Equations of state and adsorption isotherms

Secondly, if only ideality of the mixing entropy is considered, n = ni = and the Friunkin generahzed equation of state and adsorption isotherm are obtained, giving [15,26]... 

In Eq. 16, hi is another adsorption constant (independent of surface coverage) and is equal to the product of hi in Eq. 11 and the base of natural logarithm (= 2.718). For systems containing only one surfactant. Pi = Pu = 0, and Eqs. 15 and 16 reduce to the well-known Frumkin equation of state and adsorption isotherm described as... 

This implies that a smaller molecule will expel a larger one from the surface when their total concentration is increased at constant Ci/C2. Thus, a two-dimensional solution treatment which expresses the chemical potentials of the surface layer components by means of Eq. (2.7) enables us to derive equations of state and adsorption isotherms at fluid interfaces depending on the system considered (ideal or non-ideal surface layer, single surfactant or mixture of... 

The Frumkin equation of state and adsorption isotherm (2.37) - (2.38) involve one extra parameter a. Thus, the Frumkin model can better fit experimental data. The effect of the parameter a for fixed co values is illustrated by Fig. 2.2. 

The above analysis of the viscoelastic behaviour for adsorption layers of a reorientable surfactant leads to important conclusions. It is seen that the most important prerequisite for a realistic prediction of the elastic properties is the adequacy of the theoretical model used to describe the equilibrium adsorption of the surfactant. For example, when we use the von Szyszkowski-Langmuir equation instead of the reorientation model to describe the interfacial tension isotherm, this rather minor difference drastically affects the elasticity modulus of the surface layer. The elasticity modulus, therefore, can be regarded to as a much more sensitive parameter to find the correct equation of state and adsorption isotherm, rather than the surface or interfacial tension. Therefore the study of viscoelastic properties can give much more insight into the nature of subtle phenomena, like reorientation, aggregation etc. 

The application of Butler s equation has been illustrated in form of the equation of state and adsorption isotherm for non-ideal monolayers (with respect to both enthalpy and entropy) comprised of an insoluble 1 and a soluble 2 component. In this case the equation of state is Eq. (2.31), but the adsorption isotherm (2.32) is true for the soluble component 2 only... 

When the formation of large aggregates of an insoluble surfactant is stimulated by the adsorption of a soluble surfactant, the von Szyszkowski-Langmuir equation of state and adsorption isotherm for the soluble surfaetant read [157]... 

The equation of state and adsorption isotherm for the Frumkin model (which becomes the Langmuir model for a = 0, cf Chapter 2) are... 

The model for aggregation in the adsorption layer with the arbitrary aggregation number n is described by the following equation of state and adsorption isotherm... 

The equation of state and adsorption isotherm for a non-ideal surface layer of two surfactants with the same molar areas are Eq. (3.30) and... 

For a surfactant forming aggregates in the adsorption layer the equations of state and adsorption isotherms were derived in Chapter 2. In the limiting case of large aggregates these equations expressed via the molar area of monomers cd and the critical adsorption of aggregation Fic, can be written in the form of Eqs. (2.107)-(2.108). 

The Frumkin equation of state and adsorption isotherm involve an additional interaction parameter a (for a = 0 we obtain the Langmuir model). 

Table 4.3 Two-Dimensional Equations of State and Adsorption Isotherms on Homotattic Surfaces...

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