Critical packing concentration

The structures formed by polystyrene-poly(propylene imine) dendrimers have also been analyzed. Block copolymers with 8, 16, and 32 end-standing amines are soluble in water. They have a critical micelle concentration of the order of 10"7 mol/1. At 3x10 4 mol/l they form different types of micelles. The den-drimer with eight amine groups (80% PS) form bilayers. The dendrimer with 16 amine groups (65% PS) forms cylinders and the dendrimer with 32 amine groups (50% PS) forms spherical micelles [38,130,131]. These are the classical lamellar, cylindrical, and spherical phases of block copolymers. However, the boundary between the phases occurs at very different volume fractions, due to the very different packing requirements of the linear polymer and spherical dendrimer at the interphase. 

Silicone surfactants in aqueous solutions show the same general behavior as conventional hydrocarbon surfactants - the surface tension decreases with increasing concentration until a densely packed film is formed at the surface. Above this concentration, the surface tension becomes constant. The concentration at the transition is called the critical micelle concentration (CMC) or critical aggregation concentration (CAC). The surface and interfacial activity of silicone surfactants was reviewed by Hoffmann and Ulbricht [27]. Useful discussions of the dependence of the surface activity of polymeric silicone surfactants on molecular weight and structure are given by Vick [28] and for the trisiloxane surfactants by Gentle and Snow [29]. 

In general, the adsorption of ionic surfactants follows the Langmuir isotherm, as discussed in Section 4.1. The adsorption of the surfactants onto the solid surfaces is dependent on the orientation and the packing efficiency of the solid surfaces. The onset of the adsorption plateau may occur at the critical micelle concentration (c.m.c.) of the surfactant in water, as shown in Figure 4.28. If the adsorption isotherm... 

This approach can be used to give critical micellizatlpn concentrations as well as size distributions of aggregates — but is, of course, unable to distinguish between different forms of the association structures. In order to achieve this packing, restraints must be introduced. 

Amphiphilic molecules (or amphiphiles), in general, tend to aggregate in aqueous solution above some critical concentration (the critical micellar concentration or CMC) because of the hydrophobic effect (5). The aggregate structure secludes the ap-olar portions of these molecules from the aqueous medium and exposes the polar portions to water at the surface. The form of the aggregate is dictated by packing constraints (6) given... 

The concentration of vesicles has a near-Gaussian profile which peaks at an outer radius Ri close to, but slightly smaller than, the critical packing radius R. At the peak, the surface area per amphiphile is slightly greater (by 1 %) than that of the bilayer Oq, though the difference is diminished as the total amphiphile concentration increases. 

As a result of the close packing of the aqueous-phase droplets, the composition of the water phase is critical. Protein concentrates, caseinate, gelling agents, and special emulsihers have been recommended to simplify the emulsification and to stabilize the end product (93-98). For manufacture, the basic material for production is a mix that is chemically identical to the end product. This mix consists of mUkfat in the form of butter, butter oil, and fractionated butter oil or cream, in many cases, it also has milk solids, milk concentrates (including dissolved milk powder and caseinates), and emulsifiers (see Figure 10) (81). The fat mix (i.e., butter, butter oil, etc.) is melted and pasteurized. 

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