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Nigam R, Kar KK. Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:14266-14280. [PMID: 38941262 DOI: 10.1021/acs.langmuir.4c00664] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
Supercapacitors store energy due to the formation of an electric double layer (EDL) at the interface of the electrodes and electrolyte. The present article deals with the finite element study of equilibrium electric double layer capacitance (EDLC) in the mixed morphology electrodes comprising all three fundamental crystal structures, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic morphologies (FCC). Mesoporous-activated carbon forms the electrode in the supercapacitor with (C2H5)4NBF4/propylene carbonate organic electrolyte. Electrochemical interference is clearly demonstrated in the supercapacitors with the formation of the potential bands, as in the case of interference theory due to the increasing packing factor. The effects of electrode thickness varying from a wide range of 50 nm to 0.04 mm on specific EDLC have been discussed in detail. The interfacial geometry of the unit cell in contact with the electrolyte is the most important parameter determining the properties of the EDL. The critical thickness of the electrodes is 1.71 μm in all the morphologies. Polarization increases the interfacial potential and leads to EDL formation. The Stern layer specific capacitance is 167.6 μF cm-2 in all the morphologies. The maximum capacitance is in the decreasing order of interfacial geometry, as FCC > BCC > SC, dependent on the packing factor. The minimum transmittance in all the morphologies is 98.35%, with the constant figure of merit at higher electrode thickness having applications in the chip interconnects. The transient analysis shows that the interfacial current decreases with increasing polarization in the EDL. The capacitance also decreases with the increase of the scan rate.
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Affiliation(s)
- Ravi Nigam
- Advanced Nanoengineering Materials Laboratory, Materials Science Programme, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Kamal K Kar
- Advanced Nanoengineering Materials Laboratory, Materials Science Programme, Indian Institute of Technology Kanpur, Kanpur 208016, India
- Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
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Lindgren EB, Avis H, Miller A, Stamm B, Besley E, Stace AJ. The significance of multipole interactions for the stability of regular structures composed from charged particles. J Colloid Interface Sci 2024; 663:458-466. [PMID: 38417297 DOI: 10.1016/j.jcis.2024.02.146] [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: 10/27/2023] [Revised: 01/25/2024] [Accepted: 02/19/2024] [Indexed: 03/01/2024]
Abstract
Identifying the forces responsible for stabilising binary particle lattices is key to the controlled fabrication of many new materials. Experiments have shown that the presence of charge can be integral to the formation of ordered arrays; however, a complete analysis of the forces responsible has not included many of the significant lattice types that may form during fabrication. A theory of many-body electrostatic interactions has been applied to six lattice stoichiometries, AB, AB2, AB3, AB4, AB5 and AB6, to show that induced multipole interactions can make a very significant (>80 %) contribution to the total lattice energy of arrays of charged particles. Particle radii ratios which favour global minima in electrostatic energy are found to be the same or a close match to those observed by experiment. Although certain lattice types exhibit local energy minima, the calculations show that many-body rather than two-body interactions are ultimately responsible for the structures observed by experiment. For a lattice isostructural with CFe4, a particle size ratio not previously observed is found to be particularly stable due to many-body effects.
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Affiliation(s)
- Eric B Lindgren
- Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Holly Avis
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Abigail Miller
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Benjamin Stamm
- Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Elena Besley
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Anthony J Stace
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
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Siryk S, Rocchia W. Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment. J Phys Chem B 2022; 126:10400-10426. [PMID: 36473089 PMCID: PMC9761689 DOI: 10.1021/acs.jpcb.2c05564] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.
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Nigam R, Kar KK. Simulation Study of Electric Double-Layer Capacitance of Ordered Carbon Electrodes. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:12235-12247. [PMID: 36164778 DOI: 10.1021/acs.langmuir.2c01865] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Supercapacitors are electrochemical energy storage devices having high capacitance, high power density, long cycle life, low cost, easy maintenance, and negligible environmental pollution. The formation of an electric double layer at the electrode-electrolyte interface is mostly responsible for supercapacitors' energy storage. The simulation study of equilibrium electric double-layer capacitance (EDLC) in 3D arranged mesoporous carbon electrodes with a simple cubic morphology and interdigitated electrodes has been done. Continuum theory has been utilized to study the underlying processes involved in EDLC. Interfacial polarization and ion crowding depend on the electrode's critical thickness. Porosity increases the capacitance due to the increase in the electrode surface area. The diffuse-layer specific capacitance of ordered mesoporous carbon electrodes in a (C2H5)4NBF4/propylene carbonate organic electrolyte is in the range of 3.2-13.3 μF cm-2, varying according to the electrode thickness. The Stern-layer specific capacitance is 167.6 μF cm-2, and total equilibrium EDLC is in the range of 3.1-12.3 μF cm-2. The effect of the electric field at the electrode-electrolyte interface on reducing electrolyte permittivity has also been discussed. The EDLC of carbonized interdigitated electrodes is analyzed in a 6 M KOH electrolyte. The diffuse-layer specific capacitance ranges from 118.7 to 352.0 μF cm-2 depending on the width of the interdigitated electrodes. The Stern-layer specific capacitance is 91.2 μF cm-2, and the total EDLC value is 51.6-72.4 μF cm-2. The modeling and simulation approach can be applied to different mesoporous electrodes by varying the supercapacitor component's parameters and geometry.
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Affiliation(s)
- Ravi Nigam
- Advanced Nanoengineering Materials Laboratory, Materials Science Programme, Indian Institute of Technology, Kanpur 208016, India
| | - Kamal K Kar
- Advanced Nanoengineering Materials Laboratory, Materials Science Programme, Indian Institute of Technology, Kanpur 208016, India
- Advanced Nanoengineering Materials Laboratory, Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India
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Siryk SV, Bendandi A, Diaspro A, Rocchia W. Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson-Boltzmann equation model. J Chem Phys 2021; 155:114114. [PMID: 34551534 DOI: 10.1063/5.0056120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.
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Affiliation(s)
- Sergii V Siryk
- CONCEPT Lab, Istituto Italiano di Tecnologia, Via E. Melen 83, 16152 Genova, Italy
| | - Artemi Bendandi
- CHT Erzelli, Nanoscopy, Istituto Italiano di Tecnologia, Via E. Melen 83, 16152 Genova, Italy
| | - Alberto Diaspro
- CHT Erzelli, Nanoscopy, Istituto Italiano di Tecnologia, Via E. Melen 83, 16152 Genova, Italy
| | - Walter Rocchia
- CONCEPT Lab, Istituto Italiano di Tecnologia, Via E. Melen 83, 16152 Genova, Italy
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Shen KH, Fan M, Hall LM. Molecular Dynamics Simulations of Ion-Containing Polymers Using Generic Coarse-Grained Models. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02557] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Kuan-Hsuan Shen
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States
| | - Mengdi Fan
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States
| | - Lisa M. Hall
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States
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Bagchi D, Nguyen TD, Olvera de la Cruz M. Surface polarization effects in confined polyelectrolyte solutions. Proc Natl Acad Sci U S A 2020; 117:19677-19684. [PMID: 32747575 PMCID: PMC7443958 DOI: 10.1073/pnas.2007545117] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Understanding nanoscale interactions at the interface between two media with different dielectric constants is crucial for controlling many environmental and biological processes, and for improving the efficiency of energy storage devices. In this contributed paper, we show that polarization effects due to such dielectric mismatch remarkably influence the double-layer structure of a polyelectrolyte solution confined between two charged surfaces. Surprisingly, the electrostatic potential across the adsorbed polyelectrolyte double layer at the confining surface is found to decrease with increasing surface charge density, indicative of a negative differential capacitance. Furthermore, in the presence of polarization effects, the electrostatic energy stored in the double-layer structure is enhanced with an increase in the charge amplification, which is the absorption of ions on a like-charged surface. We also find that all of the important double-layer properties, such as charge amplification, energy storage, and differential capacitance, strongly depend on the polyelectrolyte backbone flexibility and the solvent quality. These interesting behaviors are attributed to the interplay between the conformational entropy of the confined polyelectrolytes, the Coulombic interaction between the charged species, and the repulsion from the surfaces with lower dielectric constant.
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Affiliation(s)
- Debarshee Bagchi
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208
| | - Trung Dac Nguyen
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208
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Filippov AV, Chen X, Harris C, Stace AJ, Besley E. Interaction between particles with inhomogeneous surface charge distributions: Revisiting the Coulomb fission of dication molecular clusters. J Chem Phys 2019; 151:154113. [PMID: 31640356 DOI: 10.1063/1.5119347] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An analytical solution describing the electrostatic interaction between particles with inhomogeneous surface charge distributions has been developed. For particles, each carrying a single charge, the solution equates to the presence of a point charge residing on the surface, which makes it particularly suitable for investigating the Coulomb fission of doubly charged clusters close to the Rayleigh instability limit. For a series of six separate molecular dication clusters, center-of-mass kinetic energy releases have been extracted from experimental measurements of their kinetic energy spectra following Coulomb fission. These data have been compared with Coulomb energy barriers calculated from the electrostatic interaction energies given by this new solution. For systems with high dielectric permittivity, results from the point charge model provide a viable alternative to kinetic energy releases calculated on the assumption of a uniform distribution of surface charge. The equivalent physical picture for the clusters would be that of a trapped proton. For interacting particles with low dielectric permittivity, a uniform distribution of charge provides better agreement with the experimental results.
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Affiliation(s)
- A V Filippov
- Troitsk Institute for Innovation and Fusion Research, Troitsk, Moscow 108840, Russia
| | - X Chen
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - C Harris
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - A J Stace
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - E Besley
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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