Surface excess surfactant

The type of behavior shown by the ethanol-water system reaches an extreme in the case of higher-molecular-weight solutes of the polar-nonpolar type, such as, soaps and detergents [91]. As illustrated in Fig. Ul-9e, the decrease in surface tension now takes place at very low concentrations sometimes showing a point of abrupt change in slope in a y/C plot [92]. The surface tension becomes essentially constant beyond a certain concentration identified with micelle formation (see Section XIII-5). The lines in Fig. III-9e are fits to Eq. III-57. The authors combined this analysis with the Gibbs equation (Section III-SB) to obtain the surface excess of surfactant and an alcohol cosurfactant. 

Tajima and co-workers [108] determined the surface excess of sodium dode-cyl sulfate by means of the radioactivity method, using tritiated surfactant of specific activity 9.16 Ci/mol. The area of solution exposed to the detector was 37.50 cm. In a particular experiment, it was found that with 1.0 x 10" Af surfactant the surface count rate was 17.0 x 10 counts per minute. Separate calibration showed that of this count was 14.5 X 10 came from underlying solution, the rest being surface excess. It was also determined that the counting efficiency for surface material was 1.1%. Calculate F for this solution. 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

Nanoparticles of the semicondnctor titanium dioxide have also been spread as mono-layers [164]. Nanoparticles of TiOi were formed by the arrested hydrolysis of titanium iso-propoxide. A very small amount of water was mixed with a chloroform/isopropanol solution of titanium isopropoxide with the surfactant hexadecyltrimethylammonium bromide (CTAB) and a catalyst. The particles produced were 1.8-2.2 nm in diameter. The stabilized particles were spread as monolayers. Successive cycles of II-A isotherms exhibited smaller areas for the initial pressnre rise, attributed to dissolution of excess surfactant into the subphase. And BAM observation showed the solid state of the films at 50 mN m was featureless and bright collapse then appeared as a series of stripes across the image. The area per particle determined from the isotherms decreased when sols were subjected to a heat treatment prior to spreading. This effect was believed to arise from a modification to the particle surface that made surfactant adsorption less favorable. 

One important advantage of the polarized interface is that one can determine the relative surface excess of an ionic species whose counterions are reversible to a reference electrode. The adsorption properties of an ionic component, e.g., ionic surfactant, can thus be studied independently, i.e., without being disturbed by the presence of counterionic species, unlike the case of ionic surfactant adsorption at nonpolar oil-water and air-water interfaces [25]. The merits of the polarized interface are not available at nonpolarized liquid-liquid interfaces, because of the dependency of the phase-boundary potential on the solution composition. 

Electroneutral substances that are less polar than the solvent and also those that exhibit a tendency to interact chemically with the electrode surface, e.g. substances containing sulphur (thiourea, etc.), are adsorbed on the electrode. During adsorption, solvent molecules in the compact layer are replaced by molecules of the adsorbed substance, called surface-active substance (surfactant).t The effect of adsorption on the individual electrocapillary terms can best be expressed in terms of the difference of these quantities for the original (base) electrolyte and for the same electrolyte in the presence of surfactants. Figure 4.7 schematically depicts this dependence for the interfacial tension, surface electrode charge and differential capacity and also the dependence of the surface excess on the potential. It can be seen that, at sufficiently positive or negative potentials, the surfactant is completely desorbed from the electrode. The strong electric field leads to replacement of the less polar particles of the surface-active substance by polar solvent molecules. The desorption potentials are characterized by sharp peaks on the differential capacity curves. 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

Li ZX, Dong CC, and Thomas RK. 1999. Neutron reflectivity studies of the surface excess of Gemini surfactants at the air-water interface. Langmuir 15(13) 4392 -396. 

It has been reported that the sonochemical reduction of Au(III) reduction in an aqueous solution is strongly affected by the types and concentration of organic additives. Nagata et al. reported that organic additives with an appropriate hydro-phobic property enhance the rate of Au(III) reduction. For example, alcohols, ketones, surfactants and water-soluble polymers act as accelerators for the reduction of Au(III) under ultrasonic irradiation [24]. Grieser and coworkers [25] also reported the effects of alcohol additives on the reduction of Au(III). They suggested that the rate of the sonochemical reduction of Au(III) is related to the Gibbs surface excess concentration of the alcohol additives. 

The classic studies of Saunders( 17) demonstrated that in the presence of excess surfactant methyl cellulose (MC) would desorb from monodispersed polystyrene latices. MC is one of the most surface active water-soluble polymers (W-SPs) and it will readily dominate the surface pressure 7T (7T = cre - cr t where cr is the surface tension of water and is the surface tension of the aqueous polymer solution) of the aqueous solution. For example, hydroxyethyl cellulose (HEC) lowers the surface tension of water much less than MC or HPMC, and when the combination of HEC and MC or HPMC in water is studied, there is no notable influence of HEC on the surface pressure (Figure 2). 

Investigations have shown that, if one carefully sucked a small amount of the surface solution of a surfactant, then one can estimate the magnitude of E The concentration of the surface-active substance was found to be 8 pmol/mL. The concentration in the bulk phase was 4 pmol/L. The data show that the surface excess is 8 pmol/mL - 4 pmol/mL = 4 pmol/mL. Further, this indicates that, when there is 8 pmol/L in the bulk of the solution, the SDS molecules completely cover the surface. The consequence of this is that, at a concentration higher than 8 pmol/L, no more adsorption at the interface of SDS takes place. Thus, y remains constant (almost). This means that the surface is completely covered with SDS molecules. The area-per-molecule data (as found to be 50 A2) indicates that the SDS molecules are oriented with the S04- groups pointing toward the water phase, while the alkyl chains are oriented away from the water phase. 

During the past decades, a few experiments have been reported, in which verification of Gibbs adsorption has been reported. One of these methods has been carried out by removing by a microtone blade the thin layer of surface of a surfactant solution. Actually, this is almost the same as the procedure of bubble extraction, that is, merely by a careful suction of the surface layer of solution. The surface excess data for a solution of SDS were found to be acceptable. The experimental data was 1.57... 

The standard approach for describing surfactant adsorption at the gas-liquid interface is based on the Gibbs methodology [16]. The Gibbs dividing surface was introduced and is mathematically defined by the interface line that divides the surface excess of the solvent into two equal parts with opposite signs, and the total surface excess of the solvent is, therefore, equal... 

In Eq. 38, the partial surface coverage, 0i, of the surfactant is defined as 01 = ri/Foo, where Ao is the surface excess of surfactant at saturation. K is the adsorption constant, which is a function of the surfactant and counterion adsorptions. The dependence is usually linear, yielding K = Ki + K20.1, where Ki and A are the equilibrium adsorption constants of the surfactant ions and their counterions. 

To resolve the problem of negative /3 values obtained with the Frumkin theory, the improved Szyszkowski-Langmuir models which consider surfactant orientational states and aggregation at the interface have been considered [17]. For one-surfactant system with two orientational states at the interface, we have two balances, i.e., Ft = Fi + F2 and Ftco = Ficoi + F2C02, which can be used in conjunction with Eq. 24 to derive two important equations for determining the total surface excess and averaged molecular area required in the calculation of surface tension, i.e.,... 

Let us consider the interface between two phases, say between a liquid and a vapour, where a solute (i) is dissolved in the liquid phase. The real concentration gradient of solute near the interface may look like Figure 3.1. When the solute increases in concentration near the surface (e.g. a surfactant) there must be a surface excess of solute nf, compared with the bulk value continued right up to the interface. We can define a surface excess concentration (in units of moles per unit area) as ... 

First, let us consider the surface density of s pfactant. The total surface excess number of moles per unit area r of surfactants is evaluated by using the relation... 

The calculated surface excesses for spheres of 1000A. radius are higher than those for a flat plate of the same potential and surfactant concentration by an amount which increases with increasing potential. Typical results of these calculations are included in Figures 3, 4, and 5. 

Soap bubbles To stabilize a bubble, surfactants are usually added to water. Assume we add a surfactant to a concentration of 2 mM. At this concentration we have a positive surface excess. As an average, each surfactant molecule occupies a surface area of 0.7 nm2. Estimate the change in pressure inside a soap bubble with a radius of 1 cm compared to a hypothetical bubble formed from pure water. 

For ionic surfactants another effect often dominates and usually salt tends to stabilize emulsions. Reason without salt the distance between surfactants in the interface is large because the molecules electrostatically repel each other. This prevents a high surface excess. The addition of salt reduces this lateral repulsion and more surfactant molecules can adsorb at the interface. Then, according to the Gibbs adsorption isotherm Eq. (3.52), the surface tension is reduced and the emulsion is stabilized. 

If we compress a surfactant film on water we observe that the surface tension decreases and the surface pressure increases. What is the reason for this decrease in surface tension We can explain it by use of the Gibbs adsorption isotherm (Eq. (3.52)). On compression, the surface excess increases and hence the surface tension has to decrease. This, however, is relatively abstract. A more illustrative explanation is that the surface tension decreases because the highly polar water surface (high surface tension) is more and more converted into a nonpolar hydrocarbon surface (low surface tension). 

With surfactant the surface tension is reduced according to the Gibbs adsorption isotherm Eq. (3.52). To apply Eq. (3.52) we need to know the surface excess ... 

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