Layer interaction

More sophisticated approaches to describe double layer interactions have been developed more recently. Using cell models, the full Poisson-Boltzmann equation can be solved for ordered stmctures. The approach by Alexander et al shows how the effective colloidal particle charge saturates when the bare particle charge is increased [4o]. Using integral equation methods, the behaviour of the primitive model has been studied, in which all the interactions between the colloidal macro-ions and the small ions are addressed (see, for instance, [44, 45]). 

The molecules in an adsorbed layer interact not only with the solid, hut also with their neighbours within the layer. The effect is negligible when the fractional coverage 0 of the surface is small and the adsorbed molecules are therefore far apart, but it becomes increasingly significant as the monolayer becomes more and more crowded. A densely occupied monolayer will act in some degree as an extension of the solid, and will be able to attract further molecules from the gas phase in the manner already described, though more... 

The multi-shell fullerenes constitute the transition from fullerenes to macroscopic graphite. They present both the closed graphitic surface of fullerenes and the stacked layers interacting by van der Waals forces, as in graphite. 

The situations would be totally different when the two surfaces are put in electrolyte solutions. This is because of formation of the electrical double layers due to the existence of ions in the gap between solid surfaces. The electrical double layers interact with each other, which gives rise to a repulsive pressure between the two planar surfaces as... 

Comparing the two optical transduction techniques (absorption or SPR) used in this work, we can conclude that SPR technique appears to be more suitable for gas sensing even if it presents some limitation regarding the suitable film thickness for SPR excitation. Moreover, the response and recovery times during the anal5fle/sensing layer interaction appears shortest in the case of optical absorption measurements. Further investigations are in... 

A bilayer forms when two lipid layers come together the hydrophobic groups in the two single layers interact and exclude water. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

At negative potentials in alkaline solutions, adsorbed NA retains K+ ions, as demonstrated by Auger spectroscopy, Figure 5-B. This retention of K+ ions is due to interaction of K+ with the pendant carboxylate moiety and greatly exceeds the amounts expected simply from diffuse double-layer interactions. Potential-dependence of K+ retention is essentially absent for compounds incapable of potential-dependent carboxylate pendancy (pyridine, picolinic acid, isonicotinic acid and 2,6-pyridine dicarboxylic acid). 

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

The same graphical method can also be used to illustrate the nature of the double layer interaction free energy and to bring out a simple physical result which can be used to check numerical algorithms commonly used to calculate the interaction free energy. 

The double layer interaction energy is given In terms of the eluant dielectric constant e by (37). 

Even though this equation is difficult to solve, many approximate methods have been used. Equation (A.3) is, however, interesting for what it tells us about the double-layer interaction. It can be rearranged in the form... 

Other modifications to the theory of Anderson and Quinn [142] have been reviewed by Deen [146]. Malone and Quinn [147] modified the above theory to include the effect of electrostatic interactions on transport in microporous membranes. Smith and Deen [148] have also looked at these electrostatic or double layer interactions. More recently, Kim and Anderson [149] investigated the hindrance of solute transport in polymer lined micropores. Also, as briefly mentioned above, an excellent review of the theories presented for transport in microporous membranes has been given by Deen [146]. 

Not only do double layers interact with double layers, the metal of one sphere also interacts with the metal of the second sphere. There is what is called the van der Waals attraction, which is essentially a dispersion interaction that depends on r-6, and the electron overlap repulsion, which varies as r-12. These interactions between the bulk... 

The total interaction between the two metal spheres can therefore be classified into two parts (1) the surface, or double-layer, interaction determined by the Gouy-Chapman potential t f0e"Krand (2) the volume, or bulk, interaction —Ar-6 + Br 12. The interaction between double layers ranges from indifference at large distances to increasing repulsion as the particles approach. The bulk interaction leads to an attraction unless the spheres get too close, when there is a sharp repulsion (Fig. 6.131). The total interaction energy depends on the interplay of the surface (double layer) and volume (bulk) effects and may be represented thus... 

Sols and Gels. The essence of the behavior characteristic of the colloidal state is that double-layer interactions are as significant as bulk interactions. In other words, surface interactions are on a par with volume interactions. This condition can therefore be realized in all systems where the surface-to-volume ratios are high, i.e., at submicroscopic dimensions. 

The term tertiary electroviscous effect is applied to the changes in the conformation of poly electrolytes that are caused by //t/ramolecular double-layer interactions. It is customary to extend this definition to include all effects in which the geometry of the system is altered as a result of double-layer interactions. 

The Electrical Double Layer and Double-Layer Interactions... 

Electrostatic and electrical double-layer interactions also create new opportunities in science and technology. We have already seen an example of this in a vignette in Chapter 1 on electrophoretic imaging devices, and another, on electrophotography, is described in the next... 

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