High performance microchanneled asymmetric

Transcription

1 Suorting Information High erformance microchanneled asymmetric Gd 0.1 Ce 0.9 O 1.95-δ -La 0.6 Sr 0.4 FeO 3-δ -based membranes for oxygen searation Shiyang Cheng *,,, Hua Huang, Simona Ovtar, Søren B. Simonsen, Ming Chen, Wei Zhang, Martin Søgaard, Andreas Kaiser, Peter Vang Hendriksen, Chusheng Chen Deartment of Energy Conversion and Storage, Technical University of Denmark, Risø camus, Frederiksborgvej 399, DK-4000 Roskilde, Denmark CAS Key Laboratory of Materials for Energy Conversion, Deartment of Materials Science and Engineering, University of Science and Technology of China, Hefei 3006, China Deartment of Materials Science and Key Laboratory of Mobile Materials MOE, Jilin University, Changchun, China * shiyanc@smn.uio.no S-1

2 1. Theoretical considerations (ECR) Electrical conductivity relaxation (ECR) is commonly utilized to measure the oxygen diffusion and surface exchange coefficients of single 1- and dual hase comosite 3-4 mixed ionic and electronic conductors (MIECs). It is based on the measurement of the total conductivity change of a dense samle uon an instantaneous change of the surrounding oxygen artial ressure. Changing the oxygen artial ressure a change in the charge carrier concentration (electrons or electron holes) is measured, which is related to the change in oxygen non-stoichiometry (δ) via the electroneutrality rincile. The following assumtions are commonly made when using ECR; i) Local electroneutrality, ii) iii) conductivity is roortional to the charge carrier concentration, the surface exchange reaction is a first order reaction with resect to the oxygen vacancy concentration;,,, J D C l t z k C l t C l z chem z ex z z (S1) where J z is the flux of oxide ions from the surface to the bulk and k ex, is the rate constant, C(±l x, t) at the surface at time t, and C(±l x, ) reresents the concentration of oxygen ions at the surface at equilibrium t. iv) The change of the oxygen artial ressure occurs much more raidly than the conductivity change of the samle. v) The chemical diffusion coefficient D chem is assumed to be constant within the O - ste range, vi) L x must be significantly larger than L y and L z. S-

3 Based on Fick s laws of diffusion with the aroriate boundary conditions, the normalized conductivity as a function of time can be written as 5 : D t ex( ) (t) (t 0) ( L ) ( L ) n, xdchemt n,y chem L ex( ) L x y l l x y n1 n, x n, x Lx x n1 n,y n,y Ly y (S) where σ denotes the conductivity after the relaxation has reached the new equilibrium, σ(t) is the conductivity at a certain time t, and σ(t=0) reresents the initial conductivity before the gas change. The above equation assumes that the gas change takes lace at time t=0. β n,x,y is the n th ositive root to the equation β n,x,ytanβ n,x,y=l x,y., where L x,y is the dimensionless number. L x,y =k ex l x,y /D chem. Eventually, the two variables k ex and D chem can be obtained by fitting an exerimental curve (normalized conductivity vs. time) with Eq. S. The characteristic thickness of the materials can be calculated as L c fd chem /k ex. (f 0.69) The larger the L c value, the more oxygen diffusion is inhibited by the surface exchange kinetics relative to the diffusion for a thin mixed ionic and electronic conductor based membrane (L<<L c ). S-3

4 . Calculation of oxide ion conductivity of 70 vol.% CGO-30. vol.% LSF Figure. S1 The calculated oxide ion conductivity of a 60 vol.% CGO-40 vol.% LSF membrane and a 70 vol.% CGO-30 vol.% LSF membrane. As shown in Fig S1, the oxide ion conductivity of the 60 vol.% CGO-40 vol.% LSF membrane is calculated in terms of the oxygen flux reorted in Ref. 6 : 16FL djo RT d ln O (S3) O '' According to Samson et al. 6, the flux of the CGO-based dual hase comosite membrane can be calculated as J O RT / O ln 16F L O O // (S4) S-4

5 where R is the gas constant, T is the temerature, F is Faraday constant, is the volume ercent of CGO, is the tortuosity, L is the thickness of the membrane, / O is the oxygen artial ressure on the feed side and // O is the oxygen artial ressure on the ermeate side. Assuming the tortuosity factor in 70 vol.% CGO-30 vol.% LSF membrane is 1.9 6, the oxide ion conductivity of a 1-mm thick 70 vol.% CGO-30 vol.% LSF membrane is simly 7/6 times that of the 1-mm thick 60 vol.% CGO-40 vol.% LSF membrane, as shown in Fig. S1. Since the total conductivity of CGO-LSF is dominated by the electronic conductivity of LSF (cf. Figure 4. of the main article), the theoretical flux of 100µm thick 70 vol.% CGO-30 vol.% LSF membrane at high O can be calculated by Wagner s equation in terms of the oxide ion conductivity in Figure. S1. 3. Calculation of electronic conductivity The calculation of effective conductivity of dual hase is based on Bruggeman-Landauer (BL) effective medium model and the Wu and Liu (WL) model 7. For a comosite consisting of two randomly-distributed hases, the effective conductivity is described as k m k 1 Z 1m k k 0 (S5) k 1 (S6) k Z is the coordination number (i.e. the number of nearest neighbouring grains), k is the conductivity of each constituent hase, k is the volume fraction of each hase, effective conductivity of the comosite. m is the The ercolation c of the dual hase comosite is, when 1 <<. Z= 6 is the commonly used coordination number for three dimensional case. Percolation is in this model descrition achieved when c 1 Z 3 (S7) In the analysis of the results carried out where Z is treated as a fitting arameter. S-5

6 4. Calculation of gas diffusion resistance The effect of Knudsen diffusion is negligible because the size of the ore far exceeds the size where Knudsen diffusion dominates. Hence, concentration driven mass transort is governed by ordinary binary diffusion through the finger-like microchannels. According to 3D tomograhy, the orosity of the finger like microchanneled substrate is 7±5%. The tortuosity of the substrate is in the range of 1.5- according to Wang s model 8 on the same structure. First, the binary diffusion coefficient of N and O is calculated by the equation: D AB kt M 1/ n AB ABD f D (S8) The effective diffusivity is influenced by orosity (ρ) and tortuosity factor (τ) D eff AB DAB (S9) The calculation of gas olarization resistance is based on Zhao et al. 9. First, the limiting current density due to concentration olarization is calculated i cs 4FD eff AB 0 RTl 0 (S10) Second the concentration olarization through the orous substrate is deduced from con RT i ln 1 4F ics (S11) The current density is related to the measured oxygen flux. i (S1) 4FJO The resistance arising from concentration olarization reads S-6

7 R con i con (S13) The total resistance is calculated as R tot V 4FJ O (S14) V RT ln 4F (S15) / O // O where V is the electromotive force (emf) of the membrane. 5. Rietveld refinement Figure. S Rietveld refinement atterns of the owder of the dual hase membrane sintered at 1300 C. The black curve is the measured attern and the red curve is calculated attern obtained from refinement. The vertical bars are the Bragg osition of each hase and the green curve means the differentiation of the fitted and exerimental atterns. R w =5.4 R =3.99 χ =4.40, Zero shift=0.1871(6). S-7

8 Table S1. Unit cell data determined from XRD for crushed sintered owder. Phase Crystal system a (Å) b (Å) C (Å) V (Å 3 ) Volume % CGO Cubic (7) (7) (7) (6) 67.5(48) LSF Rhombohedral (10) (10) (5) (40) 3.75(48) 6. Surface exchange rate (k ex ) and chemical diffusion coefficient (D chem ) versus O. Figure. S3. (a) Oxygen surface exchange (k ex ) and (b) chemical diffusion coefficient (D chem ) of CGO-LSF as a function of oxygen artial ressure. (The lines are the best linear fit for the results) 7. Leak rate Figure. S4 A comarison between the ermeated O and leaked O. S-8

9 Fig. S5 show the BSEM micrograh of a CGO-LSF samle after ECR measurement in a mixture of CO and CO. It can be clearly seen that articles with an average size of µm aear on the surface. The EDS maing confirms that the article is rich in Sr. Figure. S5 (a) BSEM micrograh and (b) EDS elemental maing of a CGO-LSF bar after ECR measurement in a mixture of CO and CO. 8. Derivation of average oxygen artial ressure in a Plug-Flow Setu and under CSTR conditions (Continuously Stirred Tank Reactor) The oxygen ermeation measurements of this work were carried out under conditions resembling either a Plug-Flow case or a CSTR. The flux measurement setu for test of the small circular membranes with a large oen volume above is best treated as a CSTR case, where the average oxygen artial ressure on the ermeate side of the membrane is equivalent to that of exit (or downstream) gas (O out =O ) since only negligible concentration gradients exist along the surface of the membrane. Hence, it is the O measured at the exit that is used when assessing the driving force for the oxygen flux. For simlicity, and to relate to directly measured quantities only, also the exit O was used when assessing the driving force over the membranes under various flows in Figure 9. However, for this setu where the extension of the cell (5 cm) is much larger than the height of the gas flow volume above it (~1 mm) the situation is much more lug-flow-like than CSTR like, i.e. there is a significant variation in O along the gas flow and thus over the active membrane area. The detailed situation will deend on the flow rate; For large gas flows it becomes lug flow like and for small flows eventually CSTR like. Therefore, the driving force for the flux decays from inlet S-9

10 towards to the outlet. To quantify the effects of the varying driving force, a simle model was setu to reresent the lug flow case allowing calculation of the average driving force over the membrane (or characteristic O ). This was done segmenting the area in n segments and conducting an averaging. The oxygen concentration in the ermeate gas in each segment is corrected for the dilution that occurs due to the ermeated oxygen that is generated from the revious segments of the membrane. n 0 RT 4F ln n / O O i V (S16) V RT 4F ln / O O avg (S17) Where V is the average emf, n is the number of the segments used in the sectioning of the membrane, O i is the oxygen artial ressure at segment i ( O 0 reresents the O at the inlet; the imurity O level in the swee gas). O avg is the average oxygen artial ressure on the ermeate side (the characteristic O (O avg which will give the correct average EMF over the membrane). The treatment here follows the one in Ref 10 but for the case of inert gases. As illustrated in Figure S6 the larger the flow the more significant is the relative variation of the oxygen artial ressure (back mixing oosite to the flow direction via diffusion is neglected in the simlified treatment). S-10

11 Figure S6 osition deendence of O at the ermeate side of the 5 5cm membrane as function of flow of swee gas at 900 C. Feed gas: O, swee gas: N. Table S Comarison between the aarent driving forces at 800 C obtained from the CSTR- and the Plug flow model. Swee rate / ml min -1 O in O out O avg Ln(O /O ) CSTR Ln(O /O ) Plug flow S-11

12 Now having a characteristic O we can lot the flux data as a function of the average driving force rather than versus the driving force revailing at outlet. This is a more correct reresentation of the situation. Results are illustrated below. The observed roortionality between flux and driving force is maintained from figure 9 but the sloe of the curves decrease. The linearity of the trend curves becomes better when using the lug flow model than when using the driving force assessment based on exit conditions. Figure S7 Comarison between the fluxes as a function of driving force obtained from CSTR model and lug flow model. S-1

13 References 1. Søgaard, M.; Hendriksen, P. V.; Mogensen, M.; Poulsen, F. W.; Skou, E., Oxygen Nonstoichiometry and Transort Proerties of Strontium Substituted Lanthanum Cobaltite. Solid State Ionics 006, 177 (37 38), Søgaard, M.; Vang Hendriksen, P.; Mogensen, M., Oxygen Nonstoichiometry and Transort Proerties of Strontium Substituted Lanthanum Ferrite. J. Solid State Chem. 007, 180 (4), Wang, Y.; Hu, B.; Zhu, Z.; Bouwmeester, H. J. M.; Xia, C., Electrical Conductivity Relaxation of Sr Fe 1.5 Mo 0.5 O 6-δ -Sm 0. Ce 0.8 O 1.9 Dual-Phase Comosites. J. Mater. Chem. A 014, (1), Zhang, Z.; Zhou, W.; Chen, Y.; Chen, D.; Chen, J.; Liu, S.; Jin, W.; Shao, Z., Novel Aroach for Develoing Dual-Phase Ceramic Membranes for Oxygen Searation through Beneficial Phase Reaction. ACS Al. Mater. Interfaces 015, 7 (41), Carslaw, H. S.; Jaeger, J. C., Conduction of Heat in Solids. Oxford: Clarendon Press, 1959, nd ed. 1959, Samson, A. J.; Søgaard, M.; Hendriksen, P. V., (Ce,Gd)O δ -Based Dual Phase Membranes for Oxygen Searation. J. Membr. Sci. 014, 470, Wu, Z.; Liu, M., Modelling of Ambiolar Transort Proerties of Comosite Mixed Ionic-Electronic Conductors. Solid State Ionics 1996, 93 (1 ), Zhiwen, W. Master thesis, University of Science and Technology of China, Zhao, F.; Armstrong, T. J.; Virkar, A. V., Measurement of O -N Effective Diffusivity in Porous Media at High Temeratures Using an Electrochemical Cell. J. Electrochem. Soc. 003, 150 (3), A49-A Jensen, S. H.; Hauch, A.; Hendriksen, P. V.; Mogensen, M., Advanced test method of solid oxide cells in a lug-flow setu. J. Electrochem. Soc. 009, 156 (6), B757-B764. S-13