Electrical Double Layer Interaction between Dissimilar Spherical Colloidal Particles and between a Sphere and a Plate:  Nonlinear Poisson−Boltzmann Theory

Carnie, Steven L.; Chan, Derek Y. C.; Gunning, James

doi:10.1021/la950384k

Cited by 106 publications

(100 citation statements)

References 27 publications

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“…For more detailed calculations which also are valid at higher potentials and which explicitly take into account the geometry see Refs. [405][406][407][408][409].…”

Section: Electrostatic Double-layer Force and Dlvo Theorymentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

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“…For more detailed calculations which also are valid at higher potentials and which explicitly take into account the geometry see Refs. [405][406][407][408][409].…”

Section: Electrostatic Double-layer Force and Dlvo Theorymentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

View full text Add to dashboard Cite

“…In the framework of mean-field dilute-solution theory, the interaction force may be calculated by solving a nonlinear Poisson-Boltzmann (PB) equation for the electric potential, followed by integration of the electric stress and hydrostatic (osmotic) pressure over the particle surface [13]. This problem is nonlinear, and exhibits multiple scales in the common case where the Debye length is small compared to system dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…Our methodology builds on what is known as the superposition approximation, saying that for thin double layers the potential is provided by adding single-particle potential distributions [13]. We further follow Refs.…”

Section: Introductionmentioning

confidence: 99%

Ray-theory approach to electrical-double-layer interactions

Schnitzer

2015

Phys. Rev. E

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A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both inter-particle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation.Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centres of all circles maximally inscribed between the two particles, the bulk stress -associated with the ray contributions interacting nonlinearly -decays exponentially with distance from the centre of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary inter-particle separations. Our theory can be generalized to arbitrary three dimensional geometries, non-ideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

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“…36,38,41,42 We remind that for heterogeneous objects is a surface integral of Π · n s with respect to surface normal n s . [43][44][45] Therefore, to find x 0 for our system, which now could depend on y, we propose to…”

Section: Disjoining Pressurementioning

confidence: 99%

Electrostatic interaction of heterogeneously charged surfaces with semipermeable membranes

2013

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In this paper we study the electrostatic interaction of a heterogeneously charged wall with a neutral semipermeable membrane. The wall consists of periodic stripes, where the charge density varies in one direction. The membrane is in a contact with a bulk reservoir of an electrolyte solution and separated from the wall by a thin film of salt-free liquid. One type of ions (small counterions) permeates into the gap and gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure due to an overlap of counterion clouds in the gap. To quantify it we use two complementary approaches. First, we propose a mean-field theory based on a linearized PoissonBoltzmann equation and Fourier analysis. These calculations allow us to estimate the effect of a heterogeneous charge pattern at the wall on the induced heterogeneous membrane potential, and the value of the disjoining pressure as a function of the gap. Second, we perform Langevin dynamics simulations of the same system with explicit ions. The results of the two approaches are in good agreement with each other at low surface charge and small gap, but differ due to nonlinearity at the higher charge. These results demonstrate that a heterogeneity of the wall charge can lead to a huge reduction in the electrostatic repulsion, which could dramatically facilitate a self-assembly in complex synthetic and biological systems.

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Electrical Double Layer Interaction between Dissimilar Spherical Colloidal Particles and between a Sphere and a Plate: Nonlinear Poisson−Boltzmann Theory

Cited by 106 publications

References 27 publications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Ray-theory approach to electrical-double-layer interactions

Electrostatic interaction of heterogeneously charged surfaces with semipermeable membranes

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