Interaction between Charged Surfaces on the Poisson−Boltzmann Level:  The Constant Regulation Approximation

Pericet-Cámara, Ramón; Papastavrou, Georg; Behrens, Sven H.; Borkovec, Michal

doi:10.1021/jp0473063

Cited by 97 publications

(183 citation statements)

References 40 publications

(142 reference statements)

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“…This solution is compatible with either of the boundary conditions (8); ζ is asymptotic to the surface potential ψ, and related to the surface charge σ by the Gouy-Chapman relation σ = 2 sinh(ζ/2). It is well known that this solution is also compatible with more general "charge regulation"-type conditions [17,41].…”

Section: Diffuse-charge Boundary Layersupporting

confidence: 52%

A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations

Schnitzer

Morozov

2015

The Journal of Chemical Physics

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Derjaguin's approximation provides the electrical-double-layer interaction force between two arbitrary convex surfaces as the product of the corresponding one-dimensional parallel-plate interaction potential and an effective radius R (function of the radii of curvature and relative orientation of the two surfaces at minimum separation). The approximation holds when both the Debye length 1/κ and minimum separation h are small compared to R. We show here that a simple transformation,yields an approximation uniformly valid for arbitrary separations h; here K i is the Gaussian curvature of particle i at minimum separation, and [ · ] is an operator which adds h/2 to all radii of curvature present in the expression on which it acts. We derive this result in two steps. First, we extend the two-dimensional ray-theory analysis of Schnitzer [Physical Review E, 91 022307 2015], valid for κh, κR 1, to three dimensions. Using this approach we obtain a general closed form expression for the force by matching nonlinear diffuse-charge boundary layers with a WKBJ description of the bulk potential, and subsequent integration via Laplace's method of the traction over the medial surface generated by all spheres maximally inscribed between the two surfaces.Second, we exploit the existence of an overlap domain, 1 κh κR, where both the ray-theory and the Derjaguin approximations hold, to systematically form the generalized mapping. The validity of the result is demonstrated by comparison with numerical computations.

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Section: Diffuse-charge Boundary Layersupporting

confidence: 52%

A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations

Schnitzer

Morozov

2015

The Journal of Chemical Physics

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“…Besides the classical boundary conditions of constant charge (CC) and constant potential (CP), we further consider the constant regulation approximation (CR). 38 For larger separations, the different boundary conditions yield the same force profile, and the diffuse layer potential and decay length can be estimated unambiguously. The fitted decay length of 23 nm coincides reasonably well with the expected Debye length of 27 nm, which was calculated from the Debye and Hu¨ckel theory with an ionic strength of 0.13 mM.…”

Section: Interaction Forces Between Bare Silica Particlesmentioning

confidence: 93%

Probing the validity of the Derjaguin approximation for heterogeneous colloidal particles

Rentsch

Pericet-Cámara

Papastavrou

et al. 2006

Phys. Chem. Chem. Phys.

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The Derjaguin approximation states that the interaction force between two curved surfaces is proportional to their effective radius, whereby the inverse effective radius is the arithmetic mean of the inverse curvature radii of the surfaces involved. The present study investigates the validity of this approximation with an atomic force microscope (AFM) by measuring interaction forces between colloidal particles of different sizes, but of identical composition. Forces were measured between silica particles of 2.0, 4.8 and 6.8 mm in diameter in KCl electrolyte solution with and without adsorbed poly(amido amine) (PAMAM) dendrimers. The Derjaguin approximation could be confirmed at all distances investigated, including those comparable with the characteristic length scales of the surface roughness or the surface charge heterogeneities. For the conditions investigated, the Derjaguin approximation turns out to be surprisingly robust.

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“…The force versus distance profiles were fitted to the full numerical solution of the Poisson-Boltzmann equation for two symmetric plates for distances above κ −1 /2 for ionic strengths <10 mM and κ −1 for 10 mM [37]. When the parameters entering the constant regulation (CR) model are determined in this fashion, one can accurately predict the force at smaller distances down to a few nanometers.…”

Section: Force Data Analysismentioning

confidence: 99%

Interaction forces and molecular adhesion between pre-adsorbed poly(ethylene imine) layers

Pericet-Cámara

Papastavrou

Behrens

et al. 2006

Journal of Colloid and Interface Science

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Interaction forces between pre-adsorbed layers of branched poly(ethylene imine) (PEI) of different molecular mass were studied with the colloidal probe technique, which is based on atomic force microscopy (AFM). During approach, the long-ranged forces between the surfaces are repulsive due to overlap of diffuse layers down to distances of a few nanometers, whereby regulation of the surface charge is observed. The ionic strength dependence of the observed diffuse layer potentials can be rationalized with a surface charge of 2.3 mC/m 2 . The forces remain repulsive down to contact, likely due to electro-steric interactions between the PEI layers. These electro-steric forces have a range of a few nanometers and appear to be superposed to the force originating from the overlap of diffuse layers. During retraction of the surfaces, erratic attractive forces are observed due to molecular adhesion events (i.e., bridging adhesion). The frequency of the molecular adhesion events increases with increasing the ionic strength. The force response of the PEI segments is dominated by rubber-like extension profiles. Strong adhesion forces are observed for low molecular mass PEI at short distances directly after separation, while for high molecular mass weaker adhesion forces at larger distances are more common. The work of adhesion was estimated by integrating the retraction force profiles, and it was found to increase with the ionic strength.

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Interaction between Charged Surfaces on the Poisson−Boltzmann Level: The Constant Regulation Approximation

Cited by 97 publications

References 40 publications

A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations

A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations

Probing the validity of the Derjaguin approximation for heterogeneous colloidal particles

Interaction forces and molecular adhesion between pre-adsorbed poly(ethylene imine) layers

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