Surface tension isotherms, surfactant

Fig. III-9. Representative plots of surface tension versus composition, (a) Isooctane-n-dodecane at 30°C 1 linear, 2 ideal, with a = 48.6. Isooctane-benzene at 30°C 3 ideal, with a = 35.4, 4 ideal-like with empirical a of 112, 5 unsymmetrical, with ai = 136 and U2 = 45. Isooctane-

The comparison of W(C) dependence with Ao(C) isotherm gives a relation between formation of black spots and films, and the adsorption layer state. It has been shown [332] that the W(Q dependences for black spot and black films of a very small radius (25 pm) coincide. The comparison of the W(C) curve of CBF from NaDoS (see Fig. 3.78) with the surface tension isotherm of the same surfactant (see Fig. 3.77) indicates that black spots begin to form when the state of adsorption layers deviates from the ideal one (Henry s region in Aa(Q isotherm). The probability for observation of a black film steeply increases with the increase in surfactant concentration to about 10 5 mol dm 3 where the adsorption layer saturation is... 

Note The surfactant adsorption isotherm and the surface tension isotherm, which are combined to ht experimental data, obligatorily must be of the same type. 

The derivative d In c ldT is calculated for each adsorption isotherm, and then the integration in Equation 5.5 is carried out analytically. The obtained expressions for J are listed in Table 5.2. Each surface tension isotherm, oCEi), has the meaning of a two-dimensional equation of state of the adsorption monolayer, which can be applied to both soluble and insoluble surfactants. ... 

Each surfactant adsorption isotherm (that of Langmuir, Volmer, Frumkin, etc.), and the related expressions for the surface tension and surface chemical potential, can be derived from an expression for the surface free energy, F, which corresponds to a given physical model. This derivation helps us obtain (or identify) the self-consistent system of equations, referring to a given model, which is to be applied to interpret a set of experimental data. Combination of equations corresponding to different models (say, Langmuir adsorption isotherm with Frumkin surface tension isotherm) is incorrect and must be avoided. 

We can check that Equation 5.13 is equivalent to the Frumkin s surface tension isotherm in Table 5.2 for a nonionic surfactant. Furthermore, eliminating ln(l - 0) between Equations 5.13 and 5.14, we obtain the Butler equation in the form ... 

FIGURE 5.6 (a) Plot of the slope coefficient 5, vs. the surfactant (DDBS) concentration the points are the values of 5, for the curves in Figure 5.5 the fine is the theoretical curve obtained using the procedure described after Equation 5.85 (no adjustable parameters), (b) Plots of the relaxation time and the Gibbs elasticity vs. the DDBS concentration is computed from the equilibrium surface tension isotherm = n (S, /Eq) is calculated using the above values of 5,. 

The Gibbs equation contains three independent variables T, a, and p (defined either via concentration or pressure, c or p, respectively), and is a typical thermodynamic relationship. Therefore, it is not possible to retrieve any particular (quantitative) data without having additional information. In order to establish a direct relationship between any two of these three variables, it is necessary to have an independent expression relating them. The latter may be in a form of an empirical relationship, based on experimental studies of the interfacial phenomena (or the experimental data themselves). In such cases the Gibbs equation allows one to establish the dependencies that are difficult to obtain from experiments by using other experimentally determined relationships. For example, the surface tension is relatively easy to measure at mobile interfaces, such as liquid - gas and liquid - liquid ones (see Chapter I). For water soluble surfactants these measurements yield the surface tension as a function of concentration (i.e., the surface tension isotherm). The Gibbs equation allows one then to convert the surface tension isotherm to the adsorption isotherm, T (c), which is difficult to obtain experimentally. 

When adsorption takes place at the surface of a highly porous solid adsorbent, the surface excess can be readily measured, e.g. by measuring the increase in the adsorbent weight in the case of adsorption from vapor, or by following the decrease in the adsorbate concentration during adsorption from solutions. Studies of the adsorption dependence on vapor pressure (or solution concentration) reveal T(p) (or T(c)) adsorption isotherms. In both cases the two-dimensional pressure isotherm can be established from the Gibbs equation (see Chapter II, 2, and Chapter VII, 4). Therefore, it is as a rule possible to establish the dependence between the two of three variables present in the Gibbs equation the surface tension isotherm, a(c), for mobile interfaces and soluble surfactants, the two-dimensional pressure, tt(c), isotherm for insoluble... 

Let us next consider the characteristic properties of interface and adsorption layers, comparing the behavior of water soluble surfactants to that of insoluble ones. We will gradually move from the simplest cases to more complex ones, revealing the nature of intermolecular interactions in the adsorption layers. In doing so, we will analyze the typical relationships that describe the properties of adsorption layers, namely the surface tension isotherm, a(c), the adsorption isotherm, F(c), the two-dimensional pressure isotherm, 7r(r), etc. 

Fig. 11-13 The surface tension isotherms plotted in a - In (c) for the three surfactants, the neighboring members of a homologous series...

The effect that the two-dimensional condensation of soluble surfactants has on the surface tension isotherm is less pronounced according to the Gibbs equation, a jump in the... 

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... 

Fig. VI-7. The surface tension isotherm of Fig. VI-8. The equivalent electric aqueous solutions containing micelle- conductivity of aqueous solutions of ionic forming surfactants surfactants as a function of surfactant...

Fig. VI-15. Schematic drawing of the Fig. VI-16. The surface tension isotherm of the mixed micelle solution of micelle-fonning surfactant in the...

Overviews of attempts to quantify the effect of impurities and to derive criteria for the purity of a liquid system for interfacial studies was given by Lunkenheimer (1984) and Miller (1987). It was shown that the absence of a minimum in a surface tension isotherm, y as a function of log(Co) is the criterion most frequently used to judge the purity of a surfactant. On the other hand, it had been shown by Krotov Rusanov (1971) that this is not sufficient. Under certain conditions such a minimum can disappear by some compensating effects as well as by addition of electrolyte (Weiner Flynn 1974). In addition, there are surfactants which do not form micelles or are not sufficiently soluble so that higher concentrations cannot be reached. 

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. 

This approximate theoretical model which attempts to explain the anomalous behaviour of protein/surfactant mixtures was recently confirmed for the HSA/CioDMPO mixture as an example [137]. The equilibrium surface tension isotherms for mixed and pure CioDMPO solutions at 22°C are shown in Fig. 2.25. It is seen that for c > 10" mol/1, the two isotherms are almost identical. For these CioDMPO concentrations the adsorption of HSA is negligible. The conclusion concerning the sharp change in the composition of the surface layer within a narrow CioDMPO concentration range is supported by the analysis of the surface shear viscosity t s of mixed monolayers [137]. 

The series of normal alcohols (C OH) is the most frequently studied homologous series of surfactants. Figure 3.1 illustrates the experimental surface tension isotherms for the aqueous solutions of alcohols in the range from C3 to C o, as summarised from the data reported elsewhere by different authors [18-24]. 

Maleic acid mono[2-(4-alkylpiperazinyl)ethyI esters] (CnPIP) also are amphoteric surfactants and the ionic form depends on the pH, [44, 45]. Four ionic forms are known, of which the most surface active one is similar to the betain, with two oppositely charged atoms bF and 0 . At pH = 6.2 approximately 99.6% of all CnPIP molecules in solution exist in the betain form, while each of the other two forms, containing one ionised atom (either N or O ) is represented by 0.2% [45]. The experimental and theoretical surface tension isotherms of C PIP solutions at pH = 6.2 and 24"C are presented in Fig. 3.21. The theoretical curves calculated from the Frumkin and reorientation models are essentially the same with similar deviations, and therefore neither model could be preferred. The dependencies of the main parameters on n for the two models are shown in Figs. 3.22 - 3.24. 

Similar results were also obtained for dodecyl trimethyl ammonium bromide (C12TAB) with different additions of NaBr (cf Fig. 2.3). However, the shape of the surface tension isotherm becomes essentially different when the mean value of the ionic product c is used instead of the surfactant concentration c. The experimental isotherms of C12TAB plotted the mean... 

It should be noted first that the Frumkin model is the most general one with respect to its application to surfactants of different nature. In spite of the fact that, e.g., for oxyethylated nonionic or ionic surfactants this model is essentially biased, in the majority of practical cases it can be recommended irrespectively of the nature of the surfactant. In the Frumkin model, three parameters are necessary to describe the adsorption and surface tension isotherm. Leaving aside the molar area co which can be estimated from the molecular geometry [16, 84], we concentrate on the results which follow from our development for the parameters a and b for surfactant molecules with linear hydrocarbon chain. Figure 3.59 illustrates the dependence of the Frumkin constant a on the molar area co of various surfactants at n<- = 10. Note that for ionic surfactants the co values are equal to the doubled values of co, from corresponding tables. 

In some cases, a better agreement with the experimental surface tension isotherms and other data (dynamic surface tension, optical methods) is provided by the reorientation or aggregation model, respectively. It follows from the presented results that the reorientation model is more appropriate for oxyethylated surfactants and for surfactants which possess relatively high molar area, ro > 2.5-lO m /mol. At the same time, the aggregation and cluster models describe better the behaviour of surfactants with a relatively large Frumkin constant and low molar area, (o< 2.5-10 m /mol. 

Fig. 5.2. Influence of added salt with the same ion as the counterion on the surface tension isotherm of usual surfactant. Broken line is the surface tension isotherm of salt-free surfactant solution the solid line is the surface tension isotherm with excess of salt. The break points on the both isotherms are the CMCs of surfactant in the corresponding solutions.

Fig. 5.3. Typical plots of surface tension isotherms for a homologous series of non-ionic surfactants.

A possible interpretation of the shape of the surface tension isotherm at the CMC was given by Rusanov and Fainerman in the framework of a quasichemical approach to micellisation [62]. The general idea is as follows the total surfactant concentration is related to the concentrations of micelles and monomers by the mass balance condition (5.18) and the mass action law in form of Eq. (5.23). From these conditions, one of two quantities can be expressed as a function of the other. For a single non-ionic surfactant this gives (see also Eq. (5.40))... 

Fig. 5.4. Surface tension isotherms of a pure surfactant (1), of a mixture of the same surfactant with a small amount of a surface active impurity (2), and the same mixture with a large amount of impurity (3).

The miceUization of binary surfactant solutions is studied by the method of tensiometry at the variation of the fraction of ionic surfactant within the range 0-1.0. The quantitative treatment of the surface tension isotherms within the framework of the phase separation modeP showed that the values of the interaction parameter p in these systems lay within the range (-0.85)-(-. 6). This indicates that in these systems synergetic behaviour occurs, i.e. the mixed aggregates are formed. The surface potential is calculated for all the systems. A decrease in the potential is shown to occur with a decrease in In... 

A surface-tension isotherm assuming surfaee-layer nonideality was presented in Refs (36, 37 and 55). For a nonideal surface layer, the unit value which enters the right-hand side of Eq. (48) should be replaeed by the aetivity eoeffieient of the solvent in the surfaee layer. It was shown in Refs 36, 37, 55 and 65 that Eq. (48) deseribes the surfaee- and interfacial-tension of anionic and cationic surfactant solutions quite well in a wide range of added inorganic electrolyte. 

Table I The Most Popular Surfactant Adsorption Isotherms and the Respective Surface Tension Isotherms ci, is the Subsurface Concentration of Surfactant Molecules...

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