Electrostatic double-layer interaction

Electrostatic double layer interaction, 12 5 Electrostatic effects, in organic separations, 21 660... 

The modulation frequency is typically in the range from 100 Hz to 3 kHz, and thus much lower than the resonance frequencies of the cantilever and the scanner. This enables better control of the forces exerted on the sample. The z-mod-ulation amplitude can be varied between 10 nm and 1 pm to ensure that that the tip is retracted from the surface. Shear forces are reduced permitting investigation of soft samples because of the small duration of the tip-surface contact, between 10 3 and 10 4 s. Pulse force mode SFM has been used to map adhesion of heterogeneous polymers in dependence of temperature and molecular weight as well as map electrostatic double-layer interactions [158-160]. 

Figure 7.1 Schematic diagram of interaction potential versus separation distance D for van der Waals and electrostatic double-layer interactions. The lower inset shows the collapse of the repulsive barrier as the electrolyte concentration is increased or the surface potential is decreased. At a separation distance of zero, there is an infinitely steep hard-core repulsive (or positive) interaction. (From Israelachvili 1991, reprinted with permission from Academic Press.)...

It is customarily assumed that the overall particle-particle interaction can be quantified by a net surface force, which is the sum of a number of independent forces. The most often considered force components are those due to the electrodynamic or van der Waals interactions, the electrostatic double-layer interaction, and other non-DLVO interactions. The first two interactions form the basis of the celebrated Derjaguin-Landau-Verwey-Overbeek (DLVO) theory on colloid stability and coagulation. The non-DLVO forces are usually determined by subtracting the DLVO forces from the experimental data. Therefore, precise prediction of DLVO forces is also critical to the determination of the non-DLVO forces. The surface force apparatus and atomic force microscopy (AFM) have been used to successfully quantify these interaction forces and have revealed important information about the surface force components. This chapter focuses on improved predictions for DLVO forces between colloid and nano-sized particles. The force data obtained with AFM tips are used to illustrate limits of the renowned Derjaguin approximation when applied to surfaces with nano-sized radii of curvature. 

Since particles in a polar solvent, like water, become electrically charged, electrostatic double-layer interaction (EDL) is important in determining particle-particle interactions. The Poisson-Boltzmann (PB) equation is used to describe the double-layer interaction. For z z valence salt solutions, the PB equation yields... 

First we consider the electrostatic (double layer) interaction between two identical charged plane parallel surfaces across a solution of symmetric Z Z electrolyte. The charge of a counterion (i.e., ion with charge opposite to that of the surface) is -Ze, whereas the charge of a coion is +Ze (Z = +1, +2,. ..) with e the elementary charge. If the separation between the two planes is very large, the number concentration of both counterions and coions would be equal to its bulk value, n, in the middle of the film. However, at finite separation, h, between the surfaces the two EDL overlap and the counterion and coion concentrations in the middle of the film, io and 2o> longer equal. Because the solution inside the film is supposed to be in electrochemical (Donnan) equilibrium with the bulk electrolyte solution of concentration q, we can write 20 0 or, alternatively,... 

Adsorption of enteric viruses on mineral surfaces in soil and aquatic environments is well recognized as an important mechanism controlling virus dissemination in natural systems. The adsorption of poliovirus type 1, strain LSc2ab, on oxide surfaces was studied from the standpoint of equilibrium thermodynamics. Mass-action free energies are found to agree with potentials evaluated from the DLVO-Lifshitz theory of colloid stability, the sum of electrodynamic van der Waals potentials and electrostatic double-layer interactions. The effects of pH and ionic strength as well as electrokinetic and dielectric properties of system components are developed from the model in the context of virus adsorption in extra-host systems. 

Poliovirus adsorption to many oxide surfaces is controlled principally by the combination of electrodynamic van der Waals interactions and electrostatic double-layer interactions, as demonstrated by the excellent correspondence of the DLVO-Lifshitz theory with experimentally determined adsorption free energies. 

Particle-particle and particle-membrane interactions can be described with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory which combines van der Waals and electrostatic double layer interactions. While these theories generally apply for smooth surfaces, Bhattacharjee et al. (1998) have... 

An electrostatic double-layer interaction arises when two charged droplets are so close together that their diffuse layers overlap. The electrostatic double-layer interaction, for two identical charged drops with a small electrostatic surface potential and a radius large compared to their separation is approximately given by ... 

Recently, Bowen et al. [27,28] and Hilal and Bowen [29] and Hilal et al. [30] applied the APM technique to study adhesion at the membrane sinface. The measurement of interaction forces between a colloid probe and a membrane smface allows quantification of the electrostatic double layer interactions when the colloid probe approaches the membrane surface, and of the adhesion force (van der Waals interaction force) when the colloid probe is withdrawn after it has been in contact with the membrane surface. Quantification of the interaction forces involved in fouling and chemical cleaning of fouled membranes is very important in order to imderstand the mechanism of fouling and to develop a favorable membrane for water treatment. 

Eirst, we consider the electrostatic (double layer) interaction between two identical charged plane parallel surfaces across solution of symmetrical Z Z electrolyte. The charge of a counterion (i.e., ion with charge opposite to that of the surface) is —Ze, whereas the charge of a coion is +Ze (Z = 1, 2,. ..) with e being the elementary charge. If the separation between the two... 

Ederth, T., Claesson, P. and Liedberg, B., Self-assembled monolayers of alkanethiolates on thin gold films as substrates for surface force measurements. Long-range hydrophobic interactions and electrostatic double-layer interactions, Langmuir, 14, 4782-4789 (1998). 

The electrostatic (double-layer) interactions across an aqueous film are due to the overlap of the double electric layers formed at two charged interfaces (e.g., interfaces covered by ionic surfactants). Moreover, electrostatic repulsion is observed even between interfaces covered by adsorption monolayers of nonionic surfactants [22,307-310]. 

Electrostatic double-layer interactions (Figure 10.18) arise when two charged surfaces are close enough for their diffuse layers to overlap. Thus, when two charged particles approach each other, their double layers begin to overlap, and they repel each other. 

Figure 10.18 Electrostatic double-layer interactions and the simplest mathematical expression for two equalsized spheres under simplifying conditions (Debye-Huckel approximation). The repulsive forces decrease exponentially with distance and added electrolyte...

H. Ohshima and T. Kondo,/. Colloid Interface Sci., 155,499 (1993). Electrostatic Double-Layer Interaction between Two Charged Ion-Penetrable Spheres An Exactly Solvable Model. 

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