Volume fraction, surfactant

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... 

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. ... 

Consider an ensemble of disk-like micelles composed of a single surfactant species. By analogy with the calculation of cylindrical micelles, find the probability distribution for finding a disk of a given size as a function of the surfactant volume fraction. Contrast the probability distribution for disks with that of cylindrical micelles (where a broad distribution of sizes exists) and comment on the reason for the difference. 

Figure 6 The position of the scattering peak as a function of the surfactant volume fraction 0 at constant / = 4.4 A, [idow = 0.1 A -, and a = 2 A. The Lifshitz line is at = 0.545. The data points are for the water-octane-C4E1 systems of Ref 94. (Redrawn from Ref 36.)...

Figure 16 Variation of the water self-diflfusion coefficient with the water + surfactant volume fraction <1> for three different dilution lines corresponding to different water/surfactant ratios in the ternary DDAB-water-dodecane system. Above a certain concentration, which depends on the water/surfactant ratio, the water diffusion coefficient increases dramatically, indicating a water droplet-to-bicontinuous transition. (Data from Ref. 48.)...

Figure 27 The relative self-diffusion coefficient (D/Do) of water plotted as a function of the surfactant volume fraction in the L3 and bicontinuous cubic phases of the AOT-water-NaCl system. Note the continuous variation of the self-diffusion coefficient across the L3-cubic phase transition, demonstrating the structural similarity of the two phases. (Data taken from Ref. 34.)...

Figure 5 Relative diffusion coefficients (D/Dq) of water (triangles) and oil (circles) plotted as a function of a reduced temperature T— 7b)/C>g, where Tq is the balance temperature and g is the surfactant volume fraction, inthemainnticroemulsion channel of a Shinoda-cut diagram. Open S5mibols refer to the Cj2E5/water/cyclohexane/tetradecane (equal weights of cyclohexane and hexadecane) system (20) and filled s)mibols to the Cj2E5/water/tetradecane system (18). The data illustrate the s)mi-metric inversion of the micro structure aroimd Jq. (For a further discussion about the chosen re...

Figure 17.7. Variation of the zero shear viscosity, x], with the surfactant volume fraction, , of solutions of the cationic gem-ini surfactant Ci2H25N(CH3)2-(CH2)2-N(CH3)2Ci2H25 +. 2Br at 20°C. (From F. Kern et al., Langmuir, 10, 1714 (1994))...

Figure 25 Morphological behavior of surfactant in aqueous solution surfactant volume fraction <1> verses molar ratio CJC of salt over surfactant concentrations. (Reprinted with permission from Ref. 66. Copyright 1994 American Chemical Society).

The variation of the percentage of TBHQ in each region with the surfactant volume fraction Oj is illustrated in Figure 4. 

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