Critical aggregation concentration, for

Mavelli and Luisi (21) have described a simple kinetic model for Walde s systems and concluded that, in both of these, there exists a critical aggregation concentration for the acids at which the monomers aggregate into vesicles in appreciable quantities. 

The cac (critical aggregate concentration) values for oleate are in the millimolar range, which means that at the operational concentration of 10-50 mM there will be a signihcant concentration of monomer in equilibrium with the aggregate. This consideration allows us to go back to the question of whether vesicles are chemical equilibrium systems. Oleate vesicles cannot be considered proper chemical equilibrium systems, however they behave in a mixed way, with some features that are typical of micelles in equilibrium (Luisi, 2001). 

Micelles and vesicles can be formed above a certain concentration. For instance, small micelles are formed above critical micellar concentration, cmc. (The latter abbreviation is often used for critical vesicle concentration, too. However, sometimes a more general term critical aggregate concentration, cac is also applied.) Bilayers of specific amphiphiles with two tails are typical of the central part of cell membranes discussed in some detail in the next chapter. Studying artificial mono- and bilayers (uniform or with built in pores) is indispensable for gaining information about the structure and functioning of cell membranes involving the transport through them. 

K-casein aggregates in aqueous medium are more complicated than those of p-casein, being composed of star-like sub-micelles, where each submicelle contains nine K-casein chains and the total degree of association may reach about 140 (Thum el al., 1987a). Payens and Vreeman (1982) used sedimentation measurements to infer a critical micelle concentration for K-casein of 0.5 mg/ml. 

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]. 

As the total mole fraction cannot exceed one, there appears automatically an upper boundary for Xj, also known as a critical aggregation concentration, or critical micelle concentration, X which is given by... 

The values obtained by dynamic light scattering (DLS) for the diameter of these vesicles are larger due to aggregation. The critical aggregation concentration (CAC) was determined with pyrene as probe molecule [56] and were for all generations... 

The variation of the surface tension with the surfactant concentration was determined for several sur tant molecules, and the critical aggregation concentration (CAC) was calculated fix>m the... 

Like other amphiphilic molecules, LPS aggregate and build up clusters in aqueous solutions. This process occurs only above a critical aggregate concentration (CAC) which has been established for a few lipids, but not, however, for LPS owing to extreme experimental difficulties. Estimations based on comparisons to values of other lipids led to the assumption of a CAC of < 10 M for hexaacyl-lipid A (O Fig. 16). For the lipid A precursor IVa (O Fig. 16) which represents a tetraacyl-lipid A, a CAC of < 10 has been reported [78]. 

Equations (2)-(4) show that the total potential energy of interaction between two colloidal spherical particles depends on the surface potential of the particles, the effective Hamaker constant, and the ionic strength of the suspending medium. It is known that the addition of an indifferent electrolyte can cause a colloid to undergo aggregation. Furthermore, for a particular salt, a fairly sharply defined concentration, called critical aggregation concentration (CAC), is needed to induce aggregation. 

The number-average diameter, for the HAP particles increases with the electrolyte KNO3 concentration until the critical aggregation concentration is reached, where the value remains approximately constant. The starting point of the maximum d corresponds to the electrolyte concentration called CAC. The last value, which depends on the electrolyte used, was found to be 1.27 x lO M for the electrolyte KNO3. 

The bile acids are 24-carbon steroid derivatives. The two primary bile acids, cholic acid and chenodeoxycholic acid, are synthesized in the hepatocytes from cholesterol by hy-droxylation, reduction, and side chain oxidation. They are conjugated by amide linkage to glycine or taurine before they are secreted into the bile (see cholesterol metabolism. Chapter 19). The mechanism of secretion of bile acids across the canalicular membrane is poorly understood. Bile acids are present as anions at the pH of the bile, and above a certain concentration (critical micellar concentration) they form polyanionic molecular aggregates, or micelles (Chapter 11). The critical micellar concentration for each bile acid and the size of the aggregates are affected by the concentration of Na+ and other electrolytes and of cholesterol and lecithin. Thus, bile consists of mixed micelles of conjugated bile acids, cholesterol, and lecithin. While the excretion of osmotically active bile acids is a primary determinant of water and solute transport across the canalicular membrane, in the canaliculi they contribute relatively little to osmotic activity because their anions aggregate to form micelles. 

Because the main driving force for surfactant self-association in polymer-surfactant mixed systems is the hydrophobic effect, the binding of surfactants to polyelectrolytes exhibits a similar dependence on the length of the alkyl chain as known for free micellization. Surfactants with longer hydrocarbon chains bind more strongly to polyions than those with shorter chains, and the binding starts a lower surfactant concentrations. In this context, a convenient parameter to characterize polyelectrolyte-surfactant systems is the critical aggregation concentration, cac, which is a counterpart of the well-known critical micellization concentration, cmc, but applies to solutions of surfactants in the presence of a polymer. It is defined as the... 

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