1
|
Prakash K, Sathian SP. Temperature-dependent differential capacitance of an ionic liquid-graphene-based supercapacitor. Phys Chem Chem Phys 2024; 26:4657-4667. [PMID: 38251719 DOI: 10.1039/d3cp05039d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2024]
Abstract
One of the critical factors affecting the performance of supercapacitors is thermal management. The design of supercapacitors that operate across a broad temperature range and at high charge/discharge rates necessitates understanding the correlation of the molecular characteristics of the device (such as interfacial structure and inter-ionic and ion-electrode interactions) with its macroscopic properties. In this study, we use molecular dynamics (MD) simulations to investigate the influence of Joule heating on the structure and dynamics of the ionic liquid (IL)/graphite-based supercapacitors. The temperature-dependent electrical double layer (EDL) and differential capacitance-potential (CD-V) curves of two different ([Bmim][BF4] and [Bmim][PF6]) IL-graphene pairs were studied under various thermal gradients. For the [Bmim][BF4] system, the differential capacitance curves transition from 'U' to bell shape under an applied thermal gradient (∇T) in the range from 3.3 K nm-1 to 16.7 K nm-1. Whereas in [Bmim][PF6], we find a positive dependence of differential capacitance with ∇T with a U-shaped CD-V curve. We examine changes in the EDL structure and screening potential (ϕ(z)) as a function of ∇T and correlate them with the trends observed in the CD-V curve. The identified correlation between the interfacial charge density and differential capacitance with thermal gradient would be helpful for the molecular design of the IL-electrode interface in supercapacitors or other chemical engineering applications.
Collapse
Affiliation(s)
- Kiran Prakash
- Department of Applied Mechanics and Biomedical Engineering, Indian Institute of Technology Madras, Chennai-600036, Tamil Nadu, India.
| | - Sarith P Sathian
- Department of Applied Mechanics and Biomedical Engineering, Indian Institute of Technology Madras, Chennai-600036, Tamil Nadu, India.
| |
Collapse
|
2
|
Sitlapersad RS, Thornton AR, den Otter WK. Charging and discharging a supercapacitor in molecular simulations. J Chem Phys 2024; 160:044111. [PMID: 38275193 DOI: 10.1063/5.0177103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 12/17/2023] [Indexed: 01/27/2024] Open
Abstract
As the world moves more toward unpredictable renewable energy sources, better energy storage devices are required. Supercapacitors are a promising technology to meet the demand for short-term, high-power energy storage. Clearly, understanding their charging and discharging behaviors is essential to improving the technology. Molecular Dynamics (MD) simulations provide microscopic insights into the complex interplay between the dynamics of the ions in the electrolyte and the evolution of the charge distributions on the electrodes. Traditional MD simulations of (dis)charging supercapacitors impose a pre-determined evolving voltage difference between the electrodes, using the Constant Potential Method (CPM). Here, we present an alternative method that explicitly simulates the charge flow to and from the electrodes. For a disconnected capacitor, i.e., an open circuit, the charges are allowed to redistribute within each electrode while the sum charges on both electrodes remain constant. We demonstrate, for a model capacitor containing an aqueous salt solution, that this method recovers the charge-potential curve of CPM simulations. The equilibrium voltage fluctuations are related to the differential capacitance. We next simulate a closed circuit by introducing equations of motion for the sum charges, by explicitly accounting for the external circuit element(s). Charging and discharging of the model supercapacitor via a resistance proceed by double exponential processes, supplementing the usual time scale set by the electrolyte dynamics with a novel time scale set by the external circuit. Finally, we propose a simple equivalent circuit that reproduces the main characteristics of this supercapacitor.
Collapse
Affiliation(s)
- Ranisha S Sitlapersad
- Department of Fluid and Thermal Engineering and MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| | - Anthony R Thornton
- Department of Fluid and Thermal Engineering and MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| | - Wouter K den Otter
- Department of Fluid and Thermal Engineering and MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| |
Collapse
|
3
|
Sitlapersad RS, Thornton AR, den Otter WK. A simple efficient algorithm for molecular simulations of constant potential electrodes. J Chem Phys 2024; 160:034107. [PMID: 38235800 DOI: 10.1063/5.0171502] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 12/21/2023] [Indexed: 01/19/2024] Open
Abstract
Increasingly, society requires high power, high energy storage devices for applications ranging from electric vehicles to buffers on the electric grid. Supercapacitors are a promising contribution to meeting these demands, though there still remain unsolved practical problems. Molecular dynamics simulations can shed light on the relevant molecular level processes in electric double layer capacitors, but these simulations are computationally very demanding. Our focus here is on the algorithmic complexity of the constant potential method (CPM), which uses dedicated electrostatics solvers to maintain a fixed potential difference between two conducting electrodes. We show how any standard electrostatics solver-capable of calculating the energies and forces on all atoms-can be used to implement CPM with a minimum of coding. As an example, we compare our generalized implementation of CPM, based on invocations of the particle-particle-particle-mesh routine of the Large-scale Atomic/Molecular Massively Parallel Simulator, with a traditional implementation based on a dedicated re-implementation of Ewald summation. Both methods yield comparable results on four test systems, with the former achieving a substantial gain in speed and improved scalability. The step from dedicated electrostatic solvers to generic routines is made possible by noting that CPM's traditional narrow Gaussian point-spread of atomic charges on the electrodes effectively endows point-like atoms with chemical hardness, i.e., an intra-atomic energy quadratic in the charge.
Collapse
Affiliation(s)
- Ranisha S Sitlapersad
- Department of Fluid and Thermal Engineering and MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| | - Anthony R Thornton
- Department of Fluid and Thermal Engineering and MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| | - Wouter K den Otter
- Department of Fluid and Thermal Engineering and MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| |
Collapse
|
4
|
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 DOI: 10.1021/acs.chemrev.2c00728] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [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.
Collapse
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
| |
Collapse
|
5
|
Panse KS, Wu H, Zhou S, Zhao F, Aluru NR, Zhang Y. Innermost Ion Association Configuration Is a Key Structural Descriptor of Ionic Liquids at Electrified Interfaces. J Phys Chem Lett 2022; 13:9464-9472. [PMID: 36198103 DOI: 10.1021/acs.jpclett.2c02768] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The structure of electric double layers (EDLs) is crucial for all types of electrochemical processes. While in dilute solutions EDL structure can be approximately treated within the Gouy-Chapman-Stern regime, in highly ionic electrolytes the description of EDL has been largely elusive. Here we study the EDL structure of an ionic liquid on a series of crystalline electrodes. Through molecular dynamics (MD) simulations, we observe strong intermolecular interaction among cations and anions and propose that the cation-anion association structure at the innermost layer is a key descriptor of the EDL. Using our recently developed electrochemical 3D atomic force microscopy (EC-3D-AFM) technique, we confirm the theoretical prediction and further find that the width of the first EDL is an experimental gauge of the ion association structure in that layer. We expect such ion association descriptors to be broadly applicable to a large range of highly ionic electrolytes on various electrode surfaces.
Collapse
Affiliation(s)
- Kaustubh S Panse
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois61801, United States
| | - Haiyi Wu
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas78712, United States
- Oden Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, Texas78712, United States
| | - Shan Zhou
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois61801, United States
| | - Fujia Zhao
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois61801, United States
| | - Narayana R Aluru
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas78712, United States
- Oden Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, Texas78712, United States
| | - Yingjie Zhang
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois61801, United States
| |
Collapse
|
6
|
Ers H, Voroshylova IV, Pikma P, Ivaništšev VB. Double layer in ionic liquids: Temperature effect and bilayer model. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119747] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
|
7
|
Ahrens-Iwers LJ, Janssen M, Tee SR, Meißner RH. ELECTRODE: An electrochemistry package for atomistic simulations. J Chem Phys 2022; 157:084801. [DOI: 10.1063/5.0099239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.
Collapse
Affiliation(s)
| | | | - Shern Ren Tee
- The University of Queensland Australian Institute for Bioengineering and Nanotechnology, Australia
| | | |
Collapse
|
8
|
Takahashi K, Nakano H, Sato H. Unified polarizable electrode models for open and closed circuits: Revisiting the effects of electrode polarization and different circuit conditions on electrode-electrolyte interfaces. J Chem Phys 2022; 157:014111. [DOI: 10.1063/5.0093095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A precise understanding of the interfacial structure and dynamics is essential for the optimal design of various electrochemical devices. Herein, we propose a method for classical molecular dynamics simulations to deal with electrochemical interfaces with polarizable electrodes under the open circuit condition. Less attention has been paid to electrochemical circuit conditions in computation despite being often essential for a proper assessment, especially comparison between different models. The present method is based on the chemical potential equalization principle, as is a method developed previously to deal with systems under the closed circuit condition. These two methods can be interconverted through the Legendre transformation, so that the difference in the circuit conditions can be compared on the same footing. Furthermore, the electrode polarization effect can be correctly studied by comparing the present method with the conventional simulations with the electrodes represented by fixed charges, since both of the methods describe systems under the open circuit condition. The method is applied to a parallel-plate capacitor composed of platinum electrodes and an aqueous electrolyte solution. The electrode polarization effects have an impact on the interfacial structure of the electrolyte solution. We found that the difference in the circuit conditions significantly affects the dynamics of the electrolyte solution. The electric field at the charged electrode surface is poorly screened by the nonequilibrium solution structure in the open circuit condition, which accelerates the motion of the electrolyte solution.
Collapse
Affiliation(s)
| | | | - Hirofumi Sato
- Department of Molecular Engineering, Kyoto University - Katsura Campus, Japan
| |
Collapse
|
9
|
Tee SR, Searles DJ. Fully periodic, computationally efficient constant potential molecular dynamics simulations of ionic liquid supercapacitors. J Chem Phys 2022; 156:184101. [DOI: 10.1063/5.0086986] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Molecular dynamics (MD) simulations of complex electrochemical systems, such as ionic liquid supercapacitors, are increasingly including the constant potential method (CPM) to model conductive electrodes at a specified potential difference, but the inclusion of CPM can be computationally expensive. We demonstrate the computational savings available in CPM MD simulations of ionic liquid supercapacitors when the usual non-periodic slab geometry is replaced with fully periodic boundary conditions. We show how a doubled cell approach, previously used in non-CPM MD simulations of charged interfaces, can be used to enable fully periodic CPM MD simulations. Using either a doubled cell approach or a finite field approach previously reported by others, fully periodic CPM MD simulations produce comparable results to the traditional slab geometry simulations with a nearly double speedup in computational time. Indeed, these savings can offset the additional cost of the CPM algorithm, resulting in periodic CPM MD simulations that are computationally competitive with the non-periodic, fixed charge equivalent simulations for the ionic liquid supercapacitors studied here.
Collapse
Affiliation(s)
- Shern R. Tee
- Australian Institute of Bioengineering and Nanotechnology, The University of Queensland, Brisbane, QLD 4072, Australia
| | - Debra J. Searles
- Australian Institute of Bioengineering and Nanotechnology, The University of Queensland, Brisbane, QLD 4072, Australia
- School of Chemistry and Molecular Biosciences, The University of Queensland, Brisbane, QLD 4072, Australia
| |
Collapse
|
10
|
Sundararaman R, Vigil-Fowler D, Schwarz K. Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface. Chem Rev 2022; 122:10651-10674. [PMID: 35522135 PMCID: PMC10127457 DOI: 10.1021/acs.chemrev.1c00800] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.
Collapse
Affiliation(s)
- Ravishankar Sundararaman
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, United States
| | - Derek Vigil-Fowler
- Materials, Chemical, and Computational Science Directorate, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Kathleen Schwarz
- Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| |
Collapse
|
11
|
de Souza JP, Pivnic K, Bazant MZ, Urbakh M, Kornyshev AA. Structural Forces in Ionic Liquids: The Role of Ionic Size Asymmetry. J Phys Chem B 2022; 126:1242-1253. [PMID: 35134297 PMCID: PMC9007453 DOI: 10.1021/acs.jpcb.1c09441] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Revised: 01/04/2022] [Indexed: 11/29/2022]
Abstract
Ionic liquids (ILs) are charged fluids composed of anions and cations of different size and shape. The ordering of charge and density in ILs confined between charged interfaces underlies numerous applications of IL electrolytes. Here, we analyze the screening behavior and the resulting structural forces of a representative IL confined between two charge-varied plates. Using both molecular dynamics simulations and a continuum theory, we contrast the screening features of a more-realistic asymmetric system and a less-realistic symmetric one. The ionic size asymmetry plays a nontrivial role in charge screening, affecting both the ionic density profiles and the disjoining pressure distance dependence. Ionic systems with size asymmetry are stronger coupled systems, and this manifests itself both in their response to the electrode polarization and spontaneous structure formation at the interface. Analytical expressions for decay lengths of the disjoining pressure are obtained in agreement with the pressure profiles computed from molecular dynamics simulations.
Collapse
Affiliation(s)
- J. Pedro de Souza
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Karina Pivnic
- School
of Chemistry, The Sackler Center for Computational Molecular and Materials
Science, Tel Aviv University, Tel Aviv, 6997801, Israel
| | - Martin Z. Bazant
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Mathematics, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Michael Urbakh
- School
of Chemistry, 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, Imperial College London, London, W12 0BZ 2AZ, United Kingdom
- Thomas
Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom
| |
Collapse
|
12
|
Gäding J, Tocci G, Busch M, Huber P, Meißner RH. Impact of confinement and polarizability on dynamics of ionic liquids. J Chem Phys 2022; 156:064703. [DOI: 10.1063/5.0077408] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Johannes Gäding
- Institute of Polymers and Composites, Hamburg University of Technology, 21073 Hamburg, Germany
| | - Gabriele Tocci
- Department of Chemistry, University of Zurich, 8057 Zürich, Switzerland
| | - Mark Busch
- Institute for Materials and X-Ray Physics, Hamburg University of Technology, 21073 Hamburg, Germany
- Deutsches Elektronen-Synchrotron DESY, Centre for X-Ray and Nano Science CXNS, 22607 Hamburg, Germany
- Centre for Hybrid Nanostructures CHyN, Hamburg University, 22761 Hamburg, Germany
| | - Patrick Huber
- Institute for Materials and X-Ray Physics, Hamburg University of Technology, 21073 Hamburg, Germany
- Deutsches Elektronen-Synchrotron DESY, Centre for X-Ray and Nano Science CXNS, 22607 Hamburg, Germany
- Centre for Hybrid Nanostructures CHyN, Hamburg University, 22761 Hamburg, Germany
| | - Robert H. Meißner
- Institute of Polymers and Composites, Hamburg University of Technology, 21073 Hamburg, Germany
- Helmholtz-Zentrum Hereon, Institute of Surface Science, 21502 Geesthacht, Germany
| |
Collapse
|
13
|
Paulista Neto AJ, da Silva DAC, Gonçalves VA, Zanin H, Freitas RG, Fileti EE. An evaluation of the capacitive behavior of supercapacitors as a function of the radius of cations using simulations with a constant potential method. Phys Chem Chem Phys 2022; 24:3280-3288. [PMID: 35048088 DOI: 10.1039/d1cp04350a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We report on the atomistic molecular dynamics, applying the constant potential method to determine the structural and electrostatic interactions at the electrode-electrolyte interface of electrochemical supercapacitors as a function of the cation radius (Cs+, Rb+, K+, Na+, Li+). We find that the electrical double layer is susceptible to the size, hydration layer volume, and cations' mobility and analyzed them. Besides, the transient potential shows an increase in magnitude and length as a function of the monocation size, i.e., Cs+ > Rb+ > K+ > Na+ > Li+. On the other hand, the charge distribution along the electrode surface is less uniform for large monocations. Nonetheless, the difference is not observed as a function of the radius of the cation for the integral capacitance. Our results are comparable to studies that employed the fixed charge method for treating such systems.
Collapse
Affiliation(s)
- Antenor J Paulista Neto
- Advanced Energy Storage Division, Center for Innovation on New Energies, Carbon Sci-Tech Labs, School of Electrical and Computer Engineering, University of Campinas; Av. Albert Einstein 400, Campinas, SP 13083-852, Brazil.
| | - Débora A C da Silva
- Advanced Energy Storage Division, Center for Innovation on New Energies, Carbon Sci-Tech Labs, School of Electrical and Computer Engineering, University of Campinas; Av. Albert Einstein 400, Campinas, SP 13083-852, Brazil.
| | - Vanessa A Gonçalves
- Institute of Physics & Department of Chemistry, Laboratory of Computational Materials, Federal University of Mato Grosso, 78060-900, Cuiabá, MT, Brazil.
| | - Hudson Zanin
- Advanced Energy Storage Division, Center for Innovation on New Energies, Carbon Sci-Tech Labs, School of Electrical and Computer Engineering, University of Campinas; Av. Albert Einstein 400, Campinas, SP 13083-852, Brazil.
| | - Renato G Freitas
- Institute of Physics & Department of Chemistry, Laboratory of Computational Materials, Federal University of Mato Grosso, 78060-900, Cuiabá, MT, Brazil.
| | - Eudes E Fileti
- Institute of Science and Technology of the Federal University of São Paulo, 12247-014, São José dos Campos, SP, Brazil.
| |
Collapse
|
14
|
Shandilya A, Schwarz K, Sundararaman R. Interfacial water asymmetry at ideal electrochemical interfaces. J Chem Phys 2022; 156:014705. [PMID: 34998343 DOI: 10.1063/5.0076038] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Controlling electrochemical reactivity requires a detailed understanding of the charging behavior and thermodynamics of the electrochemical interface. Experiments can independently probe the overall charge response of the electrochemical double layer by capacitance measurements and the thermodynamics of the inner layer with potential of maximum entropy measurements. Relating these properties by computational modeling of the electrochemical interface has so far been challenging due to the low accuracy of classical molecular dynamics (MD) for capacitance and the limited time and length scales of ab initio MD. Here, we combine large ensembles of long-time-scale classical MD simulations with charge response from electronic density functional theory to predict the potential-dependent capacitance of a family of ideal aqueous electrochemical interfaces with different peak capacitances. We show that while the potential of maximum capacitance varies, this entire family exhibits an electrode charge of maximum capacitance (CMC) between -2.9 and -2.2 μC/cm2, regardless of the details in the electronic response. Simulated heating of the same interfaces reveals that the entropy peaks at a charge of maximum entropy (CME) of -5.1 ± 0.6 μC/cm2, in agreement with experimental findings for metallic electrodes. The CME and CMC both indicate asymmetric response of interfacial water that is stronger for negatively charged electrodes, while the difference between CME and CMC illustrates the richness in behavior of even the ideal electrochemical interface.
Collapse
Affiliation(s)
- Abhishek Shandilya
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - Kathleen Schwarz
- Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Ravishankar Sundararaman
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| |
Collapse
|
15
|
Pireddu G, Scalfi L, Rotenberg B. A molecular perspective on induced charges on a metallic surface. J Chem Phys 2021; 155:204705. [PMID: 34852473 DOI: 10.1063/5.0076127] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.
Collapse
Affiliation(s)
- Giovanni Pireddu
- Sorbonne Université, CNRS, Physico-chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France
| | - Laura Scalfi
- Sorbonne Université, CNRS, Physico-chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France
| |
Collapse
|
16
|
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: 3] [Impact Index Per Article: 1.0] [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.
Collapse
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.
| |
Collapse
|
17
|
Basouli H, Mozaffari F, Eslami H. Atomistic insights into structure, ion-pairing and ionic conductivity of 1-ethyl-3-methylimidazolium methylsulfate [Emim][MeSO4] ionic liquid from molecular dynamics simulation. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115803] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
|
18
|
Abstract
Many key industrial processes, from electricity production, conversion, and storage to electrocatalysis or electrochemistry in general, rely on physical mechanisms occurring at the interface between a metallic electrode and an electrolyte solution, summarized by the concept of an electric double layer, with the accumulation/depletion of electrons on the metal side and of ions on the liquid side. While electrostatic interactions play an essential role in the structure, thermodynamics, dynamics, and reactivity of electrode-electrolyte interfaces, these properties also crucially depend on the nature of the ions and solvent, as well as that of the metal itself. Such interfaces pose many challenges for modeling because they are a place where quantum chemistry meets statistical physics. In the present review, we explore the recent advances in the description and understanding of electrode-electrolyte interfaces with classical molecular simulations, with a focus on planar interfaces and solvent-based liquids, from pure solvent to water-in-salt electrolytes.
Collapse
Affiliation(s)
- Laura Scalfi
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, CNRS 8234, Sorbonne Université, F-75005 Paris, France
| | - Mathieu Salanne
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, CNRS 8234, Sorbonne Université, F-75005 Paris, France
- Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France
| | - Benjamin Rotenberg
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, CNRS 8234, Sorbonne Université, F-75005 Paris, France
- Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France
| |
Collapse
|
19
|
Voegtle MJ, Pal T, Pennathur AK, Menachekanian S, Patrow JG, Sarkar S, Cui Q, Dawlaty JM. Interfacial Polarization and Ionic Structure at the Ionic Liquid-Metal Interface Studied by Vibrational Spectroscopy and Molecular Dynamics Simulations. J Phys Chem B 2021; 125:2741-2753. [PMID: 33689335 DOI: 10.1021/acs.jpcb.0c11232] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Ionic liquids (ILs) have both fundamental and practical value in interfacial science and electrochemistry. However, understanding their behavior near a surface is challenging because of strong Coulomb interactions and large and irregular ionic sizes, which affect both their structure and energetics. To understand this problem, we present a combined experimental and computational study using a vibrational probe molecule, 4-mercaptobenzonitrile, inserted at the junction between a metal and a variety of ILs. The vibrational frequency of the nitrile in the probe molecule reports on the local solvation environment and the electrostatic field at this junction. Within the ethylmethyl imidazolium (EMIM+) cation family of ILs, we varied the anions over a range of sizes and types. Complementing our surface spectroscopy, we also ran molecular dynamics simulations of these interfaces to better understand the ionic structures that produced the measured fields. The magnitude of the frequency shifts, and thereby fields, shows a general correlation with the size of anions, with larger anions corresponding to smaller fields. We find that the source of this correlation is partial intercalation of smaller anions into the probe monolayer, resulting in tighter packing of ionic layers near the surface. Larger anions reduce the overall lateral ion packing density near the surface, which reduces the net charge per unit area and explains the smaller observed fields. The insight from this work is important for developing a fundamental picture of concentrated electrolytes near interfaces and can help with designing ILs to create tailored electric fields near an electrode.
Collapse
Affiliation(s)
- Matthew J Voegtle
- Department of Chemistry, University of Southern California, Los Angeles, California 90007, United States
| | - Tanmoy Pal
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States
| | - Anuj K Pennathur
- Department of Chemistry, University of Southern California, Los Angeles, California 90007, United States
| | - Sevan Menachekanian
- Department of Chemistry, University of Southern California, Los Angeles, California 90007, United States
| | - Joel G Patrow
- Department of Chemistry, University of Southern California, Los Angeles, California 90007, United States
| | - Sohini Sarkar
- Department of Chemistry, University of Southern California, Los Angeles, California 90007, United States
| | - Qiang Cui
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States
| | - Jahan M Dawlaty
- Department of Chemistry, University of Southern California, Los Angeles, California 90007, United States
| |
Collapse
|
20
|
Gong Z, Padua AAH. Effect of side chain modifications in imidazolium ionic liquids on the properties of the electrical double layer at a molybdenum disulfide electrode. J Chem Phys 2021; 154:084504. [PMID: 33639754 DOI: 10.1063/5.0040172] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Knowledge of how the molecular structures of ionic liquids (ILs) affect their properties at electrified interfaces is key to the rational design of ILs for electric applications. Polarizable molecular dynamics simulations were performed to investigate the structural, electrical, and dynamic properties of electric double layers (EDLs) formed by imidazolium dicyanamide ([ImX1][DCA]) at the interface with the molybdenum disulfide electrode. The effect of side chain of imidazolium on the properties of EDLs was analyzed by using 1-ethyl-3-methylimidazolium ([Im21]), 1-octyl-3-methylimidazolium ([Im81]), 1-benzyl-3-methylimidazolium ([ImB1]), and 1-(2-hydroxyethyl)-3-methylimidazolium ([ImO1]) as cations. Using [Im21] as reference, we find that the introduction of octyl or benzyl groups significantly alters the interfacial structures near the cathode because of the reorientation of cations. For [Im81], the positive charge on the cathode induces pronounced polar and non-polar domain separation. In contrast, the hydroxyl group has a minor effect on the interfacial structures. [ImB1] is shown to deliver slightly larger capacitance than other ILs even though it has larger molecular volume than [Im21]. This is attributed to the limiting factor for capacitance being the strong association between counter-ions, instead of the free space available to ions at the interface. For [Im81], the charging mechanism is mainly the exchange between anions and octyl tails, while for the other ILs, the mechanism is mainly the exchange of counter-ions. Analysis on the charging process shows that the charging speed does not correlate strongly with macroscopic bulk dynamics like viscosity. Instead, it is dominated by local displacement and reorientation of ions.
Collapse
Affiliation(s)
- Zheng Gong
- Laboratoire de Chimie, École Normale Supérieure de Lyon and CNRS, 69364 Lyon, France
| | - Agilio A H Padua
- Laboratoire de Chimie, École Normale Supérieure de Lyon and CNRS, 69364 Lyon, France
| |
Collapse
|
21
|
Zhou S, Panse KS, Motevaselian MH, Aluru NR, Zhang Y. Three-Dimensional Molecular Mapping of Ionic Liquids at Electrified Interfaces. ACS NANO 2020; 14:17515-17523. [PMID: 33227191 DOI: 10.1021/acsnano.0c07957] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Electric double layers (EDLs), occurring ubiquitously at solid-liquid interfaces, are critical for electrochemical energy conversion and storage processes such as capacitive charging and redox reactions. However, to date the molecular-scale structure of EDLs remains elusive. Here we report an advanced technique, electrochemical three-dimensional atomic force microscopy (EC-3D-AFM), and use it to directly image the molecular-scale EDL structure of an ionic liquid under different electrode potentials. We observe not only multiple discrete ionic layers in the EDL on a graphite electrode but also a quasi-periodic molecular density distribution within each layer. Furthermore, we find pronounced 3D reconfiguration of the EDL at different voltages, especially in the first layer. Combining the experimental results with molecular dynamics simulations, we find potential-dependent molecular redistribution and reorientation in the innermost EDL layer, both of which are critical to EDL capacitive charging. We expect this mechanistic understanding to have profound impacts on the rational design of electrode-electrolyte interfaces for energy conversion and storage.
Collapse
Affiliation(s)
- Shan Zhou
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Kaustubh S Panse
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | | | - Narayana R Aluru
- Department of Mechanical Science and Engineering, University of Illinois, Urbana, Illinois 61801, United States
| | - Yingjie Zhang
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| |
Collapse
|
22
|
Takahashi K, Nakano H, Sato H. A polarizable molecular dynamics method for electrode–electrolyte interfacial electron transfer under the constant chemical-potential-difference condition on the electrode electrons. J Chem Phys 2020; 153:054126. [DOI: 10.1063/5.0020619] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Ken Takahashi
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
| | - Hiroshi Nakano
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
- Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Kyoto 615-8510, Japan
| | - Hirofumi Sato
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
- Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Kyoto 615-8510, Japan
| |
Collapse
|
23
|
Katakura S, Amano KI, Sakka T, Bu W, Lin B, Schlossman ML, Nishi N. Evolution and Reversible Polarity of Multilayering at the Ionic Liquid/Water Interface. J Phys Chem B 2020; 124:6412-6419. [PMID: 32600035 DOI: 10.1021/acs.jpcb.0c03711] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Highly correlated positioning of ions underlies Coulomb interactions between ions and electrified interfaces within dense ionic fluids such as biological cells and ionic liquids. Recent work has shown that highly correlated ionic systems behave differently than dilute electrolyte solutions, and interest is focused upon characterizing the electrical and structural properties of the dense electrical double layers (EDLs) formed at internal interfaces. It has been a challenge for experiments to characterize the progressive development of the EDL on the nanoscale as the interfacial electric potential is varied over a range of positive and negative values. Here we address this challenge by measuring X-ray reflectivity from the interface between an ionic liquid (IL) and a dilute aqueous electrolyte solution over a range of interfacial potentials from -450 to 350 mV. The growth of alternately charged cation-rich and anion-rich layers was observed along with a polarity reversal of the layers as the potential changed sign. These data show that the structural development of an ionic multilayer-like EDL with increasing potential is similar to that suggested by phenomenological theories and MD simulations, although our data also reveal that the excess charge beyond the first ionic layer decays more rapidly than predicted.
Collapse
Affiliation(s)
- Seiji Katakura
- Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto 615-8510, Japan
| | - Ken-Ichi Amano
- Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto 615-8510, Japan.,Faculty of Agriculture, Meijo University, Nagoya, Aichi 468-8502, Japan
| | - Tetsuo Sakka
- Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto 615-8510, Japan
| | - Wei Bu
- ChemMatCARS, Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, United States
| | - Binhua Lin
- ChemMatCARS, Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, United States
| | - Mark L Schlossman
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, United States
| | - Naoya Nishi
- Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto 615-8510, Japan
| |
Collapse
|
24
|
Coretti A, Scalfi L, Bacon C, Rotenberg B, Vuilleumier R, Ciccotti G, Salanne M, Bonella S. Mass-zero constrained molecular dynamics for electrode charges in simulations of electrochemical systems. J Chem Phys 2020; 152:194701. [PMID: 33687245 DOI: 10.1063/5.0007192] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Classical molecular dynamics simulations have recently become a standard tool for the study of electrochemical systems. State-of-the-art approaches represent the electrodes as perfect conductors, modeling their responses to the charge distribution of electrolytes via the so-called fluctuating charge model. These fluctuating charges are additional degrees of freedom that, in a Born-Oppenheimer spirit, adapt instantaneously to changes in the environment to keep each electrode at a constant potential. Here, we show that this model can be treated in the framework of constrained molecular dynamics, leading to a symplectic and time-reversible algorithm for the evolution of all the degrees of freedom of the system. The computational cost and the accuracy of the new method are similar to current alternative implementations of the model. The advantage lies in the accuracy and long term stability guaranteed by the formal properties of the algorithm and in the possibility to systematically introduce additional kinematic conditions of arbitrary number and form. We illustrate the performance of the constrained dynamics approach by enforcing the electroneutrality of the electrodes in a simple capacitor consisting of two graphite electrodes separated by a slab of liquid water.
Collapse
Affiliation(s)
- A Coretti
- Department of Mathematical Sciences, Politecnico di Torino, I-10129 Torino, Italy
| | - L Scalfi
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - C Bacon
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - B Rotenberg
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - R Vuilleumier
- PASTEUR, Département de chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - G Ciccotti
- Institute for Applied Computing "Mauro Picone" (IAC), CNR, Via dei Taurini 19, 00185 Rome, Italy
| | - M Salanne
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - S Bonella
- Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| |
Collapse
|
25
|
Yoshii N, Andoh Y, Okazaki S. Fast multipole method for three-dimensional systems with periodic boundary condition in two directions. J Comput Chem 2020; 41:940-948. [PMID: 31930548 DOI: 10.1002/jcc.26141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Revised: 12/01/2019] [Accepted: 12/02/2019] [Indexed: 12/11/2022]
Abstract
We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Noriyuki Yoshii
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, 464-8603, Japan.,Department of Materials Chemistry, Nagoya University, Nagoya, Japan
| | - Yoshimichi Andoh
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, 464-8603, Japan
| | - Susumu Okazaki
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, 464-8603, Japan.,Department of Materials Chemistry, Nagoya University, Nagoya, Japan
| |
Collapse
|
26
|
Katakura S, Nishi N, Kobayashi K, Amano KI, Sakka T. An electric double layer structure and differential capacitance at the electrode interface of tributylmethylammonium bis(trifluoromethanesulfonyl)amide studied using a molecular dynamics simulation. Phys Chem Chem Phys 2020; 22:5198-5210. [PMID: 32090216 DOI: 10.1039/c9cp05297f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A molecular dynamics simulation at the electrode interface of a quaternary ammonium ionic liquid, tributylmethylammonium bis(trifluoromethanesulfonyl)amide ([N1444+][TFSA-]), has been performed. Unlike the commonly used cations, such as 1-alkyl-3-methylimidazolium and 1,1-alkylmethylpyrrolidinium cations, N1444+ has multiple long-alkyl groups (three butyl groups). The behavior of ions at the electrode interface, especially these butyl groups, has been investigated. N1444+ at the first layer mainly has two types of orientations, lying and standing. The lying orientation is dominant at moderately negative potentials. However, the standing one becomes dominant at the more negative potentials. Due to this orientational change, the number of N1444+ increases at the first layer as the potential becomes negative even at the potentials where the anions are completely depleted there. The change in orientation results in the upward deviation of the differential capacitance from the theoretical prediction at the negative potentials. The results suggest that the orientational preference caused by the steric constraint between alkyl groups plays an important role in the behavior of the electric double layer of the ionic liquids.
Collapse
Affiliation(s)
- Seiji Katakura
- Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan.
| | | | | | | | | |
Collapse
|
27
|
Scalfi L, Limmer DT, Coretti A, Bonella S, Madden PA, Salanne M, Rotenberg B. Charge fluctuations from molecular simulations in the constant-potential ensemble. Phys Chem Chem Phys 2020; 22:10480-10489. [DOI: 10.1039/c9cp06285h] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Statistical mechanics of constant-potential molecular simulations yields a new fluctuation–dissipation relation for the differential capacitance.
Collapse
Affiliation(s)
- Laura Scalfi
- Sorbonne Université
- CNRS
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux
- F-75005 Paris
- France
| | - David T. Limmer
- Department of Chemistry
- University of California
- Berkeley
- USA
- Kavli Energy NanoScience Institute
| | - Alessandro Coretti
- Department of Mathematical Sciences
- Politecnico di Torino
- I-10129 Torino
- Italy
- Centre Européen de Calcul Atomique et Moléculaire (CECAM)
| | - Sara Bonella
- Centre Européen de Calcul Atomique et Moléculaire (CECAM)
- Ecole Polytechnique Fédérale de Lausanne
- 1015 Lausanne
- Switzerland
| | | | - Mathieu Salanne
- Sorbonne Université
- CNRS
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux
- F-75005 Paris
- France
| | - Benjamin Rotenberg
- Sorbonne Université
- CNRS
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux
- F-75005 Paris
- France
| |
Collapse
|
28
|
Voroshylova IV, Lembinen M, Ers H, Mišin M, Koverga VA, Pereira CM, Ivaništšev VB, Cordeiro MND. On the role of the surface charge plane position at Au(hkl)–BMImPF6 interfaces. Electrochim Acta 2019. [DOI: 10.1016/j.electacta.2019.05.058] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
29
|
Bedrov D, Piquemal JP, Borodin O, MacKerell AD, Roux B, Schröder C. Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields. Chem Rev 2019; 119:7940-7995. [PMID: 31141351 PMCID: PMC6620131 DOI: 10.1021/acs.chemrev.8b00763] [Citation(s) in RCA: 271] [Impact Index Per Article: 54.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 11/30/2022]
Abstract
Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.
Collapse
Affiliation(s)
- Dmitry Bedrov
- Department
of Materials Science & Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, Utah 84112, United States
| | - Jean-Philip Piquemal
- Laboratoire
de Chimie Théorique, Sorbonne Université,
UMR 7616 CNRS, CC137, 4 Place Jussieu, Tour 12-13, 4ème étage, 75252 Paris Cedex 05, France
- Institut
Universitaire de France, 75005, Paris Cedex 05, France
- Department
of Biomedical Engineering, The University
of Texas at Austin, Austin, Texas 78712, United States
| | - Oleg Borodin
- Electrochemistry
Branch, Sensors and Electron Devices Directorate, Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20703, United
States
| | - Alexander D. MacKerell
- Department
of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201, United
States
| | - Benoît Roux
- Department
of Biochemistry and Molecular Biology, Gordon Center for Integrative
Science, University of Chicago, 929 57th Street, Chicago, Illinois 60637, United States
| | - Christian Schröder
- Department
of Computational Biological Chemistry, University
of Vienna, Währinger Strasse 17, A-1090 Vienna, Austria
| |
Collapse
|
30
|
Raberg JH, Vatamanu J, Harris SJ, van Oversteeg CHM, Ramos A, Borodin O, Cuk T. Probing Electric Double-Layer Composition via in Situ Vibrational Spectroscopy and Molecular Simulations. J Phys Chem Lett 2019; 10:3381-3389. [PMID: 31141378 DOI: 10.1021/acs.jpclett.9b00879] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
At an electrode, ions and solvent accumulate to screen charge, leading to a nanometer-scale electric double layer (EDL). The EDL guides electrode passivation in batteries, while in (super)capacitors, it determines charge storage capacity. Despite its importance, quantification of the nanometer-scale and potential-dependent EDL remains a challenging problem. Here, we directly probe changes in the EDL composition with potential using in situ vibrational spectroscopy and molecular dynamics simulations for a Li-ion battery electrolyte (LiClO4 in dimethyl carbonate). The accumulation rate of Li+ ions at the negative surface and ClO4- ions at the positive surface from vibrational spectroscopy compares well to that predicted by simulations using a polarizable APPLE&P force field. The ion solvation shell structure and ion-pairing within the EDL differs significantly from the bulk, especially at the negative electrode, suggesting that the common rationalization of interfacial electrochemical processes in terms of bulk ion solvation should be applied with caution.
Collapse
Affiliation(s)
- Jonathan H Raberg
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
| | - Jenel Vatamanu
- Electrochemistry Branch, Sensor and Electron Devices Directorate, Power and Energy Division , U.S. Army Research Laboratory , Adelphi , Maryland 20783 , United States
- Joint Center for Energy Storage Research , U.S. Army Research Laboratory , Adelphi , Maryland 20783 , United States
| | - Stephen J Harris
- Materials Science Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | | | - Axel Ramos
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
| | - Oleg Borodin
- Electrochemistry Branch, Sensor and Electron Devices Directorate, Power and Energy Division , U.S. Army Research Laboratory , Adelphi , Maryland 20783 , United States
- Joint Center for Energy Storage Research , U.S. Army Research Laboratory , Adelphi , Maryland 20783 , United States
| | - Tanja Cuk
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
- Chemical Science Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| |
Collapse
|
31
|
Colherinhas G, Malaspina T, Fileti EE. Storing Energy in Biodegradable Electrochemical Supercapacitors. ACS OMEGA 2018; 3:13869-13875. [PMID: 30411051 PMCID: PMC6217657 DOI: 10.1021/acsomega.8b01980] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2018] [Accepted: 10/15/2018] [Indexed: 05/04/2023]
Abstract
The development of green and biodegradable electrical components is one of the main fronts of research to overcome the growing ecological problem related to the issue of electronic waste. At the same time, such devices are highly desirable in biomedical applications such as integrated bioelectronics, for which biocompatibility is also required. Supercapacitors for storage of electrochemical energy, designed only with biodegradable organic matter would contemplate both aspects, that is, they would be ecologically harmless after their service lifetime and would be an important component for applications in biomedical engineering. By means of atomistic simulations of molecular dynamics, we propose a supercapacitor whose electrodes are formed exclusively by self-organizing peptides and whose electrolyte is a green amino acid ionic liquid. Our results indicate that this supercapacitor has a high potential for energy storage with superior performance than conventional supercapacitors. In particular its capacity to store energy was estimated to be almost 20 times greater than an analogue one of planar metallic electrodes.
Collapse
Affiliation(s)
- Guilherme Colherinhas
- Departamento
de Física, CEPAE, Universidade Federal
de Goiás, 74690-900 Goiânia, Goiás, Brazil
| | - Thaciana Malaspina
- Instituto
de Ciência e Tecnologia, Universidade
Federal de São Paulo, 12247-014 São José
dos Campos, São Paulo, Brazil
| | - Eudes Eterno Fileti
- Instituto
de Ciência e Tecnologia, Universidade
Federal de São Paulo, 12247-014 São José
dos Campos, São Paulo, Brazil
| |
Collapse
|
32
|
Chaban VV, Andreeva NA, Fileti EE. Graphene/ionic liquid ultracapacitors: does ionic size correlate with energy storage performance? NEW J CHEM 2018. [DOI: 10.1039/c8nj04399j] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
Electrolytes formed by ions of similar volumes show better performance in supercapacitor applications.
Collapse
Affiliation(s)
| | - Nadezhda A. Andreeva
- Department of Physics
- St. Petersburg State University
- St. Petersburg
- Russian Federation
| | - Eudes Eterno Fileti
- Instituto de Ciência e Tecnologia
- Universidade Federal de São Paulo
- São José dos Campos
- Brazil
| |
Collapse
|
33
|
Patra CN. Spherical electric double layers containing mixed electrolytes: A case study for multivalent counterions. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.08.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
34
|
Afandak A, Eslami H. Ion-Pairing and Electrical Conductivity in the Ionic Liquid 1-n-Butyl-3-methylimidazolium Methylsulfate [Bmim][MeSO4]: Molecular Dynamics Simulation Study. J Phys Chem B 2017; 121:7699-7708. [DOI: 10.1021/acs.jpcb.7b06039] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Azam Afandak
- Department of Chemistry, College
of Sciences, Persian Gulf University, Boushehr 75168, Iran
| | - Hossein Eslami
- Department of Chemistry, College
of Sciences, Persian Gulf University, Boushehr 75168, Iran
| |
Collapse
|
35
|
Zhan C, Lian C, Zhang Y, Thompson MW, Xie Y, Wu J, Kent PRC, Cummings PT, Jiang D, Wesolowski DJ. Computational Insights into Materials and Interfaces for Capacitive Energy Storage. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2017; 4:1700059. [PMID: 28725531 PMCID: PMC5515120 DOI: 10.1002/advs.201700059] [Citation(s) in RCA: 83] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2017] [Revised: 03/25/2017] [Indexed: 05/02/2023]
Abstract
Supercapacitors such as electric double-layer capacitors (EDLCs) and pseudocapacitors are becoming increasingly important in the field of electrical energy storage. Theoretical study of energy storage in EDLCs focuses on solving for the electric double-layer structure in different electrode geometries and electrolyte components, which can be achieved by molecular simulations such as classical molecular dynamics (MD), classical density functional theory (classical DFT), and Monte-Carlo (MC) methods. In recent years, combining first-principles and classical simulations to investigate the carbon-based EDLCs has shed light on the importance of quantum capacitance in graphene-like 2D systems. More recently, the development of joint density functional theory (JDFT) enables self-consistent electronic-structure calculation for an electrode being solvated by an electrolyte. In contrast with the large amount of theoretical and computational effort on EDLCs, theoretical understanding of pseudocapacitance is very limited. In this review, we first introduce popular modeling methods and then focus on several important aspects of EDLCs including nanoconfinement, quantum capacitance, dielectric screening, and novel 2D electrode design; we also briefly touch upon pseudocapactive mechanism in RuO2. We summarize and conclude with an outlook for the future of materials simulation and design for capacitive energy storage.
Collapse
Affiliation(s)
- Cheng Zhan
- Department of ChemistryUniversity of CaliforniaRiversideCA92521United States
| | - Cheng Lian
- Department of Chemical and Environmental EngineeringUniversity of CaliforniaRiversideCalifornia92521United States
- State Key Laboratory of Chemical EngineeringEast China University of Science and TechnologyShanghai200237P. R. China
| | - Yu Zhang
- Department of Chemical and Biomolecular EngineeringVanderbilt UniversityNashvilleTennessee37235United States
| | - Matthew W. Thompson
- Department of Chemical and Biomolecular EngineeringVanderbilt UniversityNashvilleTennessee37235United States
| | - Yu Xie
- Center for Nanophase Materials SciencesOak Ridge National LaboratoryOak RidgeTennessee37831United States
| | - Jianzhong Wu
- Department of Chemical and Environmental EngineeringUniversity of CaliforniaRiversideCalifornia92521United States
| | - Paul R. C. Kent
- Center for Nanophase Materials SciencesOak Ridge National LaboratoryOak RidgeTennessee37831United States
- Computer Science and Mathematics DivisionOak Ridge National LaboratoryOak RidgeTennessee37831United States
| | - Peter T. Cummings
- Department of Chemical and Biomolecular EngineeringVanderbilt UniversityNashvilleTennessee37235United States
| | - De‐en Jiang
- Department of ChemistryUniversity of CaliforniaRiversideCA92521United States
| | - David J. Wesolowski
- Chemcial Sciences DivisionOak Ridge National LaboratoryOak RidgeTennessee37831United States
| |
Collapse
|
36
|
Vatamanu J, Bedrov D, Borodin O. On the application of constant electrode potential simulation techniques in atomistic modelling of electric double layers. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1279287] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Jenel Vatamanu
- Materials Science & Engineering Department, University of Utah, Salt Lake City, UT, USA
- Electrochemistry Branch, Sensors and Electron Devices Directorate, Army Research Laboratory, Adelphi, MD, USA
| | - Dmitry Bedrov
- Materials Science & Engineering Department, University of Utah, Salt Lake City, UT, USA
| | - Oleg Borodin
- Electrochemistry Branch, Sensors and Electron Devices Directorate, Army Research Laboratory, Adelphi, MD, USA
| |
Collapse
|
37
|
Haskins JB, Wu JJ, Lawson JW. Computational and Experimental Study of Li-Doped Ionic Liquids at Electrified Interfaces. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2016; 120:11993-12011. [PMID: 33005284 PMCID: PMC7526643 DOI: 10.1021/acs.jpcc.6b02449] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
We evaluate the influence of Li-salt doping on the dynamics, capacitance, and structure of three ionic liquid electrolytes, [pyr14][TFSI], [pyr13][FSI], and [EMIM][BF4], using molecular dynamics and polarizable force fields. In this respect, our focus is on the properties of the electric double layer (EDL) formed by the electrolytes at the electrode surface as a function of surface potential (Ψ). The rates of EDL formation are found to be on the order of hundreds of picoseconds and only slightly influenced by the addition of Li-salt. The EDLs of three electrolytes are shown to have different energy storage capacities, which we relate to the EDL formation free energy. The differential capacitance obtained from our computations exhibits asymmetry about the potential of zero charge and is consistent with the camel-like profiles noted from mean field theories and experiments on metallic electrodes. The introduction of Li-salt reduces the noted asymmetry in the differential capacitance profile. Complementary experimental capacitance measurements have been made on our three electrolytes in their neat forms and with Li-salt. The measurements, performed on glassy carbon electrodes, produce U-like profiles, and Li-salt doping is shown to strongly affect capacitance at high magnitudes of Ψ. Differences in the theoretical and experimental shapes and magnitudes of capacitance are rationalized in terms of the electrode surface and pseudocapacitive effects. In both neat and Li-doped liquids, the details of the computational capacitance profile are well described by Ψ-induced changes in the density and molecular orientation of ions in the molecular layer closest to the electrode. Our results suggest that the addition of Li+ induces disorder in the EDL, which originates from the strong binding of anions to Li+. An in-depth analysis of the distribution of Li+ in the EDL reveals that it does not readily enter the molecular layer at the electrode surface, preferring instead to be localized farther away from the surface in the second molecular layer. This behavior is validated through an analysis of the free energy of Li+ solvation as a function of distance from the electrode. Free energy wells are found to coincide with localized concentrations of Li+, the depths of which increase with Ψ and suggest a source of impedance for Li+ to reach the electrode. Finally, we make predictions of the specific energy at ideal graphite utilizing the computed capacitance and previously derived electrochemical windows of the liquids.
Collapse
Affiliation(s)
- Justin B Haskins
- AMA Inc., Thermal Materials Protection Branch, NASA Ames Research Center, Moffett Field, California 94035, USA
| | - James J Wu
- Photovoltaic and Electrochemical Systems Branch, NASA Glenn Research Center, Cleveland, Ohio 44135, USA
| | - John W Lawson
- Thermal Materials Protection Branch, NASA Ames Research Center, Moffett Field, California 94035, USA
| |
Collapse
|