Potential energy attraction-interaction-repulsion

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

When the adsorbed molecules are compressed against a solid surface, the nuclear and electronic repulsions, and the increasing electronic kinetic energy, start to overcome the attractive forces, and, therefore, the repulsion forces sharply augment in a very complicated form [43,44], This complication is avoided by proposing approximate repulsion potentials. In this sense, the terms ( )D + ( for the potential energy of interaction of a nonpolar molecule with a surface could be represented by the Lennard-Jones (L-J) (12-6) potential [10,45]... 

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. 

How was the theoretical DLVO curve in Figure 1.12 obtained The DLVO model [18, 19] postulates that the appropriate thermodynamic potential energy of interaction between two parallel flat plates can be described in terms of two components a repulsive term VR, resulting from the overlap of electrical double layers, and an attractive van der Waals interaction, VA. It also assumes that these interactions are additive, so that the total potential energy can be written as... 

Fig. 4 The total potential energy of interaction Vt as a function of distance of surface separation H for two similar oh droplets in an oil-in-water emulsion. (A) Electrostatic stabilization by a monolayer of ionic surfactant. (B) Steric stabilization by a monolayer of non-ionic surfactant. V van der Waals attractive force Vr electrostatic repulsive force Vs steric repulsive force.

In the DLVO theory the combination of the electrostatic repulsive energy 17 with the attractive potential energy Vj gives the total potential energy of interaction... 

The forces acting on a colloidal system include gravitational, diffusion, viscous, inertial, attractive Van der Waals, and electrical repulsive forces. Because most of these forces are functions of the particle size, it is important to know both particles size and size distribution. The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory describes colloid stability on the basis of pair interaction, considering only attractive van der Waals forces and repulsive electrostatic forces (Molina-Bolfvar and Ortega-Vinuesa, 1999). The total potential energy of interaction, Ujc, between two particles is defined as ... 

The total potential energy of interaction V is the sum of the potential energy of attraction VA and that of repulsion Vr ... 

Potential Energy of Attraction—Interaction—Repulsion See Gibbs Energy of... 

Figure 6. The effect of different repulsive potential energy curves VR (1) and VR (2) on the total potential energy of interaction curves V (I) and V (2), for a given attractive potential energy curve. (Reproduced with permission from reference 4. Copyright 1981 Butterworth-Heinemann.)...

Figure 3.1 Potential energy of interaction, AC(d), between two molecules a distance d apart (a) van der Waals attraction, (b) Born repulsion, (c) resultant intermolecular potential.

The total potential energy of interaction, say between two spherical particles, is obtained by summing the attractive and repulsive energies. This is illustrated schematically in Fig. 8.1.3, where three different total interaction energy curves are shown, each having been obtained by summing an attraction curve with three different electrostatic repulsion curves. 

These equations of motion can now be solved to describe completely the trajectories of the two particles. As the two particles approach, the kinetic energy increases due to the attractive potential energy of interaction and then decreases as the potential energy becomes repulsive until at the point in the trajectory when the two particles are as close as possible, Tq, the radial component of the velocity, r, is zero. At this turning point, the relationship between the impact parameter, the potential energy of interaction, and the initial energy obtained from Eq. (2-11) is... 

The total potential energy of interaction between two spherical particles is equal to the sum of attraction and repulsion energies ... 

Combining the values of repulsive and attractive potential energy, as they were found in this and the preceding, two Chapters, we find the total potential energy of interaction. 

Another way to reduce the / parameter could be owing to the increase of the total potential energy of interaction. This could succeed with the variation of the ionic strength of the carrier solution. The increase of the ionic strength decreases the repulsive forces between the particles and the accumulation wall making the van der Waals attractive forces more significant. 

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