Adsorption isotherm for single and mixed surfactant systems

Adsorption Isotherm for Single and Mixed Surfactant Systems 

The adsorption equation (2.38) of von Szyszkowski (1908) is originally an empirical relationship. Stauff (1957) later discussed the physical backgroimd of the constants a and B. 

For very low surfactant concentrations of long chain fatty acids with surface tensions close to that of the pure solvent Traube (1891) found a linear relationship between interface tension and surfactant bulk concentration 

The parameter k has the dimension of a length and results from Eq. (2.36b) as the ratio of adsorption over desorption rate constants k = k,j / kj. The description of an adsorption layer as a two dimensional gas is more thermodynamically based, 

There are two different ways of deriving the Langmuir adsorption isotherm. One of the derivations is based on kinetic transfer mechanisms of adsorption/desorption of adsorbing molecules. The second, thermodynamic derivation starts from the equivalence of the chemical potentials of adsorbing molecules in the bulk phase and in the adsorbed state. Frumkin (1925) introduced additional interaction forces between adsorbed molecules into the Langmuir adsorption isotherm. 

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