Micelles density profile

A simple scaling model of block copolymer micelles was derived by de Gennes (1978). He obtained scaling relations assuming uniformly stretched chains for the core radius, RB, of micelles with association number p.This model can be viewed as a development of the Alexander de Gennes theory (Alexander 1977 de Gennes 1976,1980) for polymer brushes at a planar interface, where the density profile normal to the interface is a step function. In the limit of short coronal (A) chains (crew-cut micelles) de Gennes (1978) predicted... 

The scaling theory for spherical polymer brushes due to Daoud and Cotton (1982) (Section 3.4.1) has been applied to analyse the coronal density profile of block copolymer micelles by Forster et al. (1996). If the density profile is of the hyperbolic form r as found by FOrster et al. (1996) for the coronal layer of block copolymer micelles, the brush height scales as... 

For the PS-P4VP micelles studied by them, Forster et al. (19%) determined that the P4VP coronal density profile can be modelled as a hyperbolic function with an exponent a between 1.05 and 1.35. 

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... 

Fig. 8 Schematic density profile of a block copolymer micelle. Uncharged micelles exhibit a simple core/shell structure whereas polyelectrolyte block copolymer micelles can show phase separation of the corona into a dense interior and a dilute outer domain...

Fig. 9 Density profiles of PEE-PSSH micelles for varying salt concentrations. The profiles were obtained by a combination of static and dynamic light scattering, small-angle neutron scattering and cryo-TEM [49]...

In reality, most micellar systems made up from polymers are not as perfect as depicted in Fig. 9. Instead, the micelles are expected to be more fuzzy and may more resemble the situation depicted in Fig. 10. In this case, the segmental distribution must be considered [44, 45, 48, 74, 79, 84-86] by calculating the scattering amplitude from a realistic density profile. In addition, the intrinsic polymer scattering must be incorporated by explicitly taking into account long-range excluded volume interactions. 

Figure 10.6 The radial electron-density profiles Ap(r) for the spherical micelles in the EC,/Sii4C3E033i [x = 7 and 9) systems (a) and those in the EC,/Sii4C3E05i [x= 1-14) systems (b) at 60°C calculated by a...

Fig. 1 SCF density profiles showing the effect of increasing the surface separation, H. The chain length is AT = 80, p = 0.0125 and yps = 2. The chains are grafted in the XY plane and the two surfaces are separated along Z. The parameter 0p is the polymer density, (a) The surfaces are highly compressed and thus, the micelles associate into bundles that extend from one surface to another, (b) Increasing H causes the micelles to absorb onto one of the surfaces, (c) Further increases in H drive the micelles to desorb and localize in the center of the gap...

Also the internal structure of block-copolymer micelles, as given by the size of core and corona and the density profile in each domain, has been carefully characterized by static and dynamic light scattering [40] and by small angle neutron scattering... 

For the amphiphilic block copolymer in the non-polar selective solvent, the unpolar blocks form the corona, which provides solubilization and stabilization, while the polar or hydrophilic and functionalized blocks form the core, which is able to dissolve metal compounds due to coordination, followed by the nucleation and growth of metal particles upon reduction. Also the internal structure of block-copolymer micelles, as given by the size of core and corona and the density profile in each domain, has been carefully characterized by static and dynamic light scattering [146] and by small angle neutron scattering using contrast variation techniques [147], The micellar corona has many of the characteristics of a spherical polymer brush. 

The experimental-theoretical study of mesophase formation in amphiphilic systems emphasizes the basic chemical, physical, and materials science aspects of the systems. The most commonly discussed mesophases, beyond the simple micelles discussed in Chapter 4, are lamellar aggregated micellar (packed in various cubic and hexagonal close-packed arrays), columnar or ribbon phases (rod-shaped micelles stacked in a two-dimensional hexagonal or rectangular array) microemulsions, and the cubic bicontinuous mesophases. The experimental techniques normally used to identify these mesophases are NMR Uneshape analysis, diffusion measurements, smaU-angle neutron and X-ray scattering, and optical texture analyses. In addition, reconstraction of electron density profiles and very low temperature transmission electron microscopy (TEM) have been used to elucidate the details of these mesostractures. 

Many types of micelle stmctures have been proposed spherical core-corona, vesicle, bmshed rod, wormlike rod, flower string, and so on. Approximating the aggregate structure with a reasonable probability density profile for the proposed stmc-ture, we can theoretically constmct a model to evaluate all the characteristics measurable by LLS in such ways as explained above. 

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