gas throughout the electrode; thus, higher electrocatalytic performances must be achieved.42 Film Thickness Effect. If a deformation of the 3D to 2D percolation network occurs in thin cermet films, it should also be possible to change a 2D percolation network into a 3D percolation network by modifying the thickness and chemistry of the secondary component in the composite of the film. Muecke et al. reported this behavior for a dense Ni/GDC thin film with thicknesses varying from 250 to 300 nm.54 Their results show that the in-plane conductivity of cermet thin films depends upon not only the composition but also the ratio between the grain size and layer thickness. A percolating metallic phase is formed at low metal volume ratios if the grain size is small compared to the film thickness. Larger metal volume ratios are needed for percolation when the grain size is comparable to the layer thickness. For the Ni/GDC film, the percolation is achieved for 31 vol % of Ni in the GDC matrix. For LSCF/GDC films, 48 vol % is needed to achieve percolation of the LSCF network. This is mostly related to the difference in the particle size (see Table S2 of the Supporting Information) because the thickness of the film is 8894

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DISCUSSION Our work shows the influence of the electrode composition and geometry of the porous network on the electrical percolation for two types of porous composite electrodes, Ni/ Gd 0.1 Ce 0.9 O 2−δ (Ni/GDC) and La 0.6 Sr0.4 Fe 0.8 Co 0.2 O 3−δ / Gd0.1Ce0.9O2−δ (LSCF/GDC). The Ni/GDC electrodes present a specific microstructure, where pores are organized in a columnar structure. The particles size is under 30 nm, smaller than the film thickness. Muecke et al. reported that a 3D percolating metallic phase is formed at low metal volume ratios (∼30 vol % Ni) if the grain size is small compared to the film thickness.54 However, in our case, the percolation modeling shows that Ni/GDC electrodes present a 2D percolation metallic phase. This is mainly related to the anisotropy observed in the film. On the contrary, for LSCF/GDC electrodes, the particle size is smaller than the particle size observed for Ni in Ni/GDC. Thus, the percolation is achieved for a higher LSCF content. Modeling has shown a 3D percolation network for LSCF in LSCF/GDC. In this case, no oriented structures (isotropic) are observed with LSCF as a mixed conductor.

the same. The difference observed between a 3D percolation network versus a 2D percolation network is related to the nature of the secondary phase. LSCF is a mixed conductor, i.e., electronic and ionic conductors, while Ni is only a metallic conductor. To study the impact of the film thickness, composite mesoporous Ni70/30GDC thin films and pure LSCF mesoporous thin films were synthesized with a thickness ranging from 120 to 500 nm. The film thickness was adjusted by depositing several layers. Between each layer, a heat treatment of 200 °C in air was applied to stabilize the hybrid film; a final heat treatment was performed at 700 °C. The total conductivity was estimated from impedance data measured at 400 °C in a reducing atmosphere for Ni/GDC and in air for LSCF. Figure 7 shows that the total conductivity for Ni/GDC

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CONCLUSION Ni/GDC and LSCF/GDC porous thin films with thicknesses between 100 and 500 nm were deposited by a dip-coating process of block-copolymer-templated sol−gel chemistry. The thin films consist of two interpenetrated networks made of pores and inorganic materials constituted of both electronic and ionic conductive phases. The porous structure was composed of multi-scale pores with dimensions ranging from macro- to nanosize and with an oriented columnar porous structure. We studied the impact of the microstructure (porous network, thickness and particle size, and secondary phase) on the total conductivity for porous composite electrode thin films (≤1 μm). We found that the dimension of the electronic percolation network and the percolation threshold depend upon the thickness/particle size ratio and the nature of the secondary phase in the composite. We demonstrated that the dimension of the percolation network is 3D-type when the secondary phase is a mixed ionic conductor. On the contrary, a 2D percolation has been found in the Ni/GDC porous electrode, where the secondary phase is only an electronic conductor. This behavior is related to the microstructure of the electrode, where pores are organized in a columnar structure, thus yielding an orientation of the inorganic network and then an orientation of the electron conductive network as well.

Figure 7. Total conductivity as a function of the thickness of the film for Ni70/30GDC and LSCF thin films.

films increases with the thickness. The conductivity is 73 × 103 S/m for 120 nm thick films and 84 × 103 S/m for 500 nm thick films. Because the difference in conductivity is not very important while the thickness is multiplied by a factor 5, this result indicates that the transition of 2D to 3D percolation occurs for a thicker film. On the contrary for LSCF/GDC thin films, this transition occurs for thinner films. The conductivity evolves from 3 × 102 to 2.5 × 103 S/m when the thickness changes from 100 to 500 nm. Thus, the total conductivity increases by a factor of ∼8 when the thickness is multiplied by a factor of ∼5. However, for a LSCF/GDC composite, LSCF is a mixed (ionic/electronic) conductor. Ion conduction occurs in both LSCF and GDC networks, even if this conduction mainly occurs through the GDC phase. This result confirms that the dimension of the percolation network depends upon both (i) the ratio between the particle size and the film thickness and (ii) the chemistry of the secondary component in the composite.28,38,54 The conductivity values for 500 nm Ni/ GDC are comparable to the value achieved by Muecke et al.54 [∼70 × 103 S/m for the Ni/GDC thin film (∼500 nm)]. In parallel, Beckel et al.54 have reported a conductivity of ∼3 × 103 S/m for the LSCF thin film (∼500 nm) that compares well to this study (2.5 × 103 S/m).

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ASSOCIATED CONTENT

S Supporting Information *

Chemical composition of the initial solutions used for the preparation of Ni/GDC and LSCF/GDC porous thin films (Table S1), FE-SEM surface images and water adsorption− desorption isotherms of (a) LSCF30/70GDC, (b) LSCF50/ 50GDC, (c) LSCF70/30GDC, and (d) LSCF porous thin films (150−250 nm) heated at 700 °C in air (Figure S1), FE-SEM surface images and particle size distributions of (a and c) LSCF50/50GDC heated at 500 °C in air and (b and d) LSCF70/30GDC 150−250 nm) heated at 700 °C in air (Figure S2), mean particle sizes of LSCF and GDC evaluated from HRTEM images for LSCF/GDC thin films calcined at 700 °C with different percentages of LSCF (Table S2), (a) XRD patterns of porous LSCF/GDC thin films calcined at 700 °C in air for 8895

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various LSCF contents and (b) average crystallite size for both LSCF and GDC measured by ex situ XRD analysis of LSCF/ GDC thin films calcined at 700 °C with different percentages of LSCF (Figure S3), average crystallite size for Ni and GDC measured by ex situ XRD analysis of Ni/GDC thin films calcined at 700 °C (NiO/GDC) and reduced at (a) different temperatures (50 vol % Ni) and (b) different percentages of Ni (400 °C) (Figure S4), (a) surface configuration layout and (b) Pt electrodes on different samples (Figure S5), scheme of GISAXS analysis (Figure S6), and dimensionality of the porous thin film used in the porosity correction eq 3 (Table S3). This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Foundation EADS for supporting the Ph.D. grant of Guillaume Muller. The authors thank D. Montero for performing FE-SEM analyses and M. Selmane for performing GISAXS analyses.

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REFERENCES

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