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Verkholyak T, Kuzmak A, Kondrat S. Capacitive energy storage in single-file pores: Exactly solvable models and simulations. J Chem Phys 2021; 155:174112. [PMID: 34742202 DOI: 10.1063/5.0066786] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion and water desalination. Exactly solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly solvable, one-dimensional off-lattice model for charging single-file pores. Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, by changing cation-anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, C ∼ u-2. This dependence follows from hard-core interactions and is not captured by the lattice model.
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Affiliation(s)
- Taras Verkholyak
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011 Lviv, Ukraine
| | - Andrij Kuzmak
- Department for Theoretical Physics, I. Franko National University of Lviv, Lviv, Ukraine
| | - Svyatoslav Kondrat
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
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2
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Frydel D. Kuramoto model with run-and-tumble dynamics. Phys Rev E 2021; 104:024203. [PMID: 34525604 DOI: 10.1103/physreve.104.024203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Accepted: 07/16/2021] [Indexed: 06/13/2023]
Abstract
This work considers an extension of the Kuramoto model with run-and-tumble dynamics-a type of self-propelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual particles is no longer fixed but can change sporadically with a new velocity drawn from a distribution g(ω). Because the Kuramoto model undergoes phase transition, it offers a simple case study for investigating phase transition for a system with self-propelled particles.
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Affiliation(s)
- Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, Santiago, Chile
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3
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Varela L, Téllez G, Trizac E. One-dimensional colloidal model with dielectric inhomogeneity. Phys Rev E 2021; 103:042603. [PMID: 34006007 DOI: 10.1103/physreve.103.042603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 03/16/2021] [Indexed: 11/07/2022]
Abstract
We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.
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Affiliation(s)
- Lucas Varela
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France.,Universidad de los Andes, Bogotá, Colombia
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4
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Groda Y, Dudka M, Kornyshev AA, Oshanin G, Kondrat S. Superionic Liquids in Conducting Nanoslits: Insights from Theory and Simulations. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2021; 125:4968-4976. [PMID: 33841607 PMCID: PMC8029497 DOI: 10.1021/acs.jpcc.0c10836] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 02/06/2021] [Indexed: 05/09/2023]
Abstract
Mapping the theory of charging supercapacitors with nanostructured electrodes on known lattice models of statistical physics is an interesting task, aimed at revealing generic features of capacitive energy storage in such systems. The main advantage of this approach is the possibility to obtain analytical solutions that allow new physical insights to be more easily developed. But how general the predictions of such theories could be? How sensitive are they to the choice of the lattice? Herein, we address these questions in relation to our previous description of such systems using the Bethe-lattice approach and Monte Carlo simulations. Remarkably, we find a surprisingly good agreement between the analytical theory and simulations. In addition, we reveal a striking correlation between the ability to store energy and ion ordering inside a pore, suggesting that such ordering can be beneficial for energy storage.
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Affiliation(s)
- Yaroslav Groda
- Department
of Mechanics and Engineering, Belarusian
State Technological University, Sverdlova str., 13a, 220006 Minsk, Belarus
| | - Maxym Dudka
- Institute
for Condensed Matter Physics of the National Academy of Sciences of
Ukraine, 1 Svientsitskii st., 79011 Lviv, Ukraine
- L Collaboration
& Doctoral College for the Statistical
Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, D-04009 Leipzig, Europe
- Institute
of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Alexei A. Kornyshev
- Department
of Chemistry, Molecular Sciences Research
Hub, White City Campus, W12 0BZ London, United Kingdom
- Thomas
Young
Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, SW7 2AZ London, United Kingdom
| | - Gleb Oshanin
- Sorbonne
Université, CNRS, Laboratoire de Physique Théorique
de la Matière Condensée, LPTMC (UMR CNRS 7600), 75252 Paris Cedex 05, France
| | - Svyatoslav Kondrat
- Institute
of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
- Max-Planck-Institut
für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany
- IV.
Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
- ,
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5
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Gomez DA, Frydel D, Levin Y. Lattice-gas model of a charge regulated planar surface. J Chem Phys 2021; 154:074706. [PMID: 33607887 DOI: 10.1063/5.0039029] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin-Fowler-Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.
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Affiliation(s)
- Daniel Alejandro Gomez
- Department of Chemistry, Federico Santa Maria Technical University, Campus San Joaquin, Santiago, Chile
| | - Derek Frydel
- Department of Chemistry, Federico Santa Maria Technical University, Campus San Joaquin, Santiago, Chile
| | - Yan Levin
- Institute of Physics, The Federal University of Rio Grande do Sul, Porto Alegre 91501-970, Brazil
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6
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Bakhshandeh A, Frydel D, Levin Y. Charge regulation of colloidal particles in aqueous solutions. Phys Chem Chem Phys 2020; 22:24712-24728. [PMID: 33104140 DOI: 10.1039/d0cp03633a] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We study the charge regulation of colloidal particles inside aqueous electrolyte solutions. To stabilize a colloidal suspension against precipitation, colloidal particles are synthesized with either acidic or basic groups on their surface. On contact with water, these surface groups undergo proton transfer reactions, resulting in colloidal surface charge. The charge is determined by the condition of local chemical equilibrium between hydronium ions inside the solution and at the colloidal surface. We use a model of Baxter sticky spheres to explicitly calculate the equilibrium dissociation constants and to construct a theory which is able to quantitatively predict the effective charge of colloidal particles with either acidic or basic surface groups. The predictions of the theory for the model are found to be in excellent agreement with the results of Monte Carlo simulations. This theory is further extended to treat colloidal particles with a mixture of both acidic and basic surface groups.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil.
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7
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Dudka M, Kondrat S, Bénichou O, Kornyshev AA, Oshanin G. Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior. J Chem Phys 2019; 151:184105. [PMID: 31731872 DOI: 10.1063/1.5127851] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop a theory of charge storage in ultranarrow slitlike pores of nanostructured electrodes. Our analysis is based on the Blume-Capel model in an external field, which we solve analytically on a Bethe lattice. The obtained solutions allow us to explore the complete phase diagram of confined ionic liquids in terms of the key parameters characterizing the system, such as pore ionophilicity, interionic interaction energy, and voltage. The phase diagram includes the lines of first- and second-order, direct and re-entrant phase transitions, which are manifested by singularities in the corresponding capacitance-voltage plots. Testing our predictions experimentally requires monodisperse, conducting ultranarrow slit pores, to permit only one layer of ions, and thick pore walls, to prevent interionic interactions across the pore walls. However, some qualitative features, which distinguish the behavior of ionophilic and ionophobic pores and their underlying physics, may emerge in future experimental studies of more complex electrode structures.
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Affiliation(s)
- Maxym Dudka
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
| | - Svyatoslav Kondrat
- Department of Complex Systems, Institute of Physical Chemistry, PAS, Kasprzaka 44/52, Warsaw, Poland
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC (UMR CNRS 7600), 75252 Paris Cedex 05, France
| | - Alexei A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub, White City Campus, London W12 0BZ, United Kingdom
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC (UMR CNRS 7600), 75252 Paris Cedex 05, France
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