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Zheng Q, Hawthorne N, Batteas JD, Espinosa-Marzal RM. Surface Curvature Enhances the Electrotunability of Ionic Liquid Lubrication. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024. [PMID: 38334102 DOI: 10.1021/acs.langmuir.3c03519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/10/2024]
Abstract
Ionic liquids (ILs) are a promising class of lubricants that allow dynamic friction control at electrified interfaces. In the real world, surfaces inevitably exhibit some degree of roughness, which can influence lubrication. In this work, we deposited single-layer graphene onto 20 nm silica nanoparticle films to investigate the effect of surface curvature and electrostatic potential on both the lubricious behavior and interfacial layering structure of 1-ethyl-3-methyl imidazolium bis(trifluoromethylsulfonyl)imide on graphene. Normal force and friction force measurements were conducted by atomic force microscopy using a sharp silicon tip. Our results reveal that the friction coefficient at the lubricated tip-graphene contacts significantly depends on surface curvature. Two friction coefficients are measured on graphene peaks and valleys with a higher coefficient measured at lower loads (pressures), whereas only one friction coefficient is measured on smooth graphene. Moreover, the electrotunability of the friction coefficient at low loads is observed to be significantly enhanced in peaks and valleys compared with smooth graphene. This is associated with the promoted overscreening of surface charge on convex interfaces and the steric hindrance at concave interfaces, which leads to more layers of ions (electrostatically) bound to the surface, i.e., thicker boundary films (electrical double layers). This work opens new avenues to control IL lubrication on the nanoscale by combining topographic features and an electric field.
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Affiliation(s)
- Qianlu Zheng
- Department of Civil and Environmental Engineering, University of Illinois at Urbana─Champaign, Urbana, Illinois 61801, United States
| | - Nathaniel Hawthorne
- Department of Chemistry, Texas A&M University, College Station, Texas 77843, United States
| | - James D Batteas
- Department of Chemistry, Texas A&M University, College Station, Texas 77843, United States
- Department of Materials Science and Engineering, Texas A&M University, College Station, Texas 77843, United States
| | - Rosa M Espinosa-Marzal
- Department of Civil and Environmental Engineering, University of Illinois at Urbana─Champaign, Urbana, Illinois 61801, United States
- Department of Materials Science and Engineering, University of Illinois at Urbana─Champaign, Urbana, Illinois 61801, United States
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2
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Kondrat S, Feng G, Bresme F, Urbakh M, Kornyshev AA. Theory and Simulations of Ionic Liquids in Nanoconfinement. Chem Rev 2023; 123:6668-6715. [PMID: 37163447 PMCID: PMC10214387 DOI: 10.1021/acs.chemrev.2c00728] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Indexed: 05/12/2023]
Abstract
Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.
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Affiliation(s)
- Svyatoslav Kondrat
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
- Institute
for Computational Physics, University of
Stuttgart, Stuttgart 70569, Germany
| | - Guang Feng
- State
Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology (HUST), Wuhan 430074, China
- Nano
Interface Centre for Energy, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Fernando Bresme
- Department
of Chemistry, Molecular Sciences Research
Hub, White City Campus, London W12 0BZ,United Kingdom
- Thomas Young
Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- London
Centre for Nanotechnology, Imperial College
London, London SW7 2AZ, United Kingdom
| | - Michael Urbakh
- School
of Chemistry and the Sackler Center for Computational Molecular and
Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Alexei A. Kornyshev
- Department
of Chemistry, Molecular Sciences Research
Hub, White City Campus, London W12 0BZ,United Kingdom
- Thomas Young
Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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3
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An R, Laaksonen A, Wu M, Zhu Y, Shah FU, Lu X, Ji X. Atomic force microscopy probing interactions and microstructures of ionic liquids at solid surfaces. NANOSCALE 2022; 14:11098-11128. [PMID: 35876154 DOI: 10.1039/d2nr02812c] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Ionic liquids (ILs) are room temperature molten salts that possess preeminent physicochemical properties and have shown great potential in many applications. However, the use of ILs in surface-dependent processes, e.g. energy storage, is hindered by the lack of a systematic understanding of the IL interfacial microstructure. ILs on the solid surface display rich ordering, arising from coulombic, van der Waals, solvophobic interactions, etc., all giving near-surface ILs distinct microstructures. Therefore, it is highly important to clarify the interactions of ILs with solid surfaces at the nanoscale to understand the microstructure and mechanism, providing quantitative structure-property relationships. Atomic force microscopy (AFM) opens a surface-sensitive way to probe the interaction force of ILs with solid surfaces in the layers from sub-nanometers to micrometers. Herein, this review showcases the recent progress of AFM in probing interactions and microstructures of ILs at solid interfaces, and the influence of IL characteristics, surface properties and external stimuli is thereafter discussed. Finally, a summary and perspectives are established, in which, the necessities of the quantification of IL-solid interactions at the molecular level, the development of in situ techniques closely coupled with AFM for probing IL-solid interfaces, and the combination of experiments and simulations are argued.
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Affiliation(s)
- Rong An
- Herbert Gleiter Institute of Nanoscience, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.
| | - Aatto Laaksonen
- Energy Engineering, Division of Energy Science, Luleå University of Technology, 97187 Luleå, Sweden.
- Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, SE-10691 Stockholm, Sweden
- Center of Advanced Research in Bionanoconjugates and Biopolymers, "Petru Poni" Institute of Macromolecular Chemistry, Iasi 700469, Romania
- State Key Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 211816, China
| | - Muqiu Wu
- Herbert Gleiter Institute of Nanoscience, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.
| | - Yudan Zhu
- State Key Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 211816, China
| | - Faiz Ullah Shah
- Chemistry of Interfaces, Luleå University of Technology, 97187 Luleå, Sweden
| | - Xiaohua Lu
- State Key Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 211816, China
| | - Xiaoyan Ji
- Energy Engineering, Division of Energy Science, Luleå University of Technology, 97187 Luleå, Sweden.
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Bresme F, Kornyshev AA, Perkin S, Urbakh M. Electrotunable friction with ionic liquid lubricants. NATURE MATERIALS 2022; 21:848-858. [PMID: 35761059 DOI: 10.1038/s41563-022-01273-7] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 05/02/2022] [Indexed: 06/15/2023]
Abstract
Room-temperature ionic liquids and their mixtures with organic solvents as lubricants open a route to control lubricity at the nanoscale via electrical polarization of the sliding surfaces. Electronanotribology is an emerging field that has a potential to realize in situ control of friction-that is, turning the friction on and off on demand. However, fulfilling its promise needs more research. Here we provide an overview of this emerging research area, from its birth to the current state, reviewing the main achievements in non-equilibrium molecular dynamics simulations and experiments using atomic force microscopes and surface force apparatus. We also present a discussion of the challenges that need to be solved for future applications of electrotunable friction.
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Affiliation(s)
- Fernando Bresme
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, London, UK.
| | - Alexei A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, London, UK.
| | - Susan Perkin
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford, UK.
| | - Michael Urbakh
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, Israel.
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5
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Di Lecce S, Kornyshev AA, Urbakh M, Bresme F. Structural effects in nanotribology of nanoscale films of ionic liquids confined between metallic surfaces. Phys Chem Chem Phys 2021; 23:22174-22183. [PMID: 34581331 DOI: 10.1039/d1cp03345j] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Room Temperature Ionic Liquids (RTILs) attract significant interest in nanotribology. However, their microscopic lubrication mechanism is still under debate. Here, using non-equilibrium molecular dynamics simulations, we investigate the lubrication performance of ultra-thin (<2 nm) films of [C2MIM]+ [NTf2]- confined between plane-parallel neutral surfaces of Au(111) or Au(100). We find that films consisting of tri-layers or bilayers, form ordered structures with a flat orientation of the imidazolium rings with respect to the gold surface plane. Tri-layers are unstable against loads >0.5 GPa, while bi-layers sustain pressures in the 1-2 GPa range. The compression of these films results in monolayers that can sustain loads of several GPa without significant loss in their lubrication performance. Surprisingly, in such ultra-thin films the imidazolium rings show higher orientational in-plane disorder, with and the rings adopting a tilted orientation with respect to the gold surface. The friction force and friction coefficient of the monolayers depends strongly on the structure of the gold plates, with the friction coefficient being four times higher for monolayers confined between Au(100) surfaces than for more compact Au(111) surfaces. We show that the general behaviour described here is independent of whether the metallic surfaces are modelled as polarizable or non-polarizable surfaces and speculate on the nature of this unexpected conclusion.
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Affiliation(s)
- Silvia Di Lecce
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College, London, W12 0BZ London, UK.
| | - Alexei A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College, London, W12 0BZ London, UK.
| | - Michael Urbakh
- School of Chemistry and The Sackler Center for Computational Molecular and Materials, Science, Tel Aviv University, 69978, Tel Aviv, Israel
| | - Fernando Bresme
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College, London, W12 0BZ London, UK.
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6
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Han M, Zhang R, Gewirth AA, Espinosa-Marzal RM. Nanoheterogeneity of LiTFSI Solutions Transitions Close to a Surface and with Concentration. NANO LETTERS 2021; 21:2304-2309. [PMID: 33616411 DOI: 10.1021/acs.nanolett.1c00167] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Water-in-salt (WIS) electrolytes composed of 21 m LiTFSI have recently emerged as a safe and environmentally friendly alternative to conventional organic electrolytes in Li-ion batteries. Several studies have emphasized the relation between the high conductivity of WIS electrolytes and their nanoscale structure. Combining force measurements with a surface forces apparatus and atomic force microscopy, this study describes the nanoheterogeneity of LiTFSI solutions as a function of concentration and distance from a negatively charged (mica) surface. We report various nanostructures coexisting in the WIS electrolyte, whose size increases with concentration and is influenced by the proximity of the mica surface. Two key concentration thresholds are identified, beyond which a transition of behavior is observed. The careful scrutinization on the concentration-dependent nanostructures lays groundwork for designing novel electrolytes in future energy storage devices.
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Affiliation(s)
- Mengwei Han
- Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Ruixian Zhang
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Andrew A Gewirth
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Rosa M Espinosa-Marzal
- Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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7
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Di Lecce S, Kornyshev AA, Urbakh M, Bresme F. Lateral Ordering in Nanoscale Ionic Liquid Films between Charged Surfaces Enhances Lubricity. ACS NANO 2020; 14:13256-13267. [PMID: 33054180 DOI: 10.1021/acsnano.0c05043] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Electric fields modify the structural and dynamical properties of room temperature ionic liquids (RTILs) providing a physical principle to develop tunable lubrication devices. Using nonequilibrium molecular dynamics atomistic simulations, we investigate the impact of the composition of imidazolium RTILs on the in-plane ordering of ionic layers in nanogaps. We consider imidazolium cations and widely used anions featuring different molecular structures, spherical ([BF4]-), elongated surfactant-like ([C2SO4]-), and elongated with a more delocalized charge ([NTf2]-). The interplay of surface charge, surface polarity, and anion geometry enables the formation of crystal-like structures in [BF4]- and [NTf2]- nanofilms, while [C2SO4]- nanofilms form disordered layers. We study how the ordering of the ionic liquid lubricant in the nanogap affects friction. Counterintuitively, we find that the friction force decreases with the ability of the RTILs to form crystal-like structures in the confined region. The crystallization can be activated or inhibited by changing the polarity of the surface, providing a mechanism to tune friction with electric fields.
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Affiliation(s)
- Silvia Di Lecce
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, W12 0BZ London, U.K
| | - Alexei A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, W12 0BZ London, U.K
| | - Michael Urbakh
- School of Chemistry and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Fernando Bresme
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, W12 0BZ London, U.K
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8
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Di Lecce S, Kornyshev AA, Urbakh M, Bresme F. Electrotunable Lubrication with Ionic Liquids: the Effects of Cation Chain Length and Substrate Polarity. ACS APPLIED MATERIALS & INTERFACES 2020; 12:4105-4113. [PMID: 31875392 DOI: 10.1021/acsami.9b19283] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Electrotunable lubrication with ionic liquids (ILs) provides dynamic control of friction with the prospect to achieve superlubrication. We investigate the dependence of the frictional and structural forces with 1-n,2-methyl-imidazolium tetrafluoroborate [CnMIM]+[BF4]- (n = 2, 4, 6) ILs as a lubricant on the molecular structure of the liquid, normal load, and polarity of the electrodes. Using non-equilibrium molecular dynamics simulations and coarse-grained force-fields, we show that the friction force depends significantly on the chain length of the cation. ILs containing cations with shorter aliphatic chains show lower friction forces, ∼40% for n = 2 as compared to the n = 6 case, and more resistance to squeeze-out by external loads. The normal load defines the dynamic regime of friction, and it determines maxima in the friction force at specific surface charges. At relatively low normal loads, ∼10 MPa, the velocity profile in the confined region resembles a Couette type flow, whereas at high loads, >200 MPa, the motion of the ions is highly correlated and the velocity profile resembles a "plug" flow. Different dynamic regimes result in distinctive slippage planes, located either at the IL-electrode interface or in the interior of the film, which ultimately lead, at high loads, to the observation of maxima in the friction force at specific surface charge densities. Instead, at low loads the maxima are not observed, and the friction is found to monotonously increase with the surface charge. Friction with [CnMIM]+[BF4]- as a lubricant is reduced when the liquid is confined between positively charged electrodes. This is due to better lubricating properties and enhanced resistance to squeeze out when the anion [BF4]- is in direct contact with the electrode.
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Affiliation(s)
- Silvia Di Lecce
- Department of Chemistry, Molecular Sciences Research Hub , Imperial College , W12 0BZ London , U.K
| | - Alexei A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub , Imperial College , W12 0BZ London , U.K
| | - Michael Urbakh
- School of Chemistry and The Sackler Center for Computational Molecular and Materials Science , Tel Aviv University , Tel Aviv 6997801 , Israel
| | - Fernando Bresme
- Department of Chemistry, Molecular Sciences Research Hub , Imperial College , W12 0BZ London , U.K
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9
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Schwaminger SP, Begovic B, Schick L, Jumani NA, Brammen MW, Fraga-García P, Berensmeier S. Potential-Controlled Tensiometry: A Tool for Understanding Wetting and Surface Properties of Conductive Powders by Electroimbibition. Anal Chem 2018; 90:14131-14136. [PMID: 30450897 DOI: 10.1021/acs.analchem.8b03475] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Potential-controlled tensiometry is a voltage-induced method which enables measuring the contact angle between a powder bed and a liquid medium through the capillary rise method. This analytical tool provides a fine-grained technique for understanding wetting behavior of powders as well as solid surfaces in connection with the application of an electrical potential. In this work, the powder bed was brought into contact with an aluminum rod connected to a portable lightweight DAC-module (digital to analog converter) powered by a lithium-polymer battery (LiPo). The presented analytical device can be charged up to ±1000 mV. Both the power source and the DAC-module are lightweight in order to be conveniently attached to a force tensiometer without incorporating complex wiring. In this setup, we tested multiwall carbon nanotubes (MWCNT) and glassy carbon particles. An influence of the potential on the wetting behavior of glassy carbon particles is observed which demonstrates the working principle of the device. Surprisingly, no significant effect of the potential on the wetting behavior of MWCNT is indicated in the range studied. This technique can be a valuable tool to analyze the effect of changing surface properties applying electrical gradients on materials.
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Affiliation(s)
- Sebastian P Schwaminger
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany
| | - Benedikt Begovic
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany
| | - Lukas Schick
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany
| | - N Aisyah Jumani
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany.,Singapore Institute of Technology , 510 Dover Road , Singapore City , Singapore 138683
| | - Markus W Brammen
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany
| | - Paula Fraga-García
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany
| | - Sonja Berensmeier
- Bioseparation Engineering Group, Department of Mechanical Engineering , Technical University of Munich , Boltzmannstraße 15 , Garching , 85748 , Germany
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10
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Breitsprecher K, Holm C, Kondrat S. Charge Me Slowly, I Am in a Hurry: Optimizing Charge-Discharge Cycles in Nanoporous Supercapacitors. ACS NANO 2018; 12:9733-9741. [PMID: 30088913 DOI: 10.1021/acsnano.8b04785] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Nanoporous supercapacitors attract much attention as green energy storage devices with remarkable cyclability and high power and energy densities. However, their use in high-frequency applications is limited by relatively slow charging processes, while accelerating charging without compromising the energy storage still remains a challenging task. Here, we study in detail the charging and discharging behavior of nanoporous supercapacitors with narrow pores, which provide exceptionally high capacitances and stored energy densities. We scrutinize the dynamic modes of charging, revealing, in particular, a transient formation of crowded and dilute ionic-liquid phases inside the pores, which leads to co-ion trapping and correspondingly slow charging. We show how trapping can be circumvented by applying a slow voltage sweep, and we demonstrate that it can accelerate the overall charging process considerably if the sweep rate is chosen appropriately. While one might be tempted to apply a similar strategy to discharging, we find that the best discharge rates are obtained when the voltage is switched off in a step-like fashion, whereby the optimal charge and discharge times differ a few-fold. We unveil the scaling laws for such optimal quantities, which allow one to predict quantitatively the charging behavior for realistically long pores. On the basis of our findings, we propose an optimal charge-discharge cycle and elaborate on optimization strategies.
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Affiliation(s)
- Konrad Breitsprecher
- Institute for Computational Physics , Universität Stuttgart , Allmandring 3 , D-70569 Stuttgart , Germany
| | - Christian Holm
- Institute for Computational Physics , Universität Stuttgart , Allmandring 3 , D-70569 Stuttgart , Germany
| | - Svyatoslav Kondrat
- Institute for Computational Physics , Universität Stuttgart , Allmandring 3 , D-70569 Stuttgart , Germany
- Department of Complex Systems , Institute of Physical Chemistry, Polish Academy of Sciences , Kasprzaka 44/52 , 01-224 Warsaw , Poland
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