Micelle shape fluctuations

Disordered solutions of spherical micelles are not particularly viscoelastic, or even viscous, unless the volume fraction of micelles becomes high, greater than 30% by volume. Figure 12-7, for example, shows the relative viscosity (the viscosity divided by the solvent viscosity) as a function of micellar volume fraction for a solution of hydrated micelles of lithium dodecyl sulfate in water. Qualitatively, these data are reminiscent of the viscosity-volume-fraction relationship for suspensions of hard spheres, shown as a dashed line (see Section 6.2.1). The micellar viscosity is higher than that of hard-sphere suspensions because of micellar ellipsoidal shape fluctuations and electrostatic repulsions. 

K. Watanabe and M. L. Klein, ]. Phys. Chem., 93, 6897 (1989). Shape Fluctuations in Ionic Micelles. 

For compact surfactant micelles, merely the size fluctuations contribute to as the shape fluctuations leave the aggregate stoichiometry unaffected. 

Thus far only processes involving motion of the surfactant as a whole have been mentioned. Other processes may occur in micellar solutions internal motion of the surfactant alkyl chains within the micelles exchange of cormterions between free and micelle-bound states and fast changes of micelle shape, among others. Also in the case of solubilized systems, i.e., micellar solutions that have solubilized compounds that are sparingly soluble in water, the solubilizate may exchange between micelles and the intermicellar solution. The dynamics of the exchange of counterions and of solubilizates are reviewed later. The dynamics of internal motions of the surfactant alkyl chains are not dealt with in this chapter, but some information and references can be found in Chapter 5, Section V. Some information on the fluctuations of micelle shapes can be found in Chapter 1, Section III.B. 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled306. The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds307, whereas the lifetime of the micellar entity is about 1-100 miliseconds307. Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

The stmcture of a micelle is dynamic and involves continuous exchange of monomers between the aggregates and those in bulk solution. But this exchange is slow, occurring on the timescale of several nanoseconds. A micelle also undergoes slow fluctuations in shape. 

Several reasons have been proposed to account for this difference between stars and micelles, which can be thought of as a peculiarity of the star polymer architecture. The most important are the fluctuations of the outer blobs of the stars with amplitude exceeding the linderman criterion limit, the weak metastable state of the stars, and the difference between stars and nricelles in relation to the presence of a well-defined, solid core in the latter. Indeed, the difference in core size and shape is important and can explain why star-like nricelles could... 

The example considered in this section suggests that the size and stability of nanoparticles built by micellization is controlled by two major factors, geometry of the amphiphilic molecules and the interfacial tension between the hydrophobic tails and water. If the shape of the molecules is not suitable for the formation of a spherical micelle, the micelle will not be stable with respect to fluctuations of curvature at constant aggregation number and cyhndrical or worm-like micelles with high polydispersity can be formed. " " ... 

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