Electrostatic, double layer repulsion forces

In the case of Brownian diffusion and interception, particle capture is enhanced by London attractive forces and reduced by electrostatic double layer repulsive forces. 

For similar micellas concentrations, the effect of electrolyte will be more severe for the anionic surfactant as it will suppress the electrostatic double-layer repulsive forces acting between the micelles. For nonionic surfactant, the repulsive force between micelles is a steric force rather than an electrostatic force, such that electrolyte has less of an effect. 

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is commonly used to describe interactions of charged surfaces across liquids [8, 9]. The DLVO theory models the interparticle interactions by superposing van der Waals attractions and electrostatic double layer repulsion forces. The direct force measurements have confirmed this theory down to surface separations of few nanometers [10]. 

O. Mondain-Monval, F. Leal-Calderon, J. PhUlip, and J. Bibette Depletion Forces in the Presence of Electrostatic Double-Layer Repulsion. Phys. Rev. lett. 75, 3364 (1995). 

One of the central questions in the stability of foams is why are liquid films between two adjacent bubbles stable, at least for some time In fact, a film of a pure liquid is not stable at all and will rupture immediately. Formally this can be attributed to the van der Waals attraction between the two gas phases across the liquid. As for emulsions, surfactant has to be added to stabilize a liquid film. The surfactant adsorbs to the two surfaces and reduces the surface tension. The main effect, however, is that the surfactant has to cause a repulsive force between the two parallel gas-liquid interfaces. Different interactions can stabilize foam films [570], For example, if we take an ionic surfactant, the electrostatic double-layer repulsion will have a stabilizing effect. 

The process of cell deposition in the presence of repulsive forces may be considered as a two-step sequence. First the cells move, primarily under the action of gravity, to a region very near to the surface. In order to move closer to the surface the particle must experience the energy barrier formed by the electrostatic double-layer repulsions and London attraction. Diffusion of cells over the energy barrier is the second step of the process. If the deposition rate is much smaller than the sedimentation rate the second step... 

It is well-known that free films of water stabilized by surfactants can exist as somewhat thicker primary films, or common black films, and thinner secondary films, or Newton black films. The thickness of the former decreases sharply upon addition of electrolyte, and for this reason its stability was attributed to the balance between the electrostatic double-layer repulsion and the van der Waals attraction. A decrease in its stability leads either to film rupture or to an abrupt thinning to a Newton black film, which consists of two surfactant monolayers separated by a very thin layer ofwater. The thickness of the Newton black film is almost independent of the concentration of electrolyte this suggests that another repulsive force than the double layer is involved in its stability. This repulsion is the result of the structuring of water in the vicinity of the surface. Extensive experimental measurements of the separation distance between neutral lipid bilayers in water as a function of applied pressure1 indicated that the hydration force has an exponential behavior, with a decay length between 1.5 and 3 A, and a preexponential factor that varies in a rather large range. 

In addition to the Laplace capillary pressure, three additional forces can operate at surfactant concentration below the cmc, namely electrostatic double layer repulsion Tj1, van der Waals attractions and steric (short-range) forces... 

Forces between DNA Double Helices. The repulsion and attraction of DNA is the molecular interaction most studied to date. In simple salts, repulsion is again exponential with decay rates of 2.8 3.3 A (II). Unlike forces between polysaccharides, the coefficient of the force depends on the type of cationic counterion, even though electrostatic double layer repulsion is low enough to suggest that the helix is largely neutralized by ion association. 

It has been well established that four types of forces can operate in aqueous film layers at low surfactant concentrations (< CMC) (a) the Laplace capillary pressure, (b) the electrostatic double-layer repulsion, Hei, (c) the van der Waals interactions rivdw and (d) the short-range hydration or structural repulsive forces caused by steric hindrance in oriented and packed layers, n t. Initially, the Deryaguin disjoining pressure, TI, encompasses two of these contributions, as follows ... 

Several types of surface forces determine the interactions across thin liquid films. In addition to the universal van der Waals forces, the adsorbed ionic surfactants enhance the electrostatic (double-layer) repulsion. On the other hand, the adsorbed nonionics give rise to a steric repulsion due to the overlap of hydrophilic polymer brushes. The presence of surfactant micelles in the continuous phase gives rise to oscillatory structural forces, which can stabilize or destabilize the liquid films (and dispersions), depending on whether the micelle volume fraction is higher or lower. These and other surface forces, related to the surfactant properties, were considered in Sec. VI. 

Two types of black films can be distinguished [754, 755] common black films, which are stabilized by electrostatic double-layer repulsion, and Newton black films, which are stabilized by short-range forces. Common black films are 6-30 nm thick. Newton black films basically consist of a bilayer of surfactant. They have a defined thickness of 4—5 nm. For lipids, it is slightly larger [756]. If we consider a Newton black film formed from an oil phase in water, we are left with a lipid bUayer that still contains some oil molecules. Such films are extremely good electric insulators and are used in electrophysiological studies of membrane proteins [757]. 

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]. 

The invention and refinement of the SFA have been among the most significant advances in experimental colloid science and have allowed researchers to identify and quantify most of the fundamental interactions occurring between surfaces in aqueous solutions as well as nonaqueous liquids. Attractive van der Waals and repulsive electrostatic double-layer forces, oscillatory (solvation or structural) forces, repulsive hydration forces, attractive hydrophobic... 

Interfacial Forces. Neighboring bubbles in a foam interact through a variely of forces which depend on the composition and thickness of liquid between them, and on the physical chemistry of their liquid—vapor interfaces. For a foam to be relatively stable, Ihe net interaction must be sufficiently repulsive at short distances to maintain a significant layer of liquid in between neighboring bubbles, Interfacial forces include ihe van der Waals inieracliun. the electrostatic double layer imeruclion. and disjoining pressure. 

Roughly 60 years ago Derjaguin, Landau, Verwey, and Overbeek developed a theory to explain the aggregation of aqueous dispersions quantitatively [66,157,158], This theory is called DLVO theory. In DLVO theory, coagulation of dispersed particles is explained by the interplay between two forces the attractive van der Waals force and the repulsive electrostatic double-layer force. These forces are sometimes referred to as DLVO forces. Van der Waals forces promote coagulation while the double layer-force stabilizes dispersions. Taking into account both components we can approximate the energy per unit area between two infinitely extended solids which are separated by a gap x ... 

For the case of purely attractive forces (such as Lon-don-van der Waals forces) the length Sjr over which they act is a useful characteristic. An attractive force which acts over a distance which is much less than Sc will not contribute substantially to the overall rate. When repulsive forces (such as the electrostatic double-layer forces) are also present, they may effectively prevent particles from arriving at the collector, even when they act only over a very short distance. For this reason the decay length alone cannot characterize the relative importance of the joint effect of attractive and repulsive farces. Useful characteristics of their combined effect may be obtained by considering the total potential energy of interaction between the particle and the collector. 

The combined effect of attraction and repulsion forces has been treated by many investigators in terms borrowed from theories of colloidal stability (Weiss, 1972). These theories treat the adhesion of colloidal particles by taking into account three types of forces (a) electrostatic repulsion force (Hogg, Healy Fuerstenau, 1966) (b) London-Van der Waals molecular attraction force (Hamaker, 1937) (c) gravity force. The electrostatic repulsion force is due to the negative charges that exist on the cell membrane and on the deposition surface because of the development of electrostatic double layers when they are in contact with a solution. The London attraction force is due to the time distribution of the movement of electrons in each molecule and, therefore, it exists between each pair of molecules and consequently between each pair of particles. For example, this force is responsible, among other phenomena, for the condensation of vapors to liquids. 

The interaction between the two plates is repulsive at small distances and becomes attractive at large distances. At small distances, the electrostatic interactions between the two plates dominate and the net force is repulsive. As the distance increases but remains smaller than the diameter of the particles, the electrostatic repulsion between the plates decreases but, because the attractive depletion force remains almost constant, the net force can become attractive. As soon as the distance between the two plates becomes larger than the particle diameter, the electrostatic and depletion contributions become comparable and the net force becomes small. The above considerations are valid when D is sufficiently large for the double layer repulsion at the distance L = D to become... 

Fig. 8. (A) Measured forces between two charged mica surfaces in 10" M KCl, where beyond 30 A (and out to 500 A) the repulsion is well described by conventional electrostatic double-layer force theory. Below 30 A there is an additional hydration repulsion, with oscillations superimposed below 15 A. (B) Forces between two uncharged lecithin bilayers in the fluid state in water. At long range there is an attractive van der Waals force, and at short range (i.e., below 25 A) there is a monotonically repulsive steric hydration force. (C) Forces between two hydrophobized mica surfaces in water where the hydrophobic interaction is much stronger than could be expected from van der Waals forces alone. From Israelachvili and Marra (1986).

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