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SUPPLEMENTARY INFORMATIONMesoporous samarium-doped ceria (SDC) powderSamarium-doped ceria (SDC60036) mesoporous powder was synthesized as a replica of the as-prepared hard template of silica KIT-6-36, by a single impregnation approach and calcined at 600 ?C for 5 h.Fig. S1a shows the nitrogen adsorption-desorption isotherms of the SDC60036. They can be classified as type IV, the typical type of mesoporous materials which show pore condensation and a H1 hysteresis loop characteristic of channel pores with narrow size. Typical values of a BET area of 121 m2/g and pore volume of 0.290 cm3/g were obtained from the measurement ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "ISSN" : "1359-7345", "PMID" : "13678168", "abstract" : "A new synthesis route to high-quality large mesoporous cubic Ia3d silica is reported, utilizing a triblock copolymer (EO20PO70EO20)-butanol mixture for the structure direction in aqueous solution.", "author" : [ { "dropping-particle" : "", "family" : "Kleitz", "given" : "Freddy", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Choi", "given" : "Shin Hei", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ryoo", "given" : "Ryong", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical communications (Cambridge, England)", "id" : "ITEM-1", "issue" : "17", "issued" : { "date-parts" : [ [ "2003", "9", "7" ] ] }, "page" : "2136-7", "title" : "Cubic Ia3d large mesoporous silica: synthesis and replication to platinum nanowires, carbon nanorods and carbon nanotubes.", "type" : "article-journal" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[1]", "plainTextFormattedCitation" : "[1]", "previouslyFormattedCitation" : "[1]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[1]. The mean pore size obtained using the BJH model at the desorption branch of the isotherm was 11.3 ± 4 nm (Fig. S1b). In agreement with Doi et al. ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/c0cc01196g", "ISSN" : "1359-7345", "author" : [ { "dropping-particle" : "", "family" : "Doi", "given" : "Yoji", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Takai", "given" : "Azusa", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Sakamoto", "given" : "Yasuhiro", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Terasaki", "given" : "Osamu", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Yamauchi", "given" : "Yusuke", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kuroda", "given" : "Kazuyuki", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Communications", "id" : "ITEM-1", "issue" : "34", "issued" : { "date-parts" : [ [ "2010" ] ] }, "page" : "6365", "title" : "Tailored synthesis of mesoporous platinum replicas using double gyroid mesoporous silica (KIT-6) with different pore diameters via vapor infiltration of a reducing agent", "type" : "article-journal", "volume" : "46" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[2]", "plainTextFormattedCitation" : "[2]", "previouslyFormattedCitation" : "[2]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[2], the use of different hydrothermal temperature during the synthesis of the KIT-6 silica template allows to selectively depositing into both pores or one single pore of the Ia3d bicontinuous structure leading to small pores of ~ 4 nm or larger pores over 10?nm. Figure S1. (a) N2 adsorption–desorption isotherms and (b) Pore size distribution from the desorption branch using the BJH method of SDC-600-36 calcined at 600 ?C.Fig. S2 shows a SEM image of mesoporous SDC-600-36 particles as synthesized at 600 ?C. The inset shows the TEM image of a typical single particle. The image presents a particle oriented in the [111] direction in order to easily measure the pore size. The pore sizes observed in both images corroborates the results obtained in the N2 physisorption measurements. The pore pattern observed in the figures correspond to filling one of the two interpenetrated channels in the original KIT-6 template structure, as expected from the low hydrothermal temperature (36 ?C) used during the template synthesis. It is demonstrated that the control of the synthesis parameters allows obtaining mesoporous oxides replicas with larger pore sizes, which further facilitates a uniform infiltration of the catalyst.Figure S2. SEM image of the mesoporous SDC-600-36 powder as synthesized at 600??C. The inset shows a TEM image of a single particle oriented in the [111] direction.Optimization of the attachment temperature of the SDC mesoporous scaffold to the SDC electrolyteThe SDC mesoporous layer was attached to the SDC electrolyte pellet at different temperatures, Tatt = 1000, 1050 and 1100 ?C. After this thermal treatment, the mesoporous scaffold was infiltrated with SSC. The morphology of the SSC-infiltrated mesoporous SDC electrodes was studied by SEM. Figure S3 shows a set of images of the electrolyte/electrode interface of the symmetrical cells SSC-SDC/SDC/SSC-SDC, with the SDC scaffold attached at different temperatures. A similar morphology of the cathodes with uniform and well-formed interface is observed for all the cells. Figure S.3. Cross-sectional SEM images of the interface of the SSC-SDC electrode and the SDC electrolyte for different attachment temperatures of the SDC mesoporous scaffold (a) Tatt = 1000 ?C, (b) Tatt = 1050 ?C and (c) Tatt = 1100 ?C.Figure S.4. shows the Nyquist plot of the symmetrical cells (SDC-SSC/SDC/SDC-SSC) obtained at 700 ?C under air. An equivalent circuit formed by a series of an inductance (L), a resistance (Rs) and a transmission line analogous to the Adler-Lane-Steele model (ALS model, see next section for a detailed description) was used to fit all the impedance spectra. The solid line observed in the figure is the result of the fitting. Figure S.4.b shows the area specific resistance (ASR) of the cathode-electrolyte interface of the same symmetrical cells in the temperature range of 500 - 750 ?C. The ASR is calculated as the sum of the chemical resistance of the ALS model and the resistance associated with gas diffusion (ASR = Rchem + Rdif). All the cells follow an Arrhenius-type law, with an activation energy (Ea) of 1.3(1), 1.4(1) and 1.2(1)?eV for the cells attached at 1000, 1050 and 1100 ?C, respectively. The best performance was observed for the cells fabricated with SDC mesoporous scaffolds attached at 1000 and 1050 ?C. This electrode-electrolyte interface should not contribute more than 0.25?Ω·cm2 to the total cell resistance, in order to obtain a typical target value of power density for SOFC applications. This value of ASR = 0.25 Ω·cm2 was attained in this work for a temperature of ca. 660 ?C for the cells attached at 1000 and 1050 ?C, demonstrating the suitability of the fabricated electrodes for IT-SOFC applications. In order to maximize the surface area of the electrode, the lowest attachment temperature of 1000??C was preferred. Moreover, the lower activation energy of the electrodes attached at 1000??C makes them presenting a slightly better behavior in the low temperature range. Figure S.4. (a) Nyquist plot obtained from EIS measurements of SSC-SDC/SDC/SDC-SSC symmetrical cells, with mesoporous SDC attached at different temperatures to the electrolyte (Tatt = 1000, 1050 and 1100 ?C) at 700 ?C under ambient air. The solid line shows the fit of the model depicted in the inset to the experimental data. (b) Arrhenius plot of the electrode/electrolyte resistance of the same cells measured in the temperature range of 500 to 750 ?C. The dashed line shows the targeted value of ASR of 0.25?Ω·cm2.Transmission Lines based Equivalent Circuit Analogous to Adler-Lane-Steele Model for MIECsAn equivalent circuit model based on transmission lines applied by Bisquert et al. in liquid electrochemistry ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/b001708f", "author" : [ { "dropping-particle" : "", "family" : "Bisquert", "given" : "Juan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Phys. Chem. Chem. Phys.", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "4185-4192", "title" : "Influence of the boundaries in the impedance of porous film electrodes", "type" : "article-journal", "volume" : "2" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[3]", "plainTextFormattedCitation" : "[3]", "previouslyFormattedCitation" : "[3]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[3] and the complete analogy between it and the analytical Adler-Lane-Steele (ALS) model ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lane", "given" : "J A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "H", "given" : "Steele B C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of The Electrochemical Society", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "1996", "11", "1" ] ] }, "language" : "en", "page" : "3554", "publisher" : "The Electrochemical Society", "title" : "Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes", "type" : "article-journal", "volume" : "143" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[4]", "plainTextFormattedCitation" : "[4]", "previouslyFormattedCitation" : "[4]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[4] is described in this section. The Adler-Lane-Steele ModelFor cathodes and in particular for mixed ionic electronic conductors (MIEC) the Adler-Lane-Steele (ALS) model is commonly used ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. 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Adler et al. defined a simple expression to quantify the impedance associated to the main non-charge transfer processes (solid-state diffusion and surface exchange). Traditionally these effects have been incorporated to the classical circuits in the form of modified charge-transfer processes or series or parallel combination of them. However, this model shows that the contribution to the total impedance of the non-charge-transfer processes take place in a convoluted manner. The expression for the non-charge transfer contribution (Znct) in the limit of a semi-infinite electrode, with no gas-phase diffusion limitations, is defined as follows:Znct=Rchem1+jωtchem (S1)where Rchem and tchem are the chemical resistance and the time constant of the chemical process, respectively. Both parameters are related to fundamental parameters as follows, (S2) (S3)Therefore, being possible to define the chemical capacitance (Cchem) associated to changes of oxygen stoichiometry in the MIEC. Since MIEC electrodes are not confined to an interface, the values of Cchem can be much larger than the typical interfacial capacitances ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lane", "given" : "J A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "H", "given" : "Steele B C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of The Electrochemical Society", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "1996", "11", "1" ] ] }, "language" : "en", "page" : "3554", "publisher" : "The Electrochemical Society", "title" : "Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes", "type" : "article-journal", "volume" : "143" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[4]", "plainTextFormattedCitation" : "[4]", "previouslyFormattedCitation" : "[4]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[4], (S4)(where δ is the penetration depth of the reduction reactions in the MIEC (from the electrolyte-electrode interface).All the nomenclature and the associated physical magnitudes for the symbols used in the previous expressions are listed below (taken from Adler et al. ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. 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An excellent work of Bisquert et al. ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/b001708f", "author" : [ { "dropping-particle" : "", "family" : "Bisquert", "given" : "Juan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Phys. Chem. Chem. Phys.", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "4185-4192", "title" : "Influence of the boundaries in the impedance of porous film electrodes", "type" : "article-journal", "volume" : "2" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[3]", "plainTextFormattedCitation" : "[3]", "previouslyFormattedCitation" : "[3]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[3] discusses the solutions for transmission lines with a single resistance in one of the channels, and either an interfacial capacitor or a RC transfer circuit at the crosswise element. A transmission line based on single resistance and RC circuits is depicted in Figure?S3 and presents an impedance given by:ZTL=R1R31+jωω3cothω3ωL12 1+jωω312 (S5)where,ω3=1R3C3 (S6)ωL=1R1C3 (S7)and R1= Lr1, R3= r3/L and C3= Lc3, with L the thickness of the electrode. Figure S3. Transmission line typically employed in liquid electrochemistryFor the particular case when R1 > R3, the expression (S5) simplifies to the following equation:ZR1>R3=R1R31+jωω3 (S8)Comparing the ALS analytical expression (S1) defined for non-charge transfer process contributions and the expression (S8) which defined the impedance of the transmission line for our particular situation; it is straightforward to obtain the formal equivalence between the ALS model and the equivalent circuit:Rchem=R1R3 (S9)Cchem=C3R3R1 (S10)The previous analogy allows understanding the Electrolyte/MIEC/Air system depicted in Figure S5a as two coupled transmission lines (Figure S5b, c): An ionic pathway for the oxide ions produced after reduction of the O2(g) by the MIEC. It represents a resistance of R1 (R1=Lr1, where L= electrode thickness).An electronic pathway to collect the electrons generated at the MIEC. The channel presents a resistance Re. Good electronic conductivity is considered for the MIEC, i.e. Re going to zero in comparison to R1.Coupling elements to connect the ionic and electronic channels. These coupling elements represent the oxygen exchange reaction at different points of the surface of the MIEC. To define these processes a typical RC in parallel is used (r3c3). The oxygen exchange reaction could take place along an extended part of the surface of the MIEC, therefore, the use of a transmission line to define the ionic pathway is required (the voltage is different depending on the distance to the electrolyte).(a) (b)(c)Figure S5. (a) Sketch of the half-cell Electrolyte/MIEC/Air and the physical phenomena associated to each part: (1) Oxygen gas phase at the surface of the MIEC; (2) Oxygen exchange at the gas/MIEC interface; (3) Oxide ions pathway to the electrolyte; (4) electrons pathway to the current collector; (b) Equivalent circuit based on transmission lines added to the sketch of the half-cell Electrolyte/MIEC/Air. (c) Schematic of the electrode reaction model based on the equivalent circuit.In addition, the analogy allows understanding the elements of the transmission line in terms of the physical parameters defined by the ALS model:The resistance of the ionic pathway (R1) refers the vacancy diffusion of the oxygen vacancies in the MIEC. Adler et al ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lane", "given" : "J A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "H", "given" : "Steele B C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of The Electrochemical Society", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "1996", "11", "1" ] ] }, "language" : "en", "page" : "3554", "publisher" : "The Electrochemical Society", "title" : "Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes", "type" : "article-journal", "volume" : "143" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[4]", "plainTextFormattedCitation" : "[4]", "previouslyFormattedCitation" : "[4]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[4] named it Z0 and gave the following expression, (S11)The resistance R3 is associated to the reaction of oxygen across the mixed conductor/gas interface. Adler et al ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lane", "given" : "J A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "H", "given" : "Steele B C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of The Electrochemical Society", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "1996", "11", "1" ] ] }, "language" : "en", "page" : "3554", "publisher" : "The Electrochemical Society", "title" : "Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes", "type" : "article-journal", "volume" : "143" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[4]", "plainTextFormattedCitation" : "[4]", "previouslyFormattedCitation" : "[4]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[4] named it ZS and gave the following expression, (S12)The capacitance C3 is associated to the reaction taking place at the surface of the MIEC. Adler et al ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lane", "given" : "J A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "H", "given" : "Steele B C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of The Electrochemical Society", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "1996", "11", "1" ] ] }, "language" : "en", "page" : "3554", "publisher" : "The Electrochemical Society", "title" : "Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes", "type" : "article-journal", "volume" : "143" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[4]", "plainTextFormattedCitation" : "[4]", "previouslyFormattedCitation" : "[4]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[4] gave the following expression, (S13)Introducing the expressions (S11), (S12) and (S13) for R1, R3 and C3, respectively, in equations (S9) and (S10) we recover the expressions for Rchem, tchem and Cchem of the ALS model, equations (2), (3) and (4), respectively. In order to complete the analogy, the parameter L of the equivalent circuit has to be defined in terms of the ALS model ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1149/1.1837252", "ISSN" : "00134651", "author" : [ { "dropping-particle" : "", "family" : "Adler", "given" : "S. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lane", "given" : "J A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "H", "given" : "Steele B C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of The Electrochemical Society", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "1996", "11", "1" ] ] }, "language" : "en", "page" : "3554", "publisher" : "The Electrochemical Society", "title" : "Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes", "type" : "article-journal", "volume" : "143" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[4]", "plainTextFormattedCitation" : "[4]", "previouslyFormattedCitation" : "[4]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[4] as follows, (S14)Using this definition of L, we can see the dependence of the expressions (S11), (S12) and (S13) with microstructural factors (ε, a and τ) and intrinsic properties (Cv, Dv, f, b and r0) and constants (F, R) for constant conditions (T): (S11bis) (S12bis) (S13bis)In conclusion, for the particular situation when R1 is higher than R3 the proposed equivalent circuit is completely analogous to the ALS-model offering a simple visualization and a useful tool for the electrochemical characterization of porous MIEC electrodes.Evolution with time of the microstructural parameters according to electrochemical experimentsThe combination of the experimental evolution with time of different measurable magnitudes (R1, R3, C3) and their dependency on microstructure parameters (S11bis, S12bis and S13bis), allowed us to determine the evolution with time of the most relevant microstructure parameters, namely, porosity (ε), surface area (a) and tortuosity?(τ). 4.1. Evolution of the porosityDirectly from (S12bis), one can obtain that the porosity is directly related to R3 but constants (for a fixed T), (1-ε)~1/R3. Since R3 experimentally increases with time (Figure 6), one can conclude that the porosity increases with time. A simple calculation allows determining the change in the porosity during the thermal stabilization process: (S15)where εi and εt are, respectively, the initial porosity and porosity at a time t. The evolution of this ratio with time is presented in Figure S6. Assuming a reasonable initial porosity of 20%, the final porosity would above 50%. Figure S6. Evolution with time of the decrease of the occupied volume (1-ε) (in black) and the increase of the porosity (in red) assuming an initial porosity of 20%. The curve is generated by using experimental values for R3.4.2. Evolution of the surface areaBy operating (S11bis) and (S13bis), one can find that the surface area is related to experimental parameters but constants (for a fixed T), a~1/C3R32. A simple calculation allows determining the change in the surface area during the thermal stabilization process with the following expression (only involving experimentally obtained quantities): (S16)where ai and at are, respectively, the initial surface area and the surface area after a certain time t. The evolution of this ratio with time is presented in Figure S7. From this figure, one can conclude that the surface area increases with time. In particular, the final surface area (electrochemically active) is 4 times the initial one.Figure S7. Evolution with time of the surface area (normalized to its initial value). The curve is generated by operation of the experimental values C3 and R3.4.3. Evolution of the tortuosityFollowing (S11bis) and (S16), it is easy to conclude that the tortuosity is related to experimental parameters but constants (for a fixed T), τ~ R1/(C3R32) (for a fixed T). A simple calculation allows determining the change in the tortuosity during the thermal stabilization process with the following expression (only involving experimentally obtained quantities): (S17)where τi and τt are, respectively, the initial tortuosity and the tortuosity after a certain time t. The evolution of this ratio with time is presented in Figure S8. From this figure, one can conclude that the tortuosity decreases with time. In particular, According to this calculation, the final tortuosity (from the electrochemical point of view) is around 50% of the original.Figure S8. Evolution with time of the tortuosity (normalized to the initial value of tortuosity). The curve is generated by using experimental values of C3, R3 and R1.4.4. Evolution of the penetration lengthA combination of the results from (S15-S17) allows the calculation of the evolution of the penetration length (δ). (S18)where δi and δf are, respectively, the initial and final penetration length. The evolution of this ratio with time is presented in Figure S9. According to this figure, the penetration length decreases with time. The final penetration length is the 60% of the initial value.Figure S9. Evolution with time of the penetration length (normalized to its initial value). The curve is generated by using experimental values of R1, R3 and C3.All in all, the evolution with time of the electrochemical performance of the mesoporous material suggests an increase of the porosity and the surface area while a decrease of the tortuosity and the penetration length in the MIEC with time. The major evolution of the microstructure takes place during the first 100h of operation.ReferencesADDIN Mendeley Bibliography CSL_BIBLIOGRAPHY [1]F. Kleitz, S.H. Choi, R. Ryoo, Cubic Ia3d large mesoporous silica: synthesis and replication to platinum nanowires, carbon nanorods and carbon nanotubes, Chem. Commun. (2003) 2136. [2]Y. Doi, A. Takai, Y. Sakamoto, O. Terasaki, Y. Yamauchi, K. Kuroda, Tailored synthesis of mesoporous platinum replicas using double gyroid mesoporous silica (KIT-6) with different pore diameters via vapor infiltration of a reducing agent, Chem. Commun. 46 (2010) 6365. [3]J. Bisquert, Influence of the boundaries in the impedance of porous film electrodes, Phys. Chem. Chem. Phys. 2 (2000) 4185. [4]S.B. Adler, J.A. Lane, Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes, J. Electrochem. Soc. 143 (1996) 3554. ................
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