Polydispersity of micellar size

Table II. Effect of Radiation Dose on the Polydispersity of Micellar Size in Solutions of Varying Concentration...

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. 

At low water content from vv = 2 to 5.5, a homogeneous reverse micellar solution (the L2 phase) is formed. In this range, the shape of the water droplets changes from spheres (below ir = 4) to cylinders. At tv — 4, the gyration radius has been determined by SAXS and found equal to 4 nm. Syntheses in isolated water-in-oil droplets show formation of a relatively small amount of copper metallic particles. Most of the particles are spherical (87%) with a low percentage (13%) of cylinders. The average size of spherical particles is characterized by a diameter of 12 nm with a size polydispersity of 14%. 

Micellar diameter and size polydispersity can be obtained directly in water or in an isotonic buffer by DLS. DLS can also provide some information on the sphericity of polymeric micelles (Kataoka et al., 1996 Nagasaki et al., 1998). Ultracentrifugation velocity studies are sometimes performed to assess the polydispersity of polymeric micelles (Yokoyama et al., 1994 Hagan et al., 1996). 

Polydispersity of simple bile salt micelles can only be assessed by modem QLS techniques employing the 2nd cumulant analysis of the time decay of the autocorrelation function [146,161]. These studies have shown, in the cases of the 4 taurine conjugates in 10 g/dl concentrations in both 0.15 M and 0.6 M NaCl, that the distribution in the polydispersity index (V) varies from 20% for small n values to 50% for large n values [6,146]. Others [112] have foimd much smaller V values (2-10%) for the unconjugated bile salts in 5% (w/v) solutions. Recently, the significance of QLS-derived polydispersities have been questioned on the basis of the rapid fluctuation in n of micellar assemblies hence V may not actually represent a micellar size distribution [167-169]. This argument is specious, since a micellar size distribution and fast fluctuations in aggregation number are identical quantities on the QLS time scale (jusec-msec) [94]. 

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... 

As mentioned earlier, studies of simple linear surfactants in a solvent (i.e, those without any third component) allow one to examine the sufficiency of coarse-grained lattice models for predicting the aggregation behavior of micelles and to examine the limits of applicability of analytical lattice approximations such as quasi-chemical theory or self-consistent field theory (in the case of polymers). The results available from the simulations for the structure and shapes of micelles, the polydispersity, and the cmc show that the lattice approach can be used reliably to obtain such information qualitatively as well as quantitatively. The results are generally consistent with what one would expect from mass-action models and other theoretical techniques as well as from experiments. For example. Desplat and Care [31] report micellization results (the cmc and micellar size) for the surfactant h ti (for a temperature of = ksT/tts = /(-ts = 1-18 and... 

Inspection of Figs 5 and 6 shows that at high probe concentration, limiting values of D tend toward Di. Thus, a reasonable estimate of D for monodisperse systems can be obtained by measuring D at relatively large probe concentrations, for example, 2 to 5 mM. For polydisperse systems, additional equilibria must be considered. A three-state model was used to develop a version of Eq. (12) for two micellar size distributions, and applied to systems with coexisting globular and rodshaped micelles [4]. 

As noted in particular in the analysis of kinetic data [10-15], there are aggregates over a wide range of aggregation numbers, from dimers and well beyond the most stable micelles. However, for surfactants with not too high a c.m.c., the size distribution curve has a very deep minimum, the least stable aggregates being present in concentrations many orders of magnitude below those of the most abundant micelles. For surfactants with predominantly spherical micelles, the polydispersity is low and there is then a particularly preferred micellar size. 

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