Shape Matters: Understanding the Effect of Electrode Geometry on Cell Resistance and Chemo-Mechanical Stress

Lin, Tiras Y.; Li, Hanyu; Brady, Nicholas W.; Cross, Nicholas R.; Ehlinger, Victoria M.; Roy, Thomas; Tortorelli, Daniel; Orme, Christine; Worsley, Marcus A.; Bucci, Giovanna

doi:10.1149/1945-7111/ad81b4

Title: Shape Matters: Understanding the Effect of Electrode Geometry on Cell Resistance and Chemo-Mechanical Stress

Journal Article · 14 October 2024 · Journal of the Electrochemical Society

DOI: https://doi.org/10.1149/1945-7111/ad81b4 · OSTI ID:2476150

^[1]; Li, Hanyu ^[1]; Brady, Nicholas W. ^[1];

^[1]; Ehlinger, Victoria M. ^[1]; Roy, Thomas ^[1]; Tortorelli, Daniel ^[1]; Orme, Christine ^[1]; Worsley, Marcus A. ^[1];

^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Rechargeable batteries that incorporate shaped three-dimensional electrodes have been shown to have increased power and energy densities when compared to a conventional geometry, i.e. a planar cathode and anode that sandwich an electrolyte. Electrodes can be shaped to enable a higher active material loading, while keeping ion transport distances small. However, the relationship between electrical and mechanical performance of shaped electrodes remains poorly understood. Many electrode designs have been explored, where the electrodes are individually shaped or intertwined, and advances in manufacturing and shape/topology optimization have made such designs a reality. Here, we explore sinusoidal half cells and interdigitated full cells. First, we use a simple electrostatics model to understand the cell resistance as a function of shape. Here we focus on low-temperature conditions, where the electrolyte conductivity decreases relative to that of the electrode; here, LiPF₆EC:DMC electrolyte and MnO₂electrode are considered. Next, we use a chemo-mechanics model to examine the stress that arises due to intercalation-driven volume expansion. We show that shaped electrodes provide a significant reduction in resistance in low-temperature conditions, however, they exhibit unfavorable stress concentrations. Overall, we find that the fully interdigitated electrodes may provide the best balance with respect to this resistance-stress trade-off.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2476150

Report Number(s):: LLNL--JRNL-864862; 1098716

Journal Information:: Journal of the Electrochemical Society, Journal Name: Journal of the Electrochemical Society Journal Issue: 10 Vol. 171; ISSN 0013-4651

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (80)

High Energy Density All-Solid-State Batteries: A Challenging Concept Towards 3D Integration Baggetto, Loıc; Niessen, Rogier A. H.; Roozeboom, Fred Advanced Functional Materials, Vol. 18, Issue 7 https://doi.org/10.1002/adfm.200701245	journal	April 2008
3D Porous Cu Current Collector/Li-Metal Composite Anode for Stable Lithium-Metal Batteries Li, Qi; Zhu, Shoupu; Lu, Yingying Advanced Functional Materials, Vol. 27, Issue 18 https://doi.org/10.1002/adfm.201606422	journal	March 2017
3D-Printing Electrolytes for Solid-State Batteries McOwen, Dennis W.; Xu, Shaomao; Gong, Yunhui Advanced Materials, Vol. 30, Issue 18 https://doi.org/10.1002/adma.201707132	journal	March 2018
3D‐Printed Structure Boosts the Kinetics and Intrinsic Capacitance of Pseudocapacitive Graphene Aerogels Yao, Bin; Chandrasekaran, Swetha; Zhang, Haozhe Advanced Materials, Vol. 32, Issue 8 https://doi.org/10.1002/adma.201906652	journal	January 2020
Ultrahigh‐Loading Manganese‐Based Electrodes for Aqueous Batteries via Polymorph Tuning Xiao, Xin; Zhang, Zewen; Wu, Yecun Advanced Materials, Vol. 35, Issue 33 https://doi.org/10.1002/adma.202211555	journal	July 2023
3D Architectures for Batteries and Electrodes Long, Jeffrey W.; Dunn, Bruce; Rolison, Debra R. Advanced Energy Materials, Vol. 10, Issue 46 https://doi.org/10.1002/aenm.202002457	journal	October 2020
Topology optimization of fluids in Stokes flow Borrvall, Thomas; Petersson, Joakim International Journal for Numerical Methods in Fluids, Vol. 41, Issue 1 https://doi.org/10.1002/fld.426	journal	January 2002
Direct Ink Writing of 3D Zn Structures as High‐Capacity Anodes for Rechargeable Alkaline Batteries Zhu, Cheng; Schorr, Noah B.; Qi, Zhen Small Structures, Vol. 4, Issue 4 https://doi.org/10.1002/sstr.202200323	journal	December 2022
Optimal shape design as a material distribution problem Bendsøe, M. P. Structural Optimization, Vol. 1, Issue 4 https://doi.org/10.1007/BF01650949	journal	December 1989
Topology optimization of channel flow problems Gersborg-Hansen, A.; Sigmund, O.; Haber, R. B. Structural and Multidisciplinary Optimization, Vol. 30, Issue 3 https://doi.org/10.1007/s00158-004-0508-7	journal	June 2005
Topology optimization approaches: A comparative review Sigmund, Ole; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 48, Issue 6 https://doi.org/10.1007/s00158-013-0978-6	journal	August 2013
Topology optimization for the design of flow fields in a redox flow battery Yaji, Kentaro; Yamasaki, Shintaro; Tsushima, Shohji Structural and Multidisciplinary Optimization, Vol. 57, Issue 2 https://doi.org/10.1007/s00158-017-1763-8	journal	July 2017
Density based topology optimization of turbulent flow heat transfer systems Dilgen, Sumer B.; Dilgen, Cetin B.; Fuhrman, David R. Structural and Multidisciplinary Optimization, Vol. 57, Issue 5 https://doi.org/10.1007/s00158-018-1967-6	journal	March 2018
Topology optimization for the design of porous electrodes Roy, Thomas; Salazar de Troya, Miguel A.; Worsley, Marcus A. Structural and Multidisciplinary Optimization, Vol. 65, Issue 6 https://doi.org/10.1007/s00158-022-03249-2	journal	May 2022
Topology optimization for the full-cell design of porous electrodes in electrochemical energy storage devices Li, Hanyu; Bucci, Giovanna; Brady, Nicholas W. Structural and Multidisciplinary Optimization, Vol. 67, Issue 11 https://doi.org/10.1007/s00158-024-03901-z	journal	November 2024
Room temperature elastic moduli and Vickers hardness of hot-pressed LLZO cubic garnet Ni, Jennifer E.; Case, Eldon D.; Sakamoto, Jeffrey S. Journal of Materials Science, Vol. 47, Issue 23, p. 7978-7985 https://doi.org/10.1007/s10853-012-6687-5	journal	July 2012
Thermal stresses in elastic multilayer systems Hsueh, C. H. Thin Solid Films, Vol. 418, Issue 2 https://doi.org/10.1016/S0040-6090(02)00699-5	journal	October 2002
Topology optimization of non-linear elastic structures and compliant mechanisms Bruns, Tyler E.; Tortorelli, Daniel A. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 26-27 https://doi.org/10.1016/S0045-7825(00)00278-4	journal	March 2001
3-D Microbatteries Hart, Ryan W.; White, Henry S.; Dunn, Bruce Electrochemistry Communications, Vol. 5, Issue 2, p. 120-123 https://doi.org/10.1016/S1388-2481(02)00556-8	journal	February 2003
A comprehensive review of lithium-ion batteries used in hybrid and electric vehicles at cold temperatures Jaguemont, J.; Boulon, L.; Dubé, Y. Applied Energy, Vol. 164 https://doi.org/10.1016/j.apenergy.2015.11.034	journal	February 2016
Design and additive manufacturing of optimized electrodes for energy storage applications Reale Batista, Mariana Desireé; Chandrasekaran, Swetha; Moran, Bryan D. Carbon, Vol. 205 https://doi.org/10.1016/j.carbon.2023.01.044	journal	March 2023
On the origin and application of the Bruggeman correlation for analysing transport phenomena in electrochemical systems Tjaden, Bernhard; Cooper, Samuel J.; Brett, Daniel JL Current Opinion in Chemical Engineering, Vol. 12 https://doi.org/10.1016/j.coche.2016.02.006	journal	May 2016
Enhancing Faradaic Charge Storage Contribution in Hybrid Pseudocapacitors Girard, Henri-Louis; Wang, Hainan; d’Entremont, Anna L. Electrochimica Acta, Vol. 182 https://doi.org/10.1016/j.electacta.2015.09.070	journal	November 2015
Computational design of flow fields for vanadium redox flow batteries via topology optimization Chen, Chih-Hsiang; Yaji, Kentaro; Yamasaki, Shintaro Journal of Energy Storage, Vol. 26 https://doi.org/10.1016/j.est.2019.100990	journal	December 2019
Topology optimization as a powerful tool to design advanced PEMFCs flow fields Behrou, Reza; Pizzolato, Alberto; Forner-Cuenca, Antoni International Journal of Heat and Mass Transfer, Vol. 135 https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.050	journal	June 2019
Enhancing heat dissipation and mass transfer of oxygen gas flow channel in a proton exchange membrane fuel cell using multiobjective topology optimization Wang, Zelin; Wang, Hui; Xiao, Heye International Journal of Hydrogen Energy, Vol. 48, Issue 83 https://doi.org/10.1016/j.ijhydene.2023.05.023	journal	October 2023
Heterogeneous damage in Li-ion batteries: Experimental analysis and theoretical modeling Xu, Rong; Yang, Yang; Yin, Fei Journal of the Mechanics and Physics of Solids, Vol. 129 https://doi.org/10.1016/j.jmps.2019.05.003	journal	August 2019
High Areal Energy Density 3D Lithium-Ion Microbatteries Hur, Janet I.; Smith, Leland C.; Dunn, Bruce Joule, Vol. 2, Issue 6 https://doi.org/10.1016/j.joule.2018.04.002	journal	June 2018
Efficient 3D Printed Pseudocapacitive Electrodes with Ultrahigh MnO2 Loading Yao, Bin; Chandrasekaran, Swetha; Zhang, Jing Joule, Vol. 3, Issue 2 https://doi.org/10.1016/j.joule.2018.09.020	journal	February 2019
Transitioning solid-state batteries from lab to market: Linking electro-chemo-mechanics with practical considerations Wang, Michael J.; Kazyak, Eric; Dasgupta, Neil P. Joule, Vol. 5, Issue 6 https://doi.org/10.1016/j.joule.2021.04.001	journal	June 2021
Controlling dendrite propagation in solid-state batteries with engineered stress Fincher, Cole D.; Athanasiou, Christos E.; Gilgenbach, Colin Joule, Vol. 6, Issue 12 https://doi.org/10.1016/j.joule.2022.10.011	journal	December 2022
Aerogels, additive manufacturing, and energy storage Chandrasekaran, Swetha; Lin, Dun; Li, Yat Joule, Vol. 7, Issue 5 https://doi.org/10.1016/j.joule.2023.03.021	journal	May 2023
Modelling electrode material utilization in the trench model 3D-microbattery by finite element analysis Zadin, Vahur; Kasemägi, Heiki; Aabloo, Alvo Journal of Power Sources, Vol. 195, Issue 18 https://doi.org/10.1016/j.jpowsour.2010.02.056	journal	September 2010
Modeling mass and density distribution effects on the performance of co-extruded electrodes for high energy density lithium-ion batteries Cobb, Corie L.; Blanco, Mario Journal of Power Sources, Vol. 249 https://doi.org/10.1016/j.jpowsour.2013.10.084	journal	March 2014
Laser-printing and femtosecond-laser structuring of LiMn2O4 composite cathodes for Li-ion microbatteries Pröll, J.; Kim, H.; Piqué, A. Journal of Power Sources, Vol. 255 https://doi.org/10.1016/j.jpowsour.2013.12.132	journal	June 2014
Effect of extreme temperatures on battery charging and performance of electric vehicles Lindgren, Juuso; Lund, Peter D. Journal of Power Sources, Vol. 328 https://doi.org/10.1016/j.jpowsour.2016.07.038	journal	October 2016
Modeling of lithium electrodeposition at the lithium/ceramic electrolyte interface: The role of interfacial resistance and surface defects Bucci, Giovanna; Christensen, Jake Journal of Power Sources, Vol. 441 https://doi.org/10.1016/j.jpowsour.2019.227186	journal	November 2019
Computational design of microarchitected porous electrodes for redox flow batteries Beck, Victor A.; Wong, Jonathan J.; Jekel, Charles F. Journal of Power Sources, Vol. 512 https://doi.org/10.1016/j.jpowsour.2021.230453	journal	November 2021
Insights into architecture, design and manufacture of electrodes for lithium-ion batteries Zhu, Pengcheng; Slater, Peter R.; Kendrick, Emma Materials & Design, Vol. 223 https://doi.org/10.1016/j.matdes.2022.111208	journal	November 2022
Finite element modelling of ion transport in the electrolyte of a 3D-microbattery Zadin, Vahur; Brandell, Daniel; Kasemägi, Heiki Solid State Ionics, Vol. 192, Issue 1 https://doi.org/10.1016/j.ssi.2010.02.007	journal	June 2011
Rate-dependent deformation of amorphous sulfide glass electrolytes for solid-state batteries Athanasiou, Christos E.; Liu, Xing; Jin, Mok Yun Cell Reports Physical Science, Vol. 3, Issue 4 https://doi.org/10.1016/j.xcrp.2022.100845	journal	April 2022
Ionic Conduction and Solution Structure in LiPF ₆ and LiBF ₄ Propylene Carbonate Electrolytes Hwang, Sunwook; Kim, Dong-Hui; Shin, Jeong Hee The Journal of Physical Chemistry C, Vol. 122, Issue 34 https://doi.org/10.1021/acs.jpcc.8b06035	journal	July 2018
High-Performance Solid-State Lithium-Ion Battery with Mixed 2D and 3D Electrodes Ashby, David S.; Choi, Christopher S.; Edwards, Martin A. ACS Applied Energy Materials, Vol. 3, Issue 9 https://doi.org/10.1021/acsaem.0c01029	journal	July 2020
Roadmap of Solid-State Lithium-Organic Batteries toward 500 Wh kg ^–1 Zhao, Lihong; Lakraychi, Alae Eddine; Chen, Zhaoyang ACS Energy Letters, Vol. 6, Issue 9 https://doi.org/10.1021/acsenergylett.1c01368	journal	August 2021
Are Three-Dimensional Batteries Beneficial? Analyzing Historical Data to Elucidate Performance Advantages Hung, Chih-Hsuan; Huynh, Phong; Teo, Katrina ACS Energy Letters, Vol. 8, Issue 1 https://doi.org/10.1021/acsenergylett.2c02208	journal	November 2022
Lithiophilic 3D Porous CuZn Current Collector for Stable Lithium Metal Batteries Zhang, Duo; Dai, Alvin; Wu, Min ACS Energy Letters, Vol. 5, Issue 1 https://doi.org/10.1021/acsenergylett.9b01987	journal	October 2019
Three-Dimensional Battery Architectures Long, Jeffrey W.; Dunn, Bruce; Rolison, Debra R. Chemical Reviews, Vol. 104, Issue 10, p. 4463-4492 https://doi.org/10.1021/cr020740l	journal	October 2004
Nanoscale Polymer Electrolytes: Ultrathin Electrodeposited Poly(Phenylene Oxide) with Solid-State Ionic Conductivity Rhodes, Christopher P.; Long, Jeffrey W.; Doescher, Michael S. The Journal of Physical Chemistry B, Vol. 108, Issue 35 https://doi.org/10.1021/jp047671u	journal	September 2004
Ultrathin, Protective Coatings of Poly(o-phenylenediamine) as Electrochemical Proton Gates: Making Mesoporous MnO₂ Nanoarchitectures Stable in Acid Electrolytes Long, Jeffrey W.; Rhodes, Christopher P.; Young, Amanda L. Nano Letters, Vol. 3, Issue 8 https://doi.org/10.1021/nl0343598	journal	July 2003
Status and challenges in enabling the lithium metal electrode for high-energy and low-cost rechargeable batteries Albertus, Paul; Babinec, Susan; Litzelman, Scott Nature Energy, Vol. 3, Issue 1 https://doi.org/10.1038/s41560-017-0047-2	journal	December 2017
Benchmarking the performance of all-solid-state lithium batteries Randau, Simon; Weber, Dominik A.; Kötz, Olaf Nature Energy, Vol. 5, Issue 3 https://doi.org/10.1038/s41560-020-0565-1	journal	March 2020
Challenges in speeding up solid-state battery development Janek, Jürgen; Zeier, Wolfgang G. Nature Energy, Vol. 8, Issue 3 https://doi.org/10.1038/s41560-023-01208-9	journal	February 2023
3D printed optimized electrodes for electrochemical flow reactors Davis, Jonathan T.; Jayathilake, Buddhinie S.; Chandrasekaran, Swetha Scientific Reports, Vol. 14, Issue 1 https://doi.org/10.1038/s41598-024-71765-w	journal	September 2024
A comparative investigation of carbon black (Super-P) and vapor-grown carbon fibers (VGCFs) as conductive additives for lithium-ion battery cathodes Cho, Inseong; Choi, Jaecheol; Kim, Kyuman RSC Advances, Vol. 5, Issue 115 https://doi.org/10.1039/C5RA19056H	journal	January 2015
Modeling of internal mechanical failure of all-solid-state batteries during electrochemical cycling, and implications for battery design Bucci, Giovanna; Swamy, Tushar; Chiang, Yet-Ming Journal of Materials Chemistry A, Vol. 5, Issue 36 https://doi.org/10.1039/C7TA03199H	journal	January 2017
Modeling gas-diffusion electrodes for CO ₂ reduction Weng, Lien-Chun; Bell, Alexis T.; Weber, Adam Z. Physical Chemistry Chemical Physics, Vol. 20, Issue 25 https://doi.org/10.1039/C8CP01319E	journal	January 2018
Chemo-mechanical expansion of lithium electrode materials – on the route to mechanically optimized all-solid-state batteries Koerver, Raimund; Zhang, Wenbo; de Biasi, Lea Energy & Environmental Science, Vol. 11, Issue 8 https://doi.org/10.1039/C8EE00907D	journal	January 2018
Review of electrical energy storage technologies, materials and systems: challenges and prospects for large-scale grid storage Gür, Turgut M. Energy & Environmental Science, Vol. 11, Issue 10 https://doi.org/10.1039/C8EE01419A	journal	January 2018
Graphene anchored on Cu foam as a lithiophilic 3D current collector for a stable and dendrite-free lithium metal anode Yang, Guanhui; Chen, Jiadong; Xiao, Peitao Journal of Materials Chemistry A, Vol. 6, Issue 21 https://doi.org/10.1039/C8TA02810A	journal	January 2018
Gradient porosity electrodes for fast charging lithium-ion batteries Yang, Jian; Li, Yejing; Mijailovic, Aleksandar Journal of Materials Chemistry A, Vol. 10, Issue 22 https://doi.org/10.1039/D2TA01707E	journal	January 2022
Thermal and Electrical Conductivity of Graphite and Carbon at Low Temperatures Buerschaper, Robert A. Journal of Applied Physics, Vol. 15, Issue 5 https://doi.org/10.1063/1.1707454	journal	May 1944
Tortuosity in electrochemical devices: a review of calculation approaches Tjaden, Bernhard; Brett, Dan J. L.; Shearing, Paul R. International Materials Reviews, Vol. 63, Issue 2 https://doi.org/10.1080/09506608.2016.1249995	journal	November 2016
Mechanical instability of electrode-electrolyte interfaces in solid-state batteries Bucci, Giovanna; Talamini, Brandon; Renuka Balakrishna, Ananya Physical Review Materials, Vol. 2, Issue 10 https://doi.org/10.1103/PhysRevMaterials.2.105407	journal	October 2018
Residual Stresses in Meta/Ceramic Bonded Strips Hsueh, C. H.; Evans, A. G. Journal of the American Ceramic Society, Vol. 68, Issue 5 https://doi.org/10.1111/j.1151-2916.1985.tb15316.x	journal	May 1985
Solid-state batteries: The critical role of mechanics Kalnaus, Sergiy; Dudney, Nancy J.; Westover, Andrew S. Science, Vol. 381, Issue 6664 https://doi.org/10.1126/science.abg5998	journal	September 2023
Transport Properties of LiPF[sub 6]-Based Li-Ion Battery Electrolytes Valo̸en, Lars Ole; Reimers, Jan N. Journal of The Electrochemical Society, Vol. 152, Issue 5 https://doi.org/10.1149/1.1872737	journal	January 2005
Theoretical Analysis of Current Distribution in Porous Electrodes Newman, John S.; Tobias, Charles W. Journal of The Electrochemical Society, Vol. 109, Issue 12 https://doi.org/10.1149/1.2425269	journal	January 1962
Numerical Simulation of Intercalation-Induced Stress in Li-Ion Battery Electrode Particles Zhang, Xiangchun; Shyy, Wei; Marie Sastry, Ann Journal of The Electrochemical Society, Vol. 154, Issue 10 https://doi.org/10.1149/1.2759840	journal	January 2007
Intercalation-Induced Stress and Heat Generation within Single Lithium-Ion Battery Cathode Particles Zhang, Xiangchun; Sastry, Ann Marie; Shyy, Wei Journal of The Electrochemical Society, Vol. 155, Issue 7 https://doi.org/10.1149/1.2926617	journal	January 2008
Modeling Current Density Non-Uniformities to Understand High-Rate Limitations in 3D Interdigitated Lithium-ion Batteries Hung, Chih-Hsuan; Allu, Srikanth; Cobb, Corie L. Journal of The Electrochemical Society, Vol. 168, Issue 10 https://doi.org/10.1149/1945-7111/ac2ac5	journal	October 2021
Topology Optimization of 3D Flow Fields for Flow Batteries Lin, Tiras Y.; Baker, Sarah E.; Duoss, Eric B. Journal of The Electrochemical Society, Vol. 169, Issue 5 https://doi.org/10.1149/1945-7111/ac716d	journal	May 2022
Lithium Concentration Dependent Elastic Properties of Battery Electrode Materials from First Principles Calculations Qi, Yue; Hector, Louis G.; James, Christine Journal of The Electrochemical Society, Vol. 161, Issue 11 https://doi.org/10.1149/2.0031411jes	journal	January 2014
Tool for Tortuosity Estimation in Lithium Ion Battery Porous Electrodes Ebner, Martin; Wood, Vanessa Journal of The Electrochemical Society, Vol. 162, Issue 2 https://doi.org/10.1149/2.0111502jes	journal	December 2014
The Effect of Stress on Battery-Electrode Capacity Bucci, Giovanna; Swamy, Tushar; Bishop, Sean Journal of The Electrochemical Society, Vol. 164, Issue 4 https://doi.org/10.1149/2.0371704jes	journal	January 2017
Temperature and Concentration Dependence of the Ionic Transport Properties of Lithium-Ion Battery Electrolytes Landesfeind, Johannes; Gasteiger, Hubert A. Journal of The Electrochemical Society, Vol. 166, Issue 14 https://doi.org/10.1149/2.0571912jes	journal	January 2019
Microscale 2.5D Batteries McKelvey, Kim; Talin, A. Alec; Dunn, Bruce Journal of The Electrochemical Society, Vol. 164, Issue 12 https://doi.org/10.1149/2.0771712jes	journal	January 2017
Evaluating Transport Properties and Ionic Dissociation of LiPF ₆ in Concentrated Electrolyte Feng, Zhange; Higa, Kenneth; Han, Kee Sung Journal of The Electrochemical Society, Vol. 164, Issue 12 https://doi.org/10.1149/2.0941712jes	journal	January 2017
A review of laser electrode processing for development and manufacturing of lithium-ion batteries Pfleging, Wilhelm Nanophotonics, Vol. 7, Issue 3 https://doi.org/10.1515/nanoph-2017-0044	journal	February 2018
Femtosecond laser structuring of graphite anodes for improved lithium-ion batteries: Ablation characteristics and process design Habedank, Jan B.; Endres, Joseph; Schmitz, Patrick Journal of Laser Applications, Vol. 30, Issue 3 https://doi.org/10.2351/1.5040611	journal	August 2018
Design of Radial Flow Channel Proton Exchange Membrane Fuel Cell Based on Topology Optimization Qu, Cheng; Zhang, Yifan; Zhang, Zhihu Processes, Vol. 11, Issue 8 https://doi.org/10.3390/pr11082482	journal	August 2023