Szyszkowski’s equation

In the following table are given the limiting values of A calculated from Milner s and v. Szyszkowski s equations by Langmuir and Harkins. 

Since c- -ac c, the number of adsorbed mols in the surface is per cm.2, or iVTco molecules per cm.2. At T=293° K., (Xq=72 5 for water, and hence the surface covered by one molecule (which is equal to 1 jFtoN) is 12 8xlO i /j3. Szyszkowski found ji3=0411, hence the surface is 31 x 10 i cm., approximately the square of the molecular diameter. Langmuir also derived an inteipretation of the constant a. Tamamushii used an approximate form of Szyszkowski s equation ... 

When water soluble surfactants adsorb at the interface between a liquid hydrocarbon and water, the trends in adsorption are very similar to those established for the air - solution interface (see Chapter II). The Traube rule remains valid, and the dependence of the surface tension on concentration can be described by Szyszkowski s equation (11.18). Moreover, at identical surfactant concentrations, the absolute values by which the surface tension is lowered at water - air and water - hydrocarbon interfaces are not that different. The surface tension isotherms for these interfaces are parallel to each other (Fig. III-6). That is due to the fact that the work of adsorption per CH2 group, given by eq. (II. 14), is determined mostly by the change in the standard part of the chemical potential of the solution bulk, q0. Similar to the air-water interface, the energy of surfactant adsorption from an aqueous solution at an... 

The adsorption-desorption energies, AG, were calculated by means of and AG =-RTlnCk /k ). They are listed in Table 1. The obtained values, however, cannot be referred to the literature ones by the static methods, since the surface excess near the CMC increases appreciably with c. Then, the effective adsorption-desorption energy near the CMC was computed by means of Szyszkowski s equation it is listed in Table 1. The values of AG obtained are in good agreement with the calculated ones. This also suggests that the proposed mechanism is reasonable. 

The interfacial activity of organophosphorus compounds 1-6 can be described by Szyszkowski s equation (72) ... 

For non-ionized monolayers the simplest equation of state is Szyszkowski s equation [30]. 

The efficiency of Pethica s equation can be shown by a simple example. Suppose that the behaviour of both surfactants in a mixed surface layer can be described by the generalised Szyszkowski-Langmuir equation (2.39)... 

As aggregation of the insoluble component occurs only when its surface concentration is sufficiently high, the description of the two components based on Volmer s equation seems to be more appropriate than that based on the Szyszkowski-Langmuir equation. If a first-order phase transition does not occur in the monolayer, i.e. no aggregates are formed, then the simultaneous solution of Volmer s equation (2.159) for the components 1 and 2, and Pethica s equation (2.152) yields the adsorption isotherm for the soluble component 2 (see [156])... 

An estimation of Ay obtained from Eq. (4.86) shows that it is essential to this non-equilibrium effect into account when Cq> S-IO" mol/cm, which coincides very good with the criterion for the non-diffusional adsorption kinetics in the Langmuir model discussed above. If we consider the von Szyszkowski-Langmuir equation, then the adsorption layer in equilibrium obeys... 

Similar conclusions as to the attainment of a finite maximum value of r as pointed out by Langmuir J.A.G.S. xxxix. 1883, 1917) can be obtained from an empiric equation put forward by V. Szyszkowski Zeit Phys. Qhem. LXiv. 385,1908) in the following form ... 

Many adsorption experiments on long chain fatty acids and other amphiphiles at the liquid/air interface and the close agreement with the von Szyszkowski equation is logically one proof of the validity of Langmuir s adsorption isotherm for the interpretation of y - log c -plots of typical surfactants in aqueous solutions (cf. Appendix 5D). This evidence is also justification for use of the kinetic adsorption/desorption mechanism based on the Langmuir model for interpreting the kinetics and dynamics of surface active molecules. 

The Szyszkowski-Langmuir (S-L) equation is often used to empirically describe measured surface tension data ... 

---