Double-layer interaction, electrostatic force

For hydrosols in gremular filtration, the external force consists of gravitational force, particle-collector surface interaction forces, such as the unretarded London attraction force (defined in (3.1.16)) and electrokinetic force (3.1.17) in the double layer, and electrostatic forces, if any, such as coulombic attraction/repulsion forces (3.1.15) (usually important in aerosol-removal processes unless the collector particles are deliberately charged). In... 

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]. 

Figures 1 and 2 summarize the results computed for the double-layer interaction between two parallel plates. Each figure presents the charge density and electrostatic potential of both interacting surfaces, together with the double-layer force per unit area (p > 0 denotes repulsion), as a function of the dimensionless separation...

As aheady noted, in a homogeneous medium a surface dipole density does not generate an electric field above the surface, and consequently such a field is ignored in the traditional theory of the double layer, which takes into account only the surface charges. In the polarization model, both the surface charge and the surface dipole densities generate electrostatic interactions (commonly denoted as double layer and hydration forces ). 

When two charged colloidal particles approach each other, their electrical double layers overlap so that the concentration of counterions in the region between the particles increases, resulting in electrostatic forces between them (Fig. 8.2). There are two methods for calculating the potential energy of the double-layer interaction between two charged colloidal particles [1,2] In the first method, one directly calculates the interaction force P from the excess osmotic pressure tensor All and... 

With this in mind, the impossibility of forming a double layer by electric forces only is obvious. Any ion that may attach to a particle will create a potential that keeps out all other ions of the same sign. Accumulation of a number of identical charges on a surface can take place only if the adsorbing ions experience a non-electric affinity for the surface so that they can move against the adverse potential. The extent to which this occurs depends on the balance between the attractive non-electrostatlc and the repulsive electric forces. In summary the reason for the formation of relaxed double layers is the nonelectric afflnlty of charge-determining ions for a surface the extent to which the double layer develops is determined by the non-electrostatlc electrostatic interaction balance. 

When the electrostatic stabilization of the emulsion is considered, the electrolytes (monovalent and divalent) added to the mixture are the major destabilizing species. The zeta potential of the emulsion particles is a function of the concentration and type of electrolytes present. Two types of emulsion particle-electrolyte (ions) interaction are proposed non-specific and specific adsorption.f H non-specific adsorption the ions are bound to the emulsion particle only by electrical double-layer interactions with the charged surface. As the electrolyte concentration is increased, the zeta potential asymptotes to zero. As the electrostatic repulsion decreases, a point can be found where the attractive van der Waals force is equal to the repulsive electrostatic force and flocculation of the emulsion occurs (Fig. 9A). This point is called the critical flocculation concentration (CFC). 

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. 

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. 

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). 

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...

This interlayer interaction is known as the Helfrich undulation interaction. In a beautiful series of X-ray diffraction experiments, Safinya O and his co-workers have demonstrated that the undulation force is dominant where any electrostatic interactions are screened out, but are ineffective in the presence of unscreened double layer interactions. 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

For solid surfaces interacting in air, the adhesion forces mainly result from van der Waals interaction and capillary force, but the effects of electrostatic forces due to the formation of an electrical double-layer have to be included for analyzing adhesion in solutions. Besides, adhesion has to be studied as a dynamic process in which the approach and separation of two surfaces are always accompanied by unstable motions, jump in and out, attributing to the instability of sliding system. 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

The surface forces apparatus (SEA) can measure the interaction forces between two surfaces through a liquid [10,11]. The SEA consists of two curved, molecularly smooth mica surfaces made from sheets with a thickness of a few micrometers. These sheets are glued to quartz cylindrical lenses ( 10-mm radius of curvature) and mounted with then-axes perpendicular to each other. The distance is measured by a Fabry-Perot optical technique using multiple beam interference fringes. The distance resolution is 1-2 A and the force sensitivity is about 10 nN. With the SEA many fundamental interactions between surfaces in aqueous solutions and nonaqueous liquids have been identified and quantified. These include the van der Waals and electrostatic double-layer forces, oscillatory forces, repulsive hydration forces, attractive hydrophobic forces, steric interactions involving polymeric systems, and capillary and adhesion forces. Although cleaved mica is the most commonly used substrate material in the SEA, it can also be coated with thin films of materials with different chemical and physical properties [12]. 

---