Charged plates, force between

In this paper, a model which takes into account the effect of a lower dielectric constant near a surface due to the presence of hairs on the surface is developed. At constant surface charge, the force between the two plates is larger than predicted by the Gouy-Chapman theory. As the dielectric constant increases, the force decreases. The nature of cations has a specific effect on the force between plates. 

If two oppositely charged plates exist in a vacuum, there is a certain force of attraction between them, as stated by Coulomb s law ... 

Dielectric Constant The dielectric constant of material represents its ability to reduce the electric force between two charges separated in space. This propei ty is useful in process control for polymers, ceramic materials, and semiconduc tors. Dielectric constants are measured with respect to vacuum (1.0) typical values range from 2 (benzene) to 33 (methanol) to 80 (water). TEe value for water is higher than for most plastics. A measuring cell is made of glass or some other insulating material and is usually doughnut-shaped, with the cylinders coated with metal, which constitute the plates of the capacitor. 

The electrostatic force (F ) between two charged plates separated by an electrolyte solution can be determined from an existing imphcit solution to the nonlinear Poisson-Boltzmann equation and can be expressed in the form [187]... 

Several repulsive and attractive forces operate between colloidal species and determine their stability [12,13,15,26,152,194], In the simplest example of colloid stability, dispersed species would be stabilized entirely by the repulsive forces created when two charged surfaces approach each other and their electric double layers overlap. The overlap causes a coulombic repulsive force acting against each surface, which will act in opposition to any attempt to decrease the separation distance (see Figure 5.2). One can express the coulombic repulsive force between plates as a potential energy of repulsion. There is another important repulsive force causing a strong repulsion at very small separation distances where the atomic electron clouds overlap, called Born repulsion. 

H. Huang, E. Ruckenstein Interaction Force between Two Charged Plates Immersed in a Solution of Charged Particles. Coupling between Double Layer and Depletion Forces, LANGMUIR 20 (2004) 5412-5417. 

Force between Two Charged Plates Immersed in an Electrolyte Solution Containing Small Charged Particles... 

In the second kind of adsorption (Fig. 2B), the dipole exposes to the solution a charge opposite of that of the surface. Correspondingly, the dipole generates a field opposite of that generated by the surface charge, and the adsorption is expected to decrease the repulsive force between the two plates. However, if the surface charge is small, then the dipoles of the adsorbed molecules alone generate repulsion. 

Fig. 1. The repulsive force between two plates at constant surface charge and various bulk NaCl concentrations. The following parameters were employed in the calculations a = —0.01 C/nr. e1 = 10, e11 = 80. S = 10 A. (1) 0.001 (2) 0.01 (3) 0.1 M NaCl. The solid lines are for the force predicted by the new model and the dashed lines for the force predicted by the Gouy-Chapman theory.

Substituting Eq. (23) into Eq. (22), a boundary condition for the surface charge density generated through the dissociation equilibrium is obtained. Equations (8) and (9) can be solved numerically for the boundary conditions (11)—(14), (23), to calculate the force between plates. 

As the dielectric constant of region I increases, the concentrations of ions near the surface increase, the magnitude of the surface charge density decreases, and the force between the two plates decreases (Fig. 17). Compared to the constant surface charge case, for which only the ion concentrations in the double layer increased with increasing dielec-... 

In this paper, a two-dimensional model is proposed, in which the polyelectrolyte chains are treated as rigid cylinders normally grafted to each of the plates. On the surface of the cylinders, ionizable sites are uniformly distributed and the surface charge of the cylinder is generated through their dissociation. Using this two-dimensional model, the repulsive force between two plates is calculated as a function of electrolyte concentration, surface density of polyelectrolyte chains on the plate, thickness of the polyelectrolyte brushes, and bulk pH (denoted in what follows as pHo). 

The electrolyte concentration affects the repulsive force between the plates through the screening effect. As the electrolyte concentration increases, the magnitudes of the electrical potential in the bmsh and the outside regions decrease (Fig. 2). Therefore, as expected, the force decreases with increasing electrolyte concentration (Fig. 3). For comparison purposes, the figure also contains the force between two plates free of polyelectrolyte chains but with the same surface charge density oj, (—0.01 C/m2) on the plates as when the chains are present. 

---