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Bernard O, Jardat M, Rotenberg B, Illien P. On analytical theories for conductivity and self-diffusion in concentrated electrolytes. J Chem Phys 2023; 159:164105. [PMID: 37873957 DOI: 10.1063/5.0165533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 09/19/2023] [Indexed: 10/25/2023] Open
Abstract
Describing analytically the transport properties of electrolytes, such as their conductivity or the self-diffusion of the ions, has been a central challenge of chemical physics for almost a century. In recent years, this question has regained some interest in light of Stochastic Density Field Theory (SDFT) - an analytical framework that allows the approximate determination of density correlations in fluctuating systems. In spite of the success of this theory to describe dilute electrolytes, its extension to concentrated solutions raises a number of technical difficulties, and requires simplified descriptions of the short-range repulsion between the ions. In this article, we discuss recent approximations that were proposed to compute the conductivity of electrolytes, in particular truncations of Coulomb interactions at short distances. We extend them to another observable (the self-diffusion coefficient of the ions) and compare them to earlier analytical approaches, such as the mean spherical approximation and mode-coupling theory. We show how the treatment of hydrodynamic effects in SDFT can be improved, that the choice of the modified Coulomb interactions significantly affects the determination of the properties of the electrolytes, and that comparison with other theories provides a guide to extend SDFT approaches in this context.
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Affiliation(s)
- Olivier Bernard
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
| | - Marie Jardat
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
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2
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Elisea-Espinoza JJ, González-Tovar E, Guerrero-García GI. Theoretical description of the electrical double layer for a mixture of n ionic species with arbitrary size and charge asymmetries. I. Spherical geometry. J Chem Phys 2023; 158:2895477. [PMID: 37294907 DOI: 10.1063/5.0151140] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Accepted: 05/08/2023] [Indexed: 06/11/2023] Open
Abstract
In this work, we propose a theoretical finite element description of the ionic profiles of a general mixture of n species of spherical charged particles dissolved in an implicit solvent, with arbitrary size and charge asymmetries, neutralizing a spherical macroion. This approach aims to close the gap between the nano- and the micro-scales in macroion solutions, taking into account the ion correlations and ionic excluded volume effects consistently. When these last two features are neglected, the classical non-linear Poisson-Boltzmann theory for n ionic species-with different ionic closest approach distances to the colloidal surface-is recovered as a limit case. As a proof of concept, we study the electrical double layer of an electroneutral mixture of oppositely charged colloids and small microions, with an asymmetry 1:333 in size and 1:10 in valence, in salt-free and added salt environments. Our theoretical approach displays a good agreement regarding the ionic profiles, the integrated charge, and the mean electrostatic potential obtained from molecular dynamics simulations with explicit-sized microions. Although the non-linear Poisson-Boltzmann colloid-colloid and colloid-microion profiles differ notably from those obtained via molecular dynamics simulations with explicit small-sized ions, the associated mean electrostatic potential agrees well with the corresponding explicit microion simulations.
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Affiliation(s)
| | - Enrique González-Tovar
- Instituto de Física de la Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - Guillermo Iván Guerrero-García
- Facultad de Ciencias de la Universidad Autónoma de San Luis Potosí, Av. Chapultepec 1570, Privadas del Pedregal, 78295 San Luis Potosí, Mexico
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3
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Avni Y, Andelman D, Orland H. Conductance of concentrated electrolytes: Multivalency and the Wien effect. J Chem Phys 2022; 157:154502. [PMID: 36272780 DOI: 10.1063/5.0111645] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The electric conductivity of ionic solutions is well understood at low ionic concentrations of up to a few millimolar but becomes difficult to unravel at higher concentrations that are still common in nature and technological applications. A model for the conductivity at high concentrations was recently put forth for monovalent electrolytes at low electric fields. The model relies on applying a stochastic density-functional theory and using a modified electrostatic pair-potential that suppresses unphysical, short-range electrostatic interactions. Here, we extend the theory to multivalent ions as well as to high electric fields where a deviation from Ohm's law known as the Wien effect occurs. Our results are in good agreement with experiments and recent simulations.
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Affiliation(s)
- Yael Avni
- School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
| | - David Andelman
- School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
| | - Henri Orland
- Institut de Physique Théorique, Université de Paris-Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
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Guerrero-García GI. Local inversion of the mean electrostatic potential, maximum charge reversal, and capacitive compactness of concentrated 1:1 salts: The crucial role of the ionic excluded volume and ion correlations. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119566] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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5
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Uchida S, Sano H, Ozaki H, Kiyobayashi T. Transport properties and solvation state of magnesium salts dissolved in propylene carbonate and γ-butyrolactone: A comparison with monovalent cation counterparts. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117692] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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6
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Falcón-González JM, Contreras-Aburto C, Lara-Peña M, Heinen M, Avendaño C, Gil-Villegas A, Castañeda-Priego R. Assessment of the Wolf method using the Stillinger-Lovett sum rules: From strong electrolytes to weakly charged colloidal dispersions. J Chem Phys 2020; 153:234901. [PMID: 33353329 DOI: 10.1063/5.0033561] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The Ewald method has been the cornerstone in molecular simulations for modeling electrostatic interactions of charge-stabilized many-body systems. In the late 1990s, Wolf and collaborators developed an alternative route to describe the long-range nature of electrostatic interactions; from a computational perspective, this method provides a more efficient and straightforward way to implement long-range electrostatic interactions than the Ewald method. Despite these advantages, the validity of the Wolf potential to account for the electrostatic contribution in charged fluids remains controversial. To alleviate this situation, in this contribution, we implement the Wolf summation method to both electrolyte solutions and charged colloids with moderate size and charge asymmetries in order to assess the accuracy and validity of the method. To this end, we verify that the proper selection of parameters within the Wolf method leads to results that are in good agreement with those obtained through the standard Ewald method and the theory of integral equations of simple liquids within the so-called hypernetted chain approximation. Furthermore, we show that the results obtained with the original Wolf method do satisfy the moment conditions described by the Stillinger-Lovett sum rules, which are directly related to the local electroneutrality condition and the electrostatic screening in the Debye-Hückel regime. Hence, the fact that the solution provided by the Wolf method satisfies the first and second moments of Stillinger-Lovett proves, for the first time, the reliability of the method to correctly incorporate the electrostatic contribution in charge-stabilized fluids. This makes the Wolf method a powerful alternative compared to more demanding computational approaches.
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Affiliation(s)
- José Marcos Falcón-González
- Unidad Profesional Interdisciplinaria de Ingeniería, Campus Guanajuato, Instituto Politécnico Nacional, Av. Mineral de Valenciana No. 200, Col. Fraccionamiento Industrial Puerto Interior, C.P. 36275 Silao de la Victoria, Guanajuato, Mexico
| | - Claudio Contreras-Aburto
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, 29050 Tuxtla Gutiérrez, Mexico
| | - Mayra Lara-Peña
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Mexico
| | - Marco Heinen
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Mexico
| | - Carlos Avendaño
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom
| | - Alejandro Gil-Villegas
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Mexico
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Mexico
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7
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Willems K, Ruić D, L R Lucas F, Barman U, Verellen N, Hofkens J, Maglia G, Van Dorpe P. Accurate modeling of a biological nanopore with an extended continuum framework. NANOSCALE 2020; 12:16775-16795. [PMID: 32780087 DOI: 10.1039/d0nr03114c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Despite the broad success of biological nanopores as powerful instruments for the analysis of proteins and nucleic acids at the single-molecule level, a fast simulation methodology to accurately model their nanofluidic properties is currently unavailable. This limits the rational engineering of nanopore traits and makes the unambiguous interpretation of experimental results challenging. Here, we present a continuum approach that can faithfully reproduce the experimentally measured ionic conductance of the biological nanopore Cytolysin A (ClyA) over a wide range of ionic strengths and bias potentials. Our model consists of the extended Poisson-Nernst-Planck and Navier-Stokes (ePNP-NS) equations and a computationally efficient 2D-axisymmetric representation for the geometry and charge distribution of the nanopore. Importantly, the ePNP-NS equations achieve this accuracy by self-consistently considering the finite size of the ions and the influence of both the ionic strength and the nanoscopic scale of the pore on the local properties of the electrolyte. These comprise the mobility and diffusivity of the ions, and the density, viscosity and relative permittivity of the solvent. Crucially, by applying our methodology to ClyA, a biological nanopore used for single-molecule enzymology studies, we could directly quantify several nanofluidic characteristics difficult to determine experimentally. These include the ion selectivity, the ion concentration distributions, the electrostatic potential landscape, the magnitude of the electro-osmotic flow field, and the internal pressure distribution. Hence, this work provides a means to obtain fundamental new insights into the nanofluidic properties of biological nanopores and paves the way towards their rational engineering.
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Affiliation(s)
- Kherim Willems
- KU Leuven, Department of Chemistry, Celestijnenlaan 200F, B-3001 Leuven, Belgium
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Roa R, Menne D, Riest J, Buzatu P, Zholkovskiy EK, Dhont JKG, Wessling M, Nägele G. Ultrafiltration of charge-stabilized dispersions at low salinity. SOFT MATTER 2016; 12:4638-4653. [PMID: 27113088 DOI: 10.1039/c6sm00660d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present a comprehensive study of cross-flow ultrafiltration (UF) of charge-stabilized suspensions, under low-salinity conditions of electrostatically strongly repelling colloidal particles. The axially varying permeate flux, near-membrane concentration-polarization (CP) layer and osmotic pressure profiles are calculated using a macroscopic diffusion-advection boundary layer method, and are compared with filtration experiments on aqueous suspensions of charge-stabilized silica particles. The theoretical description based on the one-component macroion fluid model (OCM) accounts for the strong influence of surface-released counterions on the renormalized colloid charge and suspension osmotic compressibility, and for the influence of the colloidal hydrodynamic interactions and electric double layer repulsion on the concentration-dependent suspension viscosity η, and collective diffusion coefficient Dc. A strong electro-hydrodynamic enhancement of Dc and η, and likewise of the osmotic pressure, is predicted theoretically, as compared with their values for a hard-sphere suspension. We also point to the failure of generalized Stokes-Einstein relations describing reciprocal relations between Dc and η. According to our filtration model, Dc is of dominant influence, giving rise to an only weakly developed CP layer having practically no effect on the permeate flux. This prediction is quantitatively confirmed by our UF measurements of the permeate flux using an aqueous suspension of charged silica spheres as the feed system. The experimentally detected fouling for the largest considered transmembrane pressure values is shown not to be due to filter cake formation by crystallization or vitrification.
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Affiliation(s)
- Rafael Roa
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), 52425 Jülich, Germany. and Helmholtz-Zentrum Berlin, Soft Matter and Functional Materials, 14109 Berlin, Germany
| | - Daniel Menne
- RWTH Aachen University, Chemical Process Engineering, 52064 Aachen, Germany
| | - Jonas Riest
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), 52425 Jülich, Germany. and Jülich-Aachen Research Alliance, JARA-Soft Matter
| | - Pompilia Buzatu
- RWTH Aachen University, Chemical Process Engineering, 52064 Aachen, Germany and DWI Leibniz Institute for Interactive Materials, 52074 Aachen, Germany
| | - Emiliy K Zholkovskiy
- Ukrainian Academy of Sciences, Institute of Bio-Colloid Chemistry, 03142 Kiev, Ukraine
| | - Jan K G Dhont
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), 52425 Jülich, Germany. and Jülich-Aachen Research Alliance, JARA-Soft Matter, and Physics Department, Heinrich-Heine Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Matthias Wessling
- RWTH Aachen University, Chemical Process Engineering, 52064 Aachen, Germany and Jülich-Aachen Research Alliance, JARA-Soft Matter, and DWI Leibniz Institute for Interactive Materials, 52074 Aachen, Germany
| | - Gerhard Nägele
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), 52425 Jülich, Germany. and Jülich-Aachen Research Alliance, JARA-Soft Matter, and Physics Department, Heinrich-Heine Universität Düsseldorf, 40225 Düsseldorf, Germany
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9
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Urrutia Bañuelos E, Contreras Aburto C, Maldonado Arce A. A common neighbor analysis of crystallization kinetics and excess entropy of charged spherical colloids. J Chem Phys 2016; 144:094504. [DOI: 10.1063/1.4943001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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11
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Riest J, Eckert T, Richtering W, Nägele G. Dynamics of suspensions of hydrodynamically structured particles: analytic theory and applications to experiments. SOFT MATTER 2015; 11:2821-2843. [PMID: 25707362 DOI: 10.1039/c4sm02816c] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small amount of solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.
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Affiliation(s)
- Jonas Riest
- Forschungszentrum Jülich GmbH, ICS-3 - Soft Condensed Matter, 52428 Jülich, Germany.
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12
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Roy S, Yashonath S, Bagchi B. Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics. J Chem Phys 2015; 142:124502. [DOI: 10.1063/1.4915274] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Susmita Roy
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Subramanian Yashonath
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Biman Bagchi
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
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13
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Contreras-Aburto C, Báez CA, Méndez-Alcaraz JM, Castañeda-Priego R. Long-time self-diffusion of charged spherical colloidal particles in parallel planar layers. J Chem Phys 2014; 140:244116. [DOI: 10.1063/1.4884822] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Claudio Contreras-Aburto
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Guanajuato, Mexico
| | - César A. Báez
- Departamento de Física, Cinvestav, Av. IPN 2508, Col. San Pedro Zacatenco, 07360 México, D. F., Mexico
| | - José M. Méndez-Alcaraz
- Departamento de Física, Cinvestav, Av. IPN 2508, Col. San Pedro Zacatenco, 07360 México, D. F., Mexico
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Guanajuato, Mexico
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Dhont JKG, Kang K. An electric-field induced dynamical state in dispersions of charged colloidal rods. SOFT MATTER 2014; 10:1987-2007. [PMID: 24652225 DOI: 10.1039/c3sm52277f] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The response of concentrated dispersions of charged colloids to low-frequency electric fields is governed by field-induced inter-colloidal interactions resulting from the polarization of electric double layers and the layer of condensed ions, association and dissociation of condensed ions, as well as hydrodynamic interactions through field-induced electro-osmotic flow. The phases and states that can be formed by such field-induced interactions are an essentially unexplored field of research. Experiments on concentrated suspensions of rod-like colloids (fd-virus particles), within the isotropic-nematic phase coexistence region, showed that a number of phases/states are induced, depending on the field amplitude and frequency [Soft Matter, 2010, 6, 273]. In particular, a dynamical state is found where nematic domains form and melt on a time scale of the order of seconds. We discuss the microscopic origin of this dynamical state, which is attributed to the cyclic, electric-field induced dissociation and association of condensed ions. A semi-quantitative theory is presented for the dynamics of melting and formation of nematic domains, including a model for the field-induced dissociation/association of condensed ions. The resulting equation of motion for the orientational order parameter is solved numerically for parameters complying with the fd-virus system. A limit-cycle is found, with a cycling-time that diverges at the transition line in the field-amplitude versus frequency plane where the dynamical state first appears, in accord with experimental findings.
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Affiliation(s)
- Jan K G Dhont
- Forschungszentrum Jülich, Institute of Complex Systems (ICS), Soft Condensed Matter, D-52425 Jülich, Germany.
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Contreras Aburto C, Nägele G. A unifying mode-coupling theory for transport properties of electrolyte solutions. I. General scheme and limiting laws. J Chem Phys 2013; 139:134109. [DOI: 10.1063/1.4822297] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
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