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Shigenobu K, Tsuzuki S, Philippi F, Sudoh T, Ugata Y, Dokko K, Watanabe M, Ueno K, Shinoda W. Molecular Level Origin of Ion Dynamics in Highly Concentrated Electrolytes. J Phys Chem B 2023; 127:10422-10433. [PMID: 38015036 DOI: 10.1021/acs.jpcb.3c05864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
Single-ion conducting liquid electrolytes are key to achieving rapid charge/discharge in Li secondary batteries. The Li+ transference (or transport) numbers are the defining properties of such electrolytes and have been discussed in the framework of concentrated solution theories. However, the connection between macroscopic transference and microscopic ion dynamics remains unclear. Molecular dynamics simulations were performed to obtain direct information regarding the microscopic behaviors in highly concentrated electrolytes, and the relationships between these behaviors and the transference number were determined under anion-blocking conditions. Various solvents with different donor numbers (DNs) were used along with a Li salt of the weakly Lewis basic bis(fluorosulfonyl)amide anion for electrolyte preparation. Favorable ordered Li+ structuring and a continuous Li+ conduction pathway were observed for the fluoroethylene carbonate-based electrolyte due to its low DN. The properties were less pronounced at higher DNs, e.g., for the dimethyl sulfoxide-based electrolyte. The τLi-solventlife/τdipolerelax ratio was introduced as a factor for ion dynamics, and the two mechanisms of ion transport were considered an exchange mechanism (τLi-solventlife/τdipolerelax < 1) and a vehicle mechanism (translational motion of solvated Li+) (τLi-solventlife/τdipolerelax ≥ 1). Vehicle-type transport was dominant with high DNs, while exchangeable transport was preferable at lower DNs. These findings should aid the further selection of solvents and Li salts to prepare single-ion conducting electrolytes.
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Affiliation(s)
- Keisuke Shigenobu
- Research Institute for Interdisciplinary Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan
| | - Seiji Tsuzuki
- Department of Chemistry and Life Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Frederik Philippi
- Department of Chemistry and Life Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Taku Sudoh
- Department of Chemistry and Life Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Yosuke Ugata
- Department of Chemistry and Life Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
- Advanced Chemical Energy Research Centre (ACERC), Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Kaoru Dokko
- Department of Chemistry and Life Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
- Advanced Chemical Energy Research Centre (ACERC), Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Masayoshi Watanabe
- Advanced Chemical Energy Research Centre (ACERC), Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Kazuhide Ueno
- Department of Chemistry and Life Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
- Advanced Chemical Energy Research Centre (ACERC), Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Wataru Shinoda
- Research Institute for Interdisciplinary Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan
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Affiliation(s)
- Catalin P. Gainaru
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, United States
| | - Alexei P. Sokolov
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, United States
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
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Phan AD, Ngan NK, Le NB, Thanh LTM. Toward a Better Understanding of Activation Volume and Dynamic Decoupling of Glass‐Forming Liquids under Compression. MACROMOL THEOR SIMUL 2021. [DOI: 10.1002/mats.202100035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Anh D. Phan
- Faculty of Materials Science and Engineering Phenikaa University Hanoi 12116 Vietnam
- Phenikaa Institute for Advanced Study Phenikaa University Hanoi 12116 Vietnam
| | - Nguyen K. Ngan
- Faculty of Materials Science and Engineering Phenikaa University Hanoi 12116 Vietnam
| | - Nam B. Le
- School of Engineering Physics Hanoi University of Science and Technology 1 Dai Co Viet Hanoi 10000 Vietnam
| | - Le T. M. Thanh
- Faculty of Basic Science Posts and Telecommunications Institute of Technology 122 Hoang Quoc Viet Hanoi 10000 Vietnam
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4
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Xu WS, Douglas JF, Sun ZY. Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02740] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Musiał M, Cheng S, Wojnarowska Z, Paluch M. Density, viscosity, and high-pressure conductivity studies of tricyanomethanide-based ionic liquids. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113971] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Cheng S, Wojnarowska Z, Musiał M, Paluch M. The behavior of conductivity dynamic modulus and its connection to thermodynamic bulk modulus in ionic liquids. Phys Chem Chem Phys 2020; 22:19342-19348. [PMID: 32822445 DOI: 10.1039/d0cp03422c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
In this paper, we investigate the interplay between the dynamics and thermodynamics of aprotic ionic liquids in the supercooled and normal liquid states. For this purpose, the conductivity dynamic modulus Mσp-T, being defined as the ratio of activation energy (Ep) and activation volume (VT), and its relation to bulk modulus BT under isobaric and isothermal conditions is examined. We found that both isobaric cooling and isothermal compression lead to an increase in Mσp-T. Specifically, Mσp-T(P)T rises linearly similar to BT. Consequently, a direct linear relationship between Mσp-T(P)T and BT is established under isothermal conditions.
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Affiliation(s)
- Shinian Cheng
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland.
| | - Zaneta Wojnarowska
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland.
| | - Małgorzata Musiał
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland.
| | - Marian Paluch
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland.
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7
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Xu WS, Douglas JF, Xia W, Xu X. Understanding Activation Volume in Glass-Forming Polymer Melts via Generalized Entropy Theory. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01269] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wenjie Xia
- Department of Civil and Environmental Engineering, North Dakota State University, Fargo, North Dakota 58108, United States
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Xu WS, Douglas JF, Xia W, Xu X. Investigation of the Temperature Dependence of Activation Volume in Glass-Forming Polymer Melts under Variable Pressure Conditions. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01268] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wenjie Xia
- Department of Civil and Environmental Engineering, North Dakota State University, Fargo, North Dakota 58108, United States
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Cheng S, Wojnarowska Z, Musiał M, Flachard D, Drockenmuller E, Paluch M. Access to Thermodynamic and Viscoelastic Properties of Poly(ionic liquid)s Using High-Pressure Conductivity Measurements. ACS Macro Lett 2019; 8:996-1001. [PMID: 35619493 DOI: 10.1021/acsmacrolett.9b00355] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this paper, we examine the transport properties of a 1,2,3-triazolium-based poly(ionic liquid) (PIL) at ambient and elevated pressure up to 475 MPa. We show that the isothermal and isobaric conductivity measurements analyzed in the 3D plane give a unique possibility to estimate the thermodynamic (isothermal compressibility and thermal expansion coefficient) properties for PILs having a charge transport fully controlled by viscosity. This result, providing a direct connection between thermodynamic and dynamic properties of PILs, is of significant importance for both material scientists and practical applications.
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Affiliation(s)
- Shinian Cheng
- Institute of Physics, University of Silesia, SMCEBI, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland
| | - Zaneta Wojnarowska
- Institute of Physics, University of Silesia, SMCEBI, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland
| | - Małgorzata Musiał
- Institute of Physics, University of Silesia, SMCEBI, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland
| | - Dimitri Flachard
- Univ Lyon, Université Lyon 1, CNRS, Ingénierie des Matériaux Polymères, UMR 5223, F-69003 Lyon, France
| | - Eric Drockenmuller
- Univ Lyon, Université Lyon 1, CNRS, Ingénierie des Matériaux Polymères, UMR 5223, F-69003 Lyon, France
| | - Marian Paluch
- Institute of Physics, University of Silesia, SMCEBI, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland
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Wojnarowska Z, Rams-Baron M, Knapik-Kowalczuk J, Połatyńska A, Pochylski M, Gapinski J, Patkowski A, Wlodarczyk P, Paluch M. Experimental evidence of high pressure decoupling between charge transport and structural dynamics in a protic ionic glass-former. Sci Rep 2017; 7:7084. [PMID: 28765639 PMCID: PMC5539233 DOI: 10.1038/s41598-017-07136-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Accepted: 06/23/2017] [Indexed: 11/16/2022] Open
Abstract
In this paper the relaxation dynamics of ionic glass-former acebutolol hydrochloride (ACB-HCl) is studied as a function of temperature and pressure by using dynamic light scattering and broadband dielectric spectroscopy. These unique experimental data provide the first direct evidence that the decoupling between the charge transport and structural relaxation exists in proton conductors over a wide T-P thermodynamic space, with the time scale of structural relaxation being constant at the liquid-glass transition (τα = 1000 s). We demonstrate that the enhanced proton transport, being a combination of intermolecular H+ hopping between cation and anion as well as tautomerization process within amide moiety of ACB molecule, results in a breakdown of the Stokes-Einstein relation at ambient and elevated pressure with the fractional exponent k being pressure dependent. The dTg/dP coefficient, stretching exponent βKWW and dynamic modulus Ea/ΔV# were found to be the same regardless of the relaxation processes studied. This is in contrast to the apparent activation volume parameter that is different when charge transport and structural dynamics are considered. These experimental results together with theoretical considerations create new ideas to design efficient proton conductors for potential electrochemical applications.
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Affiliation(s)
- Z Wojnarowska
- Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007, Katowice, Poland. .,Silesian Center for Education and Interdisciplinary Research, 75 Pulku Piechoty 1A, 41-500, Chorzow, Poland.
| | - M Rams-Baron
- Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007, Katowice, Poland.,Silesian Center for Education and Interdisciplinary Research, 75 Pulku Piechoty 1A, 41-500, Chorzow, Poland
| | - J Knapik-Kowalczuk
- Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007, Katowice, Poland.,Silesian Center for Education and Interdisciplinary Research, 75 Pulku Piechoty 1A, 41-500, Chorzow, Poland
| | - A Połatyńska
- Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland
| | - M Pochylski
- Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland
| | - J Gapinski
- Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland.,NanoBioMedical Centre, A. Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland
| | - A Patkowski
- Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland.,NanoBioMedical Centre, A. Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland
| | - P Wlodarczyk
- Institute of Non-Ferrous Metals, Sowinskiego 5, 44-100, Gliwice, Poland
| | - M Paluch
- Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007, Katowice, Poland.,Silesian Center for Education and Interdisciplinary Research, 75 Pulku Piechoty 1A, 41-500, Chorzow, Poland
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11
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Jedrzejowska A, Grzybowski A, Paluch M. In search of invariants for viscous liquids in the density scaling regime: investigations of dynamic and thermodynamic moduli. Phys Chem Chem Phys 2017; 19:18348-18355. [PMID: 28678273 DOI: 10.1039/c7cp01144j] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
In this paper, we report the nontrivial results of our investigations of dynamic and thermodynamic moduli in search of invariants for viscous liquids in the density scaling regime by using selected supercooled van der Waals liquids as representative materials. Previously, the dynamic modulus Mp-T (defined in the pressure-temperature representation by the ratio of isobaric activation energy and activation volume) as well as the ratio BT/Mp-T (where BT is the thermodynamic modulus defined as the inverse isothermal compressibility) have been suggested as some kinds of material constants. We have established that they are not valid in the explored wide range of temperatures T over a dozen decades of structural relaxation times τ. The temperature dependences of Mp-T and BT/Mp-T have been elucidated by comparison with the well-known measure of the relative contribution of temperature and density fluctuations to molecular dynamics near the glass transition, i.e., the ratio of isochoric and isobaric activation energies. Then, we have implemented an idea to transform the definition of the dynamic modulus Mp-T from the p-T representation to the V-T one. This idea relied on the disentanglement of combined temperature and density fluctuations involved in isobaric parameters and has resulted in finding an invariant for viscous liquids in the density scaling regime, which is the ratio of thermodynamic and dynamic moduli, BT/MV-T. In this way, we have constituted a characteristic of thermodynamics and molecular dynamics, which remains unchanged in the supercooled liquid state for a given material, the molecular dynamics of which obeys the power density scaling law.
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Affiliation(s)
- Agnieszka Jedrzejowska
- Institute of Physics, University of Silesia in Katowice, Uniwersytecka 4, 40-007 Katowice, Poland.
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Webb MA, Savoie BM, Wang ZG, Miller III TF. Chemically Specific Dynamic Bond Percolation Model for Ion Transport in Polymer Electrolytes. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b01437] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Michael A. Webb
- Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Brett M. Savoie
- Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Zhen-Gang Wang
- Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Thomas F. Miller III
- Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Stoeva Z, Lu Z, Ingram MD, Imrie CT. A new polymer electrolyte based on a discotic liquid crystal triblock copolymer. Electrochim Acta 2013. [DOI: 10.1016/j.electacta.2013.01.060] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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14
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Wojnarowska Z, Roland CM, Swiety-Pospiech A, Grzybowska K, Paluch M. Anomalous electrical conductivity behavior at elevated pressure in the protic ionic liquid procainamide hydrochloride. PHYSICAL REVIEW LETTERS 2012; 108:015701. [PMID: 22304270 DOI: 10.1103/physrevlett.108.015701] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2011] [Indexed: 05/31/2023]
Abstract
Using broadband dielectric spectroscopy, we investigated the effect of hydrostatic pressure on the conductivity relaxation time τ{σ} of the supercooled protic ionic liquid, procainamide hydrochloride, a common pharmaceutical. The pressure dependence of τ{σ} exhibited anomalous behavior in the vicinity of the glass transition T{g}, manifested by abrupt changes in activation volume. This peculiar behavior, paralleling the change in temperature dependence of τ{σ} near T{g}, is a manifestation of the decoupling between electrical conductivity and structural relaxation. Although the latter effectively ceases in the glassy state, free ions retain their mobility but with a reduced sensitivity to thermodynamic changes. This is the first observation of decoupling of ion migration from structural relaxation in a glassy conductor by isothermal densification.
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Affiliation(s)
- Z Wojnarowska
- Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice, Poland
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Bendler J, Fontanella J, Shlesinger M, Wintersgill M. Effects of pressure, temperature and volume on the electrical conductivity of polymer electrolytes. Electrochim Acta 2011. [DOI: 10.1016/j.electacta.2011.07.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Funke K, Banhatti RD, Laughman DM, Badr LG, Mutke M, Santic A, Wrobel W, Fellberg EM, Biermann C. First and Second Universalities: Expeditions Towards and Beyond. ACTA ACUST UNITED AC 2010. [DOI: 10.1524/zpch.2010.0025] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
Understanding the mechanisms of translational and localised ionic movements in disordered materials has seen intense activity spanning several decades. This article attempts to convey a concise overview of our contribution to this field over the period from 2005 to 2010 and to place it in its broad context.
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Affiliation(s)
| | - Radha D. Banhatti
- University of Münster, Department of Physical Chemistry, Münster, Deutschland
| | - D. M. Laughman
- University of Muenster, Institute of Physical Chemistry, Muenster, Deutschland
| | - L. G. Badr
- University of Muenster, Institute of Physical Chemistry, Muenster
| | | | | | | | | | - C. Biermann
- University of Muenster, Institute of Physical Chemistry, Münster, Deutschland
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Wang FM, Lee JT, Cheng JH, Cheng CS, Yang CR. The network gel polymer electrolyte based on poly(acrylate-co-imide) and its transport properties in lithium ion batteries. J Solid State Electrochem 2008. [DOI: 10.1007/s10008-008-0704-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Ingram MD, Imrie CT, Ledru J, Hutchinson JM. Unified Approach to Ion Transport and Structural Relaxation in Amorphous Polymers and Glasses. J Phys Chem B 2008; 112:859-66. [DOI: 10.1021/jp0754482] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Malcolm D. Ingram
- School of Natural and Computing Sciences, University of Aberdeen, Meston Building, Meston Walk, Aberdeen AB24 3UE, Scotland, UK, and Departament de Màquines i Motors Tèrmics, ETSEIAT, Universitat Politècnica de Catalunya, Carrer Colom 11, 08222 Terrassa, Spain
| | - Corrie T. Imrie
- School of Natural and Computing Sciences, University of Aberdeen, Meston Building, Meston Walk, Aberdeen AB24 3UE, Scotland, UK, and Departament de Màquines i Motors Tèrmics, ETSEIAT, Universitat Politècnica de Catalunya, Carrer Colom 11, 08222 Terrassa, Spain
| | - Jacques Ledru
- School of Natural and Computing Sciences, University of Aberdeen, Meston Building, Meston Walk, Aberdeen AB24 3UE, Scotland, UK, and Departament de Màquines i Motors Tèrmics, ETSEIAT, Universitat Politècnica de Catalunya, Carrer Colom 11, 08222 Terrassa, Spain
| | - John M. Hutchinson
- School of Natural and Computing Sciences, University of Aberdeen, Meston Building, Meston Walk, Aberdeen AB24 3UE, Scotland, UK, and Departament de Màquines i Motors Tèrmics, ETSEIAT, Universitat Politècnica de Catalunya, Carrer Colom 11, 08222 Terrassa, Spain
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