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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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2
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Patra CN. Spherical electric double layers containing mixed electrolytes: A case study for multivalent counterions. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.08.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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3
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Adroher-Benítez I, Martín-Molina A, Ahualli S, Quesada-Pérez M, Odriozola G, Moncho-Jordá A. Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge. Phys Chem Chem Phys 2017; 19:6838-6848. [DOI: 10.1039/c6cp08683g] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The equilibrium distribution of monovalent and trivalent ions within a thermo-responsive charged nanogel is investigated using Monte Carlo simulations and Ornstein–Zernike equations.
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Affiliation(s)
- Irene Adroher-Benítez
- Departamento de Física Aplicada
- Facultad de Ciencias
- Universidad de Granada
- 18001 Granada
- Spain
| | - Alberto Martín-Molina
- Departamento de Física Aplicada
- Facultad de Ciencias
- Universidad de Granada
- 18001 Granada
- Spain
| | - Silvia Ahualli
- Departamento de Física Aplicada
- Facultad de Ciencias
- Universidad de Granada
- 18001 Granada
- Spain
| | - Manuel Quesada-Pérez
- Departamento de Física
- Escuela Politécnica Superior de Linares
- Universidad de Jaeén
- 23700 Linares
- Spain
| | - Gerardo Odriozola
- Área de Física de Procesos Irreversibles
- División de Ciencias Básicas e Ingeniería
- Universidad Autónoma Metropolitana
- 02200 México CD de México
- Mexico
| | - Arturo Moncho-Jordá
- Departamento de Física Aplicada
- Facultad de Ciencias
- Universidad de Granada
- 18001 Granada
- Spain
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Kiyohara K, Yamagata M, Ishikawa M. Electrochemical and structural properties of the electrical double layer of two-component electrolytes in response to varied electrode potential. J Chem Phys 2016; 144:134701. [DOI: 10.1063/1.4944927] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Kenji Kiyohara
- Inorganic Functional Material Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
| | - Masaki Yamagata
- Faculty of Chemistry, Materials and Bioengineering, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan
| | - Masashi Ishikawa
- Faculty of Chemistry, Materials and Bioengineering, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan
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5
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Vereda F, Martín-Molina A, Hidalgo-Alvarez R, Quesada-Pérez M. Specific ion effects on the electrokinetic properties of iron oxide nanoparticles: experiments and simulations. Phys Chem Chem Phys 2016; 17:17069-78. [PMID: 26067087 DOI: 10.1039/c5cp01011j] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We report experimental and simulation studies on ion specificity in aqueous colloidal suspensions of positively charged, bare magnetite nanoparticles. Magnetite has the largest saturation magnetization among iron oxides and relatively low toxicity, which explain why it has been used in multiple biomedical applications. Bare magnetite is hydrophilic and the sign of the surface charge can be changed by adjusting the pH, its isoelectric point being in the vicinity of pH = 7. Electrophoretic mobility of our nanoparticles in the presence of increasing concentrations of different anions showed that anions regarded as kosmotropic are more efficient in decreasing, and even reversing, the mobility of the particles. If the anions were ordered according to the extent to which they reduced the particle mobility, a classical Hofmeister series was obtained with the exception of thiocyanate, whose position was altered. Monte Carlo simulations were used to predict the diffuse potential of magnetite in the presence of the same anions. The simulations took into account the ion volume, and the electrostatic and dispersion forces among the ions and between the ions and the solid surface. Even though no fitting parameters were introduced and all input data were estimated using Lifshitz theory of van der Waals forces or obtained from the literature, the predicted diffusion potentials of different anions followed the same order as the mobility curves. The results suggest that ionic polarizabilities and ion sizes are to a great extent responsible for the specific ion effects on the electrokinetic potential of iron oxide particles.
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Affiliation(s)
- Fernando Vereda
- Grupo de Física de Fluidos y Biocoloides, Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain.
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Ruiz-Cabello FJM, Moazzami-Gudarzi M, Elzbieciak-Wodka M, Maroni P. Forces between different latex particles in aqueous electrolyte solutions measured with the colloidal probe technique. Microsc Res Tech 2016; 80:144-152. [PMID: 26999314 DOI: 10.1002/jemt.22656] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Revised: 01/04/2016] [Accepted: 01/18/2016] [Indexed: 11/12/2022]
Abstract
In this article, a compilation of results on direct force measurements between colloidal particles in monovalent salts carried out with the colloidal probe technique based on Atomic Force Microscopy was presented. The interaction forces between similar and dissimilar particles was studied and it was concluded that, in general, these force profiles may be satisfactorily quantified by the DLVO theory down to distances of few nanometers. However, in the specific case where the charge of one of the involved particle is close to neutral, it was found that the surface potential of this particle may change its sign depending on the sign of charge of the opposite particle. In this respect, the assumption that the surface potential of a particle is a property only related to the particle surface features and the bulk properties is called into question. Microsc. Res. Tech. 80:144-152, 2017. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- F Javier Montes Ruiz-Cabello
- Biocolloid and Fluid Physics Group, Applied Physics Department, Faculty of Sciences, University of Granada, Campus de Fuentenueva s/n, Granada, 18071, Spain
| | - Mohsen Moazzami-Gudarzi
- Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, Quai Ernest-Ansermet 30, Geneva, 1205, Switzerland
| | - Magdalena Elzbieciak-Wodka
- Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Science, Krakow, 30-239, Poland
| | - Plinio Maroni
- Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, Quai Ernest-Ansermet 30, Geneva, 1205, Switzerland
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7
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Adroher-Benítez I, Ahualli S, Martín-Molina A, Quesada-Pérez M, Moncho-Jordá A. Role of Steric Interactions on the Ionic Permeation Inside Charged Microgels: Theory and Simulations. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00356] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Irene Adroher-Benítez
- Departamento
de Física Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
| | - Silvia Ahualli
- Departamento
de Física, Escuela Politécnica Superior de Linares, Universidad de Jaén, 23700 Linares, Jaén, Spain
| | - Alberto Martín-Molina
- Departamento
de Física Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
| | - Manuel Quesada-Pérez
- Departamento
de Física, Escuela Politécnica Superior de Linares, Universidad de Jaén, 23700 Linares, Jaén, Spain
| | - Arturo Moncho-Jordá
- Departamento
de Física Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
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8
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Yang G, Liu L. A systematic comparison of different approaches of density functional theory for the study of electrical double layers. J Chem Phys 2015; 142:194110. [DOI: 10.1063/1.4921376] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Guomin Yang
- Department of Chemical Engineering and Technology, Royal Institute of Technology, S-100 44 Stockholm, Sweden
| | - Longcheng Liu
- Department of Chemical Engineering and Technology, Royal Institute of Technology, S-100 44 Stockholm, Sweden
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9
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Thakore V, Hickman JJ. Charge Relaxation Dynamics of an Electrolytic Nanocapacitor. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2015; 119:2121-2132. [PMID: 25678941 PMCID: PMC4315418 DOI: 10.1021/jp508677g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2014] [Revised: 10/29/2014] [Indexed: 06/04/2023]
Abstract
Understanding ion relaxation dynamics in overlapping electric double layers (EDLs) is critical for the development of efficient nanotechnology-based electrochemical energy storage, electrochemomechanical energy conversion, and bioelectrochemical sensing devices as well as the controlled synthesis of nanostructured materials. Here, a lattice Boltzmann (LB) method is employed to simulate an electrolytic nanocapacitor subjected to a step potential at t = 0 for various degrees of EDL overlap, solvent viscosities, ratios of cation-to-anion diffusivity, and electrode separations. The use of a novel continuously varying and Galilean-invariant molecular-speed-dependent relaxation time (MSDRT) with the LB equation recovers a correct microscopic description of the molecular-collision phenomena and enhances the stability of the LB algorithm. Results for large EDL overlaps indicated oscillatory behavior for the ionic current density, in contrast to monotonic relaxation to equilibrium for low EDL overlaps. Further, at low solvent viscosities and large EDL overlaps, anomalous plasmalike spatial oscillations of the electric field were observed that appeared to be purely an effect of nanoscale confinement. Employing MSDRT in our simulations enabled modeling of the fundamental physics of the transient charge relaxation dynamics in electrochemical systems operating away from equilibrium wherein Nernst-Einstein relation is known to be violated.
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Affiliation(s)
- Vaibhav Thakore
- Department of Physics, NanoScience Technology
Center, and Department of Chemistry, University of
Central Florida, 12424
Research Parkway, Suite 400, Orlando, Florida 32826, United States
| | - James J. Hickman
- Department of Physics, NanoScience Technology
Center, and Department of Chemistry, University of
Central Florida, 12424
Research Parkway, Suite 400, Orlando, Florida 32826, United States
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11
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Shevkunov SV. Water vapor clustering in the field of a chlorine anion occurring in a planar nanopore with structureless walls. COLLOID JOURNAL 2014. [DOI: 10.1134/s1061933x14040139] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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12
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Luque-Caballero G, Martín-Molina A, Quesada-Pérez M. Polyelectrolyte adsorption onto like-charged surfaces mediated by trivalent counterions: A Monte Carlo simulation study. J Chem Phys 2014; 140:174701. [DOI: 10.1063/1.4872263] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
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13
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Liu B, Liu P, Xu Z, Zhou S. Ionic Size Effects: Generalized Boltzmann Distributions, Counterion Stratification, and Modified Debye Length. NONLINEARITY 2013; 26:2899-2922. [PMID: 24465094 PMCID: PMC3899944 DOI: 10.1088/0951-7715/26/10/2899] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Near a charged surface, counterions of different valences and sizes cluster; and their concentration profiles stratify. At a distance from such a surface larger than the Debye length, the electric field is screened by counterions. Recent studies by a variational mean-field approach that includes ionic size effects and by Monte Carlo simulations both suggest that the counterion stratification is determined by the ionic valence-to-volume ratios. Central in the mean-field approach is a free-energy functional of ionic concentrations in which the ionic size effects are included through the entropic effect of solvent molecules. The corresponding equilibrium conditions define the generalized Boltzmann distributions relating the ionic concentrations to the electrostatic potential. This paper presents a detailed analysis and numerical calculations of such a free-energy functional to understand the dependence of the ionic charge density on the electrostatic potential through the generalized Boltzmann distributions, the role of ionic valence-to-volume ratios in the counterion stratification, and the modification of Debye length due to the effect of ionic sizes.
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Affiliation(s)
- Bo Liu
- Department of Mathematics and NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
| | - Pei Liu
- Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai, 200240, P. R. China
| | - Zhenli Xu
- Department of Mathematics, Institute of Natural Sciences, and Ministry of Education Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai, 200240, P. R. China
| | - Shenggao Zhou
- Department of Mathematics and NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
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Sánchez-Arellano E, Jiménez-Ángeles F. Electrokinetic properties of a restricted primitive model electrolyte in slit-like nanopores: Effects of enhanced ionic excluded volume. J Mol Liq 2013. [DOI: 10.1016/j.molliq.2012.10.029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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15
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Moncho-Jordá A. Effective charge of ionic microgel particles in the swollen and collapsed states: The role of the steric microgel-ion repulsion. J Chem Phys 2013; 139:064906. [DOI: 10.1063/1.4817852] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Sing CE, Zwanikken JW, Olvera de la Cruz M. Effect of Ion–Ion Correlations on Polyelectrolyte Gel Collapse and Reentrant Swelling. Macromolecules 2013. [DOI: 10.1021/ma400372p] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Charles E. Sing
- Department of Materials
Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Jos W. Zwanikken
- Department of Materials
Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Monica Olvera de la Cruz
- Department of Materials
Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
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17
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Wang Z, Liu L. The Swelling Pressure of Na–Bentonite: Study with a Density Functional Approach. CHEM LETT 2012. [DOI: 10.1246/cl.2012.1346] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Zhao Wang
- Department of Chemical Engineering and Technology, Royal Institute of Technology
| | - Longcheng Liu
- Department of Chemical Engineering and Technology, Royal Institute of Technology
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18
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Vibhu I, Modak B, Patra CN, Ghosh SK. Zeta potential of colloidal particle in solvent primitive model electrolyte solution: a density functional theory study. Mol Phys 2012. [DOI: 10.1080/00268976.2012.728637] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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19
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Wang ZY, Ma YQ. A molecular simulation study on the role of ion sizes and dielectric images in near-surface ion distribution far from the strong coupling limit. J Chem Phys 2012; 136:234701. [DOI: 10.1063/1.4729311] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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Wen J, Zhou S, Xu Z, Li B. Competitive adsorption and ordered packing of counterions near highly charged surfaces: From mean-field theory to Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041406. [PMID: 22680474 PMCID: PMC3725615 DOI: 10.1103/physreve.85.041406] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2012] [Indexed: 06/01/2023]
Abstract
Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.
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Affiliation(s)
- Jiayi Wen
- Department of Mathematics, and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
| | - Shenggao Zhou
- Department of Mathematics, Zhejiang University, No. 38 Zheda Road, Hangzhou, 310027, P. R. China, and Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
| | - Zhenli Xu
- Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai, 200240, P. R. China
| | - Bo Li
- Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
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Madurga S, Rey-Castro C, Pastor I, Vilaseca E, David C, Garcés JL, Puy J, Mas F. A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: Proton binding of carboxylated latex particles as a case study. J Chem Phys 2011; 135:184103. [DOI: 10.1063/1.3658484] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zhou S, Wang Z, Li B. Mean-field description of ionic size effects with nonuniform ionic sizes: a numerical approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021901. [PMID: 21929014 PMCID: PMC3727298 DOI: 10.1103/physreve.84.021901] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2011] [Indexed: 05/14/2023]
Abstract
Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, that is, there is no explicit Boltzmann-type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such nonuniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with nonuniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson-Boltzmann theory, or the generalized Poisson-Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed.
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Affiliation(s)
- Shenggao Zhou
- Department of Mathematics, Zhejiang University, No. 38 Zheda Road, Hangzhou, 310027, P. R. China, and Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA.
| | - Zhongming Wang
- Department of Mathematics, Department of Chemistry and Biochemistry, and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA.
| | - Bo Li
- Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA.
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Wang Z, Liu L, Neretnieks I. The weighted correlation approach for density functional theory: a study on the structure of the electric double layer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:175002. [PMID: 21483081 DOI: 10.1088/0953-8984/23/17/175002] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Within the framework of density functional theory, a weighted correlation approach is developed in order to obtain the density distributions of an inhomogeneous fluid. It results in a formally exact expression, by means of the concept of a weighted pair correlation function, used to evaluate the change of the single-particle direct correlation function of the system relative to that of a reference state. When applying the approach for practical use, however, an approximation of the pair correlation function has to be made, along with an appropriate definition of a weight function. Noticeably, combining this approach with fundamental measure theory gives rise to a new method, which we call the FMT/WCA-k(2) approach, for studying the structural and thermodynamic properties of a charged hard-sphere fluid subjected to a spatially varying external potential. Application of the FMT/WCA-k(2) approach in a range of electrolyte concentrations and surface charge densities, against the Monte Carlo simulations, shows that it is superior to the typical approaches of density functional theory in predicting the ionic density profiles of both counter-ions and co-ions near a highly charged surface. It is capable of capturing the fine features of the structural properties of the electric double layers, to well reproduce the layering effect and the charge inversion phenomenon, also in strongly coupled cases where divalent counter-ions are involved. In addition, it is found that the FMT/WCA-k(2) approach even has an advantage over the anisotropic, hyper-netted chain approaches in giving better agreement with the Monte Carlo results.
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Affiliation(s)
- Zhao Wang
- Department of Chemical Engineering and Technology, Royal Institute of Technology, S-100 44 Stockholm, Sweden
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Zelko J, Iglic A, Kralj-Iglic V, Kumar PBS. Effects of counterion size on the attraction between similarly charged surfaces. J Chem Phys 2011; 133:204901. [PMID: 21133451 DOI: 10.1063/1.3506896] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Interaction between similarly charged surfaces can be attractive at high electrostatic coupling constants Ξ = l(B)Z(2)/μ(GC), where l(B) is the Bjerrum length, μ(GC) the Gouy-Chapman length, and Z the valency of counterions. While this effect has been studied previously in detail, as a function of surface charge density and valency of the pointlike counterions, much less is known about the effect of counterion size. We apply the Wang-Landau sampling Monte Carlo (MC) simulation method to compute the free energy F as a function of the scaled distance between the plates D̃=D/μ(GC) for a range of Ξ and scaled counterion radii R̃=R/μ(GC). We find that for large Ξ and small ion radius, there is a global equilibrium distance D̃=D̃(eq)=2(1+R̃), correctly giving the expected value at the point counterion limit. With increasing R̃ the global minimum in F(D̃) changes to a metastable state and finally this minimum vanishes when R̃ reaches a critical value, which depends on Ξ. We present a state diagram indicating approximate boundaries between these three regimes. The Wang-Landau MC method, as it is applied here, offers a possibility to study a wide spectrum of extended problems, which cannot be treated by the use of contact value theorem.
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Affiliation(s)
- Jasna Zelko
- Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia
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25
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Ibarra-Armenta JG, Martín-Molina A, Quesada-Pérez M. Influence of monovalent ion size on colloidal forces probed by Monte Carlo simulations. Phys Chem Chem Phys 2011; 13:13349-57. [DOI: 10.1039/c1cp21162e] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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26
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Martín-Molina A, Hidalgo-Álvarez R, Quesada-Pérez M. Additional considerations about the role of ion size in charge reversal. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:424105. [PMID: 21715840 DOI: 10.1088/0953-8984/21/42/424105] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The effect of the ion size on the charge reversal process is studied via canonical Monte Carlo simulation. To this end, a primitive model of electrolyte is used to analyze the electric double layer formed by an asymmetric electrolyte in the presence of a charged planar wall. Different values of ion diameters and surface charge densities are used so as to determine the conditions at which the charge reversal first occurs. For each case, the apparent surface charge density is calculated as a function of the distance from the charged wall for the different electrolyte concentrations in order to establish the minimal salt concentration required for the charge reversal. We will refer to this electrolyte concentration as the reversal concentration and will show how it depends on the surface charge density and on the ion size. From the apparent surface charge density profiles, the distance from the wall at which the charge reversal arises as well as its intensity can be also inferred.
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Affiliation(s)
- A Martín-Molina
- Grupo de Física de Fluidos y Biocoloides, Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, Granada 18071, Spain
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Martín-Molina A, Rodríguez-Beas C, Hidalgo-Alvarez R, Quesada-Pérez M. Effect of surface charge on colloidal charge reversal. J Phys Chem B 2009; 113:6834-9. [PMID: 19385634 DOI: 10.1021/jp900959y] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The objective of this research work is to understand the effect of the surface charge density on the charge reversal phenomenon. To this end, we use experimental results and computer simulations. In particular, we measure the electrophoretic mobility of latex particles (macroions) in the presence of a multivalent electrolyte. We have focused on the electrolyte concentration range at which a reversal in the electrophoretic mobility is expected to happen. In particular, the role of the surface charge on the charge reversal process is looked into from several latexes with the same functional group but different surface charge densities. Although the mechanism responsible for the colloidal charge reversal is still a controversial issue, it is proved that ionic correlations are behind the appearance of such phenomenon (especially near the macroion surface). This conclusion can be inferred from a great variety of theoretical models. According to them, one of the factors that determine the charge reversal is the surface charge density of the macroions. However, this feature has been rarely analyzed in experiments. Our results appear therefore as a demanded survey to test the validity of the theoretical predictions. Moreover, we have also performed Monte Carlo simulations that take the ion size into account. The correlation found between experiments and simulations is fairly good. The combination of these techniques provides new insight into the colloidal charge reversal phenomena showing the effect of surface charge.
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Affiliation(s)
- A Martín-Molina
- Grupo de Física de Fluidos y Biocoloides, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva, sn, 18071, Granada, Spain.
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29
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Martín-Molina A, Ibarra-Armenta JG, Quesada-Pérez M. Effect of ion dispersion forces on the electric double layer of colloids: a Monte Carlo simulation study. J Phys Chem B 2009; 113:2414-21. [PMID: 19199701 DOI: 10.1021/jp8019792] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work, the effect of ionic dispersion forces on the electric double layer of colloids is evaluated through Monte Carlo simulations. Particularly, the influence of these forces on the zeta-potential (as a representative electrokinetic property) is assessed. Ion polarizability is included in the primitive model with the help of the Lifshitz theory. In this way, ion specificity is not considered by means of phenomenological (and unknown a priori) parameters. Our results reveal that the ionic van der Waals forces are responsible (to some extent) for the specificity of the zeta-potential. In any case, the specific ion effects due to ion polarizability are strongly influenced by ion size. Furthermore, a preliminary study on the effect of ionic dehydration shows how this phenomenon improves the qualitative agreement between experimental data and simulations achieved in considering ionic dispersion forces.
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Affiliation(s)
- Alberto Martín-Molina
- Grupo de Física de Fluidos y Biocoloides, Departamento de Física Aplicada, Universidad de Granada, 18071 Granada, Spain
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30
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Madurga S, Garcés JL, Companys E, Rey-Castro C, Salvador J, Galceran J, Vilaseca E, Puy J, Mas F. Ion binding to polyelectrolytes: Monte Carlo simulations versus classical mean field theories. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0550-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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31
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Ibarra-Armenta JG, Martín-Molina A, Quesada-Pérez M. Testing a modified model of the Poisson–Boltzmann theory that includes ion size effects through Monte Carlo simulations. Phys Chem Chem Phys 2009; 11:309-16. [DOI: 10.1039/b811928g] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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32
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Tresset G. Generalized Poisson-Fermi formalism for investigating size correlation effects with multiple ions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061506. [PMID: 19256845 DOI: 10.1103/physreve.78.061506] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2008] [Revised: 11/21/2008] [Indexed: 05/27/2023]
Abstract
We establish a generalized Poisson-Fermi formalism to compute the electrostatic potential next to charged surfaces in the presence of multiple ion species with different sizes. A generalized Fermi-like ion distribution is deduced from the excess free energy, after expansion of the functional entropy of free space in which the ions have all the same size. The ion distribution is expressed in terms of the bulk volume fractions of each ion species rather than their bulk concentrations so as to account for the excluded volumes. We present size correlations effects such as underscreening and ion stratification, which have not been investigated before with such a simple theory. The change of dielectric properties across the space, arising from the finite spatial occupancy of ions, can be solved self-consistently through the Bruggeman model. The generalized Poisson-Fermi formalism is anticipated to be useful for interpreting electrophoretic mobility measurements and for computing the electrostatic potential over the surface of biomolecules in ionic solutions.
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Affiliation(s)
- Guillaume Tresset
- Institute of Bioengineering and Nanotechnology, 31 Biopolis Way, The Nanos 04-01, Singapore 138669.
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33
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Sang S, Huang H, Wu Q. An investigation on ion transfer resistance of cation exchange membrane/solution interface. Colloids Surf A Physicochem Eng Asp 2008. [DOI: 10.1016/j.colsurfa.2007.07.014] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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35
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Hou CH, Taboada-Serrano P, Yiacoumi S, Tsouris C. Monte Carlo simulation of electrical double-layer formation from mixtures of electrolytes inside nanopores. J Chem Phys 2008; 128:044705. [DOI: 10.1063/1.2824957] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Labbez C, Jönsson B, Pochard I, Nonat A, Cabane B. Surface charge density and electrokinetic potential of highly charged minerals: experiments and Monte Carlo simulations on calcium silicate hydrate. J Phys Chem B 2007; 110:9219-30. [PMID: 16671737 DOI: 10.1021/jp057096+] [Citation(s) in RCA: 117] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this paper, we are concerned with the charging and electrokinetic behavior of colloidal particles exhibiting a high surface charge in the alkaline pH range. For such particles, a theoretical approach has been developed in the framework of the primitive model. The charging and electrokinetic behavior of the particles are determined by the use of a Monte Carlo simulation in a grand canonical ensemble and compared with those obtained through the mean field theory. One of the most common colloidal particles has been chosen to test our theoretical approach. That is calcium silicate hydrate (C-S-H) which is the main component of hydrated cement and is known for being responsible for cement cohesion partly due to its unusually high surface charge density. Various experimental techniques have been used to determine its surface charge and electrokinetic potential. The experimental and simulated results are in excellent agreement over a wide range of electrostatic coupling, from a weakly charged surface in contact with a reservoir containing monovalent ions to a highly charged one in contact with a reservoir with divalent ions. The electrophoretic measurements show a charge reversal of the C-S-H particles at high pH and/or high calcium concentration in excellent agreement with simulation predictions. Finally, both simulation and experimental results clearly demonstrate that the mean field theory fails not only quantitatively but also qualitatively to describe a C-S-H dispersion under realistic conditions.
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Affiliation(s)
- Christophe Labbez
- LRRS, UMR CNRS 5613, Université de Bourgogne, F-21078 Dijon Cedex, France.
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37
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Madurga S, Martín-Molina A, Vilaseca E, Mas F, Quesada-Pérez M. Effect of the surface charge discretization on electric double layers: A Monte Carlo simulation study. J Chem Phys 2007; 126:234703. [PMID: 17600431 DOI: 10.1063/1.2741520] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.
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Affiliation(s)
- Sergio Madurga
- Theoretical Chemistry Research Centre (CeRQT) of Scientific Park of Barcelona (PCB), C/Josep Samitier 1-5, E-08028 Barcelona, Catalonia, Spain
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38
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Kiyohara K, Asaka K. Monte Carlo simulation of electrolytes in the constant voltage ensemble. J Chem Phys 2007; 126:214704. [PMID: 17567210 DOI: 10.1063/1.2736371] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The authors studied the structural, electrostatic, and electromechanical properties of the terlamellar structure composed of the anode, the cathode, and the electrolyte layer separating them. They used the Monte Carlo simulation technique in the constant voltage ensemble, where the electrical potential difference between the anode and the cathode is introduced as an external field. For ions, they used the primitive models of different sizes and valences in order to investigate how they affect the physical properties when an electrical field is applied between the electrodes. For electrodes, they used impermeable and permeable models, which mimic planar and porous electrodes, respectively. The asymmetry between the anions and the cations in size or valence was found to be responsible for the asymmetry in the concentration profile, the potential drop, and the stress distribution, in comparing the anode and the cathode sides. The charging/discharging process in the planar and porous electrodes is discussed at molecular level.
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Affiliation(s)
- Kenji Kiyohara
- Research Institute for Cell Engineering, National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
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39
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Martín-Molina A, Maroto-Centeno JA, Hidalgo-Alvarez R, Quesada-Pérez M. Testing one component plasma models on colloidal overcharging phenomena. J Chem Phys 2007; 125:144906. [PMID: 17042649 DOI: 10.1063/1.2357945] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, the mechanisms of overcharging of a colloidal macroion in the presence of multivalent counterions are investigated by means of Monte Carlo simulations. This computational technique appears as a powerful tool for probing the validity of semianalytical models developed for this issue. In particular, the simulations performed are compared with the predictions of two different models based on the one component plasma (OCP) theory. Therein, the multivalent ionic atmosphere confined at the macroion surface is approximated by a two-dimensional Wigner crystal. These kinds of models are largely used in the literature since (in some cases) they present quite simple equations to describe the electric double layer (EDL) of macroions with different geometries in the presence of much smaller (but still multivalent) ions. In this sense, charge inversion phenomena of membranes, polyelectrolytes, DNA molecules, etc., are straightforwardly predicted in terms of these expressions. Unfortunately, comparisons between these predictions and experimental results are scarce, mostly due to the difficulty to reproduce the experimental conditions in the laboratory. Accordingly, the goal of the present paper is to simulate EDLs under real conditions (in which overcharging phenomena are expected to happen) and use the results obtained in this way for comparing with those obtained from OCP models.
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Affiliation(s)
- Alberto Martín-Molina
- Grupo de Física de Fluidos y Biocoloides, Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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40
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Shi-Qi Z. Density functional approximation for van der Waals fluids: based on hard sphere density functional approximation. ACTA ACUST UNITED AC 2007. [DOI: 10.1088/1009-1963/16/4/052] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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41
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Bhuiyan LB, Outhwaite CW, Henderson D. Planar electric double layer for a restricted primitive model electrolyte at low temperatures. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2006; 22:10630-4. [PMID: 17129040 DOI: 10.1021/la060425k] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Monte Carlo simulation and the modified Poisson-Boltzmann theory are used to investigate the planar electric double layer for a restricted primitive model electrolyte at low temperatures. Capacitance as a function of temperature at low surface charge is determined for 1:1, 2:2, 2:1, and 3:1 electrolytes. Negative adsorption can occur for 1:1 electrolytes at low surface charge with low electrolyte concentration. The 1:1 electrolyte diffuse layer potential as a function of surface charge displays a maximum at low densities. At high densities, the diffuse layer potential is negative with a negative slope. The Gouy-Chapman-Stern theory fails in this low-temperature regime, whereas the modified Poisson-Boltzmann theory is fairly successful in this regard.
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Affiliation(s)
- L B Bhuiyan
- Laboratory of Theoretical Physics, Department of Physics, University of Puerto Rico, San Juan 00931-3343, Puerto Rico. beena.beena.cnnet.clu.edu
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42
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Moreira L, Boström M, Ninham B, Biscaia E, Tavares F. Hofmeister effects: Why protein charge, pH titration and protein precipitation depend on the choice of background salt solution. Colloids Surf A Physicochem Eng Asp 2006. [DOI: 10.1016/j.colsurfa.2005.11.021] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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44
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Luo F, Jamnik A, Su Y. Structure of Lennard–Jones fluid near large spherical particles: further test of the “universality” of adjustable parameter in perturbation density functional theory. MOLECULAR SIMULATION 2006. [DOI: 10.1080/08927020600675715] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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45
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Zhou S, Jamnik A. Further Test of Third Order + Second-Order Perturbation DFT Approach: Hard Core Repulsive Yukawa Fluid Subjected to Diverse External Fields. J Phys Chem B 2006; 110:6924-32. [PMID: 16571004 DOI: 10.1021/jp056795j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.
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Affiliation(s)
- Shiqi Zhou
- Institute of Modern Statistical Mechanics, Zhuzhou Institute of Technology, Wenhua Road, Zhuzhou city, 412008, PR China.
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46
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Fits to hypernetted chain calculations for electrostatic potential and ion concentrations for use in surface complexation. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/s1573-4285(06)80048-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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47
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Martín-Molina A, Quesada-Pérez M, Hidalgo-Alvarez R. Electric Double Layers with Electrolyte Mixtures: Integral Equations Theories and Simulations. J Phys Chem B 2005; 110:1326-31. [PMID: 16471681 DOI: 10.1021/jp053970n] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.
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Affiliation(s)
- A Martín-Molina
- Laboratoire de Physique Statistique de l'Ecole Normale Supérieure associée au CNRS, Universités Paris VI et Paris VII, 24 rue Lhomond, 75231 Paris Cedex 05, France
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48
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49
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Quesada-Pérez M, Martín-Molina A, Hidalgo-Alvarez R. Simulation of electric double layers undergoing charge inversion: mixtures of mono- and multivalent ions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2005; 21:9231-7. [PMID: 16171356 DOI: 10.1021/la0505925] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
In this paper, the electric double layer (EDL) of a charged plane in the presence of mixtures of 1:1 and 3:1 electrolytes has been investigated through Monte Carlo (MC) simulations using a nonrestrictive primitive model of EDL. In particular, the charge inversion in colloids (attributable to an accumulation of counterions on the surface) can be better understood by means of the simulations performed here. Moreover, two mechanisms proposed for charge inversion are probed: The formation of a strongly correlated layer (SCL) of multivalent counterions and excluded volume effects (to which we will also refer as ion size correlations). Our results are in agreement with the behavior found experimentally for some model colloids with increasing the concentration of monovalent salt in the presence of trivalent ions, which clearly supports the relevance of ion size correlations. In contrast, certain disagreement with predictions of SCL theories is reported.
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Affiliation(s)
- M Quesada-Pérez
- Departamento de Física, Universidad de Jaén, Escuela Universitaria Politécnica, 23700 Linares, Jaén, Spain
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50
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Matsuoka H, Yamamoto T, Harada T, Ikeda T. Effect of counterion species on colloidal crystal. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2005; 21:7105-8. [PMID: 16042430 DOI: 10.1021/la0472044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The effect of counterion species on the colloidal crystal structure in a dispersion was carefully investigated as a function of the degree of neutralization (alpha) by the ultra-small-angle X-ray scattering technique. The nearest neighbor interparticle distance (2D(exp)) first increased with decreasing alpha, and then decreased after passing through the maximum. This behavior was confirmed for K(+), Li(+), Ca(2+), TMA(+) (tetramethylammonium) as a counterion, and Na(+) in our previous report (Harada, T.; Matsuoka, H.; Ikeda, T.; Yamaoka, H. Langmuir 2000, 16, 1612). However, the alpha value of the maximum position (alpha(max)) largely depended on the counterion species, and it was in the order K(+) < Na(+) < TMA(+) approximately Li(+). This behavior was well characterized by the specific features of each ion: the alpha(max) map could be well superimposed in the Stokes radius-crystal ion radius relationship of counterions. The alpha(max) dependence on Stokes radius was very similar to that of the B coefficient by Jones and Dole except in the case of Ca(2+). In principle, the smaller the value for B, the smaller alpha(max), indicating that a water structure breaker such as K(+) can more easily destroy the colloidal crystal structure. In other words, the effect of the counterion species on colloidal crystal stability follows the Hofmeister series. Including Ca(2+), the relationship was linear for the alpha(max) values plotted as a function of the limiting equivalent conductivity of small ions. A counterion with larger conductivity would be a stronger breaker for the colloidal crystal structure.
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Affiliation(s)
- Hideki Matsuoka
- Department of Polymer Chemistry, Kyoto University, Kyoto 615-8510, Japan.
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