1
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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. [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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Zhang S, Chu HCW. Diffusioosmotic flow reversals due to ion-ion electrostatic correlations. NANOSCALE 2024. [PMID: 38651181 DOI: 10.1039/d3nr06152c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
Existing theories of diffusioosmosis have neglected ion-ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion-ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion-ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. The mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.
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Affiliation(s)
- Shengji Zhang
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
| | - Henry C W Chu
- Department of Chemical Engineering and Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA.
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3
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Ma K, Ramachandran A, Santiago JG. Analytical solutions for viscoelectric effects in electrokinetic nanochannels. Electrophoresis 2024; 45:676-686. [PMID: 38350722 DOI: 10.1002/elps.202300204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 11/21/2023] [Accepted: 12/18/2023] [Indexed: 02/15/2024]
Abstract
Understanding electrokinetic transport in nanochannels and nanopores is essential for emerging biological and electrochemical applications. The viscoelectric effect is an important mechanism implicated in the increase of local viscosity due to the polarization of a solvent under a strong electric field. However, most analyses of the viscoelectric effect have been limited to numerical analyses. In this work, we present a set of analytical solutions applicable to the physical description of viscoelectric effects in nanochannel electrokinetic systems. To achieve such closed-form solutions, we employ the Debye-Hückel approximation of small diffuse charge layer potentials compared to the thermal potential. We analyze critical parameters, including electroosmotic flow profiles, electroosmotic mobility, flow rate, and channel conductance. We compare and benchmark our analytical solutions with published predictions from numerical models. Importantly, we leverage these analytical solutions to identify essential thermophysical and nondimensional parameters that govern the behavior of these systems. We identify scaling parameters and relations among surface charge density, ionic strength, and nanochannel height.
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Affiliation(s)
- Kunlin Ma
- Department of Mechanical Engineering, Stanford University, Stanford, California, USA
| | - Ashwin Ramachandran
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey, USA
| | - Juan G Santiago
- Department of Mechanical Engineering, Stanford University, Stanford, California, USA
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4
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Kroll R, Gottlieb M, Tsori Y. Surface tension between liquids containing antagonistic and regular salts. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:116. [PMID: 38019306 DOI: 10.1140/epje/s10189-023-00378-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 11/13/2023] [Indexed: 11/30/2023]
Abstract
We investigate theoretically the surface tension between two immiscible liquids containing antagonistic and regular salts. The mean-field model includes the electrostatic energy and the Gibbs transfer energy of the ions. We find the Donnan potential difference between the liquids and solve the Poisson-Boltzmann equation to calculate the potential and ion density profiles. When the liquids contain only a regular salt, the surface tension increases when compared to the no-salt case; in contrast, the surface tension is reduced when they contain only an antagonistic salt. When both salts are present, the surface tension can either further decrease or increase depending on the preferential solvation of the ions, in agreement with published experimental observations.
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Affiliation(s)
- Roni Kroll
- Chemical Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel.
| | - Moshe Gottlieb
- Chemical Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel
| | - Yoav Tsori
- Chemical Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel
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5
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Cao Z, Wang Y, Lorsung C, Barati Farimani A. Neural network predicts ion concentration profiles under nanoconfinement. J Chem Phys 2023; 159:094702. [PMID: 37655768 DOI: 10.1063/5.0147119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 06/23/2023] [Indexed: 09/02/2023] Open
Abstract
Modeling the ion concentration profile in nanochannel plays an important role in understanding the electrical double layer and electro-osmotic flow. Due to the non-negligible surface interaction and the effect of discrete solvent molecules, molecular dynamics (MD) simulation is often used as an essential tool to study the behavior of ions under nanoconfinement. Despite the accuracy of MD simulation in modeling nanoconfinement systems, it is computationally expensive. In this work, we propose neural network to predict ion concentration profiles in nanochannels with different configurations, including channel widths, ion molarity, and ion types. By modeling the ion concentration profile as a probability distribution, our neural network can serve as a much faster surrogate model for MD simulation with high accuracy. We further demonstrate the superior prediction accuracy of neural network over XGBoost. Finally, we demonstrated that neural network is flexible in predicting ion concentration profiles with different bin sizes. Overall, our deep learning model is a fast, flexible, and accurate surrogate model to predict ion concentration profiles in nanoconfinement.
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Affiliation(s)
- Zhonglin Cao
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Yuyang Wang
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Cooper Lorsung
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Amir Barati Farimani
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Machine Learning Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
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6
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Seal A, Tiwari U, Gupta A, Govind Rajan A. Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers. Phys Chem Chem Phys 2023; 25:21708-21722. [PMID: 37551893 DOI: 10.1039/d3cp00745f] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/09/2023]
Abstract
Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.
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Affiliation(s)
- Aniruddha Seal
- School of Chemical Sciences, National Institute of Science Education and Research Bhubaneswar, Homi Bhabha National Institute, Khurda, Odisha 752050, India
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
| | - Utkarsh Tiwari
- Department of Chemical Engineering, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Zuarinagar, Goa 403726, India
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
| | - Ankur Gupta
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Ananth Govind Rajan
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
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7
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Bañuelos JL, Borguet E, Brown GE, Cygan RT, DeYoreo JJ, Dove PM, Gaigeot MP, Geiger FM, Gibbs JM, Grassian VH, Ilgen AG, Jun YS, Kabengi N, Katz L, Kubicki JD, Lützenkirchen J, Putnis CV, Remsing RC, Rosso KM, Rother G, Sulpizi M, Villalobos M, Zhang H. Oxide- and Silicate-Water Interfaces and Their Roles in Technology and the Environment. Chem Rev 2023; 123:6413-6544. [PMID: 37186959 DOI: 10.1021/acs.chemrev.2c00130] [Citation(s) in RCA: 12] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Interfacial reactions drive all elemental cycling on Earth and play pivotal roles in human activities such as agriculture, water purification, energy production and storage, environmental contaminant remediation, and nuclear waste repository management. The onset of the 21st century marked the beginning of a more detailed understanding of mineral aqueous interfaces enabled by advances in techniques that use tunable high-flux focused ultrafast laser and X-ray sources to provide near-atomic measurement resolution, as well as by nanofabrication approaches that enable transmission electron microscopy in a liquid cell. This leap into atomic- and nanometer-scale measurements has uncovered scale-dependent phenomena whose reaction thermodynamics, kinetics, and pathways deviate from previous observations made on larger systems. A second key advance is new experimental evidence for what scientists hypothesized but could not test previously, namely, interfacial chemical reactions are frequently driven by "anomalies" or "non-idealities" such as defects, nanoconfinement, and other nontypical chemical structures. Third, progress in computational chemistry has yielded new insights that allow a move beyond simple schematics, leading to a molecular model of these complex interfaces. In combination with surface-sensitive measurements, we have gained knowledge of the interfacial structure and dynamics, including the underlying solid surface and the immediately adjacent water and aqueous ions, enabling a better definition of what constitutes the oxide- and silicate-water interfaces. This critical review discusses how science progresses from understanding ideal solid-water interfaces to more realistic systems, focusing on accomplishments in the last 20 years and identifying challenges and future opportunities for the community to address. We anticipate that the next 20 years will focus on understanding and predicting dynamic transient and reactive structures over greater spatial and temporal ranges as well as systems of greater structural and chemical complexity. Closer collaborations of theoretical and experimental experts across disciplines will continue to be critical to achieving this great aspiration.
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Affiliation(s)
- José Leobardo Bañuelos
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Eric Borguet
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Gordon E Brown
- Department of Earth and Planetary Sciences, The Stanford Doerr School of Sustainability, Stanford University, Stanford, California 94305, United States
| | - Randall T Cygan
- Department of Soil and Crop Sciences, Texas A&M University, College Station, Texas 77843, United States
| | - James J DeYoreo
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Patricia M Dove
- Department of Geosciences, Department of Chemistry, Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Marie-Pierre Gaigeot
- Université Paris-Saclay, Univ Evry, CNRS, LAMBE UMR8587, 91025 Evry-Courcouronnes, France
| | - Franz M Geiger
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Julianne M Gibbs
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2Canada
| | - Vicki H Grassian
- Department of Chemistry and Biochemistry, University of California, San Diego, California 92093, United States
| | - Anastasia G Ilgen
- Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Young-Shin Jun
- Department of Energy, Environmental & Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Nadine Kabengi
- Department of Geosciences, Georgia State University, Atlanta, Georgia 30303, United States
| | - Lynn Katz
- Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - James D Kubicki
- Department of Earth, Environmental & Resource Sciences, The University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Johannes Lützenkirchen
- Karlsruher Institut für Technologie (KIT), Institut für Nukleare Entsorgung─INE, Eggenstein-Leopoldshafen 76344, Germany
| | - Christine V Putnis
- Institute for Mineralogy, University of Münster, Münster D-48149, Germany
| | - Richard C Remsing
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Kevin M Rosso
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Gernot Rother
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Marialore Sulpizi
- Department of Physics, Ruhr Universität Bochum, NB6, 65, 44780, Bochum, Germany
| | - Mario Villalobos
- Departamento de Ciencias Ambientales y del Suelo, LANGEM, Instituto De Geología, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
| | - Huichun Zhang
- Department of Civil and Environmental Engineering, Case Western Reserve University, Cleveland, Ohio 44106, United States
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8
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Nakayama Y. Nonlinear dielectric decrement of electrolyte solutions: An effective medium approach. J Colloid Interface Sci 2023; 646:354-360. [PMID: 37201463 DOI: 10.1016/j.jcis.2023.05.046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Revised: 04/28/2023] [Accepted: 05/07/2023] [Indexed: 05/20/2023]
Abstract
HYPOTHESIS The dielectric constant of an electrolyte solution, which determines electrostatic interactions between colloids and interfaces, depends nonlinearly on the salinity and also on the type of salt. The linear decrement at dilute solutions is due to the reduced polarizability in the hydration shell around an ion. However, the full hydration volume cannot explain the experimental solubility, which indicates the hydration volume should decrease at high salinity. Volume reduction of the hydration shell is supposed to weaken dielectric decrement and thus should be relevant to the nonlinear decrement. SIMULATIONS According to the effective medium theory for the permittivity of heterogeneous media, we derive an equation which relates the dielectric constant with the dielectric cavities created by the hydrated cations and anions, and the effect of partial dehydration at high salinity is taken into account. FINDINGS Analysis of experiments on monovalent electrolytes suggests that weakened dielectric decrement at high salinity originates primarily from the partial dehydration. Furthermore, the onset volume fraction of the partial dehydration is found to be salt-specific, and is correlated with the solvation free energy. Our results suggest that while the reduced polarizability of the hydration shell determines the linear dielectric decrement at low salinity, ion-specific tendency of dehydration is responsible for nonlinear dielectric decrement at high salinity.
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Affiliation(s)
- Yasuya Nakayama
- Department of Chemical Engineering, Kyushu University, Nishi-ku, Fukuoka, 819-0395, Japan.
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9
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Lesniewska N, Beaussart A, Duval JF. Electrostatics of soft (bio)interfaces: Corrections of mean-field Poisson-Boltzmann theory for ion size, dielectric decrement and ion-ion correlation. J Colloid Interface Sci 2023; 642:154-168. [PMID: 37003010 DOI: 10.1016/j.jcis.2023.03.027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 02/24/2023] [Accepted: 03/02/2023] [Indexed: 03/28/2023]
Abstract
HYPOTHESIS Electrostatics of soft (ion-permeable) (bio)particles (e.g. microorganisms, core/shell colloids) in aqueous electrolytes is commonly formulated by the mean-field Poisson-Boltzmann theory and integration of the charge contributions from electrolyte ions and soft material. However, the effects connected to the size of the electrolyte ions and that of the structural charges carried by the particle, to dielectric decrement and ion-ion correlations on soft interface electrostatics have been so far considered at the margin, despite the limits of the Gouy theory for condensed and/or multivalent electrolytes. EXPERIMENTS Accordingly, we modify herein the Poisson-Boltzmann theory for core/shell (bio)interfaces to include the aforementioned molecular effects considered separately or concomitantly. The formalism is applicable for poorly to highly charged particles in the thin electric double layer regime and to unsymmetrical multivalent electrolytes. FINDINGS Computational examples of practical interests are discussed with emphasis on how each considered molecular effect or combination thereof affects the interfacial potential distribution depending on size and valence of cations and anions, size of particle charges, length scale of ionic correlations and shell-to-Debye layer thickness ratio. The origins of here-evidenced pseudo-harmonic potential profile and ion size-dependent screening of core/shell particle charges are detailed. In addition, the existence and magnitude of the Donnan potential when reached in the shell layer are shown to depend on the excluded volumes of the electrolyte ions.
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10
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Ritt CL, de Souza JP, Barsukov MG, Yosinski S, Bazant MZ, Reed MA, Elimelech M. Thermodynamics of Charge Regulation during Ion Transport through Silica Nanochannels. ACS NANO 2022; 16:15249-15260. [PMID: 36075111 DOI: 10.1021/acsnano.2c06633] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Ion-surface interactions can alter the properties of nanopores and dictate nanofluidic transport in engineered and biological systems central to the water-energy nexus. The ion adsorption process, known as "charge regulation", is ion-specific and is dependent on the extent of confinement when the electric double layers (EDLs) between two charged surfaces overlap. A fundamental understanding of the mechanisms behind charge regulation remains lacking. Herein, we study the thermodynamics of charge regulation reactions in 20 nm SiO2 channels via conductance measurements at various concentrations and temperatures. The effective activation energies (Ea) for ion conductance at low concentrations (strong EDL overlap) are ∼2-fold higher than at high concentrations (no EDL overlap) for the electrolytes studied here: LiCl, NaCl, KCl, and CsCl. We find that Ea values measured at high concentrations result from the temperature dependence of viscosity and its influence on ion mobility, whereas Ea values measured at low concentrations result from the combined effects of ion mobility and the enthalpy of cation adsorption to the charged surface. Notably, the Ea for surface reactions increases from 7.03 kJ mol-1 for NaCl to 16.72 ± 0.48 kJ mol-1 for KCl, corresponding to a difference in surface charge of -8.2 to -0.8 mC m-2, respectively. We construct a charge regulation model to rationalize the cation-specific charge regulation behavior based on an adsorption equilibrium. Our findings show that temperature- and concentration-dependent conductance measurements can help indirectly probe the ion-surface interactions that govern transport and colloidal interactions at the nanoscale─representing a critical step forward in our understanding of charge regulation and adsorption phenomena under nanoconfinement.
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Affiliation(s)
- Cody L Ritt
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520-8286, United States
| | - J Pedro de Souza
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Michelle G Barsukov
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520-8286, United States
| | - Shari Yosinski
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - 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
| | - Mark A Reed
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - Menachem Elimelech
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520-8286, United States
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11
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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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12
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Landstorfer M, Müller R. Thermodynamic models for a concentration and electric field dependent susceptibility in liquid electrolytes. Electrochim Acta 2022. [DOI: 10.1016/j.electacta.2022.140368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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13
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Shin SJ, Kim DH, Bae G, Ringe S, Choi H, Lim HK, Choi CH, Kim H. On the importance of the electric double layer structure in aqueous electrocatalysis. Nat Commun 2022; 13:174. [PMID: 35013347 PMCID: PMC8748683 DOI: 10.1038/s41467-021-27909-x] [Citation(s) in RCA: 37] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 12/07/2021] [Indexed: 11/09/2022] Open
Abstract
To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and a structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.
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Affiliation(s)
- Seung-Jae Shin
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Republic of Korea
| | - Dong Hyun Kim
- School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, 61005, Republic of Korea
| | - Geunsu Bae
- School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, 61005, Republic of Korea
| | - Stefan Ringe
- Department of Energy Science and Engineering, Daegu Gyeongbuk Institute of Science and Technology, Daegu, 42988, Republic of Korea.,Energy Science and Engineering Research Center, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu, 42988, Republic of Korea
| | - Hansol Choi
- School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, 61005, Republic of Korea
| | - Hyung-Kyu Lim
- Division of Chemical Engineering and Bioengineering, Kangwon National University, Chuncheon, Gangwon-do, 24341, Republic of Korea
| | - Chang Hyuck Choi
- School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, 61005, Republic of Korea.
| | - Hyungjun Kim
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Republic of Korea.
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14
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Ringe S, Hörmann NG, Oberhofer H, Reuter K. Implicit Solvation Methods for Catalysis at Electrified Interfaces. Chem Rev 2021; 122:10777-10820. [PMID: 34928131 PMCID: PMC9227731 DOI: 10.1021/acs.chemrev.1c00675] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
![]()
Implicit solvation
is an effective, highly coarse-grained approach
in atomic-scale simulations to account for a surrounding liquid electrolyte
on the level of a continuous polarizable medium. Originating in molecular
chemistry with finite solutes, implicit solvation techniques are now
increasingly used in the context of first-principles modeling of electrochemistry
and electrocatalysis at extended (often metallic) electrodes. The
prevalent ansatz to model the latter electrodes and the reactive surface
chemistry at them through slabs in periodic boundary condition supercells
brings its specific challenges. Foremost this concerns the difficulty
of describing the entire double layer forming at the electrified solid–liquid
interface (SLI) within supercell sizes tractable by commonly employed
density functional theory (DFT). We review liquid solvation methodology
from this specific application angle, highlighting in particular its
use in the widespread ab initio thermodynamics approach
to surface catalysis. Notably, implicit solvation can be employed
to mimic a polarization of the electrode’s electronic density
under the applied potential and the concomitant capacitive charging
of the entire double layer beyond the limitations of the employed
DFT supercell. Most critical for continuing advances of this effective
methodology for the SLI context is the lack of pertinent (experimental
or high-level theoretical) reference data needed for parametrization.
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Affiliation(s)
- Stefan Ringe
- Department of Energy Science and Engineering, Daegu Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea.,Energy Science & Engineering Research Center, Daegu Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea
| | - Nicolas G Hörmann
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany.,Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstraße 4, D-85747 Garching, Germany
| | - Harald Oberhofer
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstraße 4, D-85747 Garching, Germany.,Chair for Theoretical Physics VII and Bavarian Center for Battery Technology (BayBatt), University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
| | - Karsten Reuter
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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15
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Huang J, Li M, Eslamibidgoli MJ, Eikerling M, Groß A. Cation Overcrowding Effect on the Oxygen Evolution Reaction. JACS AU 2021; 1:1752-1765. [PMID: 34723278 PMCID: PMC8549051 DOI: 10.1021/jacsau.1c00315] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Indexed: 05/05/2023]
Abstract
The influence of electrolyte ions on the catalytic activity of electrode/electrolyte interfaces is a controversial topic for many electrocatalytic reactions. Herein, we focus on an effect that is usually neglected, namely, how the local reaction conditions are shaped by nonspecifically adsorbed cations. We scrutinize the oxygen evolution reaction (OER) at nickel (oxy)hydroxide catalysts, using a physicochemical model that integrates density functional theory calculations, a microkinetic submodel, and a mean-field submodel of the electric double layer. The aptness of the model is verified by comparison with experiments. The robustness of model-based insights against uncertainties and variations in model parameters is examined, with a sensitivity analysis using Monto Carlo simulations. We interpret the decrease in OER activity with the increasing effective size of electrolyte cations as a consequence of cation overcrowding near the negatively charged electrode surface. The same reasoning could explain why the OER activity increases with solution pH on the RHE scale and why the OER activity decreases in the presence of bivalent cations. Overall, this work stresses the importance of correctly accounting for local reaction conditions in electrocatalytic reactions to obtain an accurate picture of factors that determine the electrode activity.
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Affiliation(s)
- Jun Huang
- Institute
of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany
- Institute
of Energy and Climate Research, IEK-13: Theory and Computation of
Energy Materials, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany
| | - Mengru Li
- Institute
of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany
| | - Mohammad J. Eslamibidgoli
- Institute
of Energy and Climate Research, IEK-13: Theory and Computation of
Energy Materials, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany
| | - Michael Eikerling
- Institute
of Energy and Climate Research, IEK-13: Theory and Computation of
Energy Materials, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany
- Jülich
Aachen Research Alliance: JARA-Energy, 52425 Jülich, Germany
| | - Axel Groß
- Institute
of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany
- Helmholtz
Institute Ulm (HIU) Electrochemical Energy Storage, 89069 Ulm, Germany
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16
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Caetano DLZ, de Carvalho SJ, Bossa GV, May S. Monte Carlo simulations and mean-field modeling of electric double layers at weakly and moderately charged spherical macroions. Phys Rev E 2021; 104:034609. [PMID: 34654110 DOI: 10.1103/physreve.104.034609] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 09/01/2021] [Indexed: 11/07/2022]
Abstract
Monte Carlo simulations are employed to determine the differential capacitance of an electric double layer formed by small size-symmetric anions and cations in the vicinity of weakly to moderately charged macroions. The influence of interfacial curvature is deduced by investigating spherical macroions, ranging from flat to moderately curved. We also calculate the differential capacitance using a previously developed mean-field model where, in addition to electrostatic interactions, the excluded volumes of the ions are taken into account using either the lattice-gas or the Carnahan-Starling equation of state. For both equations of state, we compare the mean-field model for arbitrary curvature with a recently developed second-order curvature expansion. Our Monte Carlo simulations predict an increase in the differential capacitance with growing macroion curvature if the surface charge density is small, whereas for moderately charged macroions the differential capacitance passes through a local minimum. Both mean-field models tend to somewhat overestimate the differential capacitance as compared with Monte Carlo simulations. At the same time, they do reproduce the curvature dependence of the differential capacitance, especially for small surface charge density. Our study suggests that the quality of mean-field modeling does not worsen when weakly or moderately charged macroions exhibit spherical curvature.
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Affiliation(s)
- Daniel L Z Caetano
- Institute of Chemistry, State University of Campinas (UNICAMP), Campinas, São Paulo 13083-970, Brazil and Center for Computational Engineering and Sciences, State University of Campinas (UNICAMP), Campinas, São Paulo 13083-970, Brazil
| | - Sidney J de Carvalho
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, São Paulo 15054-000, Brazil
| | - Guilherme V Bossa
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, São Paulo 15054-000, Brazil
| | - Sylvio May
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
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17
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Cats P, van Roij R. The differential capacitance as a probe for the electric double layer structure and the electrolyte bulk composition. J Chem Phys 2021; 155:104702. [PMID: 34525830 DOI: 10.1063/5.0064315] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this work, we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical density functional theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly and also how small ions dominate its behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.
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Affiliation(s)
- Peter Cats
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, Utrecht 3584 CC, The Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, Utrecht 3584 CC, The Netherlands
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18
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Lian Z, Chao H, Wang ZG. Effects of Confinement and Ion Adsorption in Ionic Liquid Supercapacitors with Nanoporous Electrodes. ACS NANO 2021; 15:11724-11733. [PMID: 34228448 DOI: 10.1021/acsnano.1c02506] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We investigate the effects of pore size and ion adsorption on the room-temperature ionic liquid capacitor with nanoporous electrodes, with a focus on optimizing the capacitance and energy storage. Using a recently developed modified BSK model accounting for both ion correlations and nonelectrostatic interactions, we find that ion crowding proximate to the electrode surface induced by the spontaneous charge separation due to strong ion correlations is responsible for the anomalous increase in the capacitance with decreasing pore sizes observed in experiments. Reducing the strength of ion correlations increases the capacitance and suppresses the anomalous size dependence. For a given pore size, the capacitance peak diverges when the ion correlation strength α reaches a critical value, αsc,L. The capacitance peak shifts to smaller pore size as α decreases because of rapid decrease of αsc,L with decreasing pore size. Asymmetric preferential ion adsorption is shown to lead to significantly enhanced energy storage close to the transition point for any pore sizes. For a given correlation strength, the energy storage is optimal at a pore size where α = αsc,L.
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Affiliation(s)
- Zengju Lian
- School of Physical Science and Technology, Ningbo University, Ningbo 315211, P. R. China
| | - Huikuan Chao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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19
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Barman SS, Bhattacharyya S, Dutta P. Electrokinetic actuation of an uncharged polarizable dielectric droplet in charged hydrogel medium. Electrophoresis 2021; 42:920-931. [PMID: 33450075 DOI: 10.1002/elps.202000343] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Revised: 12/20/2020] [Accepted: 01/04/2021] [Indexed: 12/21/2022]
Abstract
Electrokinetic transport of an uncharged nonconducting microsized liquid droplet in a charged hydrogel medium is studied. Dielectric polarization of the liquid drop under the action of an externally imposed electric field induces a non-homogeneous charge density at the droplet surface. The interactions of the induced surface charge of the droplet with the immobile charges of the hydrogel medium generates an electric force to the droplet, which actuates the drop through the charged hydrogel medium. A numerical study based on the first principle of electrokinetics is adopted. Dependence of the droplet velocity on its dielectric permittivity, bulk ionic concentration, and immobile charge density of the gel is analyzed. The surface conduction is significant in presence of charged gel, which creates a concentration polarization. The impact of the counterion saturation in the Debye layer due to the dielectric decrement of the medium is addressed. The modified Nernst-Planck equation for ion transport and the Poisson equation for the electric field is considered to take into account the dielectric polarization. A quadrupolar vortex around the uncharged droplet is observed when the gel medium is considered to be uncharged, which is similar to the induced charge electroosmosis around an uncharged dielectric colloid in free-solution. We find that the induced charge electrokinetic mechanism creates a strong recirculation of liquid within the droplet and the translational velocity of the droplet strongly depends on its size for the dielectric droplet embedded in a charged gel medium.
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Affiliation(s)
| | - Somnath Bhattacharyya
- Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India
| | - Prashanta Dutta
- School of Mechanical and Materials Engineering, Washington State University, Pullman, USA
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20
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Gupta A, Govind Rajan A, Carter EA, Stone HA. Ionic Layering and Overcharging in Electrical Double Layers in a Poisson-Boltzmann Model. PHYSICAL REVIEW LETTERS 2020; 125:188004. [PMID: 33196271 DOI: 10.1103/physrevlett.125.188004] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Revised: 09/06/2020] [Accepted: 09/30/2020] [Indexed: 06/11/2023]
Abstract
Electrical double layers (EDLs) play a significant role in a broad range of physical phenomena related to colloidal stability, diffuse-charge dynamics, electrokinetics, and energy storage applications. Recently, it has been suggested that for large ion sizes or multivalent electrolytes, ions can arrange in a layered structure inside the EDLs. However, the widely used Poisson-Boltzmann models for EDLs are unable to capture the details of ion concentration oscillations and the effect of electrolyte valence on such oscillations. Here, by treating a pair of ions as hard spheres below the distance of closest approach and as point charges otherwise, we are able to predict ionic layering without any additional parameters or boundary conditions while still being compatible with the Poisson-Boltzmann framework. Depending on the combination of ion valence, size, and concentration, our model reveals a structured EDL with spatially oscillating ion concentrations. We report the dependence of critical ion concentration, i.e., the ion concentration above which the oscillations are observed, on the counter-ion valence and the ion size. More importantly, our model displays quantitative agreement with the results of computationally intensive models of the EDL. Finally, we analyze the nonequilibrium problem of EDL charging and demonstrate that ionic layering increases the total charge storage capacity and the charging timescale.
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Affiliation(s)
- Ankur Gupta
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Ananth Govind Rajan
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India
| | - Emily A Carter
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, California 90095, USA
- Office of the Chancellor, University of California, Los Angeles, Los Angeles, California 90095, USA
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
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21
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Quadre AB, de Carvalho SJ, Bossa GV. How charge regulation and ion-surface affinity affect the differential capacitance of an electrical double layer. Phys Chem Chem Phys 2020; 22:18229-18238. [PMID: 32776041 DOI: 10.1039/d0cp02360d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The differential capacitance of an electrical double layer is a topic of great importance to develop more efficient and environment-friendly energy storage devices: electric double layer supercapacitors. In addition to the bare electrostatic interactions, recent experimental and computational studies suggest that electrodes covered by ionizable groups do interact selectively with specific ion types, an effect that can increase the maximal conductivity and voltage of a supercapacitor. Inspired by this, in the present work we investigate how ion-specific non-electrostatic interactions modify the differential capacitance of a flat electrode whose surface is covered by ionizable groups subject to a charge regulation process. The incorporation of hydration interactions by means of ion-specific Yukawa potential into the Poisson-Boltzmann theory allows our model to describe different scenarios of ion-surface affinity and, hence, the selective depletion or accumulation of specific ion types close to a charged surface. We obtained larger capacitance values when considering electrodes that favor the accumulation of cations and the depletion of anions.
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Affiliation(s)
- Amanda B Quadre
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, SP 15054-000, Brazil.
| | - Sidney J de Carvalho
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, SP 15054-000, Brazil.
| | - Guilherme Volpe Bossa
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, SP 15054-000, Brazil.
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22
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Gupta A, Zuk PJ, Stone HA. Charging Dynamics of Overlapping Double Layers in a Cylindrical Nanopore. PHYSICAL REVIEW LETTERS 2020; 125:076001. [PMID: 32857551 DOI: 10.1103/physrevlett.125.076001] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 05/03/2020] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
The charging of electrical double layers inside a cylindrical pore has applications to supercapacitors, batteries, desalination and biosensors. The charging dynamics in the limit of thin double layers, i.e., when the double layer thickness is much smaller than the pore radius, is commonly described using an effective RC transmission line circuit. Here, we perform direct numerical simulations (DNS) of the Poisson-Nernst-Planck equations to study the double layer charging for the scenario of overlapping double layers, i.e., when the double layer thickness is comparable to the pore radius. We develop an analytical model that accurately predicts the results of DNS. Also, we construct a modified effective circuit for the overlapping double layer limit, and find that the modified circuit is identical to the RC transmission line but with different values and physical interpretation of the capacitive and resistive elements. In particular, the effective surface potential is reduced, the capacitor represents a volumetric current source, and the charging timescale is weakly dependent on the ratio of the pore radius and the double layer thickness.
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Affiliation(s)
- Ankur Gupta
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Pawel J Zuk
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106 Warsaw, Poland
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
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23
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Malossi RM, Girotto M, dos Santos AP, Levin Y. Simulations of electrolyte between charged metal surfaces. J Chem Phys 2020; 153:044121. [DOI: 10.1063/5.0012073] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rodrigo Mór Malossi
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil
| | - Matheus Girotto
- Instituto de Fisica, Universidade de Sao Paulo, Rua do Matao, 1371, 05508-090 Sao Paulo, SP, Brazil
| | - Alexandre P. dos Santos
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil
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24
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Horng TL. Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation. ENTROPY 2020; 22:e22060632. [PMID: 33286407 PMCID: PMC7517166 DOI: 10.3390/e22060632] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Revised: 06/03/2020] [Accepted: 06/04/2020] [Indexed: 01/20/2023]
Abstract
The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.
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Affiliation(s)
- Tzyy-Leng Horng
- Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan
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25
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Zou WX, Peng J, Xiu WN, Liu XM. Principles of surface potential estimation in mixed electrolyte solutions: Taking into account dielectric saturation. CHINESE J CHEM PHYS 2020. [DOI: 10.1063/1674-0068/cjcp1907132] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Wen-xin Zou
- Chongqing key Laboratory of Soil Multi-scale Interfacial Process, College of Resources and Environment, Southwest University, Chongqing 400715, China
| | - Jing Peng
- Chongqing key Laboratory of Soil Multi-scale Interfacial Process, College of Resources and Environment, Southwest University, Chongqing 400715, China
| | - Wei-ning Xiu
- Institute of Agricultural Engineering, Chongqing Academy of Agricultural Sciences, Chongqing 401329, China
| | - Xin-min Liu
- Chongqing key Laboratory of Soil Multi-scale Interfacial Process, College of Resources and Environment, Southwest University, Chongqing 400715, China
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26
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Kumar R, Mahalik JP, Silmore KS, Wojnarowska Z, Erwin A, Ankner JF, Sokolov AP, Sumpter BG, Bocharova V. Capacitance of thin films containing polymerized ionic liquids. SCIENCE ADVANCES 2020; 6:eaba7952. [PMID: 32637617 PMCID: PMC7319767 DOI: 10.1126/sciadv.aba7952] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 05/15/2020] [Indexed: 06/11/2023]
Abstract
Electrode-polymer interfaces dictate many of the properties of thin films such as capacitance, the electric field experienced by polymers, and charge transport. However, structure and dynamics of charged polymers near electrodes remain poorly understood, especially in the high concentration limit representative of the melts. To develop an understanding of electric field-induced transformations of electrode-polymer interfaces, we have studied electrified interfaces of an imidazolium-based polymerized ionic liquid (PolyIL) using combinations of broadband dielectric spectroscopy, specular neutron reflectivity, and simulations based on the Rayleigh's dissipation function formalism. Overall, we obtained the camel-shaped dependence of the capacitance on applied voltage, which originated from the responses of an adsorbed polymer layer to applied voltages. This work provides additional insights related to the effects of molecular weight in affecting structure and properties of electrode-polymer interfaces, which are essential for designing next-generation energy storage and harvesting devices.
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Affiliation(s)
- Rajeev Kumar
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
| | - Jyoti P. Mahalik
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
| | - Kevin S. Silmore
- Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Zaneta Wojnarowska
- Institute of Physics,University of Silesia,SMCEBI, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland
| | - Andrew Erwin
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- School of Materials Science and Engineering, Georgia Tech, Atlanta, GA 30332, USA
| | - John F. Ankner
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Alexei P. Sokolov
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA
- Department of Chemistry, University of Tennessee, Knoxville, TN 37996, USA
| | - Bobby G. Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Vera Bocharova
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
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27
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Qing L, Lei J, Zhao T, Qiu G, Ma M, Xu Z, Zhao S. Effects of Kinetic Dielectric Decrement on Ion Diffusion and Capacitance in Electrochemical Systems. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:4055-4064. [PMID: 32233504 DOI: 10.1021/acs.langmuir.0c00353] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Diffusion of ionic components in electrolytes not only eliminates the gradients of ionic concentrations but also alters the local dielectric environment, and the coupling effect between kinetic dielectric decrement and ionic concentration gradient on the diffusion dynamics is not well understood. Herein, taking the charging process in electrical double layer systems as a case study, we conduct a multiscale investigation of ion diffusions in aqueous electrolytes by combining the dynamic density functional theory and an ion-concentration-dependent dielectric constant model. By properly considering the time evolutions of local dielectric constant coupled with ion density, we report an interesting phenomenon on the suppression of surface charge density that is not captured by conventional models. In addition, we show that the usage of aqueous electrolyte with small dielectric decrement coefficients promotes the capacitance, in quantitative agreement with experimental measurements.
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Affiliation(s)
- Leying Qing
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, 200237 Shanghai, China
| | - Jun Lei
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, 200237 Shanghai, China
| | - Teng Zhao
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, 200237 Shanghai, China
| | - Genlong Qiu
- Guangxi Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology and School of Chemistry and Chemical Engineering, Guangxi University, Nanning 530004, China
| | - Manman Ma
- School of Mathematical Sciences, Tongji University, 200092 Shanghai, China
| | - Zhenli Xu
- School of Mathematical Sciences, Institute of Natural Sciences, and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, 200240 Shanghai, China
| | - Shuangliang Zhao
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, 200237 Shanghai, China
- Guangxi Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology and School of Chemistry and Chemical Engineering, Guangxi University, Nanning 530004, China
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28
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Chao H, Wang ZG. Effects of Surface Transition and Adsorption on Ionic Liquid Capacitors. J Phys Chem Lett 2020; 11:1767-1772. [PMID: 32040914 DOI: 10.1021/acs.jpclett.0c00023] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Room-temperature ionic liquids (RTILs) are synthetic electrolytes with electrochemical stability superior to that of conventional aqueous-based electrolytes, allowing a significantly enlarged electrochemical window for application as capacitors. In this study, we propose a variant of an existing RTIL model for solvent-free RTILs, accounting for both ion-ion correlations and nonelectrostatic interactions. Using this model, we explore the phenomenon of spontaneous surface charge separation in RTIL capacitors and find that this transition is a common feature for realistic choices of the model parameters in most RTILs. In addition, we investigate the effects of asymmetric preferential ion adsorption on this charge separation transition and find that proximity of the transition in this case can result in greatly enhanced energy storage. Our work suggests that differential chemical treatment of electrodes can be a simple and useful means for optimizing energy storage in RTIL capacitors.
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Affiliation(s)
- Huikuan Chao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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29
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Heo M, Shin GR, Kim SC. Capacitance of electrolytes with hydration-mediated interaction in planar electric double layers. Mol Phys 2020. [DOI: 10.1080/00268976.2019.1610196] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Minhye Heo
- Department of Physics, Andong National University, Andong, Korea
| | - Ghi Ryang Shin
- Department of Physics, Andong National University, Andong, Korea
| | - Soon-Chul Kim
- Department of Physics, Andong National University, Andong, Korea
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30
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Qiao C, Zhang J, Jiang P, Zhao S, Song X, Yu J. A molecular approach for predicting phase diagrams of ternary aqueous saline solutions. Chem Eng Sci 2020. [DOI: 10.1016/j.ces.2019.115278] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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31
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Nattino F, Truscott M, Marzari N, Andreussi O. Continuum models of the electrochemical diffuse layer in electronic-structure calculations. J Chem Phys 2019; 150:041722. [PMID: 30709273 DOI: 10.1063/1.5054588] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science, it remains unclear which features are necessary in order to accurately describe interface-related observables such as the differential capacitance (DC) of metal electrode surfaces. We present here a critical comparison of continuum diffuse-layer models that can be coupled to an atomistic first-principles description of the charged metal surface in order to account for the electrolyte screening at electrified interfaces. By comparing computed DC values for the prototypical Ag(100) surface in an aqueous solution to experimental data, we validate the accuracy of the models considered. Results suggest that a size-modified Poisson-Boltzmann description of the electrolyte solution is sufficient to qualitatively reproduce the main experimental trends. Our findings also highlight the large effect that the dielectric cavity parameterization has on the computed DC values.
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Affiliation(s)
- Francesco Nattino
- Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Matthew Truscott
- Department of Physics, University of North Texas, Denton, Texas 76207, USA
| | - Nicola Marzari
- Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Oliviero Andreussi
- Department of Physics, University of North Texas, Denton, Texas 76207, USA
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32
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Melander MM, Kuisma MJ, Christensen TEK, Honkala K. Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials. J Chem Phys 2019; 150:041706. [PMID: 30709274 DOI: 10.1063/1.5047829] [Citation(s) in RCA: 74] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed ion and electrode potentials. In this work, a general framework within density functional theory (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including (i) the combination of classical and electronic DFTs within the GC ensemble and (ii) on the simplest level a chemically and physically sound way to obtain various (modified) Poisson-Boltzmann (mPB) implicit solvent models. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some of the constraints and coarse-graining if needed. We implement various mPB models within a linear dielectric continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.
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Affiliation(s)
- Marko M Melander
- Nanoscience Center, Department of Chemistry, University of Jyväskylä, P.O. Box 35 (YN), FI-40014 Jyväskylä, Finland
| | - Mikael J Kuisma
- Nanoscience Center, Department of Chemistry, University of Jyväskylä, P.O. Box 35 (YN), FI-40014 Jyväskylä, Finland
| | | | - Karoliina Honkala
- Nanoscience Center, Department of Chemistry, University of Jyväskylä, P.O. Box 35 (YN), FI-40014 Jyväskylä, Finland
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33
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González-Tovar E, Lozada-Cassou M, Bhuiyan LB, Outhwaite CW. Comparison of zeta potentials and structure for statistical mechanical theories of a model cylindrical double layer. J Mol Liq 2018. [DOI: 10.1016/j.molliq.2017.12.044] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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34
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Gupta A, Stone HA. Electrical Double Layers: Effects of Asymmetry in Electrolyte Valence on Steric Effects, Dielectric Decrement, and Ion-Ion Correlations. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:11971-11985. [PMID: 30153029 DOI: 10.1021/acs.langmuir.8b02064] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the effects of asymmetry in electrolyte valence (i.e., non z: z electrolytes) on mean field theory of the electrical double layer. Specifically, we study the effect of valence asymmetry on finite ion-size effects, the dielectric decrement, and ion-ion correlations. For a model configuration of an electrolyte near a charged surface in equilibrium, we present comprehensive analytical and numerical results for the potential distribution, electrode charge density, capacitance, and dimensionless salt uptake. We emphasize that the asymmetry in electrolyte valence significantly influences the diffuse-charge relations, and prior results reported in the literature are readily extended to non z: z electrolytes. We develop scaling relations and invoke physical arguments to examine the importance of asymmetry in electrolyte valence on the aforementioned effects. We conclude by providing implications of our findings on diffuse-charge dynamics and other electrokinetic phenomena.
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Affiliation(s)
- Ankur Gupta
- Department of Mechanical and Aerospace Engineering , Princeton University , Princeton , New Jersey 08544 , United States
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering , Princeton University , Princeton , New Jersey 08544 , United States
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35
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McEldrew M, Goodwin ZAH, Kornyshev AA, Bazant MZ. Theory of the Double Layer in Water-in-Salt Electrolytes. J Phys Chem Lett 2018; 9:5840-5846. [PMID: 30229648 DOI: 10.1021/acs.jpclett.8b02543] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
One challenge in developing the next generation of lithium-ion batteries is the replacement of organic electrolytes, which are flammable and most often contain toxic and thermally unstable lithium salts, with safer, environmentally friendly alternatives. Recently developed water-in-salt electrolytes (WiSEs), which are nonflammable, nontoxic, and also have enhanced electrochemical stability, are promising alternatives. In this work, we develop a simple modified Poisson-Fermi theory for WiSEs, which demonstrates the fine interplay between electrosorption, solvation, and ion correlations. The phenomenological parameters are extracted from molecular dynamics simulations, also performed here. The theory reproduces the WiSEs' electrical double-layer structure with remarkable accuracy.
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Affiliation(s)
- Michael McEldrew
- Department of Chemical Engineering , Massachusetts Institute of Technology , Cambridge , Massachusetts , United States
| | - Zachary A H Goodwin
- Department of Physics, CDT Theory and Simulation of Materials , Imperial College of London, South Kensington Campus , London SW7 2AZ , U.K
- Department of Chemistry , Imperial College of London, South Kensington Campus , London SW7 2AZ , U.K
| | - Alexei A Kornyshev
- Department of Chemistry , Imperial College of London, South Kensington Campus , London SW7 2AZ , U.K
- Thomas Young Centre for Theory and Simulation of Materials , Imperial College of London, South Kensington Campus , London SW7 2AZ , U.K
| | - Martin Z Bazant
- Department of Chemical Engineering , Massachusetts Institute of Technology , Cambridge , Massachusetts , United States
- Department of Mathematics , Massachusetts Institute of Technology , Cambridge , Massachusetts , United States
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36
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Bossa GV, Caetano DLZ, de Carvalho SJ, Bohinc K, May S. Modeling the camel-to-bell shape transition of the differential capacitance using mean-field theory and Monte Carlo simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:113. [PMID: 30259300 DOI: 10.1140/epje/i2018-11723-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2018] [Accepted: 08/30/2018] [Indexed: 06/08/2023]
Abstract
Mean-field electrostatics is used to calculate the differential capacitance of an electric double layer formed at a planar electrode in a symmetric 1:1 electrolyte. Assuming the electrolyte is also ion-size symmetric, we derive analytic expressions for the differential capacitance valid up to fourth order in the surface charge density or surface potential. Our mean-field model accounts exclusively for electrostatic interactions but includes an arbitrary non-ideality in the mixing entropy of the mobile ions. The ensuing criterion for the camel-to-bell shape transition of the differential capacitance is analyzed using commonly used mixing models (one based on a lattice gas and the other based on the Carnahan-Starling equation of state) and compared with Monte Carlo simulations. We observe a reasonable agreement between all our mean-field models and the simulation data for the camel-to-bell shape transition. The absolute value of the differential capacitance for an uncharged (or weakly charged) electrode is, however, not reproduced by our mean-field approaches, not even upon introducing a Stern layer with a thickness equal of the ion radius. We show that, if a Stern layer is introduced, its thickness dependence on the ion size is non-monotonic or, depending on the salt concentration, even inversely proportional.
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Affiliation(s)
- Guilherme V Bossa
- Department of Physics, North Dakota State University, 58108-6050, Fargo, ND, USA
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, 15054-000, São José do Rio Preto, SP, Brazil
| | - Daniel L Z Caetano
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, 15054-000, São José do Rio Preto, SP, Brazil
| | - Sidney J de Carvalho
- Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, 15054-000, São José do Rio Preto, SP, Brazil
| | - Klemen Bohinc
- Faculty of Health Sciences, University of Ljubljana, Poljanska 26a, 1000, Ljubljana, Slovenia
| | - Sylvio May
- Department of Physics, North Dakota State University, 58108-6050, Fargo, ND, USA.
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37
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Podgornik R. General theory of charge regulation and surface differential capacitance. J Chem Phys 2018; 149:104701. [PMID: 30219025 DOI: 10.1063/1.5045237] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A generalization of the mean-field approach will be derived that will take into account the ion-ion as well as ion-surface non-electrostatic effects on an equal footing, being based on the bulk and surface equations of state in the absence of electrostatic interactions. This approach will be applied to the analysis of a single planar surface with dissociable sites with several models of the specific ion-surface non-electrostatic interactions, providing a general thermodynamic insight into the characteristics of the surface differential capacitance. The ion-surface interactions and ion-ion packing considerations at the surface will be shown to be more relevant than the bulk packing constraints for ions vicinal to the surface, as well as to set in prior to the conditions where the bulk packing constraints would become relevant.
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Affiliation(s)
- Rudolf Podgornik
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; Department of Theoretical Physics, Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia; and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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38
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López-García JJ, Horno J, Grosse C. Diffuse double-layer structure in mixed electrolytes considering ions as dielectric spheres. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:102. [PMID: 30191427 DOI: 10.1140/epje/i2018-11713-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Accepted: 08/08/2018] [Indexed: 06/08/2023]
Abstract
The structure of the diffuse part of the electric double layer at solid-electrolyte solution interfaces is examined using a theoretical model that takes into account the finite ion size by modeling the solution as a suspension of polarizable insulating spheres in water. This formalism is applied to mixed electrolyte solutions using the "Boublik-Mansoori-Carnahan-Starling-Leland" (BMCSL) theory for the steric interactions among ions. It is shown that the ionic size differences have a strong bearing on the diffuse part of the electric double-layer structure of these systems. Moreover, for strong potential values, the different size-related effects become important even for binary electrolyte solutions due to the presence of H+ and OH- ions that are substantially smaller than hydrated ions originated from salt dissociation. The obtained results display some of the qualitative features observed in experiments on aqueous systems that are generally interpreted in terms of totally different mechanisms.
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Affiliation(s)
- J J López-García
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071, Jaén, Spain.
| | - J Horno
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071, Jaén, Spain
| | - C Grosse
- Departamento de Física, Universidad Nacional de Tucumán, Av. Independencia 1800, 4000, San Miguel de Tucumán, Argentina
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39
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Uematsu Y, Netz RR, Bonthuis DJ. Analytical Interfacial Layer Model for the Capacitance and Electrokinetics of Charged Aqueous Interfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:9097-9113. [PMID: 29495657 DOI: 10.1021/acs.langmuir.7b04171] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We construct an analytical model to account for the influence of the subnanometer-wide interfacial layer on the differential capacitance and the electro-osmotic mobility of solid-electrolyte interfaces. The interfacial layer is incorporated into the Poisson-Boltzmann and Stokes equations using a box model for the dielectric properties, the viscosity, and the ionic potential of mean force. We calculate the differential capacitance and the electro-osmotic mobility as a function of the surface charge density and the salt concentration, both with and without steric interactions between the ions. We compare the results from our theoretical model with experimental data on a variety of systems (graphite and metallic silver for capacitance and titanium oxide and silver iodide for electro-osmotic data). The differential capacitance of silver as a function of salinity and surface charge density is well reproduced by our theory, using either the width of the interfacial layer or the ionic potential of mean force as the only fitting parameter. The differential capacitance of graphite, however, needs an additional carbon capacitance to explain the experimental data. Our theory yields a power-law dependence of the electro-osmotic mobility on the surface charge density for high surface charges, reproducing the experimental data using both the interfacial parameters extracted from molecular dynamics simulations and fitted interfacial parameters. Finally, we examine different types of hydrodynamic boundary conditions for the power-law behavior of the electro-osmotic mobility, showing that a finite-viscosity layer explains the experimental data better than the usual hydrodynamic slip boundary condition. Our analytical model thus allows us to extract the properties of the subnanometer-wide interfacial layer by fitting to macroscopic experimental data.
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Affiliation(s)
- Yuki Uematsu
- Department of Chemistry , Kyushu University , Fukuoka 819-0395 , Japan
- Fachbereich Physik , Freie Universität Berlin , 14195 Berlin , Germany
| | - Roland R Netz
- Fachbereich Physik , Freie Universität Berlin , 14195 Berlin , Germany
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40
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Majee PS, Bhattacharyya S. Electroosmotic flow around a dielectric uncharged particle by considering the dielectric decrement effects. Colloids Surf A Physicochem Eng Asp 2018. [DOI: 10.1016/j.colsurfa.2018.03.037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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41
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Daniels L, Scott M, Mišković Z. The effects of dielectric decrement and finite ion size on differential capacitance of electrolytically gated graphene. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.04.030] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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42
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Uematsu Y, Netz RR, Bonthuis DJ. The effects of ion adsorption on the potential of zero charge and the differential capacitance of charged aqueous interfaces. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:064002. [PMID: 29297853 DOI: 10.1088/1361-648x/aaa4d4] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Using a box profile approximation for the non-electrostatic surface adsorption potentials of anions and cations, we calculate the differential capacitance of aqueous electrolyte interfaces from a numerical solution of the Poisson-Boltzmann equation, including steric interactions between the ions and an inhomogeneous dielectric profile. Preferential adsorption of the positive (negative) ion shifts the minimum of the differential capacitance to positive (negative) surface potential values. The trends are similar for the potential of zero charge; however, the potential of zero charge does not correspond to the minimum of the differential capacitance in the case of asymmetric ion adsorption, contrary to the assumption commonly used to determine the potential of zero charge. Our model can be used to obtain more accurate estimates of ion adsorption properties from differential capacitance or electrocapillary measurements. Asymmetric ion adsorption also affects the relative heights of the characteristic maxima in the differential capacitance curves as a function of the surface potential, but even for strong adsorption potentials the effect is small, making it difficult to reliably determine the adsorption properties from the peak heights.
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Affiliation(s)
- Yuki Uematsu
- Department of Chemistry, Kyushu University, Fukuoka 819-0395, Japan. Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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43
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Persson RAX. On the dielectric decrement of electrolyte solutions: a dressed-ion theory analysis. Phys Chem Chem Phys 2018; 19:1982-1987. [PMID: 28009858 DOI: 10.1039/c6cp07515k] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Based on the dressed-ion theory and a simple physical argument regarding the conductivity of the solution, we derive a relation between the ionic strength and dielectric constant of an electrolyte solution. At its simplest, this model gives the dielectric constant at low ionic strength I as εr(I) = εr(0)(1 + αI)-1, where α (the excess polarization) is directly related to the dressed-ion charge. One contribution to the origin of the dielectric decrement is thus seen to stem from the electrostatic screening of the ions in solution, with no solvent contributions necessary.
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Affiliation(s)
- Rasmus A X Persson
- Department of Chemistry & Molecular Biology, University of Gothenburg, Gothenburg, Sweden.
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44
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Bohinc K, Bossa GV, May S. Incorporation of ion and solvent structure into mean-field modeling of the electric double layer. Adv Colloid Interface Sci 2017; 249:220-233. [PMID: 28571611 DOI: 10.1016/j.cis.2017.05.001] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Revised: 04/28/2017] [Accepted: 05/02/2017] [Indexed: 01/13/2023]
Abstract
An electric double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the electric double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded volume effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theoretical models predict structural properties of the electric double layer such as the differential capacitance and compare some of these predictions with computer simulations.
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Affiliation(s)
- Klemen Bohinc
- Faculty of Health Sciences, University of Ljubljana, Ljubljana SI-1000, Slovenia.
| | | | - Sylvio May
- Department of Physics, North Dakota State University, Fargo, ND 58108-6050, USA
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45
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López-García JJ, Horno J, Grosse C. Differential capacitance of the diffuse double layer at electrode-electrolyte interfaces considering ions as dielectric spheres: Part I. Binary electrolyte solutions. J Colloid Interface Sci 2017; 496:531-539. [PMID: 28259019 DOI: 10.1016/j.jcis.2017.02.043] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Revised: 02/17/2017] [Accepted: 02/17/2017] [Indexed: 11/25/2022]
Abstract
A full theoretical account of the differential capacitance of the diffuse part of the electric double layer at electrode-electrolyte solution interfaces is presented. It builds upon the standard electrokinetic model adding all the additional effects related to the finite ionic size. This includes steric interactions among ions by means of either the Bikerman or Carnahan-Starling expressions and all the permittivity related effects that arise when ions are represented as dielectric spheres. These include the solution permittivity dependence on the local ionic concentration, calculated by means of the Maxwell mixture formula, and two additional forces acting on the ions, namely the Born and the dielectrophoretic forces that depend on the permittivity and the electric field gradients, respectively. The obtained results show that the diffuse double layer behavior is sufficient to qualitatively account for the observed differential capacitance dependence on the electrode voltage. Moreover, when combined with an inner layer capacitance and using the Carnahan-Starling expression, a remarkably good quantitative agreement is achieved.
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Affiliation(s)
- J J López-García
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071 Jaén, Spain.
| | - J Horno
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071 Jaén, Spain
| | - C Grosse
- Departamento de Física, Universidad Nacional de Tucumán, Av. Independencia 1800, 4000 San Miguel de Tucumán, Argentina
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46
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Shevkunov SV. Mechanisms for ion retention in molecular water clusters in a planar nanopore against the background of thermal fluctuations. COLLOID JOURNAL 2017. [DOI: 10.1134/s1061933x17030140] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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47
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Ringe S, Oberhofer H, Reuter K. Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions. J Chem Phys 2017; 146:134103. [DOI: 10.1063/1.4978850] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Stefan Ringe
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Harald Oberhofer
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Karsten Reuter
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
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48
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Daniels L, Scott M, Mišković ZL. The role of Stern layer in the interplay of dielectric saturation and ion steric effects for the capacitance of graphene in aqueous electrolytes. J Chem Phys 2017. [DOI: 10.1063/1.4976991] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lindsey Daniels
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Matthew Scott
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Z. L. Mišković
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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49
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Sundararaman R, Schwarz K. Evaluating continuum solvation models for the electrode-electrolyte interface: Challenges and strategies for improvement. J Chem Phys 2017; 146:084111. [PMID: 28249432 PMCID: PMC5569893 DOI: 10.1063/1.4976971] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Ab initio modeling of electrochemical systems is becoming a key tool for understanding and predicting electrochemical behavior. Development and careful benchmarking of computational electrochemical methods are essential to ensure their accuracy. Here, using charging curves for an electrode in the presence of an inert aqueous electrolyte, we demonstrate that most continuum models, which are parameterized and benchmarked for molecules, anions, and cations in solution, undersolvate metal surfaces, and underestimate the surface charge as a function of applied potential. We examine features of the electrolyte and interface that are captured by these models and identify improvements necessary for realistic electrochemical calculations of metal surfaces. Finally, we reparameterize popular solvation models using the surface charge of Ag(100) as a function of voltage to find improved accuracy for metal surfaces without significant change in utility for molecular and ionic solvation.
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Affiliation(s)
- Ravishankar Sundararaman
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110 8th St, Troy, NY 12180 (USA)
| | - Kathleen Schwarz
- National Institute of Standards and Technology, Material Measurement Laboratory, 100 Bureau Dr, Gaithersburg, MD, 20899 (USA)
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50
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Caetano DLZ, Bossa GV, de Oliveira VM, Brown MA, de Carvalho SJ, May S. Differential capacitance of an electric double layer with asymmetric solvent-mediated interactions: mean-field theory and Monte Carlo simulations. Phys Chem Chem Phys 2017; 19:23971-23981. [DOI: 10.1039/c7cp04672c] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The differential capacitance of an electrical double layer is directly affected by properties of the electrolyte solution such as temperature, salt concentration, ionic size, and solvent structure.
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Affiliation(s)
- Daniel L. Z. Caetano
- Department of Physics
- Sao Paulo State University (UNESP)
- Institute of Biosciences
- Humanities and Exact Sciences (Ibilce)
- Brazil
| | | | - Vinicius M. de Oliveira
- Department of Physics
- Sao Paulo State University (UNESP)
- Institute of Biosciences
- Humanities and Exact Sciences (Ibilce)
- Brazil
| | - Matthew A. Brown
- Laboratory for Surface Science and Technology
- Department of Materials
- ETH Zürich
- CH-8093 Zurich
- Switzerland
| | - Sidney J. de Carvalho
- Department of Physics
- Sao Paulo State University (UNESP)
- Institute of Biosciences
- Humanities and Exact Sciences (Ibilce)
- Brazil
| | - Sylvio May
- Department of Physics
- North Dakota State University
- Fargo
- USA
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