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Jeanmairet G, Rotenberg B, Salanne M. Microscopic Simulations of Electrochemical Double-Layer Capacitors. Chem Rev 2022; 122:10860-10898. [PMID: 35389636 PMCID: PMC9227719 DOI: 10.1021/acs.chemrev.1c00925] [Citation(s) in RCA: 35] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
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Electrochemical double-layer
capacitors (EDLCs) are devices allowing
the storage or production of electricity. They function through the
adsorption of ions from an electrolyte on high-surface-area electrodes
and are characterized by short charging/discharging times and long
cycle-life compared to batteries. Microscopic simulations are now
widely used to characterize the structural, dynamical, and adsorption
properties of these devices, complementing electrochemical experiments
and in situ spectroscopic analyses. In this review,
we discuss the main families of simulation methods that have been
developed and their application to the main family of EDLCs, which
include nanoporous carbon electrodes. We focus on the adsorption of
organic ions for electricity storage applications as well as aqueous
systems in the context of blue energy harvesting and desalination.
We finally provide perspectives for further improvement of the predictive
power of simulations, in particular for future devices with complex
electrode compositions.
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Affiliation(s)
- Guillaume Jeanmairet
- Sorbonne Université, CNRS, Physico-chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France.,Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-chimie des Electrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France.,Réseau sur le Stockage Électrochimique de l'Énergie (RS2E), FR CNRS 3459, 80039 Amiens, France
| | - Mathieu Salanne
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens, France.,Sorbonne Université, CNRS, Physico-chimie des Electrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France.,Institut Universitaire de France (IUF), 75231 Paris Cedex 05, France
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2
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Guo P, Qian F, Zhang W, Yan H, Wang Q, Zhao C. Radial basis function interpolation supplemented lattice Boltzmann method for electroosmotic flows in microchannel. Electrophoresis 2021; 42:2171-2181. [PMID: 34549443 DOI: 10.1002/elps.202100155] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Revised: 08/24/2021] [Accepted: 09/09/2021] [Indexed: 01/19/2023]
Abstract
Large gradients of physical variables near the channel walls are characteristic of EOF. The previous numerical simulations of EOFs with the lattice Boltzmann method (LBM) utilize uniform lattice and are not efficient, especially when the electric double layer (EDL) thickness is significantly smaller than the channel height. The efficient LBM simulation of EOF in microchannel calls for a nonuniform mesh which is dense in the EDL region and sparse in the bulk region. In this article, we formulate a radial basis function (RBF)-based interpolation supplemented LBM (ISLBM) to solve the governing equations of EOF, that is, the Poisson, Nernst-Planck, and Navier-Stokes equations, in a nonuniform mesh system. Unlike the conventional ISLBM, the RBF-ISLBM determines the prestreaming distribution functions by using the local RBF-based interpolation over circular supporting regions and is particularly suitable for nonuniform meshes. The RBF-ISLBM is validated by the EOFs in infinitely long and finitely long microchannels. The results show that the RBF-ISLBM possesses excellent robustness and accuracy. Finally, we use the RBF-ISLBM to simulate the EOFs with the hitherto highest electrokinetic parameter, κa, defined by the ratio of channel height a to EDL thickness κ-1 , in LBM simulations of EOF.
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Affiliation(s)
- Panpan Guo
- MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China
| | - Fang Qian
- MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China
| | - Wenyao Zhang
- MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China
| | - Huilong Yan
- MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China
| | - Qiuwang Wang
- MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China
| | - Cunlu Zhao
- MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China
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3
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Asta AJ, Palaia I, Trizac E, Levesque M, Rotenberg B. Lattice Boltzmann electrokinetics simulation of nanocapacitors. J Chem Phys 2019; 151:114104. [DOI: 10.1063/1.5119341] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adelchi J. Asta
- Sorbonne Universités, CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Ivan Palaia
- LPTMS, UMR 8626, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Emmanuel Trizac
- LPTMS, UMR 8626, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Maximilien Levesque
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Universités, CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
- Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, Amiens, France
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4
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Asta A, Levesque M, Rotenberg B. Moment propagation method for the dynamics of charged adsorbing/desorbing species at solid-liquid interfaces. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1461944] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Adelchi Asta
- Sorbonne Université, CNRS, Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX , Paris, France
| | - Maximilien Levesque
- PASTEUR, Département de chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS , 75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX , Paris, France
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5
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Plümper O, Botan A, Los C, Liu Y, Malthe-Sørenssen A, Jamtveit B. Fluid-driven metamorphism of the continental crust governed by nanoscale fluid flow. NATURE GEOSCIENCE 2017; 10:685-690. [PMID: 28890735 PMCID: PMC5584665 DOI: 10.1038/ngeo3009] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Accepted: 07/19/2017] [Indexed: 05/25/2023]
Abstract
The transport of fluids through the Earth's crust controls the redistribution of elements to form mineral and hydrocarbon deposits, the release and sequestration of greenhouse gases, and facilitates metamorphic reactions that influence lithospheric rheology. In permeable systems with a well-connected porosity, fluid transport is largely driven by fluid pressure gradients. In less permeable rocks, deformation may induce permeability by creating interconnected heterogeneities, but without these perturbations, mass transport is limited along grain boundaries or relies on transformation processes that self-generate transient fluid pathways. The latter can facilitate large-scale fluid and mass transport in nominally impermeable rocks without large-scale fluid transport pathways. Here, we show that pervasive, fluid-driven metamorphism of crustal igneous rocks is directly coupled to the production of nanoscale porosity. Using multi-dimensional nano-imaging and molecular dynamics simulations, we demonstrate that in feldspar, the most abundant mineral family in the Earth's crust, electrokinetic transport through reaction-induced nanopores (10-100 nm) can potentially be significant. This suggests that metamorphic fluid flow and fluid-mediated mineral transformation reactions can be considerably influenced by nanofluidic transport phenomena.
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Affiliation(s)
- Oliver Plümper
- Department of Earth Sciences, Utrecht University, Budapestlaan 4, 3584CD Utrecht, The Netherlands
| | - Alexandru Botan
- Physics of Geological Processes (PGP), Departments of Geosciences
and Physics, University of Oslo, Blindern, N-0136 Oslo, Norway
- Centre for Materials Science and Nanotechnology, University of Oslo, Blindern, N-0318 Oslo, Norway
| | - Catharina Los
- Department of Geosciences, University of Bremen, Klagenfurter Strasse 2, 28359 Bremen, Germany
| | - Yang Liu
- Department of Earth Sciences, Utrecht University, Budapestlaan 4, 3584CD Utrecht, The Netherlands
- Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, the Netherlands
| | - Anders Malthe-Sørenssen
- Physics of Geological Processes (PGP), Departments of Geosciences
and Physics, University of Oslo, Blindern, N-0136 Oslo, Norway
| | - Bjørn Jamtveit
- Physics of Geological Processes (PGP), Departments of Geosciences
and Physics, University of Oslo, Blindern, N-0136 Oslo, Norway
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Šamaj L, Trizac E. Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls. Phys Rev E 2016; 93:012601. [PMID: 26871116 DOI: 10.1103/physreve.93.012601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Indexed: 11/07/2022]
Abstract
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).
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Affiliation(s)
- Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
| | - Emmanuel Trizac
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
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7
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Luo K, Wu J, Yi HL, Tan HP. Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids. Phys Rev E 2016; 93:023309. [PMID: 26986441 DOI: 10.1103/physreve.93.023309] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Indexed: 06/05/2023]
Abstract
In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.
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Affiliation(s)
- Kang Luo
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Jian Wu
- GeoRessources Laboratory, Université de Lorraine (ENSG), CNRS, CREGU, F-54501, Vandoeuvre-les-Nancy, France
| | - Hong-Liang Yi
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - He-Ping Tan
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
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8
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Ceratti DR, Obliger A, Jardat M, Rotenberg B, Dahirel V. Stochastic rotation dynamics simulation of electro-osmosis. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1037370] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Davide R. Ceratti
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
- Collège de France, UMR 7574, Chimie de la Matière Condensée de Paris
| | - Amaël Obliger
- Concrete Sustainability Hub, Department of Civil and Environmental Engineering, and MIT-CNRS Joint Laboratory, Massachusetts Institute of Technology , Cambridge, MA, United States
| | - Marie Jardat
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| | - Benjamin Rotenberg
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| | - Vincent Dahirel
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
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9
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Yoshida H, Mizuno H, Kinjo T, Washizu H, Barrat JL. Molecular dynamics simulation of electrokinetic flow of an aqueous electrolyte solution in nanochannels. J Chem Phys 2015; 140:214701. [PMID: 24908029 DOI: 10.1063/1.4879547] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electrokinetic flows of an aqueous NaCl solution in nanochannels with negatively charged surfaces are studied using molecular dynamics simulations. The four transport coefficients that characterize the response to weak electric and pressure fields, namely, the coefficients for the electrical current in response to the electric field (M(jj)) and the pressure field (M(jm)), and those for the mass flow in response to the same fields (M(mj) and M(mm)), are obtained in the linear regime using a Green-Kubo approach. Nonequilibrium simulations with explicit external fields are also carried out, and the current and mass flows are directly obtained. The two methods exhibit good agreement even for large external field strengths, and Onsager's reciprocal relation (M(jm) = M(mj)) is numerically confirmed in both approaches. The influence of the surface charge density on the flow is also considered. The values of the transport coefficients are found to be smaller for larger surface charge density, because the counter-ions strongly bound near the channel surface interfere with the charge and mass flows. A reversal of the streaming current and of the reciprocal electro-osmotic flow, with a change of sign of M(mj) due to the excess co-ions, takes places for very high surface charge density.
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Affiliation(s)
- Hiroaki Yoshida
- Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan
| | - Hideyuki Mizuno
- Laboratory for Interdisciplinary Physics, UMR 5588, Université Grenoble 1 and CNRS, 38402 Saint Martin d'Hères, France
| | - Tomoyuki Kinjo
- Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan
| | - Hitoshi Washizu
- Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan
| | - Jean-Louis Barrat
- Laboratory for Interdisciplinary Physics, UMR 5588, Université Grenoble 1 and CNRS, 38402 Saint Martin d'Hères, France
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10
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Ancian B, Bernard O, Chevalet J, Dahirel V, Devilliers D, Dubois E, Dufrêche JF, Durand-Vidal S, Groult H, Jardat M, Lantelme F, Malikova N, Marry V, Mériguet G, Perzynski R, Rollet AL, Rotenberg B, Salanne M, Simon C. Pierre Turq, an inspirational scientist in charge and at interfaces. Mol Phys 2014. [DOI: 10.1080/00268976.2014.885094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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11
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Obliger A, Jardat M, Coelho D, Bekri S, Rotenberg B. Pore network model of electrokinetic transport through charged porous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:043013. [PMID: 24827338 DOI: 10.1103/physreve.89.043013] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2014] [Indexed: 06/03/2023]
Abstract
We introduce a method for the numerical determination of the steady-state response of complex charged porous media to pressure, salt concentration, and electric potential gradients. The macroscopic fluxes of solvent, salt, and charge are computed within the framework of the Pore Network Model (PNM), which describes the pore structure of the samples as networks of pores connected to each other by channels. The PNM approach is used to capture the couplings between solvent and ionic flows which arise from the charge of the solid surfaces. For the microscopic transport coefficients on the channel scale, we take a simple analytical form obtained previously by solving the Poisson-Nernst-Planck and Stokes equations in a cylindrical channel. These transport coefficients are upscaled for a given network by imposing conservation laws for each pores, in the presence of macroscopic gradients across the sample. The complex pore structure of the material is captured by the distribution of channel diameters. We investigate the combined effects of this complex geometry, the surface charge, and the salt concentration on the macroscopic transport coefficients. The upscaled numerical model preserves the Onsager relations between the latter, as expected. The calculated macroscopic coefficients behave qualitatively as their microscopic counterparts, except for the permeability and the electro-osmotic coupling coefficient when the electrokinetic effects are strong. Quantitatively, the electrokinetic couplings increase the difference between the macroscopic coefficients and the corresponding ones for a single channel of average diameter.
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Affiliation(s)
- Amaël Obliger
- Sorbonne Universités, UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France and CNRS, UMR 8234 PHENIX, 75005 Paris, France and Andra, Parc de la Croix-Blanche, 1-7, rue Jean-Monnet, 92298 Châtenay-Malabry cedex, France
| | - Marie Jardat
- Sorbonne Universités, UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France and CNRS, UMR 8234 PHENIX, 75005 Paris, France
| | - Daniel Coelho
- Andra, Parc de la Croix-Blanche, 1-7, rue Jean-Monnet, 92298 Châtenay-Malabry cedex, France
| | - Samir Bekri
- IFP Energies nouvelles, 1-4 Avenue de Bois-Préau, Rueil-Malmaison 92852, France
| | - Benjamin Rotenberg
- Sorbonne Universités, UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France and CNRS, UMR 8234 PHENIX, 75005 Paris, France
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