The adsorption equation (2.38) of von Szyszkowski (1908) is originally an empirical relationship. Stauff (1957) later discussed the physical backgroimd of the constants a and B. [Pg.48]

The Szyszkowski equation has proved useful for describing the relatively simple adsorptions under consideration. However, its foundation is at issue because the Langmuir equation was not derived for mobile but for localized adsorbates the translational entropy is not properly accounted for. We return to this issue below, in the mean time accepting [4.3.13] as a useful empirical expression. [Pg.479]

These two equations represent the generalized Szyszkowski-Langmuir adsorption model. [Pg.31]

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]

This example emphasizes the danger of using the ideal Langmuir-Szyszkowski equation of state in converting surface tension-time data into adsorption—time data even for very dilute monolayers. Also it clearly shows that any conclusion about the existence or non-existence of an [Pg.293]

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] [Pg.171]

Fig. 2.9 Equilibrium surface pressure for BHBCi solutions symbols - experimental data from [13,25], curves -theoretical calculations curve 1 - Langmuir-Szyszkowski equation curves 2 - 5 - reorientation model for 2, 3, 7 and over 50 adsorption states of the BHBCie molecule, respectively (n j =2.52 lO mVmol, |

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]

The general principles of the adsorption of surfactants at liquid/gas interfaces and the structure of adsorption layers are well described in detail for example in [10] as well as in Chapter 2. The main effect of adsorption is the substantial change of the interfacial pressure n of a given interface. This property is described in a first approximation by the Langmuir- von Szyszkowski equation (2.16) [Pg.513]

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 [Pg.323]

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]

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]

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]

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]

We have considered the surface tension behavior of several types of systems, and now it is desirable to discuss in slightly more detail the very important case of aqueous mixtures. If the surface tensions of the separate pure liquids differ appreciably, as in the case of alcohol-water mixtures, then the addition of small amounts of the second component generally results in a marked decrease in surface tension from that of the pure water. The case of ethanol and water is shown in Fig. III-9c. As seen in Section III-5, this effect may be accounted for in terms of selective adsorption of the alcohol at the interface. Dilute aqueous solutions of organic substances can be treated with a semiempirical equation attributed to von Szyszkowski [89,90] [Pg.67]

Measurement of the high frequency modulus, c0, as a function of the equilibrium surface pressure, tt, should provide a sensitive criterion for interaction for monolayers that are quite soluble by normal standards, which involve much longer time spans than the inverse frequency of the compression/expansion experiment. A numerical example of the greater sensitivity of an e0 vs. tt plot, compared with that of the ir vs. log c relationship is shown in Figure 1 for a hypothetical case. The specific defini-nition of surface interactions used here to arrive at numerical values includes all mechanisms that produce deviations from Szyszkowski-Langmuir adsorption behavior. Ideal behavior, with zero surface interactions, then is represented by zero values of In fis in the equation of state [Pg.283]

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