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Duff B, Corti L, Turner B, Han G, Daniels LM, Rosseinsky MJ, Blanc F. Revealing the Local Structure and Dynamics of the Solid Li Ion Conductor Li 3P 5O 14. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2024; 36:7703-7718. [PMID: 39220613 PMCID: PMC11360135 DOI: 10.1021/acs.chemmater.4c00727] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 05/31/2024] [Accepted: 05/31/2024] [Indexed: 09/04/2024]
Abstract
The development of fast Li ion-conducting materials for use as solid electrolytes that provide sufficient electrochemical stability against electrode materials is paramount for the future of all-solid-state batteries. Advances on these fast ionic materials are dependent on building structure-ionic mobility-function relationships. Here, we exploit a series of multinuclear and multidimensional nuclear magnetic resonance (NMR) approaches, including 6Li and 31P magic angle spinning (MAS), in conjunction with density functional theory (DFT) to provide a detailed understanding of the local structure of the ultraphosphate Li3P5O14, a promising candidate for an oxide-based Li ion conductor that has been shown to be a highly conductive, energetically favorable, and electrochemically stable potential solid electrolyte. We have reported a comprehensive assignment of the ultraphosphate layer and layered Li6O16 26- chains through 31P and 6Li MAS NMR, respectively, in conjunction with DFT. The chemical shift anisotropy of the eight resonances with the lowest 31P chemical shift is significantly lower than that of the 12 remaining resonances, suggesting the phosphate bonding nature of these P sites being one that bridges to three other phosphate groups. We employed a number of complementary 6,7Li NMR techniques, including MAS variable-temperature line narrowing spectra, spin-alignment echo (SAE) NMR, and relaxometry, to quantify the lithium ion dynamics in Li3P5O14. Detailed analysis of the diffusion-induced spin-lattice relaxation data allowed for experimental verification of the three-dimensional Li diffusion previously proposed computationally. The 6Li NMR relaxation rates suggest sites Li1 and Li5 (the only five-coordinate Li site) are the most mobile and are adjacent to one another, both in the a-b plane (intralayer) and on the c-axis (interlayer). As shown in the 6Li-6Li exchange spectroscopy NMR spectra, sites Li1 and Li5 likely exchange with one another both between adjacent layered Li6O16 26- chains and through the center of the P12O36 12- rings forming the three-dimensional pathway. The understanding of the Li ion mobility pathways in high-performing solid electrolytes outlines a route for further development of such materials to improve their performance.
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Affiliation(s)
- Benjamin
B. Duff
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
- Stephenson
Institute for Renewable Energy, University
of Liverpool, L69 7ZF Liverpool, U.K.
| | - Lucia Corti
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
- Leverhulme
Research Centre for Functional Materials Design, Materials Innovation
Factory, University of Liverpool, L7 3NY Liverpool, United Kingdom
| | - Bethan Turner
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
| | - Guopeng Han
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
| | - Luke M. Daniels
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
| | - Matthew J. Rosseinsky
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
- Leverhulme
Research Centre for Functional Materials Design, Materials Innovation
Factory, University of Liverpool, L7 3NY Liverpool, United Kingdom
| | - Frédéric Blanc
- Department
of Chemistry, University of Liverpool, L69 7ZD Liverpool, U.K.
- Stephenson
Institute for Renewable Energy, University
of Liverpool, L69 7ZF Liverpool, U.K.
- Leverhulme
Research Centre for Functional Materials Design, Materials Innovation
Factory, University of Liverpool, L7 3NY Liverpool, United Kingdom
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2
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Wimperis S, Rudman GE, Johnston KE. Biexponential I = 3/2 Spin-Lattice Relaxation in the Solid State: Multiple-Quantum 7Li NMR as a Probe of Fast Ion Dynamics. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2024; 128:5453-5460. [PMID: 38595772 PMCID: PMC11000215 DOI: 10.1021/acs.jpcc.4c00262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/14/2024] [Revised: 03/05/2024] [Accepted: 03/07/2024] [Indexed: 04/11/2024]
Abstract
Spin-lattice relaxation measurements are used in 7Li NMR studies of materials of potential use in solid-state Li-ion batteries as a probe of ion mobility on a fast (nanosecond to picosecond) time scale. The relaxation behavior is often analyzed by assuming exponential behavior or, equivalently, a single T1 time constant. However, the spin-lattice relaxation of spin I = 3/2 nuclei, such as 7Li, is in general biexponential; this is a fundamental property of I = 3/2 nuclei and unrelated to any compartmentalization within the solid. Although the possibility of biexponential 7Li (and other I = 3/2 nuclei) spin-lattice relaxation in the solid state has been noted by a number of authors, it can be difficult to observe unambiguously using conventional experimental NMR techniques, such as inversion or saturation recovery. In this work, we show that triple-quantum-filtered NMR experiments, as previously exploited in I = 3/2 NMR of liquids, can be used in favorable circumstances to observe and readily quantify biexponential 7Li spin-lattice relaxation in solids with high ion mobility. We demonstrate a triple-quantum-filtered inversion-recovery experiment on the candidate solid electrolyte material Li2OHCl at 325 K, which has previously been shown to exhibit fast ion mobility, and we also introduce a novel triple-quantum-filtered saturation-recovery experiment. The results of these solid-state NMR experiments are less straightforward than those in liquids as a consequence of the unwanted direct excitation of triple-quantum coherences by the weak (compared with the unaveraged 7Li quadrupolar interaction) pulses used, but we show that this unwanted excitation can be accounted for and, in the example shown here, does not impede the extraction of the two 7Li spin-lattice relaxation times.
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Affiliation(s)
- Stephen Wimperis
- Department
of Chemistry, Faraday Building, Lancaster
University, Lancaster LA1 4YB, U.K.
| | - George E. Rudman
- Department
of Chemistry, Durham University, Durham DH1 3LE, U.K.
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3
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Chometon R, Deschamps M, Dugas R, Quemin E, Hennequart B, Deschamps M, Tarascon JM, Laberty-Robert C. Targeting the Right Metrics for an Efficient Solvent-Free Formulation of PEO:LiTFSI:Li 6PS 5Cl Hybrid Solid Electrolyte. ACS APPLIED MATERIALS & INTERFACES 2023; 15:58794-58805. [PMID: 38055784 DOI: 10.1021/acsami.3c11542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
Hybrid solid electrolytes (HSEs) aim to combine the superior ionic conductivity of inorganic fillers with the scalable process of polymer electrolytes in a unique material for solid-state batteries. Pursuing the goal of optimizing the key metrics (σion ≥ 10-4 S·cm-1 at 25 °C and self-standing property), we successfully developed an HSE based on a modified poly(ethylene oxide):LiTFSI organic matrix, which binds together a high loading (75 wt %) of Li6PS5Cl particles, following a solvent-free route. A rational study of available formulation parameters has enabled us to understand the role of each component in conductivity, mixing, and mechanical cohesion. Especially, the type of activation mechanism (Arrhenius or Vogel-Fulcher-Tammann (VFT)) and its associated energy are proposed as a new metric to unravel the ionic pathway inside the HSE. We showed that a polymer-in-ceramic approach is mandatory to obtain enhanced conduction through the HSE ceramic network, as well as superior mechanical properties, revealed by the tensile test. Probing the compatibility of phases, using electrochemical impedance spectroscopy (EIS) alongside 7Li nuclear magnetic resonance (NMR), reveals the formation of an interphase, the quantity and resistivity of which grow with time and temperature. Finally, electrochemical performances are evaluated by assembling an HSE-based battery, which displays comparable stability as pure ceramic ones but still suffers from higher polarization and thus lower capacity. Altogether, we hope these findings provide valuable knowledge to develop a successful HSE, by placing the optimization of the right metrics at the core of the formulation.
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Affiliation(s)
- Ronan Chometon
- Collège de France, Chaire de Chimie du Solide et de l'Energie, UMR8260, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
- Laboratoire de Chimie de la Matière Condensée Sorbonne Université, UMR7574, 4 place Jussieu, 75005 Paris, France
- Blue Solutions, Odet, 29500 Ergué-Gabéric, France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Michaël Deschamps
- CNRS-CEMHTI, UPR3079, Université d'Orléans, 1D avenue de la Recherche Scientifique, Orléans Cedex, 45071 France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Romain Dugas
- Collège de France, Chaire de Chimie du Solide et de l'Energie, UMR8260, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Elisa Quemin
- Collège de France, Chaire de Chimie du Solide et de l'Energie, UMR8260, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Benjamin Hennequart
- Collège de France, Chaire de Chimie du Solide et de l'Energie, UMR8260, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | | | - Jean-Marie Tarascon
- Collège de France, Chaire de Chimie du Solide et de l'Energie, UMR8260, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Christel Laberty-Robert
- Laboratoire de Chimie de la Matière Condensée Sorbonne Université, UMR7574, 4 place Jussieu, 75005 Paris, France
- Réseau sur le Stockage Électrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
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4
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Duff B, Elliott SJ, Gamon J, Daniels LM, Rosseinsky MJ, Blanc F. Toward Understanding of the Li-Ion Migration Pathways in the Lithium Aluminum Sulfides Li 3AlS 3 and Li 4.3AlS 3.3Cl 0.7 via 6,7Li Solid-State Nuclear Magnetic Resonance Spectroscopy. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2023; 35:27-40. [PMID: 36644214 PMCID: PMC9835825 DOI: 10.1021/acs.chemmater.2c02101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Revised: 11/23/2022] [Indexed: 06/17/2023]
Abstract
Li-containing materials providing fast ion transport pathways are fundamental in Li solid electrolytes and the future of all-solid-state batteries. Understanding these pathways, which usually benefit from structural disorder and cation/anion substitution, is paramount for further developments in next-generation Li solid electrolytes. Here, we exploit a range of variable temperature 6Li and 7Li nuclear magnetic resonance approaches to determine Li-ion mobility pathways, quantify Li-ion jump rates, and subsequently identify the limiting factors for Li-ion diffusion in Li3AlS3 and chlorine-doped analogue Li4.3AlS3.3Cl0.7. Static 7Li NMR line narrowing spectra of Li3AlS3 show the existence of both mobile and immobile Li ions, with the latter limiting long-range translational ion diffusion, while in Li4.3AlS3.3Cl0.7, a single type of fast-moving ion is present and responsible for the higher conductivity of this phase. 6Li-6Li exchange spectroscopy spectra of Li3AlS3 reveal that the slower moving ions hop between non-equivalent Li positions in different structural layers. The absence of the immobile ions in Li4.3AlS3.3Cl0.7, as revealed from 7Li line narrowing experiments, suggests an increased rate of ion exchange between the layers in this phase compared with Li3AlS3. Detailed analysis of spin-lattice relaxation data allows extraction of Li-ion jump rates that are significantly increased for the doped material and identify Li mobility pathways in both materials to be three-dimensional. The identification of factors limiting long-range translational Li diffusion and understanding the effects of structural modification (such as anion substitution) on Li-ion mobility provide a framework for the further development of more highly conductive Li solid electrolytes.
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Affiliation(s)
- Benjamin
B. Duff
- Department
of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K.
- Stephenson
Institute for Renewable Energy, University
of Liverpool, Liverpool L69 7ZF, U.K.
| | - Stuart J. Elliott
- Department
of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K.
| | - Jacinthe Gamon
- Department
of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K.
| | - Luke M. Daniels
- Department
of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K.
| | - Matthew J. Rosseinsky
- Department
of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K.
- Leverhulme
Research Centre for Functional Materials Design, Materials Innovation
Factory, University of Liverpool, Liverpool L7 3NY, U.K.
| | - Frédéric Blanc
- Department
of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K.
- Stephenson
Institute for Renewable Energy, University
of Liverpool, Liverpool L69 7ZF, U.K.
- Leverhulme
Research Centre for Functional Materials Design, Materials Innovation
Factory, University of Liverpool, Liverpool L7 3NY, U.K.
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5
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Sharon D, Deng C, Bennington P, Webb MA, Patel SN, de Pablo JJ, Nealey PF. Critical Percolation Threshold for Solvation-Site Connectivity in Polymer Electrolyte Mixtures. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00988] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel Sharon
- Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Chuting Deng
- Pritzker School of Molecular Engineering, University of Chicago, 5640 S Ellis Ave, Chicago, Illinois 60637, United States
| | - Peter Bennington
- Pritzker School of Molecular Engineering, University of Chicago, 5640 S Ellis Ave, Chicago, Illinois 60637, United States
| | - Michael A. Webb
- Department of Chemical and Biological Engineering, Princeton University, 41 Olden Street, Princeton, New Jersey 08540, United States
| | - Shrayesh N. Patel
- Pritzker School of Molecular Engineering, University of Chicago, 5640 S Ellis Ave, Chicago, Illinois 60637, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, 5640 S Ellis Ave, Chicago, Illinois 60637, United States
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, United States
| | - Paul F. Nealey
- Pritzker School of Molecular Engineering, University of Chicago, 5640 S Ellis Ave, Chicago, Illinois 60637, United States
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, United States
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6
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Messinger RJ, Vu Huynh T, Bouchet R, Sarou-Kanian V, Deschamps M. Magic-angle-spinning-induced local ordering in polymer electrolytes and its effects on solid-state diffusion and relaxation NMR measurements. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2020; 58:1118-1129. [PMID: 32324938 DOI: 10.1002/mrc.5033] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Revised: 04/15/2020] [Accepted: 04/17/2020] [Indexed: 06/11/2023]
Abstract
Magic-angle-spinning (MAS) enhances sensitivity and resolution in solid-state nuclear magnetic resonance (NMR) measurements. MAS is obtained by aerodynamic levitation and drive of a rotor, which results in large centrifugal forces that may affect the physical state of soft materials, such as polymers, and subsequent solid-state NMR measurements. Here, we investigate the effects of MAS on the solid-state NMR measurements of a polymer electrolyte for lithium-ion battery applications, poly(ethylene oxide) (PEO) doped with the lithium salt LiTFSI. We show that MAS induces local chain ordering, which manifests itself as characteristic lineshapes with doublet-like splittings in subsequent solid-state 1 H, 7 Li, and 19 F static NMR spectra characterizing the PEO chains and solvated ions. MAS results in distributions of stresses and hence local chain orientations within the rotor, yielding distributions in the local magnetic susceptibility tensor that give rise to the observed NMR anisotropy and lineshapes. The effects of MAS were investigated on solid-state 7 Li and 19 F pulsed-field-gradient (PFG) diffusion and 7 Li longitudinal relaxation NMR measurements. Activation energies for ion diffusion were affected modestly by MAS. 7 Li longitudinal relaxation rates, which are sensitive to lithium-ion dynamics in the nanosecond regime, were essentially unchanged by MAS. We recommend that NMR researchers studying soft polymeric materials use only the spin rates necessary to achieve the desired enhancements in sensitivity and resolution, as well as acquire static NMR spectra after MAS experiments to reveal any signs of stress-induced local ordering.
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Affiliation(s)
- Robert J Messinger
- Department of Chemical Engineering, The City College of New York, CUNY, New York, NY, 10031, USA
| | - Tan Vu Huynh
- CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans, F-45071, France
- RS2E, Réseau sur le Stockage Électrochimique de l'Énergie, FR CNRS 3459, F-80039, Amiens, France
| | - Renaud Bouchet
- LEPMI, CNRS UMR 5279, Université Grenoble Alpes, Grenoble, F-38000, France
| | - Vincent Sarou-Kanian
- CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans, F-45071, France
- RS2E, Réseau sur le Stockage Électrochimique de l'Énergie, FR CNRS 3459, F-80039, Amiens, France
| | - Michaël Deschamps
- CEMHTI, CNRS UPR 3079, Université d'Orléans, Orléans, F-45071, France
- RS2E, Réseau sur le Stockage Électrochimique de l'Énergie, FR CNRS 3459, F-80039, Amiens, France
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7
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Mongcopa KIS, Tyagi M, Mailoa JP, Samsonidze G, Kozinsky B, Mullin SA, Gribble DA, Watanabe H, Balsara NP. Relationship between Segmental Dynamics Measured by Quasi-Elastic Neutron Scattering and Conductivity in Polymer Electrolytes. ACS Macro Lett 2018; 7:504-508. [PMID: 35619350 DOI: 10.1021/acsmacrolett.8b00159] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Quasi-elastic neutron scattering experiments on mixtures of poly(ethylene oxide) and lithium bis(trifluoromethane)sulfonimide salt, a standard polymer electrolyte, led to the quantification of the effect of salt on segmental dynamics in the 1-10 Å length scale. The monomeric friction coefficient characterizing segmental dynamics on these length scales increases exponentially with salt concentration. More importantly, we find that this change in monomeric friction alone is responsible for all of the observed nonlinearity in the dependence of ionic conductivity on salt concentration. Our analysis leads to a surprisingly simple relationship between macroscopic ion transport in polymers and dynamics at monomeric length scales.
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Affiliation(s)
- Katrina Irene S. Mongcopa
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, United States
| | - Madhusudan Tyagi
- National Institute of Standards and Technology Center for Neutron Research, Gaithersburg, Maryland 20899, United States
- Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, United States
| | - Jonathan P. Mailoa
- Research and Technology Center, Robert Bosch LLC, Cambridge, Massachusetts 02139, United States
| | - Georgy Samsonidze
- Research and Technology Center, Robert Bosch LLC, Cambridge, Massachusetts 02139, United States
| | - Boris Kozinsky
- Research and Technology Center, Robert Bosch LLC, Cambridge, Massachusetts 02139, United States
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | | | - Daniel A. Gribble
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, United States
| | - Hiroshi Watanabe
- Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Nitash P. Balsara
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, United States
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Joint Center for Energy Storage Research, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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8
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Timachova K, Villaluenga I, Cirrincione L, Gobet M, Bhattacharya R, Jiang X, Newman J, Madsen LA, Greenbaum SG, Balsara NP. Anisotropic Ion Diffusion and Electrochemically Driven Transport in Nanostructured Block Copolymer Electrolytes. J Phys Chem B 2018; 122:1537-1544. [DOI: 10.1021/acs.jpcb.7b11371] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ksenia Timachova
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California, United States
- Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States
| | - Irune Villaluenga
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California, United States
- Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States
| | - Lisa Cirrincione
- Department
of Physics and Astronomy, Hunter College, City University of New York, New York, New York, United States
| | - Mallory Gobet
- Department
of Physics and Astronomy, Hunter College, City University of New York, New York, New York, United States
| | - Rajashree Bhattacharya
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California, United States
| | - Xi Jiang
- Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States
| | - John Newman
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California, United States
| | - Louis A. Madsen
- Department
of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States
| | - Steven G. Greenbaum
- Department
of Physics and Astronomy, Hunter College, City University of New York, New York, New York, United States
| | - Nitash P. Balsara
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California, United States
- Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States
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