Volmer (1925) was the first who mentioned the equivalence of the Langmuir and the von Szyszkowski isotherm, given by von Szyszkowski in the following from. [Pg.48]

FIGURE 2.8 The Szyszkowski isotherms,

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. [Pg.27]

The comparison of the empirical Szyszkowski equation (II. 18) with the Gibbs equation (II.5) indicates that Langmuir adsorption isotherm (11.22) is well suited also for the description of adsorption at the air - surfactant solution interface. It is interesting to point out that at the gas - solid interface, for which eq. (11.22) was originally derived various deviations from Langmuirian behavior are often observed. [Pg.104]

The applicability of eq. (11.22) to a successful description of adsorption from a solution was established by Langmuir himself, when he compared his adsorption isotherm to the Gibbs equation and ended up with the Szyszkowski equation as a result. The transition from localized to non-localized adsorption (which can be viewed as the transition from fixed adsorption sites to moving ones) does not, therefore, change general trends in the adsorption in the cases described. One should also keep in mind that the liquid interface is more uniform in terms of energy than the solid interface, which contains active sites with different interaction potentials.4 The latter is probably the reason why... [Pg.104]

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... [Pg.178]

These adsorption isotherms are known as Henry (1801), von Szyszkowski (1908), Langmuir (1916), Frumkin (1925), Volmer (1925) or HOckel-Cassel-isotherm (Huckel 1932, Cassel 1944), respectively. The constants in these isotherms refer to kinetic models of adsorption/desorption, interactions between adsorbed molecules and/or to the minimum area of adsorbed species. [Pg.44]

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. [Pg.48]

The thermodynamics and dynamics of interfacial layers have gained large interest in interfacial research. An accurate description of the thermodynamics of adsorption layers at liquid interfaces is the vital prerequisite for a quantitative understandings of the equilibrium or any non-equilibrium processes going on at the surface of liquids or at the interface between two liquids. The thermodynamic analysis of adsorption layers at liquid/fluid interfaces can provide the equation of state which expresses the surface pressure as the function of surface layer composition, and the adsorption isotherm, which determines the dependence of the adsorption of each dissolved component on their bulk concentrations. From these equations, the surface tension (pressure) isotherm can also be calculated and compared with experimental data. The description of experimental data by the Langmuir adsorption isotherm or the corresponding von Szyszkowski surface tension equation often shows significant deviations. These equations can be derived for a surface layer model where the molecules of the surfactant and the solvent from which the molecules adsorb obey two conditions ... [Pg.99]

It is seen from the von Szyszkowski-Langmuir surface tension isotherm, Eq. (2.41), that at a given temperature the shape of the surface tension isotherm is determined by only one parameter cOg =cO =cd. The other parameter b enters this equation as a dimensionless variable be, in combination with the concentration. Therefore, the value of b does not affect the shape of surface tension isotherm, and only scales this curve with respect to the concentration axis. It should be noted that this dependence on b is characteristic to all the equations presented above. The dependence of the surface pressure isotherm on the molar area co is illustrated by Fig. 2.1. It is seen, that the lower ro is, hence the higher the limiting adsorption T = 1/co, the steeper is the slope of the n(c)-curve. [Pg.112]

The von Szyszkowski equation (2.41) and Frumkin equations (2.37)-(2.38) have been used for the description of experimental surface tension isotherms of ionic surfactants [40, 58]. Thus the constant a in the Eqs. (2.37)-(2.38) reflects simultaneously intermolecular attractive (van der Waals) and interionic repulsive interactions. As a result, for the ionic surfactants the constant a can have either a positive or negative sign. [Pg.113]

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. [Pg.130]

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. [Pg.136]

Fig. 2.17. Surface pressure isotherm for 1-decanol solutions O -experimental data [36, 37] calculations from the von Szyszkowski equation (1), Frumkin equation (2), and aggregation model (3). |

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])... [Pg.171]

Thus, for any time t the value of a can be calculated from Eqs (71) and (72). If we assume a Langmuir-Szyszkowski adsorption isotherm and interfacial tension equations, the parameters % and can be expressed via the values of the dynamic and equilibrium interfacial pressures, Yl(t) and... [Pg.14]

It is seen from the von Szyszkowski-Langmuir surface tension isotherm, that at a given temperature the shape of the surface tension isotherm is determined only by the parameter co, while parameter b enters this equation as a dimensionless variable be. The dependence of the surface pressure isotherm on the molar area CO is illustrated by Fig. 2. For lower co steeper curves 11(c) are obtained. [Pg.61]

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