Area per surfactant ion

The above treatment, however, requires knowledge of the Hamaker constant, and a, the area per surfactant ion. To obtain these quantities the experimental data of the polymer-free raicroemulsion system containing 5 gm/dl TRS 10-410 and 3 gm/dl XBA have been utilized. From the solubilization data, the volume fraction of drops at different salinities was calculated. This is indicated by the dotted line in Figure 13. The radius of the droplets has been reported as a function of salinity by Mukherjee (26). For the salinity range of interest, the radius a in °A is empirically related as follows 0... 

As mentioned above, i"2 can be calculated from the slope of the linear position of the curves shown in Figure 5.2, just before the cmc is reached. The area per surfactant ion or molecule can be calculated from F-, since... 

As discussed in Chapter 5, the area per surfactant ion or molecule gives information on the orientation of surfactant ions or molecules at the interface. This information is relevant for the stability of the suspension. For example, for the vertical orientation of surfactant ions (e.g., dodecyl sulphate anions), which is essential to produce a high surface charge (and hence an enhanced electrostatic... 

It can be seen that for the A/W interface y decreases from the value for water (72 mNm at 20 °C) reaching about 25-30 mNm near the cmc. This is clearly schematic since the actual values depend on the surfactant nature. For the 0/W case, y decreases from a value of about 50 mNm (for a pure hydrocarbon-water interface) to 1-5 mNm near the cmc (again depending on the nature of the surfactant). F2 can be calculated from the slope of the linear position of the curves shown in Fig. 3.2 just before the cmc is reached. From F2, the area per surfactant ion or molecule can be calculated since... 

The electrostatic contribution to the energy when the only ions present in the solution are those of the counterions of the surfactant molecules, hence in the absence of an added electrolyte, is calculated by integrating the electrostatic pressure from infinity to the distance xi. Denoting the surface charge o, = a, e/A, where a, is the degree of dissociation and A is the area per surfactant molecule adsorbed on the interface, the electrostatic energy per unit area is given by (see Appendix B)... 

The adsorption isotherm is represented by a plot of Tj versus Cj. In most cases, the adsorption increases gradually with increase of Cj, and a plateau Ff is reached at ftiU coverage corresponding to a surfactant monolayer. The area per surfactant molecule or ion at full saturation can be calculated from ... 

The same qualitative conclusions can be drawn from the analysis of curves in Fig.2b. At free pH (pH 6.5 before adsorption), alumina sample represents a moderately-charged hydrophilic substrate because the pH value is close to the pzc. The maximum quantity of adsorption corresponds to the area of 0.52 nm per one adsorbed molecule (cf. 0.35 nm at the water-air interface). For pH 3 surfactant ions achieve a close-packed arrangement in the adsorbed bilayer and the density of bilayer adsorption at the plateau (0.11 nm /molecule) is even less than the air-water interfacial density. At the same time, the cmc is markedly diminished by a decrease in the pH. Both effects can be attributed to the appearance of a non-ionized surfactant species in a solution. The neutral form of the surfactant is less soluble in water and thus exhibits a greater affinity for a hydrophobic surface of alumina modified with grafted aliphatic chains. The decresed repulsion between uncharged heads causes a closer packing of the adsorbate in a mixed surface structure. 

Recently it has been also shown that the surface tension of micellar solutions above the CMC can respond to the transition between spherical and rodlike micelles taking place in micellar solutions of certain surfactants in the presence of multivalent ions, such as Al [65], The qualitative explanation of this phenomenon is connected with the ability of ion to bind three surfactant headgroups, and, consequently, to lower the area per headgroup. According to Israelachvili et al., [11] this can induce a transition from spherical to rodlike micelles. On the other hand, the new micelles adsorb additional Al ions from the bulk. This leads also to a lower adsorption of Al at the solution-gas interface because the competitive adsorption of the counterions follows the same tendency as their bulk concentration. The desorption of Ap causes sharp increase of the surface tension with increasing molar ratio. 

It is remarkable that the minimal (excluded) area per adsorbed surfactant molecule, a = 1/F , obtained from the best fit of surface tension data by the van der Waals isotherm practically coincides with the value of a estimated by molecular size considerations (i.e., from the maximal cross-sectional area of an amphiphilic molecule in a dense adsorption layer) see for example Figure 7.1 in Ref. [36]. This is illustrated in Table 4.5, which contains data for alkanols, alkanoic acids, (SDS), (DDES), cocamidopropyl betaine (CAPE), and C -trimethyl ammonium bromides (n = 12, 14, and 16). The second column of Table 4.5 gives the group whose cross-sectional area is used to calculate a. For molecules of circular cross section, we can calculate the cross-sectional area from the expression a = %r, where r is the respective radius. For example [54], the radius of the S04 " ion is r = 3.09 A, which yields a = = 30.0 A. In the fits of surface tension data by the van der Waals... 

The adsorption of ionic surfactants on hydrophobic polar surfaces resembles that for carbon black [8, 9]. For example, Saleeb and Kitchener [8] found a similar limiting area for cetyltrimethylammonium bromide on Graphon and polystyrene ( 0.4 nm ). As with carbon black, the area per molecule depends on the nature and amount of added electrolyte. This can be accounted for in terms of reduction of head group repulsion and/or counter ion binging. 

The lamellar phase consists of aqueous layers with thickness, 2L, alternating with surfactant bilayers, thickness 2b, as illustrated in figure 2. The surfactant molecules are assumed to be totally incorporated into the lamella making the average charge density determined by the composition and the area per molecule. The ions X and X are assumed to reside in the aqueous layer, where they partly have the role of counterions, or X depending on the A /A ratio, and partly the role of a screening electrolyte. 

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