The Forces Between a Charged Particle Surface and an Ionic Solution

Origin of particle surface charge The attraction between a charged surface and a concentration of counterions in the diffuse double layer adjacent to the particle surface will be the source of increased interaction energies. The charge density on the surface of the solid particles, and hence the potential gradients in the diffuse double layers, is determined by the degree to which the intermolecular forces at the crystal surface are non-compensated. These are related to the structure of the crystal lattice and to the orientation of the cleavage planes at the surface.

As a consequence of a surface charge, to a greater or lesser extent hydrated ions will be adsorbed, the energy of attachment being related to the charge density on the particle surface. As both orthorhombic sulfur and graphite exhibit comparatively weak residual surface forces with strong non-polar bonds being localized within the unit cells of the crystal lattice, the attachment energy of hydroxyl and hydrated ions will be low giving the surfaces their hydrophobic character.

On the other hand, for ionic crystals the uncom-pensated electrostatic forces at the surface may be high and can lead to strong attachment of water. As the electrostatic forces operate over significantly longer distances than do the London-van der Waals forces they will give hydrated layer thicknesses of the order 20-60 A. According to Klassen and Mokrousov who quote Derjaguin and Derjaguin, Karasiev and Zorin, the hydrated layer has an increased viscosity over that of the bulk water and the change in viscosity is discontinuous.

Diffuse boundary layer To illustrate the previous observations consider a plane surface with a uniform charge density a0 in contact with water with a bulk ionic concentration n0. If the solid-water interface has a positive electrical potential, the potential in the solution will decrease to 0 as one proceeds in a normal direction away from the surface into the solution. Close to the positively charged surface, however, there will be an excess of negative ions. If n # and n~ are the concentrations of the positive and negative ions, of equal and opposite charge, + z and — z, respectively, at a point in the solution then the net charge density p at that point in the solution will be:

Using the Boltzmann factor, the ionic concentrations can be linked to the local potential at a point in the solution:

and:

from which:

The integral of p to infinity will give the total excess charge in the solution per unit cross-sectional area which is equal to but opposite in sign to the charge density on the surface a. The situation is that of a double layer of charge, the one localized on the solid surface and the other in the diffuse region.

To link the potential in the solution with the normal distance x from the surface the Debye-Hiickel treatment may be followed. This uses Poisson's equation which relates the divergence of the gradient of the electrical potential at a given point to the charge density at that point:

solution of eqn [28] reduces to:

where V2 is the Laplace operator and D is the dielectric constant of the medium (for water = 78). For small values of zep with respect to kT, eqn [25] can be expressed as:

Solar Panel Basics

Solar Panel Basics

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