Binding isotherm equation derivation

Derivation of the Enzyme-Ligand Binding Isotherm Equation... 

On the assumption that the forces that produce condensation are chiefly responsible for the binding energy of multilayer adsorption, ey proceeded to derive an isotherm equation for multilayer adsorption by a method that was a generalization of Langmuir s treatment of the unimolecular layer. The generalization of the ideal localized monolayer treatment is effected by assuming that each first layer adsorbed molecule serves as a site for the adsorption of a molecule into the second layer and so on. Hence, the concept of localization prevails at all layers and forces of mutual interaction are neglected. 

The binding energy in field adsorption can be derived from consideration of the kinetics of field adsorption. Specifically, it can be determined from a temperature dependence of the probability of field adsorption on an adsorption site, or the degree of coverage of field adsorption on a plane. As will be shown, a consideration of the probability of field adsorption based on adsorption time and desorption time leads to an equation equivalent to the Langmuir adsorption isotherm, but specific to the problem of field adsorption.112115 Let us focus on one surface atom. The average time it takes to have an image gas atom field adsorbed on the surface atom, ra, is... 

The Tempkin isotherm describes the adsorbent-adsorbate interactions, which assumes that the adsorption heat decreases linearly rather than logarithmic as the coverage proceeds [7]. Besides, the derivation of this adsorption is characterized by a uniform distribution of binding energy, which can up to some maximum binding energy. The equation for this model is expressed as ... 

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