Micellar core radius

Fig. 3.24 Micellar core radius, RB, as a function of Ng for PS-poly(caesium acrylate) (A) and PS-poly(caesium methacrylate) ( ) in toluene (Nguyen el al. 1994). A linear relationship is anticipated by the scaling theories of Zhulina and Birshtein (1985) and Halperin (1987,1990) for type IV micelles.

Table 8.4 Calculated d spacings from measured and indexed Bragg peaks for hexagonal and cubic Si CjEOsi 6/D4 mixtures at 58°C, and derived micellar core radius Reore and interfacial area per molecule, as.

Example 5.5 Molecular volume of asphaltene and other substances, and asphaltene-micellar core radius Calculate the molecular volume in A from mass density and molecular weight. Calculate also the number of asphaltene molecules in the asphaltene core from the asphaltene micellar core radius of Fig. 5.17. 

From Fig. 5.17 the micellar core radius of the Weyburn reservoir fluid before mixing with CO2 is about 30 A. The number of asphaltene molecules in the core is given by... 

Electrolytes are obviously solubilized only in the aqueous micellar core. Adding electrolytes in water-containing AOT-reversed micelles has an effect that is opposite to that observed for direct micelles, i.e., a decrease in the micellar radius and in the intermicellar attractive interactions is observed. This has been attributed to the stabilization of AOT ions at the water/surfactant interface [128]. 

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. 3.23 Coronal thickness, A a. plotted as a function of NX fv f°r micelles formed by PS-poly(2-cinnamoylethyl metharylate) diblocks in cyclopentane (Tao et at. 1997). This yields a straight line in accord with the predictions of scaling theory for the micellar radius (the core radius for these micelles was small enough to be neglected, then RA - R).

Roe and co-workers (Nojima et al. 1990 Rigby and Roe 1984,1986 Roe 1986) have used SAXS to characterize micelles formed by PS-PB diblocks at low concentrations in blends with low-molecular-weight PB. Micellar dimensions and association numbers were determined for symmetric and asymmetric diblocks (Rigby and Roe 1984,1986). The effective hard sphere radius, the core radius and volume fraction of hard spheres were determined using the Percus-Yevick model (Rigby and Roe 1986). These results were compared (Roe 1986) to the predictions of the theory of Leibler et al (1983). The theory qualitatively reproduced the observed trend for the cmc to increase with temperature for blends containing a particular diblock. The cmc was found to decrease at a fixed temperature... 

Important parameters that control the size of micelles are the degree of polymerization of the polymer blocks, NA and NB, and the Flory-Huggins interaction parameter %. The micellar structure is characterized by the core radius Rc, the overall radius Rm, and the distance b between adjacent blocks at the core/shell-interface as shown in Fig. 1. b is often called grafting distance for comparisons to polymer brush models, b2 is the area per chain which compares to the area per head group in case of surfactant micelles. In the case of spherical micelles, the core radius Rc and the area per chain b2 are directly related to the number of polymers per micelles, i.e., the aggregation number Z=4nR2clb2. 

The internal structure of polyelectrolyte block copolymer micelles such as their core radius Rc and micellar radius Rm can be determined by a variety of methods involving static and dynamic light scattering (SLS, DLS), small-angle X-ray (SAXS) and neutron scattering (SANS) as well as imaging techniques such as transmission electron microscopy (TEM) or atomic force mi-... 

It is usually assumed that the micellar corona is a continuous phase extending from the micellar core to the micellar radius Rm. The internal structure of the micelle can be described by a density profile as shown in Fig. 8. The micellar core is a homogeneous melt or glass of insoluble polymer blocks. For hydrophobic blocks in aqueous solutions, the polymer volume fraction in the micellar core is 0C 1. The micellar shell is swollen with water or aqueous salt solution and has a polymer segment density that is expected to decrease in the radial direction as 0(r) r-a as typical for star polymers or... 

PB-core. The micellar core has a radius of Rc= 17 nm in good agreement with scattering experiments. It is surrounded by a thin dark layer which represents the dense interior part of the polyelectrolyte corona containing a high concentration of condensed counterions. 

In deriving eq 16-19, the surface area A is taken as the surface area of the micellar core since it is based on the volume of the hydrophobic core. In reality the surface area should account for the surface roughness due to the presence of the head groups. The actual surface area can be calculated by increasing the radius of the micellar core by a value .3b A is calculated using eq 10 where ro is now given... 

The data from the SANS study were fitted to a poly-disperse spherical core-plus-shell (or corona) model assuming no intermicellar interactions. The model Sharma and Bhatia used essentially fits three parameters, namely the radius of the micelle core, / i, the radius of the micelle shell, R2 and the micelle aggregation number. To fit the SANS data to the model, the authors assumed that the micellar cores were comprised only of hydrophobe (PPO) and D2O, while the shell was assumed to comprise only of hydrophile (PEO) and D2O, with no intermixing of the PPO and PEO chains. 

Figure 34 Schematic representation of the models for bilayered micelles with separate (a) and interdigitated (b) EO chains. ( ) Water molecule. E = thickness of peripheral layer and R = radius of micellar core. (From Ref. 348.)...

In the case of strongly asymmetric block copolymers Na Nb), the size of the micellar core, Rears, is much smaller than the radius / corona of the corona. In this case, starlike micelles with spherical cores are formed (Fig. la). In the opposite limit of short hydrophilic block, Na Nb, the size of micellar core. Rears, exceeds by far the thickness of the corona. The coronae of these crew-cut micelles can be viewed as quasi-planar polymer brushes [51, 52], see Fig. lb. 

Under certain conditions, cylindrical micelles or even vesicles can be formed instead of spherical symmetric micelles. Cylindrical micelles are usually formed as a consequence of a delicate balance between the different terms, most notably governed by the chain stretching in the micellar core. Compared to spherical micelles, the core radius of a cylinder for an equivalent area or volume can easily be evaluated to be 2/3 smaller. Hence, in a cylindrical micelle, the amount of chain stretching is expected to be less pronounced than in a spherical one. On the other hand, chain interactimis in the corona of a cylindrical micelle is expected to be more severe due to the smaller area available for each chain. All terms must thus be included and a more detailed thermodynamic evaluation should be performed. For vesicles, the bending modules is additionally expected to be important [46]. 

We came above to a simple characterization of the micelle core as a hydrocarbon droplet with a radius equalling the length of the extended alkyl chain of the surfactant. We noted also that, since the cross-sectional area per chain decreases radially towards the centre, only one chain can be fully extended while the others are more or less folded. The aggregation number, A, can be expressed as the ratio between the micellar core volume, Vniic and the volume, u, of one chain as follows ... 

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