The models of adsorption and surface charge

As mentioned above, the adsorption of ions at interface can be divided into different cases. The solid can be an extended surface or can consist of disperse particle, such as latices and specific and non-specific adsorption is possible. At the solid surface active sites are distributed. This active sites are the geometrical spots for localised adsorption. Two different planes of adsorption are possible. The first one is the solid/liquid interface itself. We could take the adsorption of negatively charged phosphate ions of amino groups as part of a solid siuface as an example of this. The phosphate groups are a classical case of non-point charges which can 

is the fraction of surface sites covered by specifically adsorbed ions i, W. is the specific Gibbs energy of adsorption, C /55.5 is the mole fraction of i and ZjF Fs, the coulomb contribution to the adsorption energy. 

In contrast, the liquid interface can be considered homogeneous which is a precondition for a non-localised adsorption. Any free space at the liquid interface is available for ion adsorption. At the transition from a localised to a non-localised adsorption the exponential term of the Stem-Langmuir equation can be preserved and the pre-exponential multiplier must be changed. This was done by Martynov (1979). The basis of this approach is the notation of a homogeneous potential well along the liquid interface as a whole. 

The homogeneity of a liquid surface leads to identical conditions for the adsorption at any place of the surface which is reflected by the notion of a homogeneous potential well in a layer of thickness A. Its depth is equal to the adsorption energy, its thickness represents the decay of interaction between ions and the interface as the distance increases. Martynov considered this decay and initially introduced the potential well of a complicated configuration. In the framework of this model the adsorption is characterised as the total quantity of the ions within the potential well, i.e. as the product of the well thickness and the ion concentration within it. 

The recombination of Martynov s theory, which is based on a Boltzmann distribution and a Lennard-Jones potential, the isotherm for a smeared adsorption can simplified to 

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