The distribution of ions in an electric field near a charged surface

The Distribution of Ions in an Electric Field Near a Charged Surface 

The distribution of ions in the diffuse layer in the form of a concentration profile is the result of electrostatic attraction forces and the thermal equilibrium. 

Thus the counterions migrate toward the surface under the action of the electric field. Since their concentration increases in this direction, this electromigration is fiilly compensated for by the diffusion current. The conditions for compensation of electromigration in diffusion can be mathematically represented in the following form 

We consider two equations for the three functions Pci(x) C, (x) and can express the ion concentration distribution through the potential distribution. By separation of the variables one can carry out the integration which yields 

As expected, the ions are distributed across the double layer according to Boltzmann s formula. As a result, the general relationship between the electric potential (x) and the density of the 

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