Surface tension curved interface

Figure 12.6 In a curved interface, surface tension generates a net force normal to the surface. This must be balanced by a pressure difference across the interface (black arrow).

The area occupied by a surfactant at the air-water interface can be obtained from the slope of the curve of surface tension, /, versus the logarithm of surfactant concentration. In C, using the Gibbs equation, which can be expressed as follows ... 

In the microemulsion systems the primary alcohols are frequently considered as cosurfactants, which are usually weakly amphiphilic molecules that help the amphiphilic surfactants to reduce the surface tension of the interface between the immiscible components of the system. In this way they usually enhance and emphasize the internal structure of the system at the colloidal level. Remarkably, the short-chain alcohols, which are sufficiently soluble in water, themselves show surfactant-like behavior in plain binary water mixtures. As was shown by Kahlweit et al. [87], this specific behavior can be observed from the break in the curves of surface tension versus molar fraction of alcohol in water. Similar breaks were observed by Zana et al. [7] in the curves of fluorescence intensity versus molar fraction of alcohol, where changes in the environment polarity are sensed by the pyrene fluorescence probe. Interestingly, with increasing the length of the... 

Fig. 3. Two-dimensional schematic illustrating the distribution of Hquid between the Plateau borders and the films separating three adjacent gas bubbles. The radius of curvature r of the interface at the Plateau border depends on the Hquid content and the competition between surface tension and interfacial forces, (a) Flat films and highly curved borders occur for dry foams with strong interfacial forces, (b) Nearly spherical bubbles occur for wet foams where...

Measurement of the differential capacitance C = d /dE of the electrode/solution interface as a function of the electrode potential E results in a curve representing the influence of E on the value of C. The curves show an absolute minimum at E indicating a maximum in the effective thickness of the double layer as assumed in the simple model of a condenser [39Fru]. C is related to the electrocapillary curve and the surface tension according to C = d y/dE. Certain conditions have to be met in order to allow the measured capacity of the electrochemical double to be identified with the differential capacity (see [69Per]). In dilute electrolyte solutions this is generally the case. 

Gross et al. [3] and Reid et al. [30] measured surface tension of the water-nitrobenzene interface in the presence of bromides of sodium and tetra-alkylammonium ions in water and tetra-alkylammonium tetraphenylborates in nitrobenzene, i.e., tetra-alkylammonium served as the potential-determining ion, cf. the scheme (13). The surface tension vs. the potential difference A p plot (electrocapillary curve), cf. Eq. (15), was constructed by varying the concentration of tetra-alkylammonium bromide in water, while holding... 

Kakiuchi and Senda [36] measured the electrocapillary curves of the ideally polarized water nitrobenzene interface by the drop time method using the electrolyte dropping electrode [37] at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. An example of the electrocapillary curve for this system is shown in Fig. 2. The surface excess charge density Q, and the relative surface excess concentrations T " and rppg of the Li cation and the tetraphenylborate anion respectively, were evaluated from the surface tension data by using Eq. (21). The relative surface excess concentrations and of the d anion and the... 

Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water-1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water-nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of —0.225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41]. 

Koryta et al. [48] first stressed the relevance of adsorbed phospholipid monolayers at the ITIES for clarification of biological membrane phenomena. Girault and Schiffrin [49] first attempted to characterize quantitatively the monolayers of phosphatidylcholine and phos-phatidylethanolamine at the ideally polarized water-1,2-dichloroethane interface with electrocapillary measurements. The results obtained indicate the importance of the surface pH in the ionization of the amino group of phosphatidylethanolamine. Kakiuchi et al. [50] used the video-image method to study the conditions for obtaining electrocapillary curves of the dilauroylphosphatidylcholine monolayer formed on the ideally polarized water-nitrobenzene interface. This phospholipid was found to lower markedly the surface tension by forming a stable monolayer when the interface was polarized so that the aqueous phase had a negative potential with respect to the nitrobenzene phase [50,51] (cf. Fig. 5). 

Jarvis, N.L. and Zisman, W.A. "Surface Activity of Fluorinated Organic Compounds at Organic-Liquid/Air Interfaces Part II. Surface Tension vs Concentration Curves, Adsorption Isotherms, and Force-Area Isotherms for Partially Fluorinated Carboxylic Esters," Naval Research Labs Report 5364, Surface Chemistry Branch, Chemistry Division, October 8, 1959. 

Figure 2.1 (a) A schematic representation of the apparatus employed in an electrocapillarity experiment, (b) A schematic representation of the mercury /electrolyte interface in an electro-capillarity experiment. The height of the mercury column, of mass m and density p. is h, the radius of the capillary is r, and the contact angle between the mercury and the capillary wall is 0. (c) A simplified schematic representation of the potential distribution across the metal/ electrolyte interface and across the platinum/electrolyte interface of an NHE reference electrode, (d) A plot of the surface tension of a mercury drop electrode in contact with I M HCI as a function of potential. The surface charge density, pM, on the mercury at any potential can be obtained as the slope of the curve at that potential. After Modern Electrochemistry, J O M. 

Thus, we now have a reasonable model of the interface in terms of the classical Helmholtz model that can explain the parabolic dependence of y on the applied potential. The various plots predicted by equation (2.18) are shown in Figures 2.5(a) to (c). The variation in the surface tension of the mercury electrode with the applied potential should obey equation (2.18). Obtaining the slope of this curve at each potential V (i.e. differentiating equation (2.18)), gives the charge on the electrode, [Pg.49]

What characterizes surfactants is their ability to adsorb onto surfaces and to modify the surface properties. At the gas/liquid interface this leads to a reduction in surface tension. Fig. 4.1 shows the dependence of surface tension on the concentration for different surfactant types [39]. It is obvious from this figure that the nonionic surfactants have a lower surface tension for the same alkyl chain length and concentration than the ionic surfactants. The second effect which can be seen from Fig. 4.1 is the discontinuity of the surface tension-concentration curves with a constant value for the surface tension above this point. The breakpoint of the curves can be correlated to the critical micelle concentration (cmc) above which the formation of micellar aggregates can be observed in the bulk phase. These micelles are characteristic for the ability of surfactants to solubilize hydrophobic substances in aqueous solution. So the concentration of surfactant in the washing liquor has at least to be right above the cmc. 

Surface tension-potential difference curves for each electrolyte against mercury are plotted in the capillary electrometer, the result being shown in Fig. 16. At P there is, according to Helmholtz, no potential difference between Hg — KC1, and at R none between Hg — KI. If the effects at the interface were purely electrostatic, i.e., dependent only on the lines of force, and if the anions had no specific influence, then QS should be zero. Actually, however, it represents a potential difference of 0 2 volt. 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

Helfrich has shown [18] that the surface tension of a curved interface can be expressed as a Taylor series up to second order in the radius of curvature ... 

Equation 9.6 determines the conditions of a mechanical equilibrium of the curved interface. This can be illustrated with an example of a spherical bubble of radius r. To compete the surface tension the pressure inside the bubble should exceed the external pressure with AP, which is determined from the work, W, for virtual change of r dll APdl adl. Under equilibrium, dll = 0 and APdU=erd4, thus... 

If surface tension, analogous to that in liquids, really exists in solids, then also capillary pressure Pc must exist (Laplace 1805). The pressure at any point on the concave (convex) side of a curved interface would be by... 

It will be shown here that, due to the presence of surface tension in liquids, a pressure difference exists across the curved interfaces of liquids (such as drops or bubbles). This capillary force will be analyzed later. 

The r, N curve for the adsorption of pyridine from an aqueous solution at a water-uncharged mercury interface. The surface tension measurements employed are those found by Gouy Ann. de Ghimie et de Physique, vill. ix. 130, 1906), whilst the pyridine activities are derived from the vapour pressure data of Zadwiski... 

The profiles of pendant and sessile bubbles and drops are commonly used in determinations of surface and interfacial tensions and of contact angles. Such methods are possible because the interfaces of static fluid particles must be at equilibrium with respect to hydrostatic pressure gradients and increments in normal stress due to surface tension at a curved interface (see Chapter 1). It is simple to show that at any point on the surface... 

Is It Possible to Measure Surface Tension of Solid Metal and Solution Interfaces In contrast to measurement of surface tension for liquids, the direct measurement of surface tension for solids can be considered an impossible task. However, it is possible to apply indirect measurements to obtain electrocapillary curves of solid electrodes and therefore the information from these curves. 

The surface tension was stated (Section 6.4.5), on general grounds, to be related to the surface excess of species in the interphase. The surface excess in turn represents in some way the structure of the interface. It follows therefore that electrocapillaiy curves must contain many interesting messages about the double layer at the electrode/ electrolyte interface. To understand such messages, one must learn to decode the electrocapillary data. It is necessary to derive quantitative relations among surface tension, excess charge on the metal, cell potential, surface excess, and solution composition. 

With liquid metals, the most convenient method of determining the pzc is by making electrocapillary measurements. From the y versus V curve, the qM versus V curve can be found and thus the value of 0 or E. The pzc, however, is such a fundamental characteristic of the interface that there is a considerable need to know its value for interfaces involving solid electrodes. Here, surface tensions cannot be determined with capillary electrodes, and one must resort to other methods of pzc determination. Some values of the pzc for solid metals are given in Table 6.4. 

The presence of surface tension has an important implication for the pressures across a curved interface and, as a consequence, for phase equilibria involving curved interphase boundaries. The equation that relates the pressure difference across an interface to the radii of curvature, known as the Laplace equation, is derived in Section 6.4, and the implications for phase equilibria are considered for some specific cases in Section 6.5. 

SURFACE TENSION IMPLICATIONS FOR CURVED INTERFACES AND CAPILLARITY... 

Equation (42) provides a thermodynamically valid way to determine y for an interface involving a solid. The thermodynamic approach makes it clear that curvature has an effect on activity for any curved surface. The surface free energy interpretation of y is more plausible for solids than the surface tension interpretation, which is so useful for liquid surfaces. Either interpretation is valid in both cases, and there are situations in which both are useful. From solubility studies on a particle of known size, y5 can be determined by the method of Example 6.2. 

Surface tensions for the interface between air and aqueous solutions generally display one of the three forms indicated schematically in Figure 7.14. The type of behavior indicated by curves 1 and 3 indicates positive adsorption of the solute. Since dy/dc and therefore dy/d In c are negative, E must be positive. On the other hand, the positive slope for curve 2 indicates a negative surface excess, or a surface depletion of the solute. Note that the magnitude of negative adsorption is also less than that of positive adsorption. 

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