Critical aggregate concentration

Additives, whether hydrophobic solutes, other surfactants or polymers, tend to nucleate micelles at concentrations lower than in the absence of additive. Due to this nucleating effect of polymers on micellization there is often a measurable erne, usually called a critical aggregation concentration or cac, below the regular erne observed in the absence of added polymer. This cac is usually independent of polymer concentration. The size of these aggregates is usually smaller than that of free micelles, and this size tends to be small even in the presence of added salt (conditions where free micelles tend to grow in size). 

The distinction between pairwise and bulk hydrophobic interactions is often made, although some authors doubt the existence of an intrinsic difference between the two ". Pairwise hydrophobic interactions denote the interactions behveen two isolated nonpolar solutes in aqueous solution. They occur in the regime where no aggregation takes place, hence below the critical aggregation concentration or solubility limit of the particular solute. If any breakdown of the hydrophobic hydration shell occurs, it will be only transient. 

FIGURE 3.3 Surface tension y plotted against the concentration c of lysine derivative 3.20. Critical aggregate concentration (O) cM=2430mg/L=2.43mM, yc =58mN/m. (Reprinted from Nalum Naess, S. et al., Chem. Phys. Lipids, 148, 63, 2007. With permission.)M... 

The SC nanogels had 70 nm mean diameter with narrow size distribution, significantly lower critical aggregation concentration (CAC), and stronger thermodynamic stability compared with those of the corresponding l- or D-isomer nanogels [163]. 

Self-aggregating amphiphiles can broadly be divided into hydrotropes and surfactants. The main difference between hydrotropes and surfactants lies in the fact that hydrotropes are typically not sufficiently hydrophobic to cooperatively self-aggregate and form organized structures, whereas surfactants form distinct aggregates such as micelles and vesicles above their critical aggregation concentrations. 

Our group [124] has used pyrene and pyrene labeled poly(acrylic acid) as a fluorescent probe to investigate the interaction between poly(acrylic acid) (PAA) and dodecyltrimethylammonium bromide (DTAB) in water. We have measured the Is /1 ratio of pyrene as a function of DTAB in the presence of 1 g/L PAA. A sharp decrease in polarity is found well below the CMC of DTAB (1.3 X 10 M, Fig. 17). The onset of this polymer-induced association is referred to as the critical aggregation concentration. The CAC has been measured at various pH and NaCl levels (Fig. 18). It was observed that the... 

Fig. 18 Critical aggregate concentration, CAC of DTAB in 1 g/L sodium polyacrylate in 0 and 0.03 M added NaCl...

Fig. 22 Comparison of critical aggregate concentration, determined by excimer formation of covalently labeled polymer and micropolarity response of free pyrene...

Figure 5.3 Self-assembly of a vesicle. Water-soluble molecules can be entrapped inside, ionic molecules on the polar head groups of the surface, amphiphatic molecules in the hydrophobic bilayer, (cac critical aggregate concentration).

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. 

FIGURE 13.7 Effect of polymer concentration and temperature on the critical aggregation concentration of nystatin, as interpreted from dynamic light scattering data. (Reproduced from Croy, S. R. and G. S. Kwon. 2004. J. Control. Rel.95 161-171. With permission from Elsevier Ltd.)... 

Y. Li, S. Zhang, Q. Wang, and J. Yang, Study on surface activity and critical aggregation concentration of sucrose esters containing different isomers of mono-, di- and polyesters, Ten-side Surfactants Deterg., 41 (2004) 26-30. 

G. Garofalakis, B. S. Murray, and D. B. Sarney, Surface activity and critical aggregation concentration of pure sugar esters with different sugar headgroups, J. Colloid Interface Sci., 229 (2000) 391-398. 

Aurell, C.A., Wistrom, A.O., Critical aggregation concentrations of Gram-negative bacterial lipopolysaccharides (LPS). Biochem Biophys Res Commun 253 (1998) 119-123. 

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