Theory of Surface Forces in Multivalent Electrolytes

Misra, Rahul Prasanna; Souza, J. Pedro de; Blankschtein, Daniel; Bazant, Martin Z.

doi:10.1021/acs.langmuir.9b01110

Cited by 67 publications

(86 citation statements)

References 76 publications

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“…However, these assumptions should be carefully scrutinized in other applications such as highly charged surfaces. Bazant et al have recently developed more consistent and general boundary conditions for their fourth-order model by enforcing continuity of the Maxwell stress at a charged interface [ 171 , 172 ].…”

Section: Generalized Debye-hückel Theorymentioning

confidence: 99%

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

Liu

Eisenberg

2020

Entropy

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We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

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Section: Generalized Debye-hückel Theorymentioning

confidence: 99%

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

Liu

Eisenberg

2020

Entropy

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“… 44 , 47 Additionally, particles with a higher charge density would involve stronger ion–particle binding and consequently the multivalent ion-mediated like-charge attraction generally becomes stronger for higher particle charges. 83 , 84 However, until now, the covered range of particle charge densities is rather limited in previous works, thus it is still unclear how the multivalent ion-mediated attraction between like-charged particles depends on the particle charge in a wide range. 85 …”

Section: Introductionmentioning

confidence: 99%

“…Such an enhanced multivalent ion-mediated like-charge attraction by higher particle charges is in accordance with previous works. 52 , 54 , 83 The comparison between a 2:2 salt and a 3:3 salt indicates that trivalent counterions bind more tightly to charged colloidal particles and can cause a stronger effective attraction with a lower PMF minimum and a slightly closer equilibrium separation between like-charged colloidal particles.…”

Section: Introductionmentioning

confidence: 99%

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge

et al. 2021

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Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a “critical” value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the “critical” particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the “critical” particle charge based on the Lindemann melting law.

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“…For this purpose, Poisson–Boltzmann theory is often used for calculating the potential profile in the vicinity of the charged wall [15]. The Poisson–Boltzmann theory is in a very good agreement with the experimental data in case of lower surface charge density, high solvent dielectric permittivity, and electrolytes of lower valency [16,17]. The study of the diffuse layer is often limited to strong monovalent electrolytes such as sodium chloride.…”

Section: Introductionmentioning

confidence: 99%

Mathematical model of electromigration allowing the deviation from electroneutrality

Novotný

Gaš

2020

Electrophoresis

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The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern–Gouy–Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G‐function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.

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Theory of Surface Forces in Multivalent Electrolytes

Cited by 67 publications

References 76 publications

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge

Mathematical model of electromigration allowing the deviation from electroneutrality

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