Surface tension isotherms

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-

Uncertain due to the non-distinct slope of the surface tension isotherm... 

Figure 6.58 Surface tension isotherms for poly(fluorooxetane)s K ),2( ), and 3M Fluorad FC-1 29 (A) in pH 8-buffered aqueous solution. Structures are shown in Figure 6.59.

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... 

Figure 2. Surface tension isotherms on the EA-water interface 1—SLS, 2—APGS, 3-C-30 ( j, 4-TX-100(S) ( Aj. T = 298°K.

The adsorption isotherms in Table 5.2 can be applied to both fluid and solid interfaces. The surface tension isotherms in Table 5.2, which relate a and Fj, are usually apphed to fluid interfaces, although they could also be used for sohd-liquid interfaces if a is identified with the Gibbs superficial tension. (The latter is defined as the force per unit length that opposes every increase of the wet area without any deformation of the sohd.)... 

The surface tension isotherms in Table 5.2 are deduced from the respective adsorption isotherms in the following way. Integration of Equation 5.2 yields... 

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 ... 

The long-time portions of the curves in Figure 5.5, plotted as o vs. comply very well with straight lines, whose slopes, S are plotted in Figure 5.6a — the points. The theoretical curve for Si is calculated using the procedure given after Equation 5.85. The curve is obtained using only the parameters of the equilibrium surface tension isotherm and the diffusion coefficients of the ionic... 

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 Equations (l)-(7) have been used to describe the equilibrium surface tension isotherms. The fitting was based on a software package that was developed recently and is explained in ref. 4. 

The surface tension isotherms y as a function of protein bulk concentration c are shown in Figure 2. The data are obtained from the time dependencies of the measured y(t) curves shown in Figure 3 and Figure 4 by extrapolation via... 

Fig. II-3. The surface tension isotherms for the surface active (1) and surface inactive (2) substances...

A substance that has lower surface tension is usually a surface active one. If component A is surface active with respect to component B, then the component B is inactive with respect to A, i.e. the surface tension, a(c), isotherms usually exhibit a monotonous behavior. The isotherms with a minimum are rarely encountered. They may be observed in systems consisting of substances whose surface tension values are close, such as, e.g., a carbon disulfide - dichloroethane system. When the components have limited solubility in each other, the surface tension isotherms consist of two separate sections separated by a gap, the borders of which correspond to the concentrations of saturated solutions. It is essential to point out that when the mutual solubility of components is limited, an interface with a very low interfacial tension may form between two saturated solutions (see Chapter III, 2). 

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. 

Equations of state for surface layers, adsorption isotherms (below referred to as simply isotherms ) and surface tension isotherms can be derived by equating the expressions for the chemical potentials at the surface, Eq. (2.7), to those in the solution bulk... 

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. 

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. 

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