Sphere electrostatic repulsive force between

Fig. 7.13. The separation dependence of the normalized force FR, between the silanated glass sphere R = 9 im) and silanated LaSF glass plate in 8CB at T — Tivj = 7.1 K. The solid line is a fit to an electrostatic repulsive force given by (7.6). The fit parameters are u = 1 x 10 (1 0.07) Asm, Ad = 73(1 0.07) 10 m. Inset shows the same data in a log-lin scale, to emphasize the exponential dependence of the force on the separation.

Calculate (a) the repulsion force between the 2 negative spheres, (b) the force of attraction of the positive sphere for each negative sphere. Which force is greater What statement can you make about the stabilization of the Rutherford atom by electrostatic forces only ... 

Vakarelski et al. [88] also investigated the adhesive forces between a colloid particle and a flat surface in solution. In their case they investigated a sihca sphere and a mica surface in chloride solutions of monovalent cations CsCl, KCl, NaCl, and LiCl. The pH was kept at 5.6 for all the experiments. To obtain the adhesive force in the presence of an electrostatic interaction, they summed the repulsive force and the pull-off force (coined foe by the authors ) to obtain a value for the adhesive force that is independent of the electrostatic component. 

The number of forces separating the particles is smaller. Repulsive forces act between particles with the same electrostatic charge. The mixing of fiuids leads to the development of shear forces, which try to separate the particles. The maximum hydrodynamic force acting on spheres in a uniform shear field can be expressed as [22,24] ... 

Electrostatic Model. A simple model that can account for the observed bond angles in a qualitative way comes from a consideration of electrostatic repulsions of electron pairs. Let us consider electron pairs around an atom as concentrations of charge placed on a more or less spherical surface, and let us assume that the electrons can move in pairs. Barring other forces, the most likely arrangement will be the one where the electron pairs exert the minimum repulsion on each other. This will be achieved when the electrons get as far away from each other as possible. Since the electrons are restricted by our assumption to a sphere, the maximum distance of separation corresponds to a maximum angle between their positions and the center of the sphere. 

These trajectory methods have been used by numerous researchers to further investigate the influence of hydrodynamic forces, in combination with other colloidal forces, on collision rates and efficiencies. Han and Lawler [3] continued the work of Adler [4] by considering the role of hydrodynamics in hindering collisions between unequal-size spheres in Brownian motion and differential settling (with van der Waals attraction but without electrostatic repulsion). The results indicate the potential significance of these interactions on collision efficiencies that can be expected in experimental systems. For example, collision efficiency for Brownian motion will vary between 0.4 and 1.0, depending on particle absolute size and the size ratio of the two interacting particles. For differential... 

It is well known [4,5] that in the case of hard spheres di = d.2 = 0), the electrostatic force between two dissimilar spheres with charges of unlike sign is attractive for large kH but becomes repulsive at small kH, that is, there is a minimum in the interaction energy except when a lox =1. The case of nonzero Kd and xd2,... 

In addition, if the spheres are in water, there will be a repulsive electrostatic force between them. Under usual conditions of stability, this force is quite strong and its range is on the order of the sphere s radii. It is easy to see that the location of this repulsive wall with respect to the thickness 5 of the adsorbed layers will determine the type of binding which will be possible. If the wall is within the adsorbed layer ((7. 5)> unsaturated spheres will experience a short range attraction and... 

Stable Systems. The viscoelastic response of a concentrated noncoagulating suspension is strong when the average distance between the suspended particles is of the same order as the distance at which the interparticle repulsive forces become important. Hence, the viscoelastic behavior originates from the interparticle repulsive potential. Several studies have been carried out on hard sphere systems (72, 204, 205), steric systems (88, 94, 203, 206), and electrostatic systems (163,... 

Dispersion forces are attractive forces between atoms at close distances. Even molecules with no permanent dipole moment have, due to the movement of their electrons, local dipole moments which induce dipoles in the opposite molecule, leading to fluctuating electrostatic attractions. At a closer distance repulsive forces develop due to an unfavorable overlap of the van der Waals spheres of both molecules. These relationships are typically described by the Lennard Jones potential, with an r attractive term and an r repulsive term (Figure 2) [59, 116]. Dipole-dipole interactions and dispersion forces are much weaker than other electrostatic interactions. Nevertheless, if there is a close contact between both molecules over a relatively large surface area, they may sum up to large values of overall interaction energies. 

Electrostatic forces are repulsive forces caused by electric double layers at the surfaces of particles or drops. The electrostatic potential for two various spheres of radii R and R2 (Ri > R2) with the distance r between its centers is equal to [52]... 

An expression for the force of electrostatic repulsion between two charged crossed hemicylindrical surfaces is given in Equation (3.5) and in fact this turns out to be equivalent to interaction between a sphere and a flat plate. Integration of this expression leads directly to the potential energy of electrostatic repulsion, namely. 

A typical force measurement that indicates the presence of the electrostatic force, is presented in Fig. 7.13. Here, the force between a silanated 10 /rm glass sphere and a flat surface of a silanated glass plate is measured in the isotropic phase of 8CB at a temperature 7.1 K above the phase transition temperature into the nematic phase (Tni). A very strong repulsive force can be observed. As one can see from the inset, this force decreases exponentially with increasing separation and can be detected even at a separation of 300 nm. At smaller separations of 20 nm, we have observed an attractive force, which is a result of the capillary condensation of the partially ordered isotropic Uquid crystal into the developed nematic phase, as already reported [58]. The exponentially decaying repulsive force showed no temperature dependence in a wide range of temperatures above the nematic to isotropic phase transition temperature. 

Fig. 8 Force between a silica sphere and a gold electrode in an aqueous solution of 1 X 10 mol dm KCl, and 1 x 10 mol dm (inset) KCl at 25 °C, and pH 5.5, as a function of the applied electrode potential. The curves correspond to, from top to bottom, electrode potentials of—700, —500, —400, —300, —200, —100, 0, and -1-100 mV (versus SCE). Electrostatic repulsion decreases as the electrode potential increases from —700 to 100 mV (after Ref [41]).

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