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Patterned electrodes are widely used in the development of novel electrodes of solid oxide fuel cells (SOFCs) because of their well-controlled geometries, distinguishable catalytically active sites and simple transport paths. In the existing studies the patterned electrodes are usually adopted to reveal relevant reaction mechanisms and to investigate the electrochemical characteristics of new materials of SOFCs, however, the effects of electrode geometry are not taken into consideration. In the present paper, a lattice Boltzmann model for simulating the charge transport and electrochemical reaction in an SOFC patterned anode is established, and the key dimensionless parameters governing the above electrode process are deduced. This model is then used to investigate the effects of the key dimensionless parameters on the electrochemical performance of a patterned anode. More importantly, the influences of the patterned anode geometry on the coupling of the charge transport and electrochemical reaction are unraveled. According to the sensitivity of the electrode performance to the dimensionless parameters, a dimensionless phase map, which is divided into maximum area, transition area and minimum area, is built. It is concluded that the transition area, in which the electrode performance varies dramatically with the parameters of design and operation, is regarded as the optimal range for studying the relevant reaction mechanism. Meanwhile, it is found that although the electron transport does not restrict the electrode performance, the moderate decrease of the height-to-width ratio of electronic conductor is capable of enlarging the transition area, which is beneficial to revealing the relevant reaction mechanism. Conversely, the ion transport is the rate-limiting step, however, the transition area remains unchanged under different ionic conductor geometries. The present numerical method and conclusions could offer guidance for rationally designing and operating the patterned electrodes.
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Keywords:
- solid oxide fuel cell /
- patterned anode /
- phase map /
- transition area
[1] Chen Y, deGlee B, Tang Y, Wang Z, Zhao B, Wei Y, Zhang L, Yoo S, Pei K, Kim J, Ding Y, Hu P, Tao F, Liu M 2018 Nat. Energy 3 1042
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Chen M N, Zhang L, Gao H Y, Xuan Y, Ren J F, Lin Z J 2018 Acta Phys. Sin. 67 088202
Google Scholar
[3] Mahato N, Banerjee A, Gupta A, Omar S, Balani K 2015 Prog. Mater Sci. 72 141
Google Scholar
[4] Li W, Shi Y, Luo Y, Wang Y, Cai N 2015 J. Power Sources 276 26
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[5] Patel H, Tabish A, Comelli F, Aravind P 2015 Appl. Energy 154 912
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[6] Luo Y, Li W, Shi Y, Cai N 2017 J. Power Sources 366 93
Google Scholar
[7] Doppler M, Fleig J, Bram M, Opitz A 2018 J. Power Sources 380 46
Google Scholar
[8] Chen Y, Choi Y, Yoo S, Ding Y, Yan R, Pei K, Qu C, Zhang L, Chang I, Zhao B, Zhang Y, Chen H, Chen Y, Yang C, deGlee B, Murphy R, Liu J, Liu M 2018 Joule 2 938
Google Scholar
[9] Luo Y, Li W, Shi Y, Wang Y, Cai N 2017 Int. J. Hydrogen Energy 42 25130
Google Scholar
[10] Liu M, Lynch M E, Blinn K, Alamgir F M, Choi Y 2011 Mater. Today 14 534
Google Scholar
[11] Liu J, Ciucci F 2017 Phys. Chem. Chem. Phys. 19 26310
Google Scholar
[12] Patel H, Tabish A, Aravind P 2015 Electrochim. Acta 182 202
Google Scholar
[13] Yao W, Croiset E 2014 J. Power Sources 248 777
Google Scholar
[14] Yurkiv V, Utz A, Weber A, Ivers-Tiffée E, Volpp H R, Bessler W G 2012 Electrochim. Acta 59 573
Google Scholar
[15] Lynch M, Liu M 2010 J. Power Sources 195 5155
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[16] Vogler M, Bieberle-Hütter A, Gauckler L, Warnatz J, Bessler W G 2009 J. Electrochem. Soc. 156 B663
Google Scholar
[17] Lynch M, Mebane D, Liu Y, Liu M 2008 J. Electrochem. Soc. 155 B635
Google Scholar
[18] Qu Z P, Aravind P V, Boksteen S Z, Dekker N J J, Janssen A H H, Woudstra N, Verkooijen A H M 2011 Int. J. Hydrogen Energy 36 10209
Google Scholar
[19] Chan S H, Khor K A, Xia Z T 2001 J. Power Sources 93 130
Google Scholar
[20] Xu H, Chen Y, Kim J, Dang Z, Liu M 2019 Int. J. Hydrogen Energy 44 30293
Google Scholar
[21] Feng D, Bao C, Gao T 2020 J. Power Sources. 449 227499
Google Scholar
[22] 刘高洁, 郭照立, 施保昌 2016 物理学报 65 014702
Google Scholar
Liu G J, Guo Z L, Shi B C 2016 Acta Phys. Sin. 65 014702
Google Scholar
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图 1 (a) 模式阳极结构示意图; (b) 本文计算区域与边界条件
Figure 1. (a) Schematic of a patterned anode; (b) computational domain and boundary conditions of the model in the present study.
图 2 本文LB模型验证
Figure 2. Model validation of the present LB model.
图 3 模式阳极在基准工况下的性能 (a) 整个阳极电势分布; (b) 电子导体与离子导体交界面(z/Hion = 1.0)电势分布; (c) 电子导体和离子导体分别在TPB处的电势分布; (d) 无量纲电势(Fϕ0/RT)对无量纲平均电流密度(iav/i0)的影响; (e) 无量纲交换电流密度(iex/i0)对iav/i0的影响; (f) iex/i0与Fϕ0/RT对iav/i0的耦合影响; (g) 指导模式阳极设计与运行的无量纲相图
Figure 3. Patterned anode performance at standard case: (a) Potential distribution in the entire anode; (b) potential distribution at z/Hion = 1.0; (c) potential distribution at TPBs; (d) effect of dimensionless potential (Fϕ0/RT) on dimensionless average current density (iav/i0); (e) effect of dimensionless exchange current density (iex/i0) on iav/i0; (f) combined effect of iex/i0 and Fϕ0/RT on iav/i0; (e) phase map generated based on panel (f) for rational design and operation of patterned anode.
图 4 电子导体高宽比(Hele/Lele)对模式阳极性能的影响 (a) 不同电子导体高宽比下无量纲交换电流密度(iex/i0)与无量纲电势(Fϕ0/RT)对无量纲平均电流密度(iav/i0)的耦合影响; (b) 不同电子导体高宽比下指导模式阳极设计与运行的无量纲相图
Figure 4. Effect of height-to-width ratio of electronic conductor (Hele/Lele) on patterned anode performance: (a) Combined effect of dimensionless exchange current density (iex/i0) and dimensionless potential (Fϕ0/RT) on dimensionless average current density (iav/i0); (b) phase maps under different Hele/Lele generated based on panel (a) for rational design and operation of patterned anode.
图 5 电子导体宽度与间距比(Lele/ΔL)对模式阳极性能的影响 (a) 不同电子导体宽度与间距比下无量纲交换电流密度(iex/i0)与无量纲电势(Fϕ0/RT)对无量纲平均电流密度(iav/i0)的耦合影响; (b) 不同电子导体宽度与间距比下指导模式阳极设计与运行的无量纲相图
Figure 5. Effect of width-to-spacing ratio of electronic conductor (Lele/ΔL) on patterned anode performance: (a) Combined effect of dimensionless exchange current density (iex/i0) and dimensionless potential (Fϕ0/RT) on dimensionless average current density (iav/i0); (b) phase maps under different Lele/ΔL generated based on panel (a) for rational design and operation of patterned anode.
图 6 离子导体高宽比(Hion/Lion)对模式阳极性能的影响 (a) 不同离子导体高宽比下无量纲交换电流密度(iex/i0)与无量纲电势(Fϕ0/RT)对无量纲平均电流密度(iav/i0)的耦合影响; (b) 不同离子导体高宽比下指导模式阳极设计与运行的无量纲相图
Figure 6. Effect of height-to-width ratio of ionic conductor (Hion/Lion) on patterned anode performance: (a) Combined effect of dimensionless exchange current density (iex/i0) and dimensionless potential (Fϕ0/RT) on dimensionless average current density (iav/i0); (b) phase maps under different Hion/Lion generated based on panel (a) for rational design and operation of patterned anode.
表 1 本文的边界条件
Table 1. Boundary conditions of the present study.
坐标 边界条件 z* = 0 ϕ* = 0 z* = 1 + Hele/Hion ϕ* = 1 x* = 0, Lion/Hion,
电子导体左右边界${ {\partial \phi ^*} / {\partial x^* = 0} }$ z* = 1 (非TPBs) ${ {\partial \phi ^*} / {\partial z^* = 0} }$ z* = 1 (TPBs) ${\left. { {{i} }^*} \right|_{ {\rm{el} } } } = {\left. { - \sigma ^*\nabla \phi ^*} \right|_{ {\rm{el} } } } = {\left. { {{i} }^*} \right|_{ {\rm{ion} } } } = {\left. { - \nabla \phi ^*} \right|_{ {\rm{ion} } } }$ 
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[1] Chen Y, deGlee B, Tang Y, Wang Z, Zhao B, Wei Y, Zhang L, Yoo S, Pei K, Kim J, Ding Y, Hu P, Tao F, Liu M 2018 Nat. Energy 3 1042
Google Scholar
[2] 陈美娜, 张蕾, 高慧颖, 宣言, 任俊峰, 林子敬 2018 物理学报 67 088202
Google Scholar
Chen M N, Zhang L, Gao H Y, Xuan Y, Ren J F, Lin Z J 2018 Acta Phys. Sin. 67 088202
Google Scholar
[3] Mahato N, Banerjee A, Gupta A, Omar S, Balani K 2015 Prog. Mater Sci. 72 141
Google Scholar
[4] Li W, Shi Y, Luo Y, Wang Y, Cai N 2015 J. Power Sources 276 26
Google Scholar
[5] Patel H, Tabish A, Comelli F, Aravind P 2015 Appl. Energy 154 912
Google Scholar
[6] Luo Y, Li W, Shi Y, Cai N 2017 J. Power Sources 366 93
Google Scholar
[7] Doppler M, Fleig J, Bram M, Opitz A 2018 J. Power Sources 380 46
Google Scholar
[8] Chen Y, Choi Y, Yoo S, Ding Y, Yan R, Pei K, Qu C, Zhang L, Chang I, Zhao B, Zhang Y, Chen H, Chen Y, Yang C, deGlee B, Murphy R, Liu J, Liu M 2018 Joule 2 938
Google Scholar
[9] Luo Y, Li W, Shi Y, Wang Y, Cai N 2017 Int. J. Hydrogen Energy 42 25130
Google Scholar
[10] Liu M, Lynch M E, Blinn K, Alamgir F M, Choi Y 2011 Mater. Today 14 534
Google Scholar
[11] Liu J, Ciucci F 2017 Phys. Chem. Chem. Phys. 19 26310
Google Scholar
[12] Patel H, Tabish A, Aravind P 2015 Electrochim. Acta 182 202
Google Scholar
[13] Yao W, Croiset E 2014 J. Power Sources 248 777
Google Scholar
[14] Yurkiv V, Utz A, Weber A, Ivers-Tiffée E, Volpp H R, Bessler W G 2012 Electrochim. Acta 59 573
Google Scholar
[15] Lynch M, Liu M 2010 J. Power Sources 195 5155
Google Scholar
[16] Vogler M, Bieberle-Hütter A, Gauckler L, Warnatz J, Bessler W G 2009 J. Electrochem. Soc. 156 B663
Google Scholar
[17] Lynch M, Mebane D, Liu Y, Liu M 2008 J. Electrochem. Soc. 155 B635
Google Scholar
[18] Qu Z P, Aravind P V, Boksteen S Z, Dekker N J J, Janssen A H H, Woudstra N, Verkooijen A H M 2011 Int. J. Hydrogen Energy 36 10209
Google Scholar
[19] Chan S H, Khor K A, Xia Z T 2001 J. Power Sources 93 130
Google Scholar
[20] Xu H, Chen Y, Kim J, Dang Z, Liu M 2019 Int. J. Hydrogen Energy 44 30293
Google Scholar
[21] Feng D, Bao C, Gao T 2020 J. Power Sources. 449 227499
Google Scholar
[22] 刘高洁, 郭照立, 施保昌 2016 物理学报 65 014702
Google Scholar
Liu G J, Guo Z L, Shi B C 2016 Acta Phys. Sin. 65 014702
Google Scholar
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