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Bossa GV, Caetano DLZ. Differential capacitance of curved electrodes: role of hydration interactions and charge regulation. Phys Chem Chem Phys 2024; 26:16774-16781. [PMID: 38819431 DOI: 10.1039/d4cp00372a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
The functioning of supercapacitors relies on establishing electrostatic double-layer capacitance across a larger surface area, offering numerous advantages over conventional batteries, such as an extended lifespan and elevated safety standards. The differential capacitance is a fundamental property within the electrical double layer, playing a pivotal role in the advancement of electrical double-layer supercapacitors. In addition to electrostatic interactions, multiple theoretical and experimental studies have indicated that the differential capacitance is influenced by factors such as the physical structure of the electrode, solvent-mediated hydration interactions, and the specific type of electrolyte utilized. In this work, we incorporate hydration interactions into the Poisson-Boltzmann theory to explore curved electrodes whose surfaces can be covered by either acidic or basic groups. We examine how the electrostatic interaction, charge regulation, hydration effects, and the finite size of ions collectively modify the differential capacitance. Furthermore, we explore different scenarios of electrode curvature and how it may be used to achieve larger capacitance depending on the electrolyte type and pH.
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Affiliation(s)
- Guilherme Volpe Bossa
- Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile.
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2
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Cats P, Härtel A. In-plane structure of the electric double layer in the primitive model using classical density functional theory. J Chem Phys 2023; 159:184707. [PMID: 37955323 DOI: 10.1063/5.0176309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 10/24/2023] [Indexed: 11/14/2023] Open
Abstract
The electric double layer (EDL) has a pivotal role in screening charges on surfaces as in supercapacitor electrodes or colloidal and polymer solutions. Its structure is determined by correlations between the finite-sized ionic charge carriers of the underlying electrolyte, and, this way, these correlations affect the properties of the EDL and of applications utilizing EDLs. We study the structure of EDLs within classical density functional theory (DFT) in order to uncover whether a structural transition in the first layer of the EDL that is driven by changes in the surface potential depends on specific particle interactions or has a general footing. This transition has been found in full-atom simulations. Thus far, investigating the in-plane structure of the EDL for the primitive model (PM) using DFT has proved a challenge. We show here that the use of an appropriate functional predicts the in-plane structure of EDLs in excellent agreement with molecular dynamics simulations. This provides the playground to investigate how the structure factor within a layer parallel to a charged surface changes as a function of both the applied surface potential and its separation from the surface. We discuss pitfalls in properly defining an in-plane structure factor and fully map out the structure of the EDL within the PM for a wide range of electrostatic electrode potentials. However, we do not find any signature of a structural crossover and conclude that the previously reported effect is not fundamental but rather occurs due to the specific force field of ions used in the simulations.
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Affiliation(s)
- Peter Cats
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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3
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Dawlaty JM, Perkin S, Salanne M, Willard AP. The chemical physics of electrode-electrolyte interfaces. J Chem Phys 2023; 159:150401. [PMID: 37846953 DOI: 10.1063/5.0177099] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 09/25/2023] [Indexed: 10/18/2023] Open
Affiliation(s)
- Jahan M Dawlaty
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Susan Perkin
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Mathieu Salanne
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Adam P Willard
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 01239, USA
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4
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Eckert T, Stuhlmüller NCX, Sammüller F, Schmidt M. Local measures of fluctuations in inhomogeneous liquids: statistical mechanics and illustrative applications. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:425102. [PMID: 37414000 DOI: 10.1088/1361-648x/ace50c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 07/06/2023] [Indexed: 07/08/2023]
Abstract
We show in detail how three one-body fluctuation profiles, namely the local compressibility, the local thermal susceptibility, and the reduced density, can be obtained from a statistical mechanical many-body description of classical particle-based systems. We present several different and equivalent routes to the definition of each fluctuation profile, facilitating their explicit numerical calculation in inhomogeneous equilibrium systems. This underlying framework is used for the derivation of further properties such as hard wall contact theorems and novel types of inhomogeneous one-body Ornstein-Zernike equations. The practical accessibility of all three fluctuation profiles is exemplified by grand canonical Monte Carlo simulations that we present for hard sphere, Gaussian core and Lennard-Jones fluids in confinement.
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Affiliation(s)
- Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Nico C X Stuhlmüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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Xiao T, Song X. A Gaussian field approach to the planar electric double layer structures in electrolyte solutions. J Chem Phys 2023; 158:2887562. [PMID: 37125713 DOI: 10.1063/5.0138568] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 04/17/2023] [Indexed: 05/02/2023] Open
Abstract
In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.
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Affiliation(s)
- Tiejun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
| | - Xueyu Song
- Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
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6
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Mechanism of oscillation of aqueous electrical double layer capacitance: Role of solvent. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119943] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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7
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Dočkal J, Lísal M, Moučka F. Molecular dynamics of preferential adsorption in mixed alkali–halide electrolytes at graphene electrodes. J Chem Phys 2022; 157:084704. [DOI: 10.1063/5.0097425] [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
Understanding the microscopic behavior of aqueous electrolyte solutions in contact with graphene and related carbon surfaces is important in electrochemical technologies, such as capacitive deionization or supercapacitors. In this work, we focus on preferential adsorption of ions in mixed alkali–halide electrolytes containing different fractions of Li+/Na+ or Li+/K+ and/or Na+/K+ cations with Cl− anions dissolved in water. We performed molecular dynamics simulations of the solutions in contact with both neutral and positively and negatively charged graphene surfaces under ambient conditions, using the effectively polarizable force field. The simulations show that large ions are often intuitively attracted to oppositely charged electrodes. In contrast, the adsorption behavior of small ions tends to be counterintuitive. In mixed-cation solutions, one of the cations always supports the adsorption of the other cation, while the other cation weakens the adsorption of the first cation. In mixed-cation solutions containing large and small cations simultaneously, adsorption of the larger cations varies dramatically with the electrode charge in an intuitive way, while adsorption of the smaller cations changes oppositely, i.e., in a counterintuitive way. For (Li/K)Cl mixed-cation solutions, these effects allow the control of Li+ adsorption by varying the electrode charge, whereas, for LiCl single-salt solutions, Li+ adsorption is nearly independent of the electrode charge. We rationalize this cation–cation lever effect as a result of a competition between three driving forces: (i) direct graphene–ion interactions, (ii) the strong tendency of the solutions to saturate the network of non-covalent intermolecular bonds, and (iii) the tendency to suppress local charge accumulation in any region larger than typical interparticle distances. We analyze the driving forces in detail using a general method for intermolecular bonding based on spatial distribution functions and different contributions to the total charge density profiles. The analysis helps to predict whether an ion is more affected by each of the three driving forces, depending on the strength of the ion solvation shells and the compatibility between the contributions of the charge density profiles due to the ion and water molecules. This approach is general and can also be applied to other solutions under different thermodynamic conditions.
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Affiliation(s)
- Jan Dočkal
- Department of Physics, Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem, Pasteurova 3544/1, 400 96 Ústí nad Labem, Czech Republic and Department of Molecular and Mesoscopic Modelling, The Czech Academy of Sciences, Institute of Chemical Process Fundamentals, Rozvojová 135/1, Prague, Czech Republic
| | - Martin Lísal
- Department of Physics, Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem, Pasteurova 3544/1, 400 96 Ústí nad Labem, Czech Republic and Department of Molecular and Mesoscopic Modelling, The Czech Academy of Sciences, Institute of Chemical Process Fundamentals, Rozvojová 135/1, Prague, Czech Republic
| | - Filip Moučka
- Department of Physics, Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem, Pasteurova 3544/1, 400 96 Ústí nad Labem, Czech Republic and Department of Molecular and Mesoscopic Modelling, The Czech Academy of Sciences, Institute of Chemical Process Fundamentals, Rozvojová 135/1, Prague, Czech Republic
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8
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Tschopp SM, Sammüller F, Hermann S, Schmidt M, Brader JM. Force density functional theory in- and out-of-equilibrium. Phys Rev E 2022; 106:014115. [PMID: 35974621 DOI: 10.1103/physreve.106.014115] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 06/06/2022] [Indexed: 06/15/2023]
Abstract
When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In-equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.
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Affiliation(s)
- Salomée M Tschopp
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Joseph M Brader
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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9
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Wu J. Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics. Chem Rev 2022; 122:10821-10859. [PMID: 35594506 DOI: 10.1021/acs.chemrev.2c00097] [Citation(s) in RCA: 99] [Impact Index Per Article: 49.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.
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Affiliation(s)
- Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
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10
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Bruch D, Balzer C, Wang ZG. Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential. J Chem Phys 2022; 156:174704. [DOI: 10.1063/5.0089260] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.
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Affiliation(s)
- Dorian Bruch
- Chemistry and Chemical Engineering, California Institute of Technology Division of Chemistry and Chemical Engineering, United States of America
| | | | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, United States of America
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11
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Ma K, Janssen M, Lian C, van Roij R. Dynamic density functional theory for the charging of electric double layer capacitors. J Chem Phys 2022; 156:084101. [DOI: 10.1063/5.0081827] [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)
- Ke Ma
- School of Materials Science and Engineering, Tianjin University of Technology, China
| | | | - Cheng Lian
- East China University of Science and Technology, China
| | - Rene van Roij
- Institute for Theoretical Physics, Utrecht University Institut for Theoretical Physics, Netherlands
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12
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Pelagejcev P, Glatzel F, Härtel A. Extension of the primitive model by hydration shells and its impact on the reversible heat production during the buildup of the electric double layer. J Chem Phys 2022; 156:034901. [DOI: 10.1063/5.0077526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Philipp Pelagejcev
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Fabian Glatzel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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