Repulsive barrier

The charge on a droplet surface produces a repulsive barrier to coalescence into the London-van der Waals primary attractive minimum (see Section VI-4). If the droplet size is appropriate, a secondary minimum exists outside the repulsive barrier as illustrated by DLVO calculations shown in Fig. XIV-6 (see also Refs. 36-38). Here the influence of pH on the repulsive barrier between n-hexadecane drops is shown in Fig. XIV-6a, while the secondary minimum is enlarged in Fig. XIV-6b [39]. The inset to the figures contains t,. the coalescence time. Emulsion particles may flocculate into the secondary minimum without further coalescence. 

Although reduction or elimination of the repulsion barrier is a necessary prerequisite of successful flocculation, the actual flocculation in such a destabilized suspension is effected by particle—particle collisions. Depending on the mechanism that induces the collisions, the flocculation process may be either perikinetic or orthokinetic. 

However, as follows from the results presented in Fig. 1(b), the behavior of the PMF for the case of adsorbed dispersion in the matrix at Pm< m — 0.386 contains interesting features in addition to those shown in Fig. 1(a). We observe that the PMF is modulated by the presence of solvent species and in addition is modulated by the presence of matrix particles. The structural repulsive barrier appears, due to matrix particles. An additional weak attractive minimum exists at separations corresponding to matrix-separated colloids. It is interesting that the effects of solvent modulation of the PMF in the adsorbed dispersion are seen for matrix separated colloids. The matrix particles are larger than colloids adsorption of solvent species on the surface of a matrix particle is stronger than on the surface of a colloid. Therefore, the solvent modulating effects of the PMF result from colloids separated by a matrix particle covered by a single layer of solvent species. 

The major impediment to fusion reactions is that the reacting nuclei must have very high kinetic energies to overcome the electrical repulsion between positive particles. The fusion of two hydrogen nuclei has the lowest possible repulsion barrier because it involves two Z — I nuclei. Even so, this reaction requires kinetic energies... 

C22-0042. Is the repulsive barrier for fusion of H and Ll larger, smaller, or about the same as that for 4... 

With the addition of a pseudopotential interaction between electrons and metal ions, the density-functional approach has been used82 to calculate the effect of the solvent of the electrolyte phase on the potential difference across the surface of a liquid metal. The solvent is modeled as a repulsive barrier or as a region of dielectric constant greater than unity or both. Assuming no specific adsorption, the metal is supposed to be in contact with a monolayer of water, modeled as a region of 3-A thickness (diameter of a water molecule) in which the dielectric constant is 6 (high-frequency value, appropriate for nonorientable dipoles). Beyond this monolayer, the dielectric constant is assumed to take on the bulk liquid value of 78, although the calculations showed that the dielectric constant outside of the monolayer had only a small effect on the electronic profile. 

The prominent feature of the triplet curve in the long-range region R > 1.8 A is a double-humped repulsive barrier. This is evidently associated with successive... 

If the electrostatic barrier is removed either by specific ion adsorption or by addition of electrolyte, the rate of coagulation (often followed by measuring changes in turbidity) can be described fairly well from simple diffusion-controlled kinetics and the assumption that all collisions lead to adhesion and particle growth. Overbeek (1952) has derived a simple equation to relate the rate of coagulation to the magnitude of the repulsive barrier. The equation is written in terms of the stability ratio ... 

It is not necessary to restrict ourselves to bonds that are described by Morse potentials. We can regard eqn. (56) as a quadratic equation in x, use any form of the potential energy V(R) with the usual shape (i.e., a minimum, a repulsive barrier at short distances, and a monotonical increase at large distances), and determine x to get another definition of the bond order. This is called the unity bond index quadratic exponential potential (UBI QEP) method by Shustor-ovich and Sellers. ... 

Let us now consider coagulation of particles in the absence of any repulsive barrier. In addition, we assume that, although there are no interparticle forces that contribute to the transport of particles toward each other, there is sufficient attraction between the particles on contact for them to form a permanent bond. As early as 1917, Smoluchowski formulated the equations for the collision rate for particles transported by diffusion alone (Smoluchowski 1917), and we develop the same idea here. 

When the repulsion barrier is large (i.e., < max is about 10 kBTor larger), one can evaluate the integral in the expression for Wusing what are known as asymptotic techniques and obtain the following expression (Derjaguin 1989, p. 162) ... 

A further consequence of intermediate-range interactions adding up are very high almost isotropic repulsive barriers around compact clusters. This has consequences for the density scaling [32] and favors small islands with more narrow distributions of sizes and spacings than the ones obtained without interactions [29]. We finally note that atomic superlattices with smaller lattice constant may be stabilized by dipolar interactions of relatively short range. The most prominent examples for such interactions are alkali metals on metal surfaces. A phase transition from a dilute liquid into a well-ordered solid has been reported for Cs/Ag/Si(lll)-( /3 x %/3) [33]. 

Recently, this problem was treated by a rigorous quantum chemistry calculation by Bakalov et al. [28], First, the authors calculated ab initio the interatomic interaction V(R,r, ) between an atomcule pHe- and a He atom based on the Born-Oppenheimer approximation. Since the rotational frequency of the p (of order of 1015 s-1) is much higher than the collision frequency (of order of 1012 s-1), the angular dependence is smeared out, and typically, the Van der Waals minimum occurs around R 5.5 a.u., and the repulsive barrier starts around R 5 a.u. The potential V(R) depends on (n,l), and thus, a small difference AV(R) occurs between an initial state and a final state. It is this difference that causes pressure shifts and broadening in the resonance line. 

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