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]

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]

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]

FIGURE 2.8 The Szyszkowski isotherms,

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]

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]

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]

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). |

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]

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]

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]

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]

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]

© 2019 chempedia.info