Polydisperse micellar systems

The classic biological example of these systems is bile salt (BS)-lecithin (L)-cholesterol (Ch) micelles which have been studied in detail by QLS [239], In TC-L-Ch systems, particle size and polydispersity were studied as functions of Ch mole fraction (= 0-15%), L/TC molar ratio (0-1.6), temperature (5-85°C), and total lipid concentration (3 and 10 g/dl) in 0.15 M NaCl. For values below the established solubilization limits (A )> added Ch has little influence on the size of simple TC micelles, on the coexistence of simple and mixed TC-L micelles, or on the growth of mixed disk TC-L micelles. For supersaturated systems >1), 10 g/dl simple micellar systems (L/TC = 0) exist as metastable micellar solutions even at = 5.3. Metastability is decreased in coexisting systems... 

Further, a change in the micellar system including the type of surfactant (e.g. AOT in place of CTAB) could cause a change in the droplet size and hence, change in polydispersity [353]. 

Although the polydispersity of micelle size is an important property of a micellar system it has so far, except for a few isolated cases, eluded direct measurement. The reason for this is purely a question of the limitations of experimental technique. 

There is considerable evidence for polydispersity in micellar systems of CTAB and SDS at surfactant and salt concentrations of 0.1 M or abovei 38-40. por example, for CTAB in 0.1 M alkali bromide solutions, both spherical and larger rod-like aggregates were proposed to coexist on the basis of light scattering and NMR results . Extrapolating from these studies. Mi is probably spherical or globular and M2 larger and rodlike. 

Thus, models based on multisite binding equilibria successfully describe the dependence of D on Cx at a fixed micelle concentration when the electroactive probe is almost totally bound to the micelles. The electrode reaction of the probe must not be accompanied by adsorption or chemical reaction. Nonlinear regression analysis of the data enables an assessment of the importance of polydispersity and an accurate estimate of diffusion coefficients of the micelles. Parameters proportional to binding constants are also obtained, and these can be converted to apparent binding constants if the micelle concentrations are known. The models also quantitatively predict the observed z decrease in measured diffusion coefficient with concentration of micelles. This work shows that the micellar system we have used for electrocatalysis are probably polydisperse. 

The different location of polar and amphiphilic molecules within water-containing reversed micelles is depicted in Figure 6. Polar solutes, by increasing the micellar core matter of spherical micelles, induce an increase in the micellar radius, while amphiphilic molecules, being preferentially solubihzed in the water/surfactant interface and consequently increasing the interfacial surface, lead to a decrease in the miceUar radius [49,136,137], These effects can easily be embodied in Eqs. (3) and (4), aUowing a quantitative evaluation of the mean micellar radius and number density of reversed miceUes in the presence of polar and amphiphilic solubilizates. Moreover it must be pointed out that, as a function of the specific distribution law of the solubihzate molecules and on a time scale shorter than that of the material exchange process, the system appears polydisperse and composed of empty and differently occupied reversed miceUes [136],... 

Fig. 3.19 Critical micelle temperature versus the polymer concentration calculated for an aqueous solution of Pluronic P105 (PEO37PPO56PEO37) (Linse 1994b). Results from a polydisperse model (MJMn = 1.2) are shown as solid lines and for the monodisperse polymer as a dashed line. The curves for the polydisperse system are labelled in terms of the number of components representing the polydisperse polymer. Points with constant micellar volume fractions (criterion of the cmc) are represented by dotted curves, the volume fraction being indicated. Experimental data from Alexandridis et al. (1994a) are also included as filled squares.

The light scattering methods provide statistically averaged quantities when applied to polydisperse samples (e.g., micellar or polymer solutions). The case of independent scatterers can be rigorously treated 2 by using the mass distribution function of the particles, f M). By definition, dm =f(M)dM is the mass of particles in the range between M and (M + dM), scaled by the total particle mass. As shown by Zimm, the scattering law in such a system can be presented similarly to the case of monodisperse particles (see Equation 5.405) ... 

Scattering techniques provide the most definite proof of micellar aggregation. Zielinski et aL (34) employed SANS to study the droplet structures in these systems. Conductivity measurements (35) and SANS (36) were also used to study droplet interactions at high volume fraction in w/c microemulsions formed with a PFPE-COO NH4 surfactant (MW = 672). Scattering data were successfully fitted by Schultz distribution of polydisperse spheres (see footnote 37). A range of PFPE-COO NH/ surfactants were also shown to form w/c emulsions consisting of equal amount of CO2 and brine (38-40). 

A more rigorous approach to the description of the colloid surfactant diffusion to the interfaee was proposed by Noskov [133]. The reduced diffusion equations for micelles and monomers, which take into account the multistep nature of micellisation and the polydispersity of micelles, were derived for time intervals corresponding to the fast and slow processes using the method applied initially by Aniansson and Wall to uniform systems. Analogous equations have been derived later by Johner and Joanny [135] and also by Dushkin et al. [137]. Recently Dushkin has studied also the adsorption kinetics in the framework of a simplified model of quasi-monodisperse micelles. In this case the assumption of the existence of two kinds of micelles permits to study the main features of the surface tension relaxation in real micellar solution [138]. The main steps of the derivation of surfactant diffusion equations in micellar solutions are presented below [133, 134]. 

Eq. (5.223) coincides with the monomer diffusion equation proposed by Evans et al. [149] if the rate constant Rb in [149] is replaced by c°[rc ,(c + a c, )]. However, the obtained result is not restricted to the interpretation of the coefficients only, which have been used before. Eq. (5.224) does not coincide with the corresponding diffusion equation in [149] even if we replace Rb by this expression. Unlike the equations derived in the preceding works, the system (5.223) and (5.224) takes into account the polydispersity of micelles and the two-step nature of the micellisation. Actually, the release or incorporation of monomers in the second step of disintegration or formation of micelles is determined not only by their transition from the micellar to the premicellar region and their subsequent disintegration (as characterised by the parameter J) but also by the alteration of the size distribution of micelles. The latter change... 

Vesicles are closed bilayers that can be observed in two forms. At low surfactant concentration, the vesicles are unilamellar and behave like a colloidal suspension of polydisperse particles. At more concentrated surfactant solutions, small multilayered vesicles are formed [134], Multilamellar vesicles (known also as spherulites) have also been observed in the lamellar phases of surfactant-brine (or even pure water-alcohol) systems [218]. The surfactant may be SDS [218,223] or DDAB (didodecyldimethylammonium bromide) [224]. In alcohol-containing systems the bilayer structural transformations are controlled by the alcohol/surfactant ratio [134].Thus, in many SDS-brine (or water)-alcohol systems, a vesicle (L4) phase is located between the micellar phase and the lamellar (L ) phase. At fixed surfactant concentration, the sequence of phases L4 -La-L3 (in water) is obtained by increasing the alcohol content, and the sequence L2 -La-L3 (in oil) is obtained by decreasing the alcohol content [ 134]. 

---