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Kalyuzhnyi YV, Nezbeda I, Cummings PT. Integral equation theory for mixtures of spherical and patchy colloids. 2. Numerical results. SOFT MATTER 2021; 17:3513-3519. [PMID: 33662078 DOI: 10.1039/d0sm02284e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Thermodynamic properties and structure of binary mixtures of patchy and spherical colloids are studied using a recently developed theory [Y. V. Kalyuzhnyi, et al., Soft Matter, 2020, 16, 3456]. The theory is based on a solution of the multidensity Ornstein-Zernike equation and provides completely analytical expressions for the structure factors of these systems and for all their major thermodynamical quantities. The considered mixtures are made up of particles of different size and with a different number of patches. A set of molecular simulation data has been generated to enable a systematic comparison and to access thus accuracy of the theoretical predictions. In general, the predictions of the theory appear to be in good agreement with computer simulation data. For the models with a lower number of patches (np = 1, 2) the theoretical results show very good accuracy. Less accurate are the predictions for the four-patch versions of the model. While theoretical results for the radial distribution functions are, generally, relatively accurate for all the models, results for thermodynamics deteriorate with increasing concentration of the spherical colloids. Possible ways to improve the theory are briefly outlined.
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Affiliation(s)
- Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., Lviv 79011, Ukraine.
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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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Kalyuzhnyi YV, Nezbeda I, Cummings PT. Integral equation theory for a mixture of spherical and patchy colloids: analytical description. SOFT MATTER 2020; 16:3456-3465. [PMID: 32201867 DOI: 10.1039/c9sm02309g] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
An analytic theory for the structure and thermodynamics of two-component mixtures of patchy and spherical colloids is developed. The theory is based on an analytical solution of the multidensity Ornstein-Zernike equation supplemented by the associative Percus-Yevick closure relations. We derive closed-form analytic expressions for the partial structure factors and thermodynamic properties using the energy route for the model with arbitrary number of patches and any hard-sphere size ratio of the particles. To assess the accuracy of the theoretical predictions we compare them against existing and newly generated set of computer simulation data. In our numerical calculations we consider the model with equal hard-sphere sizes and one patch. Very good agreement between results of the theory and simulation for the pair correlation functions, excess internal energy and pressure is observed for almost all values of the system density, temperature and composition studied. Only in the region of low concentrations of spherical colloids the theoretical results become less accurate.
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Affiliation(s)
- Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., Lviv 79011, Ukraine.
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González-Tovar E, Lozada-Cassou M. Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration. Adv Colloid Interface Sci 2019; 270:54-72. [PMID: 31181349 DOI: 10.1016/j.cis.2019.05.009] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2019] [Revised: 05/23/2019] [Accepted: 05/24/2019] [Indexed: 10/26/2022]
Abstract
In charged colloidal dispersion systems the interest is in finding their stability conditions, phase transitions, and transport properties, either in bulk or confinement, among other physicochemical quantities, for which the knowledge of the dispersions' molecular structure and the associated macroion-macroion forces is crucial. To investigate these phenomena simple models have been proposed. Most of the theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence, these studies have been focused on the electrolyte structure around one or two isolated central particle(s), where phenomena as charge reversal, charge inversion and surface charge amplification have been shown to be relevant. However, experimental studies at finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. A simple, yet useful, model is the Colloidal Primitive Model, in which the colloidal dispersion is modeled as a mixture of size (and charge) asymmetrical hard spheres, at finite volume fraction. In this paper we review recent integral equations solutions for this model, where very long-range attractive-repulsive forces, as well as new long-range, giant charge inversions are reported. The calculated macroions radial distribution functions, charge distributions, and macroion-macroion forces are qualitatively consistent with existing experimental results, and Monte Carlo and molecular dynamics simulations.
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Prslja P, Aupic J, Urbic T. Thermodynamics and structure of a two-dimensional asymmetric electrolyte by integral equation theory. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1307469] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Paulina Prslja
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna pot 113, 1000 Ljubljana, Slovenia
| | - Jana Aupic
- Department of Synthetic Biology and Immunology, National Institute of Chemistry, Hajdrihova, Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna pot 113, 1000 Ljubljana, Slovenia
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El-Moudny S, Badia M, Benhamou M. Structure and thermodynamics of Pickering emulsions stabilized by adsorbed charged particles. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.11.044] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Luchko T, Joung IS, Case DA. Integral Equation Theory of Biomolecules and Electrolytes. INNOVATIONS IN BIOMOLECULAR MODELING AND SIMULATIONS 2012. [DOI: 10.1039/9781849735049-00051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
The so-called three-dimensional version (3D-RISM) can be used to describe the interactions of solvent components (here we treat water and ions) with a chemical or biomolecular solute of arbitrary size and shape. Here we give an overview of the current status of such models, describing some aspects of “pure” electrolytes (water plus simple ions) and of ionophores, proteins and nucleic acids in the presence of water and salts. Here we focus primarily on interactions with water and dissolved salts; as a practical matter, the discussion is mostly limited to monovalent ions, since studies of divalent ions present many difficult problems that have not yet been addressed. This is not a comprehensive review, but covers a few recent examples that illustrate current issues.
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Affiliation(s)
- Tyler Luchko
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
| | - In Suk Joung
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
| | - David A. Case
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
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Jardat M, Dahirel V, Durand-Vidal S, Lucas I, Bernard O, Turq P. Effective charges of micellar species obtained from Brownian dynamics simulations and from an analytical transport theory. Mol Phys 2006. [DOI: 10.1080/00268970600997564] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Avendaño C, Gil-Villegas A. Monte Carlo simulations of primitive models for ionic systems using the Wolf method. Mol Phys 2006. [DOI: 10.1080/00268970600551155] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Jardat M, Durand-Vidal S, Da Mota N, Turq P. Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: Comparison between experiments, analytical calculations and numerical simulations. J Chem Phys 2004; 120:6268-73. [PMID: 15267514 DOI: 10.1063/1.1652427] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.
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Affiliation(s)
- M Jardat
- Laboratoire Liquides Ioniques et Interfaces Chargees, UMR CNRS 7612, boite postale 51, Universite P. et M. Curie, 4 place Jussieu, F-75252 Paris Cedex 05, France.
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Spohr E, Hribar B, Vlachy V. Mechanism of Macroion−Macroion Clustering Induced by the Presence of Trivalent Counterions. J Phys Chem B 2002. [DOI: 10.1021/jp013811d] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- E. Spohr
- Department of Theoretical Chemistry, University of Ulm, D-89069 Ulm, Germany
| | - B. Hribar
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000 Ljubljana, Slovenia
| | - V. Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000 Ljubljana, Slovenia
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Jardat M, Cartailler T, Turq P. Counterion and polyion dynamics in highly asymmetrical electrolyte solutions. J Chem Phys 2001. [DOI: 10.1063/1.1376425] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Linse P, Lobaskin V. Electrostatic attraction and phase separation in solutions of like-charged colloidal particles. J Chem Phys 2000. [DOI: 10.1063/1.480943] [Citation(s) in RCA: 119] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lobaskin V, Linse P. Computer simulation of highly asymmetric electrolytes with charge asymmetry 60:1 and 60:2. J Mol Liq 2000. [DOI: 10.1016/s0167-7322(99)00116-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Lobaskin V, Linse P. Simulation of an asymmetric electrolyte with charge asymmetry 60:1 using hard-sphere and soft-sphere models. J Chem Phys 1999. [DOI: 10.1063/1.479728] [Citation(s) in RCA: 88] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Linse P. On the convergence of simulation of asymmetric electrolytes with charge asymmetry 60:1. J Chem Phys 1999. [DOI: 10.1063/1.478217] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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González-Mozuelos P, Carbajal-Tinoco MD. Effective pair potentials for charged colloidal particles. J Chem Phys 1998. [DOI: 10.1063/1.477745] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lobaskin V, Linse P. Accurate simulation of highly asymmetric electrolytes with charge asymmetry 20:1 and 20:2. J Chem Phys 1998. [DOI: 10.1063/1.476948] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hribar B, Krienke H, Kalyuzhnyi Y, Vlachy V. Dilute solutions of highly asymmetrical electrolytes in the primitive model approximation. J Mol Liq 1997. [DOI: 10.1016/s0167-7322(97)00073-1] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Reščič J, Vlachy V, Bhuiyan LB, Outhwaite CW. Monte Carlo simulation studies of electrolyte in mixture with a neutral component. J Chem Phys 1997. [DOI: 10.1063/1.474718] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Hribar B, Vlachy V. Evidence of Electrostatic Attraction between Equally Charged Macroions Induced by Divalent Counterions. J Phys Chem B 1997. [DOI: 10.1021/jp970007b] [Citation(s) in RCA: 75] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- B. Hribar
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000 Ljubljana, Slovenia
| | - V. Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000 Ljubljana, Slovenia
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V. VLACHY L. B. BHUIYAN C. W. OUTHW. electrolyte in mixture with a neutral component: effects of counterion charge. Mol Phys 1997. [DOI: 10.1080/002689797172264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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