Surface tension variation with concentration

At appreciable concentrations, the variation of the surface tension y with concentration c of aqueous solutions of the lower fatty acids is given by y = A + B log c, where A is a constant for each acid and B is approximately the same for all the acids. Show that the extent of adsorption of a fatty acid at the surface of its aqueous solution is then roughly independent of the concentration of the solution and of the nature of the acid. Suggest a physical interpretation of this result. 

The surface tension of soap solution is typically about one third that of water, which has a surface tension of 72.25 dynes per cm at 20 °C, and varies with the concentration, c, of the soap solution. Fig. 1.16 shows the variation of the surface tension, a, with concentration, c. It has the value for distilled water at c = 0 and decreases monotonically until it reaches its smallest value at the c.m.c., as indicated in Fig. 1.16. 

Because the Gibbs elasticity eo involves a derivative of the surface tension with respect to the surface concentration and the surface concentration is itself a derivative of the surface tension with respect to the bulk concentration, Sc is proportional to d y/dc. The Gibbs elasticity is, therefore, sensitive to very small differences in surface tension variation with surfactant bulk concentration, more sensitive than the surface coverage itself. Both r and e cannot be evaluated by the preceding two equations when the bulk concentration is above the cmc. However, in general, the surface coverage does not change appreciably above the cmc, and the surface properties determined at this concentration can be used as a first approximation for the more concentrated solutions. 

The surface-active properties of the ii.onomers were also confirmed by surface-tension experiments. Figure 3 shows the variation of the surface tension 7 with the concentration of a cationic monomer (MADQUAT) (29) and a neutral one (AM) (Graillat, C.. Pichot, C. unpublished results). The surface-tension drops for example from 70 dyn./cm to 40 dyn/cm when the MADQUAT concentration varies from 10 to eibout 3M (a 3M is the monomer concentration based on the aqueous phase used in most polymerization reactions). However, the amphiphilic character of monomers is not sufficiently pronounced to give rise to micellization since no sharp transition corresponding to the C.M.C. is detectable. 

During the 1870 s, Carlo Marangoni, who was apparently aware of Carra-dori s work but not of Thompson s, formulated a rather complete theory of surface tension driven flow (M2, M3). He noted that flow could result from surface tension variations as they are caused by differences in temperature and superficial concentration, and that, conversely, variations in temperature and concentration could be induced by an imposed surface flow. Marangoni ascribed several new rheological properties to the surface (notably surface viscosity, surface elasticity, and even surface plasticity), while remarking that perhaps some of these properties could be associated only with surface contamination. Most present-day authors ascribe the first explanation of surface tension driven flow to Marangoni, and term such flow a Maragoni effect. ... 

Figure 11 shows the variation of surface tension of 15 wt% HCl with mutual solvent (ethylene glycol monobutylether, EGMBE) concentration. The surface tension decreases with mutual solvent concentration up to 10 wt%, then remains constant. Mutual solvent acts as a surface-active species. A similar behavior was noted by D Angelo and Santucci [63] when mutual solvent was added to distilled water. 

Figure 13.5 shows the variations of surface tension versus surfactant concentration for pure surfactant system and the mixture of polymer/surfactant where the polymer concentration is constant. In the case of pure surfactant solution, a sharp decrease in the surface tension occurs with the increase in surfactant concentration up to the critical micelle concentration (CMC). For surfactant concentrations higher than the CMC, the surface tension remains constant. In the mixture of polymer and surfactant, the surface tension plot shows two break points. The first point is the CAC point where the interaction between the polymer and the surfactant begins. The second point is the PSP point where the polymer chains become saturated with the surfactant. When the interaction between the polymer and surfactant is weak, CAC and PSP values are close to the CMC of pure surfactant (Mohsenipour 2011). 

Extensive surface tension measurements have been performed on aqueous solutions of gemini surfactants with the purpose of investigating their behavior at the air solution interface (measurement of surface area a occupied by one surfactant molecule at the interface) and determining CMCs. The surface areas a were obtained from the slope of the variation of the surface tension 7 with In C (C = surfactant concentration) using the Gibbs expression of the surface excess concentration T ... 

Figure 4.14 Variation of surface tension, y, with log molal concentration, m, for...

Figure 1.5 Dependence of various properties of a solution of an ionic surfactant with the surfactant concentration C. Variations of the refractive index R, density D, specific conductance turbidity T and solubility S of a water-insoluble dye (Orange OT) with C (plots in continuous line), of the osmotic coefficient g and of the equivalent conductance A, with (plots in broken line), and of the surface tension o with log C (plot in dotted line). Reproduced from reference 15 with permission of Elsevier Publishing Co.

Figure 15.3 shows the variation of surface tension y with log HMI concentration. The results clearly show that y decreases linearly with an increase in HMI concentration till a critical concentration is reached above which y remains virtually constant with a further increase in polymer concentration. The break point at the critical concentration can be identified with the CAC. The latter was found to be 6.6 x 10 mol/dm, which is significantly lower than the value obtained using light scattering. It is well known that the CAC value depends on the technique used for its measurement [9]. 

For dilute solutions, solute-solute interactions are unimportant (i.e., Henry s law will hold), and the variation of surface tension with concentration will be linear (at least for nonelectrolytes). Thus... 

The surface tension of an aqueous solution varies with the concentration of solute according to the equation y = 72 - 350C (provided that C is less than 0.05Af). Calculate the value of the constant k for the variation of surface excess of solute with concentration, where k is defined by the equation V = kC. The temperature is 25°C. 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

In Fig. 2.58 (Hetsroni et al. 2001b) the dependencies of the surface tension of the various surfactants a divided on the surface tension of water ow are shown. One can see that beginning from some particular value of surfactant concentration (which depends on the kind of surfactant), the value of the relative surface tension almost does not change with further increase in the surfactant concentration. It should be emphasized that the variation of the surface tension as a function of the solution concentration shows the same behavior for anionic, non-ionic, and cationic surfactants at various temperatures. 

Other experiments performed by Bergeron [34] on air foams stabilized with ionic surfactants reveal that the so-called Gibbs or dilatational elasticity e may play an important role in the coalescence process. The Gibbs elasticity measures the variation of surface tension yi t associated to the variation of the surfactant surface concentration F ... 

The foaming ability of a liquid mixture depends on the magnitude of the variation of surface-tension with concentration, but not on its sign 95). In practice, however, the effect of surface tension on plate efficiency... 

Recently the surface properties of the supramolecular inclusion complex (ICs) obtained from the threading of a-CD onto poly(ethylene oxide) (PEO) free in solution was studied [28], The complex were characterized by IR, H NMR spectroscopy, and thermal analisis. The variation of the interfacial tension, yjnt, with inclusion complex (IC) concentration and temperature were determined. The results were compared with those found for PEO under the same conditions. a-CD does not present surface activity [28], To quantify the adsorption process of IC and PEO in aqueous medium, the following form of Gibbs equation was used [29],... 

Solutions of soaps and other long-chain Colloidal electrolytes. The surface tension of soaps has been very extensively studied,1 but for the most part the results in the literature are discordant far beyond the usual error of measurement of surface tension. In general the surface tension diminishes rapidly with increasing concentration, reaching a steady, or nearly steady, low value after a certain concentration is reached this concentration is naturally lower the longer the hydrocarbon chain. The variation between the results obtained by different experimenters, and even by the same experimenter under different conditions, may... 

Fig. 1 [2] presents the variation of surface tension with concentration, at 25°C. 

Variations to improve accuracy, facilitate handling, or render the method applicable to special systems have been proposed. For instance, Richards and Carver ) developed a capillary with a reflush device (a wider tube, parallel to the vertical capillary) to facilitate rejuvenation of the liquid surface. This apparatus was modified by Young and Gross ). Ramakrishnan and Hartland ) developed a procedure of measuring surface tensions in the annular ring between two concentric cylinders. This approach was duplicated by Agrawal and Menon ). Long ago Sentis ) experimented with an isolated capillary on the lower end of which a... 

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