Radius of micelles

Hydrodynamic radius of micelles formed, RH Radius of gyration, RG... 

Eigure 9.12 shows the variation of (ymin) as a function of a/R (encounter radius to radius of micelle) obtained by varying the concentration for the survival probability, which is given as... 

Fig. 9.12 Variation of (ymin) as a function of a/R (encounter radius to radius of micelle) at zero time. The micelle contains a 1 scavenger, b 5 scavengers and c 10 scavengers. Encounter distance was varied using a fixed sphere radius of 30 A. Smol and Sphere refer to Eqs. (9.47) and (9.49) respectively. Units of y-axis are in units of A...

FIG. 11 Eigenvalues of the radius of gyration tensor (dots largest, squares middle triangles smallest) of micelles vs aggregation number N in an oif-lattiee model of H2T2 surfaetants. The mieelle size distribution for this partieular system has a peak at 28. (From Viduna et al. [144].)... 

The overall radius of the micelle, R, is dominated by the corona whose thickness is, from Table 1, Lcorona f1/5NA/5a and leads to ... 

Highly monodisperse reversed micelles are formed by sodium bis(2-ethylhexyl) sul-fosuccinate (AOT) dissolved in hydrocarbons that are in equilibrium with monomers whose concentration (cmc) is 4 X 10 M, have a mean aggregation number of about 23, a radius of 15 A, exchange monomers with the bulk in a time scale of 10 s, and dissolve completely in a time scale of 10 s [1,2,4,14], Other very interesting surfactants able to form reversed micelles in a variety of apolar solvents have been derived from this salt by simple replacing the sodium counterion with many other cations [15,16],... 

FIG. 4 Onion model of spherical water-containing reversed micelles. Solvent molecules are not represented. A, surfactant alkyl chain domain B, head group plus hydration water domain C, hulk water domain. (For water-containing AOT-reversed micelles, the approximate thickness of layer A is 1.5 nm, of layer B is 0.4 nm, whereas the radius of C is given hy the equation r = 0.17R nm.)... 

With the development of new instrumental techniques, much new information on the size and shape of aqueous micelles has become available. The inceptive description of the micelle as a spherical agglomerate of 20-100 monomers, 12-30 in radius (JJ, with a liquid hydrocarbon interior, has been considerably refined in recent years by spectroscopic (e.g. nmr, fluorescence decay, quasielastic light-scattering), hydrodynamic (e.g. viscometry, centrifugation) and classical light-scattering and osmometry studies. From these investigations have developed plausible descriptions of the thermodynamic and kinetic states of micellar micro-environments, as well as an appreciation of the plurality of micelle size and shape. 

Figure 3 Example of SANS curves at two times of the reaction. The lines are calculations of the form factor. (A) prior to TEOS addition, the micelles are well described by core-shell spheres, with an external radius of 7.1 ran. ( ) 15 minutes after the beginning of the reaction, the micelles can be viewed as cylinders of length 50 nm and radius 6.9 nm.

The reverse microemulsion method can be used to manipulate the size of silica nanoparticles [25]. It was found that the concentration of alkoxide (TEOS) slightly affects the size of silica nanoparticles. The majority of excess TEOS remained unhydrolyzed, and did not participate in the polycondensation. The amount of basic catalyst, ammonia, is an important factor for controlling the size of nanoparticles. When the concentration of ammonium hydroxide increased from 0.5 (wt%) to 2.0%, the size of silica nanoparticles decreased from 82 to 50 nm. Most importantly, in a reverse microemulsion, the formation of silica nanoparticles is limited by the size of micelles. The sizes of micelles are related to the water to surfactant molar ratio. Therefore, this ratio plays an important role for manipulation of the size of nanoparticles. In a Triton X-100/n-hexanol/cyclohexane/water microemulsion, the sizes of obtained silica nanoparticles increased from 69 to 178 nm, as the water to Triton X-100 molar ratio decreased from 15 to 5. The cosurfactant, n-hexanol, slightly influences the curvature of the radius of the water droplets in the micelles, and the molar ratio of the cosurfactant to surfactant faintly affects the size of nanoparticles as well. 

The translational diffusion coefficient of micelles loaded with a fluorophore can be determined from the autocorrelation function by means of Eqs (11.8) or (11.9). The hydrodynamic radius can then be calculated using the Stokes-Einstein relation (see Chapter 8, Section 8.1) ... 

In contrast to the above results, all three "picket fence" porphyrins are solubilized in an oil-in-water microemulsion to yield a clear solution having a Soret band at 419-421 nm resembling that of H2PF,TPro solubilized in micelles. In this case the microemulsion (composed of SDS, n-pentanol and dodecane) consists of oil "droplets" dissolved in bulk water the radius of the droplet has been estimated to be 37 A ( ), well over twice that estimated for an SDS micelle (16 A). Since the droplet in the microemulsion contains a much larger "interior", it is reasonable that it may be a better medium for solubilizing the porphyrin. 

The radius of the spherical micelle is reported to be 20 A, which increases to 23 A for the nonspherical micelle. 

Size analyses of (using light scatter) some spherical micelles of SDS have indeed shown that the radius of the micelle is almost the same as the length of the SDS molecule. However, if the solute interferes with the outer polar part of the micelle, then the micelle system may change in such a way that the CMC and other properties change. This is observed in the case of the addition of dodecanol to SDS solutions. However, very small additions of solutes show very little effect on CMC. The data in Figure 3.18 show the change in the solubility of naphthalene in SDS aqueous solutions. 

An illustration of the effect of micelle/nanoparticle volume fraction on contact line motion is found in [57]. They used 0.1 M NaCl solution to reduce the electrical double layer thickness surrounding the NaDS micelle. At a given number concentration of micelles, decreasing the size of each micelle decreases the volume fraction greatly, since the volume of each spherical micelle varies as the third power of the radius. Thus, the addition of electrolyte effectively reduced the micellar volume fraction in the aqueous medium. The authors found that the oil droplet that would otherwise become completely detached from the solid surface, came back to reattach itself to the solid when electrolyte was present. They rationalized this finding as being caused by the inability of the weakened structural disjoining forces to counteract the attraction of the oil drop to the solid surface. 

The effect of increasing only the radius of curvature of the oil drop on the displacement of the contact fine while keeping the interfacial tension constant at 20 dyn/cm, is illustrated in Figs. 9 and 11. Figure 11 shows that for a radius of a curvature of 100 xm, there is virtually no movement of the contact fine from the base case due to the presence of nanoparticles/micelles even at volume fraction 0.25. However, when the radius of curvature is increased to 500 xm (recall Fig. 9), thereby decreasing the capillary pressure, the presence of nanoparticles at the same concentration moves the contact fine by 1 xm. 

The parameter Wi which takes the concentration of the non-aggregated surfactant in the oil into account - the cpc - is directly proportional to the radius of the reverse micelles rrev. mic. because of the volume to surface ratio of spherical droplets [64-66] ... 

Figure 9.6 Aqueous micelles from sodium dodecylsulfate (SDS) and their physical properties. Average radius of a micelle (7 h), 2.2 nm average aggregation number, 62 approximate relative mass of a micelle (Mr), 1.8 x 10 average half-life of a SDS molecule in the micelle, 0.1 ms CMC (25 °C, H2O), 8.1 x 10 M i.e., monomer concentration by 10 g SDS 1 (35 mM), 2.3 g 1 ...

Figure 9.10 Some structural details and dynamic properties of reverse micelles 50 irtM AOT/isooctane, Wo = 11.1 (= 10 p lHoOperml), 25°C 3.2% AOT (w/w), 1.4% H2O (w/w) mean water pool radius 20 A, mean hydrohynamic radius 32 A concentration of micelles 400 (xM, monomer AOT concentration 0.6-0.9 mM aggregation number 125 total interfacial area 14 m mC (Adapted from Fletcher and Robinson, 1981, and Harada and Schelly, 1982.)...

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