Surface excess concentration measurement

In summary, molecular dynamics has confirmed what was expected from surface excess concentration measurements—that the more miscible the solvents, the rougher the interface, the lower the interfacial tension. It has also confirmed that lipophilic ions are specifically adsorbed on the organic side of the interface. In addition, it has introduced the concept of water protrusions or water fingers in the organic phase. It has clearly shown that the presence of ionic species enhances the formation of protrusions. In the case of solvents with a hydrocarbon chain such as hexanol, heptanone, or nitrophenyloctyle-ther, molecular dynamics has demonstrated the layering of the first organic solvent molecules. 

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... 

The surface excess is measurable. There are essentially two approaches to its measurement. One approach is to make use of the fact that the surface excess of a species is approximately equal to its adsorption on the electrode when the bulk concentration of that species is extremely low. Under these conditions, the surface excess can be approximately known by directly measuring adsorption. How can this be done ... 

EXAMPLE 7.4 Determination of Surface Excess Concentration from Surface Tension Data. The slope of the 25°C line in Figure 7.15 on the low-concentration side of the break is about -16.7 mN m 1. Calculate the surface excess and the area per molecule for the range of concentrations shown. How would Figure 7.15 be different if accurate measurements could be made over several more decades of concentration in the direction of higher dilution Could the data still be interpreted by Equation (49) in this case ... 

When a solute avoids the interface (T < 0), the surface tension increases by adding the substance. Experimentally Equation (3.52) can be used to determine the surface excess by measuring the surface tension versus the bulk concentration. If a decrease in the surface tension is observed, the solute is enriched in the interface. If the surface tension increases upon addition of solute, then the solute is depleted in the interface. 

For equilibrium pressures higher than px, for which surface excess concentration can be measured, the value of the integral term of Equation (2.34) is obtained by evaluation of the area under the curve n/p - i(p), between pressures p, and p. 

The basic information in the study of sorption processes is the quantity of substances on the interfaces. In order to measure the sorbed quantity accurately, very sensitive analytical methods have to be applied because the typical amount of particles (atoms, ions, and molecules) on the interfaces is about I0-5 mol/m2. In the case of monolayer sorption, the sorbed quantity is within this range. As the sorbed quantity is defined as the difference between quantities of a given substance in the solution and/or in the solid before and after sorption processes (surface excess concentration, Chapter 1, Section 1.3.1), all methods suitable for the analysis of solid and liquid phases can be applied here, too. These methods have been discussed in Sections 4.1 and 4.2. In addition, radioisotopic tracer method can also be applied for the accurate measurement of the sorbed quantities. On the basis of the radiation properties of the available isotopes, gamma and beta spectroscopy can be used as an analytical method. Alpha spectroscopy may also be used, if needed however, it necessitates more complicated techniques and sample preparation due to the significant absorption of alpha radiation. The sensitivity of radioisotopic labeling depends on the half-life of the isotopes. With isotopes having medium half-time (days-years), 10 14-10-10 mol can be measured easily. 

For the liquid vapor interface, the surface tension is easUy measured as a function of the concentration as shown in Figure 9.10. The preceding equation can he used to determine the surface excess concentration of surfactant as a function of the sur ctant concentration if the sur ce tension of the solution as a fimction of surfactant concentration is known. For dilute aqueous solutions of organic substrates, the semi-empirical equation for the surface tension, y, of a solution of concentration C2,... 

A study of iron, cadmium and lead mobility in remote mountain streams of California by Erel et al. (1990) showed that the excess of atmospheric pollution-derived lead and cadmium is rapidly removed downstream. The comparison of truly dissolved, colloidal, and surface particle concentrations measured in the stream with the results of a model of equilibrium adsorption indicates that the mechanism of removal in this organic-poor environment is essentially by uptake onto hydrous iron oxides. The experimentally determined partition coefficients (Dzomback and Morel, 1990) explain the behavior of lead however, they fail to explain the cadmium removal. It is proposed by the authors that cadmium is taken up by surfaces other than hydrous iron oxides. 

The surface excess concentration ( surface concentration) at surface saturation Tm is a useful measure of the effectiveness of adsorption of the surfactant at the L/G or L/L interface, since it is the maximum value that adsorption can attain. The effectiveness of adsorption is an important factor in determining such properties of the surfactant as foaming, wetting, and emulsification, since tightly packed, coherent interfacial films have very different interfacial properties than loosely packed, noncoherent films. Table 2-2 lists values for the effectiveness of adsorption Tm, in mol/cm2, and the area per molecule at the interface at surface saturation asm, in square angstroms (which is inversely proportional to the effectiveness of adsorption) for a wide variety of anionic, cationic, nonionic, and zwitterionic surfactants at various interfaces. 

Cosorption Lines Contours of equal surface activity as measured by the Gibbs surface excess concentrations plotted on phase diagrams. See p 131 of reference 9. 

Surface chemists, who are used to these sorts of problems, have defined a quantity called the surface excess, a measure of surface concentration per unit area which can be related to macroscopic, measurable thermodynamic variables such as the change in interfacial tension. The surface excess, denoted P, of a soluble surfactant is defined as the excess amount per unit area present in a finite section through the surface (i.e., including some of each phase) compared to the amount that would be present in an identical section of the aqueous bulk phase containing the same number of moles of water as the surface section. It can be shown that such a definition implies the existence of a plane such that the excess of water present in the fuzzy air phase above is balanced by the depleted amount of water in the fuzzy water phase below. The surface excess of the water is thus taken as zero. If this plane is taken as the zero of a depth scale into the bulk solution and c(x) is the profile of concentration of a surface-adsorbed species, it can be shown that ... 

For most of the conventional amphiphiles it was demonstrated by Rosen [141] that at a surface pressure H = 20 mN/m the surface excess concentration reaches 84-100 % of its saturation value. Then, the (l/c)n=2o value can be related to the change in free energy of adsorption at infinite dilution AG , the saturation adsorption F and temperature T using the Langmuir and von Szyszkowski equations. The negative logarithm of the amphiphile concentration in the bulk phase required for a 20 mN/m reduction in the surface or interfacial tension can be used as a measure of the efficiency of the adsorbed surfactant ... 

The results of flic interfacial rheological studies on asphaltene adsorption at oil-water interfaces teach us a great deal about the behavior of asphaltenes and their role in emulsion stabili2ation. The conclusions drawn are based largely on the assumption that the rheological properties measured, namely flic elastic film modulus G are directly related to the surface excess concentration of asphaltenes. F. It is understood diat die elastic modulus actually depends on both the surface excess concenlration and the relative conformation (i.e., coimectivity) of the adsorbed asphaltenes. It is further understood that a minimum adsorbed level is required to observe a finite value of G and that the relationship between G and G is not linear. With these caveats in mind, we can conclude die following ... 

The preceding discussion of the Gibbs adsorption equation was referenced to a fluid-fluid interface in which the surface excess, T, is calculated based on a measured quantity, a, the interfacial tension. For a sohd-fluid interface, the interfacial tension cannot be measured directly, but the surface excess concentration of the adsorbed species can be, so that the equation is equally useful. In the latter case. Equation (9.16) provides a method for determining the surface tension of the interface based on experimentally accessible data. 

It is well known that the air/solution interface of an amphiphile solution is well populated (Clint, 1992) by the adsorbed molecules. Accordingly, it has been shown that the concentration of the surfactant is always greater at the surface due to adsorption over and above the concentration of surfactant in the bulk. For calculation of Gibbs free energy changes, required different surface properties (e.g., the surface excess concentration, Tmax, minimum area per surfactant molecule at the air/water interface, Amin etc.). The surface excess concentration is an effective measure of the Gibbs adsorption at liquid/air interface, which was calculated by applying equation (Chattoraj Birdi, 1984)... 

On the other hand, the changes caused by specific adsorption of anions in the solution side of the double layer can also be followed through the measurement of TCO4 adsorption. Specifically adsorbed anions depending on the extent of their adsorption compensate the positive charge of a protonated surface therefore, the negative charge on the solution side, i.e., the surface excess concentration of nonspecifically adsorbed anions, should decrease. This effect is well demonstrated by the curve presented in Fig. 9. 

Back in 1983, the concept of mixed solvent layer [16] resulted from the determination of water surface excess concentrations at different interfaces by interfacial tension measurements that showed that, in the case of the H2O-DCE interface, and unlike the liquid water-vapor or the water-heptane interfaces, the water excess concentration was less than a monolayer as expected for aqueous 1 1 electrolyte. The molecular dynamics results of Wick and Dang seem therefore to corroborate this early concept of interfacial structure in the presence of electrolytes in the aqueous phase. 

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 ... 

The characterization of the adsorption of surfactant at a water-solid interface is more difficult than at the water-air interface for two reasons First, the interfacial tension cannot be measured directly and, second, its relation to the surfactant surface excess concentration is not always straightforward. 

The surface excess concentration under conditions of surface saturation, T, may conveniently be used as a measure of the maximum extent of adsorption of a surfactant. Several factors determine the maximum amount of surfactant which can be adsorbed at an interface. 

Tadros [37] determined the area per molecule for Monflor surfactants from surface tension measurements. The area per molecule in the adsorbed monolayer was calculated from the surface excess concentration, F, determined from the linear portion of the y-log C curve above cmc (Fig. 4.4). Equation (7) was used for nonionic and Eq. (12) for ionic surfactants (Table 4.2). 

Here, F is the surface excess of the solute and a is its activity. The change in surface tension of the liquid is at constant temperature that is the reason why Eq. (6.65) is called isotherm. Equation (6.65) tells us that when a solute is enriched at the interface (F > 0), the surface tension decreases when the solution concentration is increased. Such solutes are said to be surface active and they are called surfactants or surface-active agents. Often, the term amphiphilic molecule or simply amphi-phUe is used. When a solute avoids the interface (F < 0), the surface tension increases by adding the substance. Experimentally, Eq. (6.65) can be used to determine the surface excess by measuring the surface tension versus the bulk concentration. If a decrease in the surface tension is observed, the solute is enriched in the interface. If the surface tension increases upon addition of solute, then the solute is depleted in the interface. 

In systems where the interfacial energy can be directly determined (e.g., in L/L and LfV systems), Eq. (3.10) can be used to determine the surface excess concentration of the adsorbed species and, in principle, to relate that quantity to the structure of the molecule. It therefore becomes a useful tool for characterizing a surfactant species at the molecular level and aids in the interpretation of surface phenomena on the basis of chemical composition and molecular structure. In systems where the interfacial energy cannot be measured directly (e.g., in systems involving a solid interface) but the surface concentration can, the equation allows one to calculate changes in the interfacial energy of the system that would otherwise be inaccessible. 

McBain reports the following microtome data for a phenol solution. A solution of 5 g of phenol in 1000 g of water was skimmed the area skimmed was 310 cm and a 3.2-g sample was obtained. An interferometer measurement showed a difference of 1.2 divisions between the bulk and the scooped-up solution, where one division corresponded to 2.1 X 10 g phenol per gram of water concentration difference. Also, for 0.05, 0.127, and 0.268M solutions of phenol at 20°C, the respective surface tensions were 67.7, 60.1, and 51.6 dyn/cm. Calculate the surface excess Fj from (a) the microtome data, (b) for the same concentration but using the surface tension data, and (c) for a horizontally oriented monolayer of phenol (making a reasonable assumption as to its cross-sectional area). 

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