Surfactants Volume

The lowest value of Qeff corresponds to different structures for different along the bifurcation line. The sequence of phases is always the same for various strengths of surfactant (with 7 > 27/4) and for increasing p it is L—>G—>D—>P—>C. For 7 = 50 (strong surfactant, like C10E5) the portion of the phase diagram corresponding to the stable cubic phases is shown in Fig. 14(b). For surfactants weaker than in the case shown in Fig. 14 the cubic phases occur for a lower surfactant volume fraction for example, for 7=16 cubic phases appear for p 0.45. 

The ratio E/ps, calculated for different phases below the bifurcation, is shown in Fig. 15. In the special case of the C phase the surface intersects itself therefore, in the computation of S/p we have subtracted the volume occupied along the lines of intersection, since it would be counted twice otherwise. The surface area per volume is an increasing function of the surfactant volume fraction and it determines the sequence of phases. Moreover, we have found that the effect of broadening of the interface on the value S/p in different phases is different, and we have a quantitative... 

FIG. 15 The projected surface area per unit volume S, divided by the surfactant volume fraction for different structures along the bifurcation line as a function of surfactant volume fraction Note that due to the geometrical constraints this quantity cannot exceed the length of the surfactant a. Here we set a = 1 for convenience. 

FiG. 16 Average Gaussian curvature for 7 = 50 at fixed temperature r = 2.7. is a surfactant volume fraction and a length unit is the size of a surfactant molecule (a bare thickness of the monolayer). 

The first observation of depletion flocculation by surfactant micelles was reported by Aronson [3]. Bibette et al. [4] have studied the behavior of silicone-in-water emulsions stabilized by sodium dodecyl sulfate (SDS). They have exploited the attractive depletion interaction to size fractionate a crude polydisperse emulsion [5]. Because the surfactant volume fraction necessary to induce flocculation is always lower than 5%, the micelle osmotic pressure can be taken to be the ideal-gas value ... 

The observations were interpreted using a well-known similarity solution based on binary diffusion. In each phase j surfactant volume fraction (Pj is given by... 

Anon. (1991) Environmental and Human Safety of Major Surfactants. Volume 1 Anionic Surfactants. Part 1. Linear Alkylbenzene Sulfonates. Part 2. Alcohol Ethyl Sulfates. Part 3. Alkyl Sulfates. Part 4. Alpha Olgin Sulfonates. Volume 2 Nonionic Surfactants, Alcohol Ethoxylates and Alkylphenol Ethoxylates. Government Reports Announcements Index (GRA I). 

The demixing curves in the W/S pseudoternary diagrams for the hexanol and pentanol systems have been calculated according to the above theoretical treatment. These lines have been determined in the following way. The calculation of the state equation is applied to a dilution line along such a line the inverse micelles have a constant radius R. The micelles contain the whole water (volume Vw), the surfactant (volume V ) and a part of the alcohol V. The rest of alcohol is in the oil continuous phase. We suppose that the alcohol-oil ratio in the continuous phase is constant and is equal to k. Besides, in the calculation of the micellar radius R one assumes that the surfactant and the alcohol molecules which are situated at the interface have a constant area per chain s. In mos of the previous studies s has been found constant and equal to 25 A2. This value is taken equal for the alcohol and surfactant chains. Consequently ... 

Refer again to Figure 7.13. First, measure the perpendiculars from the overall composition point to the three sides of the triangle—s, o, and w. Then the total surfactant volume (VJ, total water volume (V ), and total oil volume (V ,) in the... 

Note that the surfactant volume in the microemulsion phase (Vs ) is the same as that in the total system (V,). In other words, all the surfactant is in the microemulsion phase. 

As mentioned earlier, we sometimes conduct an alkalinity scan by changing alkali concentration while the salinity is fixed. Then the activity map can be presented by alkali concentration versus oil volume percent or the ratio of oil volume percent to surfactant volume or weight percent, schematically shown in Figure 12.5. 

A general pattern of microemulsion phase behavior exists for systems containing comparable amounts of water and a pure hydrocarbon or hydrocarbon mixture together with a few percent surfactant. For somewhat hydrophilic conditions, the surfactant films tend to bend in such a way as to form a water-continuous phase, and an oil in water microemulsion coexists with excess oil. Drops in the microemulsion are spherical with diameters of order 10 nm. Both drop size and solubilization expressed as (VJVX the ratio of oil to surfactant volume in the microemulsion, increase as the system becomes less hydrophilic. At the same time interfacial tension between the microemulsion and oil phases decreases. Just the opposite occurs for somewhat lipophilic conditions. That is, a water in oil microemulsion coexists with excess water with drop size and solubilization of water (VJV,) increasing and interfacial tension decreasing as the system becomes less lipophilic. When the hydrophilic and lipophilic properties of the surfactant films are nearly balanced, a bicontinuous microemulsion phase coexists with both excess oil and excess water. For a balanced film (VJV,) and (VJV ) in the microemulsion are nearly equal, as are 7, 0 and... 

Figure 8.2 Fraction of surfactant in monomers (Pi) and in micelles (Pm) for a model where there is only one preferred size m n ox N Af. The critical micelle concentration is denoted by (f)c and (f)s is the surfactant volume fraction.

Since R [ 1), unless (ps is exponentially small. For stiff membranes, where 1, this implies that the vesicles can only exist as a dilute solution for surfactant volume fractions, volume fractions, the lowest free energy state is probably lamellar. Including the effects of the renormalization of the bending modulus to lower values due to long-wavelength fluctuations (see Chapter 6), changes the distribution of Eq. (8.21) from a simple exponential to the product of a power law in N and an exponential. ... 

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