Polydispersity of micelles

Diffusion CoefQcient, Size, Shape, and Polydispersity of Micelles... 

For small disturbances of the adsorption layer from equilibrium, Lucassen (1976) derived an analytical solution (cf Section 6.1.1). An analysis of the effect of a micellar kinetics mechanism of stepwise aggregation-disintegration and the role of polydispersity of micelles was made by Dushkin Ivanov (1991) and Dushkin et al. (1991). Although it results in analytical expressions, it is based on some restricting linearisations, for example with respect to adsorption isotherm, and therefore, it is valid only for states close to equilibrium. 

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... 

Physicochemical characterisation was characterised of self-assembled nanoparticles based on glycol chitosan-bearing 5p-cholanic acid and their surfactant activity . Fluorescence spectroscopy and pulsed field gradient NMR (PFG-NMR) revealed information concerning the polydispersity of micelle polymers - chiral polymeric surfactants developed over the past decade for use as chiral selectors in the analytical separation of enantiomers . The authors suggest that polydispersity is a crucial factor in understanding the chiral interactions of these species. 

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. 

Templates made of surfactants are very effective in order to control the size, shape, and polydispersity of nanosized metal particles. Surfactant micelles may enclose metal ions to form amphiphilic microreactors (Figure 11a). Water-in-oil reverse micelles (Figure 11b) or larger vesicles may function in similar ways. On the addition of reducing agents such as hydrazine nanosized metal particles are formed. The size and the shape of the products are pre-imprinted by the constrained environment in which they are grown. 

The micelle formation is not restricted to solvents for polystyrene but also occurs in very unpolar solvents, where the fluorinated block is expected to dissolve. Comparing the data, we have to consider that the micelle structure is inverted in these cases, i.e., the unpolar polystyrene chain in the core and the very unpolar fluorinated block forming the corona. The micelle size distribution is in the range we regard as typical for block copolymer micelles in the superstrong segregation limit.2,5,6 The size and polydispersity of some of these micelles, measured by DLS, are summarized in Table 10.3. 

The preparation and characterization of these colloids have thus motivated a vast amount of work (17). Various colloidal methods are used to control the size and/or the polydispersity of the particles, using reverse (3) and normal (18,19) micelles, Langmuir-BIodgett films (4,5), zeolites (20), two-phase liquid-liquid system (21), or organometallic techniques (22). The achievement of accurate control of the particle size, their stability, and a precisely controllable reactivity of the small particles are required to allow attachment of the particles to the surface of a substrate or to other particles without leading to coalescence and hence losing their size-induced electronic properties. It must be noted that, manipulating nearly monodis-persed nanometer size crystallites with an arbitrary diameter presents a number of difficulties. 

From these data it is concluded that the size, shape, and polydispersity of nanoparticles depend critically on the colloidal structure in which the synthesis is performed. This is well demonstrated when, by changing the water content, similar colloidal structures (reverse micelles or interconnected cylinders) are obtained ... 

NaAOT-heptane and toluene-H20 reversed micelles Size-quantized CdS particles generated in situ in reversed micelles Low [H2Oj and reversed-micelle interface were important in controlling the size and polydispersity of CdS 617... 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

It is difficult to obtain meaningful results on colloidal interactions unless the samples have low polydispersity. Studies of colloidal interactions between whole casein micelles can be affected by the polydispersity of native casein micelles. (Stothart,1987b). To circumvent the problem of polydispersity, the food system can be deposited on monodisperse silica spheres (Rouw and de Kruif,1989). 

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). 

This equation relates the standard deviation to the rate of change of mean aggregation number with respect to micelle concentration (S—Zj). Clearly, a rapid change of N with concentration is evidence of a large distribution of polydispersity in micelle size (at a given concentration). 

Two points can be made. First, even if hn = Pm for all N > M, as will shown below N cannot exceed M by very much for dilute lipid solutions. In fact N will be found in section 4 to be somewhat smaller than the optimal value M. Second, if the spread of micelle size is not large, the cmc will be given to a good approximation by neglecting polydispersity and assuming N = M. Whence (solving Xi — Xm for Zf), we have... 

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