Repulsive double-layer force

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] ... 

Measurements of the rate of deposition of particles, suspended in a moving phase, onto a surface also change dramatically with ionic strength (Marshall and Kitchener, 1966 Hull and Kitchener, 1969 Fitzpatrick and Spiel-man, 1973 Clint et al., 1973). This indicates that repulsive double-layer forces are also of importance to the transport rates of particulate solutes. When the interactions act over distances that are small compared to the diffusion boundary-layer thickness, the rate of transport can be computed (Ruckenstein and Prieve, 1973 Spiel-man and Friedlander, 1974) by lumping the interactions into a boundary condition on the usual convective-diffusion equation. This takes die form of an irreversible, first-order reaction on tlie surface. A similar analysis has also been performed for the case of unsteady deposition from stagnant suspensions (Ruckenstein and Prieve, 1975). 

The forces experienced after adding 20 ppm of chito-san-E045 oligomers are quite different. Firstly, the repulsive double-layer force is significantly weaker, which is due to adsorption of cationic groups on the negatively charged surface. Secondly, at distances below lOnm, the... 

What the majority of these systems rely on is the stability of the colloidal dispersions involved. This in turn requires the existence of a repulsive force between the charged entities i.e., a repulsive double layer force. 

The mechanism of Ca2+ binding is not clear yet. However, increase in repulsive double layer forces between neutral diacylphosphatidylcholine bilayer in aqueous media in the presence of divalent ions has been identified by other methods as well [293-296]. These systems differ from the foam- film model by virtue of their interface ordered lipid phase/water in place of the air/water interface of foam films. Nevertheless, the CaCb concentration where the transition from NBF to silver films is observed in experiments with foam films is very close to the concentrations where increase in the distance between the bilayers was found [293,294,296]. Results with microscopic films are also in good agreement with the established increase in the free energy of formation of macroscopic films stabilised with lysolecithin in the presence of CaCl2 [287]. 

The stability of the concentrated emulsions has a kinetic origin. Repulsive double layer forces together with hydration forces are responsible for stability when the surfactant which is adsorbed upon the surface of the thin films is ionic steric repulsion as well as hydration forces are involved in stability when the adsorbed surfactant is non-ionic. 

Here by contrast, it is the overlap of the inhomogeneous profiles of electrolyte concentrations induced by the charged surface of the particle that gives rise to the osmotic (double-layer) force (titeme (ii)). When the repulsive double-layer forces win out, the suspension is stable. On addition of sufficient salt, the range of these forces decreases, the attractive forces take over, and the system of particles flocculates. 

Note first that in this older picture, for both the attractive (van der Waals) forces and for the repulsive double-layer forces, the water separating two surfaces is treated as a continuum (theme (i) again). Extensions of the theory within that restricted assumption are these van der Waals forces were presumed to be due solely to electronic correlations in the ultra-violet frequency range (dispersion forces). The later theory of Lifshitz [3-10] includes all frequencies, microwave, infra-red, ultra and far ultra-violet correlations accessible through dielectric data for the interacting materials. All many-body effects are included, as is the contribution of temperature-dependent forces (cooperative permanent dipole-dipole interactions) which are important or dominant in oil-water and biological systems. Further, the inclusion of so-called retardation effects, shows that different frequency responses lock in at different distances, already a clue to the specificity of interactions. The effects of different geometries of the particles, or multiple layered structures can all be taken care of in the complete theory [3-10]. 

Equation (5.174) is generally used for particles brought into close proximity by Brownian motion and neglecting any type of short-range fluid-dynamic interaction. In fact, the only interactions considered are those related to attractive Van der Waal forces and repulsive double-layer forces. Huid-dynamic effects are accounted for by modifying Eq. (5.174) as follows ... 

The forces measured between the AFM tip and the PCMA coated mica surface across a 1 cmc (8.3 X 10 3 M) SDS solution are shown in Figure 12. At repulsive double-layer force dominates the long-range interaction, whereas two pronounced steps with a periodicity of 40 A are observed at small separations. We can thus conclude that the adsorbed layer is heterogeneous both parallel and perpendicular to the surface. Two other surface force techniques, the MASIF and the SFA, were used to explore this further. 

At the SDS concentration of 0.1 cmc it was noted that the forces measured on the first approach were significantly different from those measured on subsequent approaches (Figure 15). The repulsive double-layer force is stronger, and oscillations are now present in the force curve. This demonstrates that the act of separating the surfaces from contact changes the structure of the adsorbed layer. It seems likely that some polyelectrolyte chains will be stretched out from the surface during the separation process, and that these chains will interact more favorably with the surfactants than the part of the polyelectrolyte that is in close contact with the surface. Hence, surfactants associate readily with the stretched chains, and the amount of surfactants associated with the polyelectrolyte layer increases, which results in an increased double-layer force. The surfactants that associate with the extended chains also counteract readsorption of the chains to the surface. 

X 10 3 M) results in a strong increase in the repulsive double-layer force but no change in the final layer thickness see Figure 28. 

The DLVO model (named after its principal creators, Deqaguin, Landau, Verwey and Overbeek) is the most widely used to describe inter-particle surface force potential (1,2). It assumes that the total inter-particle potential is the sum of an attractive van der Waals force and a repulsive double-layer force. The repulsive force due to the double-layer coulombic interaction between equal spheres separated by a distance D generates a positive potential energy Vr. If the radius r of the spheres is large compared to the double-layer thickness 1/k (Kr l, with K the Debye-Hiickel parameter), Fr is described approximately by ... 

Addition of SDS to a concentration of 0.01 or 0.02 cmc (cmc = 8.3 X 10 M) does not result in any change in the measured long-range interaction (Fig. 2) or pull-off force. However, as the SDS concentration is increased further to 0.1 cmc a long-range repulsive double-layer force appears, showing that SDS is incorporated in the adsorbed layer. The repulsive force is overcome by an attraction at a separation of 110 A. This attraction pulls the surface inwards to a separation of 40 A. A further increase in the compres-sional force hardly affects the surface separation, indicating a dense layer structure. Clearly, the layers on the... 

An increase in surfactant concentration results in an increased incorporation of SDS in the adsorbed layer and at an SDS concentration of 0.2 cmc pronounced oscillations appear in the force curve (Fig. 3). It is possible to identify three oscillations. The innermost one is located at a separation between 40 and 50 A, the next one in the distance interval 70-90 A, and the outermost one at a separation of 120-130 A. The oscillations thus have a periodicity of about 40 A, and it is observed that both the repulsive and the attractive branch increase in magnitude as the surfaces are moved from an outer to an inner oscillation. The reason for the presence of these oscillations are discussed below. At separations larger than 130 A a repulsive double-layer force dominates the interaction. 

A further increase in surfactant concentration to 2 cmc does not affect the qualitative behavior of the interaction (Fig. 4). At large separations a repulsive double-layer force dominates the interaction, and at separations of about 120, 80 and 40 A are three clear oscillations observed. Hence, the periodicity of the oscillations remains unchanged when the SDS concentration is increased. One or two less steep and less-pronounced oscillations in the force profile can also be distinguished at larger separations. 

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