Ideal surface layers and model isotherms

For ideal (with respect to the enthalpy) surface layers of a surfactant capable of adsorbing in two states (1 and 2) with different partial molar areas cOj (coi 2) and different adsorption equilibrium constants, Eqs. (2.26) and (2.27) can be transformed into a generalised von Szyszkowski-Langmuir equation of state [25] 

The corresponding values of equilibrium adsorption in these two states are Ti and P2, respectively, with the total adsorption expressed as F = F + F2. The ratio of the adsorption values and the average molar area are given by the expressions 

The pre-exponential factor p expresses the relative activity of the states of the surfactant molecule with different areas, and involves two co-factors the first results from the theory which takes into account the non-ideality of the surface layer entropy caused by differences in the molar areas, while the second co-factor (involving the constant a) reflects the effect of the additional surface activity of state 1 as compared with state 2. 

Let us consider now the dependence of the shape of surface pressure isotherms on the parameters of the reorientation model. The dependence of surface pressure on the maximum area C0 is illustrated in Fig. 2.5. Here Eqs. (2.84)-(2.88) are employed with (02 = const and a = 0. All calculated curves are normalised in such a way that for the concentration 1 O mol/1, the surface pressure is 30 mN/m. One can see in Fig. 2.5 that with the increase of (Oj the inflection of the isotherm becomes more pronounced, however, for the ratio a)i/( 2 = 4 the calculated curve almost coincides with the one calculated from the von Szyszkowski-Langmuir equation (2.41) which assumes only one adsorption state with (Oo = = const. 

For lower ratios CO1/CO2 the shape of the isotherms is less convex than for the Langmuir isotherm. For non-zero a, which are especially characteristic for oxyethylated alcohols [87], this difference becomes even more significant. For example, the isotherms calculated for various a values (0 to 5) and 1/0)2 = 4 are presented in Fig. 2.6, while the calculations performed for the same a range and / 2 = 8 are illustrated by Fig. 2.7. 

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