Area per surfactant molecule

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The surfactant heads are treated as a monolayer adsorbed at the micellar interface, and thei interactions are a function of the head cross-sectional areas of both surfactants as well as the com position. The larger the surfactant heads, the higtjeA smaller area per surfactant molecule, as in cylindrical micelles, leads to a highga, while a larger area per surfactant molecule, as in spherical micelles, leads to a loweafet (Shiloach and Blankschtein, 1998). 

Consequently, a particular O/W or W/O droplet can be completely characterized by three geometrical variables. A set of convenient variables is (i) the surface area of the droplet in contact with water per surfactant molecule, a, (ii) the ratio of alcohol-to-surfactant molecules in the interfacial layer, gAi/gsi, and (iii) the ratio of oil-to-surfactant molecules in the interfacial layer, goi/gsi- For a flat interfacial layer, denoting the layer thickness by Ro — J wIf and the area per surfactant molecule of the flat interface by ap, one can write the following on the basis of molecular packing considerations ... 

For given values of the control variables Xsw and. Xaw, the maximum in Xgo (or Xgw) was found, using the IMSL subroutine ZXMWD, by solving the implicit eq 3.1 in combination with eq 3.4. As mentioned in section 2, the area per surfactant molecule a, the alcohol-to-surfactant ratio gAi4 si, and the oil-to-surfactant ratio golgsi in the interfacial layer were selected as the three independent variables with respect to which the maximization was carried out. The total volume fraction 4>s of surfactant present in the microemulsion is given by... 

The maximum of Qf is determined with respect to the two independent variables, the area per surfactant molecule of the interface, aF, and the alcohol-to-surfactant ratio in the interfacial layer, (gAs/gsih- In contrast to that in the droplet-type microemulsion, the oil-to-surfactant ratio in the interfacial layer, (goi/gsi)F, is not an independent variable but is determined by the packing constraint (eq 2.7) for flat layers. 

Figure 6. Thicknesses of the interfacial layers of droplets (circles) and areas per surfactant molecule of the droplets at an oil-water interface (squares) as functions of the volume ratios of alcohol to surfactant in microemulsions for systems containing O/W (filled symbols) and W/O (open symbols) droplets. All the system characteristics are identical to those described for Figure 3.

These deviations were accounted by Strey et al.,8 who carried out experiments with the binary water—C12E5 system, by noting that the amplitude of the thermal undulations increased with the repeat distance d. If one considers the total area of the interface a constants which depends only on the number of surfactant molecules, the projection So of the total area on a plane perpendicular to d will decrease with increasing d. Hence, the apparent area per surfactant molecule, which is defined as the ratio between So and the total number of surfactant molecules, decreases with increasing d, while the ideal dilution law implies that the apparent area per surfactant molecule is a constant. The excess area, defined as AS = S — So, was related to the bending modulus of the interface,8 and the experimental results for the deviations from the ideal dilution law were used to determine. Kc-3,11 However, it should be noted that there are binary systems for which the deviations from the ideal dilution law occur in the opposite directions. For instance, in the binary systems of fatty acid alkali soaps/water, the apparent area per headgroup increases with water dilution, because of the incorporation of water in the interface.1... 

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 high homogeneity and rather well-defined character of those latexes is clearly observed. Again, already surfactant loads as low as 1.8% relative to the dispersed phase result in stable latexes. The particle size is getting smaller with increasing amounts of the surfactant, and the surface area per surfactant molecule Asurf is between 18 nm2 at low surfactant amounts (1.8 rel.%) and 7 nm2 for higher surfactant amounts (7.1 rel.%), depending on the particle size. 

A crucial parameter-free test of the theory is provided by its application to micelle formation from ionic surfactants in dilute solution [47]. There, if we accept that the Poisson-Boltzmann equation provides a sufficiently reasonable description of electrostatic interactions, the surface free energy of an aggregate of radius R and aggregation number N can be calculated horn the electrostatic free energy analytically. The whole surface free energy can be decomposed into two terms, one electrostatic, and another due to short-range molecular interactions that, from dimensional considerations, must be proportional to area per surfactant molecule, i.e. 

The area per surfactant molecule at the hydrophobic-hydrophilic interface -the head-group area - is prescribed by the temperature, water content, steric effects and ionic concentration for ionic surfactants. Assume for now that the area per each surfactant "block" making up the assembly is set a priori. This assumption implies that the surface to volume ratio of the mixture (assumed to be homogeneous) is set by the concentration of the surfactant. So the interfacial topology is predetermined by this global constraint, the surface to volume ratio. 

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 ... 

Total interfacial area = Total number of surfactant molecules (n ) x area per surfactant molecule (A ) -H total number of cosurfactant molecules x area per cosurfactant molecule... 

Ruckenstein and Chi presented a thermodynamic treatment of a microemulsion consisting of fixed amounts of oil, water, and surfactant. The analysis yielded an optimum droplet diameter, demonstrated that the entropy of dispersion made an important contribution to microemulsion free energy, and confirmed that a very low interfacial tension of the droplets was required for thermodynamic stability. Indeed, to a first approximation, we can often estimate droplet size by taking the area per surfactant molecule as that for which interfacial tension would be zero. 

Calculate the number of polymerizing particles per liter of water using the following additional data surface area per surfactant molecule = 5x10 cm rate of volume increase of latex particle = 4x10 cm s kd of K2S2O8 at 60°C = 6x10" s-i. 

The addition of an alcohol that adsorbs at the interface, such as n-pentanol, decreases Acw by increasing the interfacial area per surfactant molecule. The addition of electrolyte, in the case of an ionic surfactant, decreases ACw and increases Ahh- All these changes result in an increase in the value of R. 

DTAB and PAMPS for which x = 10 and 25%. For the smallest degree of charge, the CAC is no longer well defined. One rather observes an inflection point around 1 mM of DTAB, after which the solutions become turbid. If we apply Equation 3 to evaluate the area per surfactant molecule for x = 10% we find close to CAC ... 

Assuming that the surface area per surfactant molecule is everywhere equal or close to the optimum area ao non-spherical micelles can occur alternatively when v/aok > 1/3. Similar critical conditions for the formation of cylindrical micelles and planar bilayers, respectively, are... 

In connection with Eqs. (5.100) and (5.101) Israelachvili et al noted that regardless of the shape all aggregates must satisfy the following two criteria No point within the structure can be farther from the hydrocarbon-water surface than Ic. The total hydrocarbon core volume of the structure Vtot and the total surface area A must satisfy the condition V ot/v = A/oo = ni. The last criterion is only approximate since it assumes that the mean surface area per surfactant molecule is equal to ao. 

As mentioned in the discussion around Eqs. (21)-(24), we need values of the five parameters listed in Eqs. (53) and of the surfactant concentration, Csa, to be able to calculate values of various properties of microemulsions (O/W + O or W/O-fW). Of these five parameters the area per surfactant molecule, (t.,., can be determined accurately from the Gibbs adsorption equation, Eq. (1), and there is only a small uncertainty regarding the values of / and c. 

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