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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 30, 1975 - Issue 5
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Original Articles

Mean spherical model for asymmetric electrolytes

I. Method of solution

L. Blum Physics Department, University of Puerto Rico, Rio Piedras, PR, 00931
Pages 1529-1535 | Received 10 May 1975, Published online: 23 Aug 2006

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Crossref
Marta Hvozd, Oksana Patsahan, Taras Patsahan & Myroslav Holovko. (2022) Fluid-fluid phase behaviour in the explicit hard spherocylinder solvent ionic model confined in a disordered porous medium. Journal of Molecular Liquids 346, pages 117888.
Crossref
Pierre J. Walker, Xiaodong Liang & Georgios M. Kontogeorgis. (2022) Importance of the Relative Static Permittivity in electrolyte SAFT-VR Mie Equations of State. Fluid Phase Equilibria 551, pages 113256.
Crossref
Andrew S. Ylitalo, Christopher Balzer, Pengfei Zhang & Zhen-Gang Wang. (2021) Electrostatic Correlations and Temperature-Dependent Dielectric Constant Can Model LCST in Polyelectrolyte Complex Coacervation. Macromolecules 54:24, pages 11326-11337.
Crossref
Dirk Gillespie, Mónika Valiskó & Dezső Boda. (2021) Electrostatic correlations in electrolytes: Contribution of screening ion interactions to the excess chemical potential. The Journal of Chemical Physics 155:22.
Crossref
Pengfei Zhang & Zhen-Gang Wang. (2021) Interfacial Structure and Tension of Polyelectrolyte Complex Coacervates. Macromolecules 54:23, pages 10994-11007.
Crossref
Julian Self, Helen K. Bergstrom, Kara D. Fong, Bryan D. McCloskey & Kristin A. Persson. (2021) A Theoretical Model for Computing Freezing Point Depression of Lithium-Ion Battery Electrolytes. Journal of The Electrochemical Society 168:12, pages 120532.
Crossref
Alejandro Gallegos, Gary M. C. Ong & Jianzhong Wu. (2021) Thermodynamic non-ideality in charge regulation of weak polyelectrolytes. Soft Matter 17:40, pages 9221-9234.
Crossref
Li Sun & Jierong Liang. (2021) Thermodynamic modeling of gas solubility in aqueous sodium chloride solution. Chinese Journal of Chemical Engineering 38, pages 184-195.
Crossref
Victor P. Stepanov. (2021) Adiabatic compressibility of biphasic salt melts. Zeitschrift für Naturforschung A 76:8, pages 723-730.
Crossref
Christopher Balzer, Leying Qing & Zhen-Gang Wang. (2021) Preferential Ion Adsorption in Blue Energy Applications. ACS Sustainable Chemistry & Engineering 9:28, pages 9230-9239.
Crossref
Alfredo González-Calderón & Marcelo Lozada-Cassou. (2021) Violation of the local electroneutrality condition in an inhomogeneous macroions solution. The European Physical Journal Special Topics 230:4, pages 1113-1120.
Crossref
Li Sun & Jierong Liang. (2021) Solubility Calculations of Methane and Ethane in Aqueous Electrolyte Solutions. Journal of Solution Chemistry 50:6, pages 920-940.
Crossref
Christopher Balzer, Jian Jiang, Ryan L. Marson, Valeriy V. Ginzburg & Zhen-Gang Wang. (2021) Nonelectrostatic Adsorption of Polyelectrolytes and Mediated Interactions between Solid Surfaces. Langmuir 37:18, pages 5483-5493.
Crossref
Qiyuan Qiu, Xiaofei Xu & Yanwei Wang. (2021) Phase Behavior of Partially Charged Polyelectrolyte Solutions with Salt: A Theoretical Study. Macromolecular Theory and Simulations 30:3.
Crossref
Zsófia Sarkadi, Dávid Fertig, Zoltán Ható, Mónika Valiskó & Dezső Boda. (2021) From nanotubes to nanoholes: Scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes. The Journal of Chemical Physics 154:15.
Crossref
Jian Jiang & Dirk Gillespie. (2021) Revisiting the Charged Shell Model: A Density Functional Theory for Electrolytes. Journal of Chemical Theory and Computation 17:4, pages 2409-2416.
Crossref
Mingge Zhao, Xiang Li & Junhan Cho. (2021) Pressure Effects on Self-Assembly in Mixtures Containing Zwitterionic Amphiphiles. Langmuir 37:13, pages 3882-3896.
Crossref
S. Zhou. (2021) Surface electrostatic force in presence of dimer counter-ion. Journal of Molecular Liquids 328, pages 115225.
Crossref
P. Cats, R. Evans, A. Härtel & R. van Roij. (2021) Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations. The Journal of Chemical Physics 154:12.
Crossref
Andrés González de Castilla, Simon Müller & Irina Smirnova. (2021) On the analogy between the restricted primitive model and capacitor circuits: Semi-empirical alternatives for over- and underscreening in the calculation of mean ionic activity coefficients. Journal of Molecular Liquids 326, pages 115204.
Crossref
Jalel M'halla, Sondes Boughammoura & Anis Ghazouani. (2021) Translational dielectric friction on a pearl-necklace-like polyelectrolyte chain. Journal of Molecular Liquids 326, pages 115173.
Crossref
Zhenshu Wen, Lijun Zhang & Mingji Zhang. (2020) Dynamics of Classical Poisson–Nernst–Planck Systems with Multiple Cations and Boundary Layers. Journal of Dynamics and Differential Equations 33:1, pages 211-234.
Crossref
Jian Jiang. (2021) Non-monotonic Effects of Intrinsic Stiffness and Concentration of Polyelectrolytes on the Electro-Sorption. Macromolecules 54:4, pages 1801-1810.
Crossref
Seanea Jang & Ghi Ryang Shin. (2020) Long-range interactions in model colloidal dispersions with surface charge distributions. Journal of the Korean Physical Society 78:3, pages 210-218.
Crossref
Salaheddine Chabab, Alain Valtz, Snaide Ahamada & Christophe Coquelet. (2020) Hydrate Stability of Carbon Dioxide + Oxygen Binary Mixture (CO 2 + O 2 ) in Pure Water: Measurements and Modeling . Journal of Chemical & Engineering Data 66:1, pages 767-779.
Crossref
L. B. Bhuiyan. (2021) Structure and thermodynamics in the linear modified Poisson-Boltzmann theories in restricted primitive model electrolytes. Condensed Matter Physics 24:2, pages 23801.
Crossref
Samira Farzam & Farzaneh Feyzi. (2021) Experimental investigation and thermodynamic modeling of equilibrium extraction of gold(III) from hydrochloric acid in 1-butyl-3-methylimidazolium hexafluorophosphate. Fluid Phase Equilibria 527, pages 112839.
Crossref
Andrew J. Haslam, Alfonso González-Pérez, Silvia Di Lecce, Siti H. Khalit, Felipe A. Perdomo, Spiros Kournopoulos, Maximilian Kohns, Tom Lindeboom, Malak Wehbe, Sara Febra, George Jackson, Claire S. Adjiman & Amparo Galindo. (2020) Expanding the Applications of the SAFT-γ Mie Group-Contribution Equation of State: Prediction of Thermodynamic Properties and Phase Behavior of Mixtures. Journal of Chemical & Engineering Data 65:12, pages 5862-5890.
Crossref
Xiaofei Xu, Qiyuan Qiu, Changjie Lu & Shuangliang Zhao. (2020) Responsive Properties of Grafted Polyanion Chains: Effects of Dispersion Interaction and Salt. Journal of Chemical & Engineering Data 65:12, pages 5708-5717.
Crossref
Alejandro Gallegos & Jianzhong Wu. (2020) Charge Regulation of Natural Amino Acids in Aqueous Solutions. Journal of Chemical & Engineering Data 65:12, pages 5630-5642.
Crossref
Ezat Keshavarzi & Mahsa Abareghi. (2020) The effect of electro-neutrality violation inside a charged spherical cavity on the capacitance curve shape in DFT approach and interpretation of mean electrostatic potential. Journal of Molecular Liquids 318, pages 114271.
Crossref
Salaheddine Chabab, Pascal Théveneau, Christophe Coquelet, Jérôme Corvisier & Patrice Paricaud. (2020) Measurements and predictive models of high-pressure H2 solubility in brine (H2O+NaCl) for underground hydrogen storage application. International Journal of Hydrogen Energy 45:56, pages 32206-32220.
Crossref
Husnain Manzoor, Muaz A. Selam, Samer Adham, Ho Kyong Shon, Marcelo Castier & Ahmed Abdel-Wahab. (2020) Energy recovery modeling of pressure-retarded osmosis systems with membrane modules compatible with high salinity draw streams. Desalination 493, pages 114624.
Crossref
Wilko Verweij & Jean-Pierre Simonin. (2020) Implementing the Mean Spherical Approximation Model in the Speciation Code CHEAQS Next at High Salt Concentrations. Journal of Solution Chemistry 49:11, pages 1319-1327.
Crossref
Chandra N. Patra. (2020) Size and charge correlations in spherical electric double layers: a case study with fully asymmetric mixed electrolytes within the solvent primitive model. RSC Advances 10:64, pages 39017-39025.
Crossref
Ryuichi Okamoto, Kenichiro Koga & Akira Onuki. (2020) Theory of electrolytes including steric, attractive, and hydration interactions. The Journal of Chemical Physics 153:7.
Crossref
Marc Theiss & Joachim Gross. (2020) Perturbation approaches for describing dipolar fluids and electrolyte solutions. The Journal of Chemical Physics 153:4, pages 044102.
Crossref
Alexandre P. dos Santos, Yuki Uematsu, Alexander Rathert, Philip Loche & Roland R. Netz. (2020) Consistent description of ion-specificity in bulk and at interfaces by solvent implicit simulations and mean-field theory. The Journal of Chemical Physics 153:3.
Crossref
Maximilian Kohns, Georgia Lazarou, Spiros Kournopoulos, Esther Forte, Felipe A. Perdomo, George Jackson, Claire S. Adjiman & Amparo Galindo. (2020) Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulphuric, and carbonic acids. Physical Chemistry Chemical Physics 22:27, pages 15248-15269.
Crossref
Xiaofei Xu, Hao Shi & Fuhan Wang. (2020) Near-Critical Phase Behavior in Polyelectrolyte Solutions: Effect of Charge Fluctuations. The Journal of Physical Chemistry B 124:20, pages 4203-4210.
Crossref
Husnain Manzoor, Muaz A. Selam, Fahim Bin Abdur Rahman, Samer Adham, Marcelo Castier & Ahmed Abdel-Wahab. (2020) A tool for assessing the scalability of pressure-retarded osmosis (PRO) membranes. Renewable Energy 149, pages 987-999.
Crossref
Vincent Dahirel, Olivier Bernard & Marie Jardat. (2020) Can we describe charged nanoparticles with electrolyte theories? Insight from mesoscopic simulation techniques. Journal of Molecular Liquids 303, pages 111942.
Crossref
Mahsa Abareghi & Ezat Keshavarzi. (2020) Ion selectivity by charged spherical cavities and investigation of intersection point for average cavity density versus electric potential (a DFT study). Journal of Molecular Liquids 302, pages 112283.
Crossref
Samuel W. Coles, Chanbum Park, Rohit Nikam, Matej Kanduč, Joachim Dzubiella & Benjamin Rotenberg. (2020) Correlation Length in Concentrated Electrolytes: Insights from All-Atom Molecular Dynamics Simulations. The Journal of Physical Chemistry B.
Crossref
Marc Theiss & Joachim Gross. (2020) Nonprimitive Model Electrolyte Solutions: Comprehensive Data from Monte Carlo Simulations. Journal of Chemical & Engineering Data 65:2, pages 634-639.
Crossref
Isabelle Raspo & Evelyne Neau. (2020) An empirical correlation for the relative permittivity of liquids in a wide temperature range: Application to the modeling of electrolyte systems with a GE/EoS approach. Fluid Phase Equilibria 506, pages 112371.
Crossref
Samaneh Bandehali, Hamidreza Sanaeepur, Abtin Ebadi Amooghin & Abdolreza Moghadassi. 2020. Modeling in Membranes and Membrane‐Based Processes. Modeling in Membranes and Membrane‐Based Processes 201 235 .
Dirk Gillespie, Dimiter N. Petsev & Frank van Swol. (2020) Electric Double Layers with Surface Charge Regulation Using Density Functional Theory. Entropy 22:2, pages 132.
Crossref
Chongzhi Qiao, Jie Zhang, Peng Jiang, Shuangliang Zhao, Xingfu Song & Jianguo Yu. (2020) A molecular approach for predicting phase diagrams of ternary aqueous saline solutions. Chemical Engineering Science 211, pages 115278.
Crossref
Jian Jiang, Valeriy V. Ginzburg & Zhen-Gang Wang. (2019) On the origin of oscillatory interactions between surfaces mediated by polyelectrolyte solution. The Journal of Chemical Physics 151:21.
Crossref
S. Zhou. (2019) Role of neutral and non-hard sphere interaction in differential capacitance of electrical double-layer. Journal of Molecular Liquids 295, pages 111620.
Crossref
Salaheddine Chabab, Pascal Théveneau, Jérôme Corvisier, Christophe Coquelet, Patrice Paricaud, Céline Houriez & Elise El Ahmar. (2019) Thermodynamic study of the CO2 – H2O – NaCl system: Measurements of CO2 solubility and modeling of phase equilibria using Soreide and Whitson, electrolyte CPA and SIT models. International Journal of Greenhouse Gas Control 91, pages 102825.
Crossref
Jalel M’halla, Sondes Boughammoura & Anis Ghazouani. (2019) Some New Contributions to the Theory of Polyelectrolyte Solutions: Prediction of Polyion Conformation and Interpretation of Some Deviations from Kohlrausch’s Law According to the Superposition Principle and the Dielectric Friction Effect. Journal of Solution Chemistry 48:11-12, pages 1685-1715.
Crossref
Dávid Fertig, Bartłomiej Matejczyk, Mónika Valiskó, Dirk Gillespie & Dezső Boda. (2019) Scaling Behavior of Bipolar Nanopore Rectification with Multivalent Ions. The Journal of Physical Chemistry C 123:47, pages 28985-28996.
Crossref
Fuhan Wang, Xiaofei Xu & Shuangliang Zhao. (2019) Complex Coacervation in Asymmetric Solutions of Polycation and Polyanion. Langmuir 35:47, pages 15267-15274.
Crossref
Silvia Di Lecce, Georgia Lazarou, Siti H. Khalit, Claire S. Adjiman, George Jackson, Amparo Galindo & Lisa McQueen. (2019) Modelling and prediction of the thermophysical properties of aqueous mixtures of choline geranate and geranic acid (CAGE) using SAFT-γ Mie. RSC Advances 9:65, pages 38017-38031.
Crossref
S. Zhou. (2019) Solvent granularity in the differential electrical capacitance of supercapacitor and mechanism analysis. Physica A: Statistical Mechanics and its Applications 533, pages 121905.
Crossref
Andrew R. Crothers, Clayton J. Radke & John M. Prausnitz. (2019) 110th Anniversary : Theory of Activity Coefficients for Lithium Salts in Aqueous and Nonaqueous Solvents and in Solvent Mixtures . Industrial & Engineering Chemistry Research 58:39, pages 18367-18377.
Crossref
Pablo Lodeiro, María Martínez-Cabanas, Roberto Herrero, José L. Barriada, Teresa Vilariño, Pilar Rodríguez-Barro & Manuel E. Sastre de Vicente. (2019) The proton binding properties of biosorbents. Environmental Chemistry Letters 17:3, pages 1281-1298.
Crossref
Minhye Heo, Ghi Ryang Shin & Soon-Chul Kim. (2019) Differential capacitance of uniformly charged hard-sphere ions in planar electric double layers. Journal of Statistical Mechanics: Theory and Experiment 2019:8, pages 083207.
Crossref
S. Zhou. (2019) Effects of interionic non-hard sphere neutral interaction and solvent crowding on differential capacitance curve of electrical double layer. The Journal of Chemical Physics 151:6.
Crossref
Enrique González-Tovar & Marcelo Lozada-Cassou. (2019) Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration. Advances in Colloid and Interface Science 270, pages 54-72.
Crossref
Cheng Lian, Haiping Su, Chunzhong Li, Honglai Liu & Jianzhong Wu. (2019) Non-Negligible Roles of Pore Size Distribution on Electroosmotic Flow in Nanoporous Materials. ACS Nano 13:7, pages 8185-8192.
Crossref
M. Hvozd, T. Patsahan, O. Patsahan & M. Holovko. (2019) Fluid-fluid phase behaviour in the explicit solvent ionic model: Hard spherocylinder solvent molecules. Journal of Molecular Liquids 285, pages 244-251.
Crossref
Ricardo Macías-Salinas. (2019) A Simple G -Excess Model for Concentrated Aqueous Electrolyte Solutions . Journal of Chemical & Engineering Data 64:5, pages 2193-2206.
Crossref
Adelina Voukadinova & Dirk Gillespie. (2019) Energetics of counterion adsorption in the electrical double layer. The Journal of Chemical Physics 150:15.
Crossref
Shiqi Zhou. (2019) Effective electrostatic potential between two oppositely charged cylinder rods in primitive model and extended primitive model electrolytes. Journal of Statistical Mechanics: Theory and Experiment 2019:3, pages 033213.
Crossref
Marc Theiss & Joachim Gross. (2019) Dipolar Hard Spheres: Comprehensive Data from Monte Carlo Simulations. Journal of Chemical & Engineering Data 64:2, pages 827-832.
Crossref
O.V. Patsahan & T.M. Patsahan. (2019) Phase behaviour in ionic solutions: Restricted primitive model of ionic liquid in explicit neutral solvent. Journal of Molecular Liquids 275, pages 443-451.
Crossref
Stanisław Lamperski & Shiqi Zhou. (2019) Structural and electrical properties of an electric double layer formed inside a cylindrical pore investigated by Monte Carlo and classical density functional theory. Microfluidics and Nanofluidics 23:2.
Crossref
Seanea Jang, Ghi Ryang Shin & Soon-Chul Kim. (2019) Electrostatic Adsorption of Uniformly Charged Sphere Ions Confined between Two Charged Plates. Journal of the Korean Physical Society 74:1, pages 30-35.
Crossref

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