Surface tension of pure components

We shall only consider flat, macroscopic fluid-fluid, one- or two-component systems, meaning that for the moment only surface tensions of pure liquids against their vapour and interfacial tensions between two, immiscible but mutually... 

The calculations with Equation 11.23 and Table 11.3 are in reasonably good agreement with the reported values for the Lifshitz-van der Waals surface tension component in the literature [4-6,28]. As an example, the y calculated from Equation 11.23 for methanol, ethanol, glycerol, and water are 17.23, 18.03, 31.97, and 21.13 mN/m, respectively, while the corresponding reported values [28] are 18.5, 20.1, 34.0, and 21.8 mN/m, respectively. Having the partial surface tensions of pure solvents, we may now proceed to the next step and propose a method for the surface-tension characterization of polymers and solid surfaces. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

The principal point of interest to be discussed in this section is the manner in which the surface tension of a binary system varies with composition. The effects of other variables such as pressure and temperature are similar to those for pure substances, and the more elaborate treatment for two-component systems is not considered here. Also, the case of immiscible liquids is taken up in Section IV-2. 

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]... 

In general, the surface tension of a Hquid mixture is not a simple function of the pure component surface tensions because the composition of the mixture surface is not the same as the bulk. For nonaqueous solutions of n components, the method of Winterfeld, Scriven, and Davi is apphcable ... 

In the case of the interfacial tension of two pure liquids we have had to deal with the superficial system in equilibrium with a two phase two component system of three dimensions. If we add to this system a third component the problem becomes still more complicated. The simplest case is that in which the added substance is soluble in one phase and completely insoluble in the other, the original liquids being themselves mutually insoluble. The change of interfacial tension should then run parallel to the change of surface tension of the liquid in which the third component dissolves. 

If the original liquids are again partially miscible, and the added component soluble in either the mutual solubility may be increased if so the interfacial tension will probably diminish whatever may be the effect on the surface tensions of the two pure liquids. Clearly, if sufficient of the third component be added to make the two phases completely soluble the interfacial tension must disappear altogether. 

Results for the various binary mixed surfactant systems are shown in figures 1-7. Here, experimental results for the surface tension at the cmc (points) for the mixtures are compared with calculated results from the nonideal mixed monolayer model (solid line) and results for the ideal model (dashed line). Calculations of the surface tension are based on equation 17 with unit activity coefficients for the ideal case and activity coefficients determined using the net interaction 3 (from the mixed micelle model) and (equations 12 and 13) in the nonideal case. In these calculations the area per mole at the surface for each pure component, tOj, is obtained directly from the slope of the linear region in experimental surface tension data below the cmc (via equation 5) and the maximum surface pressure, from the linear best fit of... 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

On the molar volumes of pure components, we used the following values in Equation (13) by assuming that the temperature dependence of the molar volume and the volume change due to the melting are neglected because the effect of the excess Gibbs energy and the surface tension on the phase equilibria is focused. 

The surface tension of most concentrated aqueous solutions of inorganic salts, such as those employed in OD as strip solutions, is considerably greater than that of pure water. Intrusion of these solutions into microporous, hydrophobic membranes of the types used in OD is, therefore, unlikely under moderate operating pressures. However, some aqueous feeds contain amphiphilic components that may depress the liquid surface tension, and thereby reduce the critical penetration pressure. In such cases it may be necessary to use a membrane with a pore diameter of less than 0.1 p, to prevent liquid intrusion. For most applications however, membranes with a nominal pore diameter of 0.2 p have been found to be suitable. 

From Eq. (6.42) it follows that in the ideal solutions, the surface adsorption is proportional to the difference in the surface tension of the pure components. 

Values of Yq are often taken to be the surface tension of the pure components, Y and have also been obtained by iterative procedures. Figure 4a shows a typical plot of Y as a function of x for a binary slag and the individual x Yi contributions have also been included. These methods work well for certain slag mixtures but break down when surface-active constituents, such as P205 are present. These components migrate preferentially to the surface and cause a sharp decrease in the surface tension and consequently only very small concentrations are required to cause an appreciable decrease in Y. Thus some unreported or undetected impurity could have a marked effect on the surface tension of the slag and thereby produce an apparent error in the value estimated by the model. In this respect surface tension differs from all the other physical properties which are essentially bulk properties. 

This is a useful equation relating the thickness of the supposedly homogeneous interfacial layer to properties of pure components (surface tensions and molar volumes), to the bulk composition, and to the interaction parameters (5 and %. It is worth observing that the more negative the % parameter (the more favorable the interaction between components 1 and 2), the smaller the thickness of the interfacial layer. If the thickness is estimated from independent studies. Equation 2.C13 could be used for obtaining the lipophobicity constant or the composition of the interfacial layer. 

The effect of temperature on the surface tension of mixtures of n-propanol/ -heptane has been investigated. The variation of surface tension by temperature (K) for pure components was... 

The rigorous equation of state for mixed surface layers can be transforms into a simple relationship (3.41) for surfactants possessing different adsorption parameters. To calculate the surface tension of the surfactant mixtures one can use various types of surface tension information of the individual components, either experimental values for a given concentration in the pure solutions, or the parameters of the corresponding adsorption isotherms. 

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