Surface potential, change with number

The popular applications of the adsorption potential measurements are those dealing with the surface potential changes at the water/air and water/hydrocarbon interface when a monolayer film is formed by an adsorbed substance. " " " Phospholipid monolayers, for instance, formed at such interfaces have been extensively used to study the surface properties of the monolayers. These are expected to represent, to some extent, the surface properties of bilayers and biological as well as various artificial membranes. An interest in a number of applications of ordered thin organic films (e.g., Langmuir and Blodgett layers) dominated research on the insoluble monolayer during the past decade. 

As before, the x direction has been taken normal to the metal surface. In electrochemistry, the dipole moment mx associated with an adsorbate bond can be defined in the following way For simplicity suppose that the electrode has unit area. At the beginning the electrode surface is bare and kept at the pzc. Then a number nad of ions with charge number z are adsorbed simultaneously a counter charge —zeon is allowed to flow onto the metal surface. The change A(j> in the electrode potential is related to the dipole moment through ... 

The potential in the diffuse layer decreases exponentially with the distance to zero (from the Stem plane). The potential changes are affected by the characteristics of the diffuse layer and particularly by the type and number of ions in the bulk solution. In many systems, the electrical double layer originates from the adsorption of potential-determining ions such as surface-active ions. The addition of an inert electrolyte decreases the thickness of the electrical double layer (i.e., compressing the double layer) and thus the potential decays to zero in a short distance. As the surface potential remains constant upon addition of an inert electrolyte, the zeta potential decreases. When two similarly charged particles approach each other, the two particles are repelled due to their electrostatic interactions. The increase in the electrolyte concentration in a bulk solution helps to lower this repulsive interaction. This principle is widely used to destabilize many colloidal systems. 

For thermodynamic vectorial forces, such as a difference in chemical potential of component /, proper spatial characteristics must be assigned for the description of local processes. For this purpose, we consider all points of equal as the potential surface. For the two neighboring equipotential surfaces with chemical potentials p, and /z, + dp the change in p, with number of moles N is dpJdN, which is the measure of the local density of equipotential surfaces. At any point on the potential surface, we construct a perpendicular unit vector with the direction corresponding to the direction of maximal change in p,. With the unit vectors in the direction x, y, and z denoted by i, j, and k, respectively, the gradient of the field in Cartesian coordinates is... 

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