Aggregation number of micelle

With monomeric molecules, the aggregation number of micelles is determined by equilibrium thermodynamics. In polymeric molecules, however, topological constraints are imposed on the system. If the degree of polymerization exceeds the aggregation number of the monomeric micelle, unsaturated sites of the polymeric molecules become available (directed to the aqueous phase) and inter-molecular interactions (agglomeration) occur. In the case of polymer with Mw= 6.23x105, typical surfactant behavior was found. 

As a general result, we conclude that micelle and vesicle formation cannot be explained by cone or cylinder shapes of the monomeric amphiphiles. The key criterion for the curvature of molecular assemblies lies in the saturation solubility or cmc of the amphiphile. A cmc above 10 M usually means appreciable dissociation leading to small aggregation numbers of micelles. A cmc below 10 M means large planar bilayers or, upon their disruption, vesicles. 

The effect of neutral electrolyte on the aggregation number of micelles of POE nonionics in aqueous solution is somewhat unclear, with both increases and decreases being observed on the addition of electrolyte. In either case, however, the effect appears to be small. 

The viscosity of the copolymer-surfactant solution depends upon the nature and extent of association of the hydrophobic blocks (27). Figure 2 illustrates the possibilities. If no surfactant is present (top of Figure 2), the hydrophobic blocks can associate intermolecularly, intramolecularly, or a combination of both. If the system is swamped with surfactant (middle of Figure 2), each hydrophobic block is completely solvated by surfactant so that there is no cross-linldng. As heat, electrolyte, or other additives affect the number and aggregation number of micelles, various amounts of inter-molecular or intramolecular cross-linldng are produced (bottom of Figure... 

Figure 7.1 shows the concentration dependence of the apparent aggregation number of micelles at different temperatures obtained from the following equations... 

FIGURE 10 Distribution of a representative micelle population as a function of aggregation number /. The dashed curve indicates the redistribution after a small perturbation of the system that leads to dissociation and decrease of the mean aggregation number of micelles. The dotted line is the final equilibrium distribution, and 2 are the characteristic relaxation times of the process indicated by the arrows. [From Schelly, Z. A. etal. (1979). In Solution Chemistry of Surfactants, pp. 323-325. Plenum, New York, as discussed in Fendler, J. H. (1982). Membrane Mimetic Chemistry, Wiley, New York.]... 

We can find the osmotic pressure n from the chemical potential of the solvent A/u-o-The number average aggregation number of micelles is given by... 

Benrraou M, Bales BL, Zana R (2003) Effect of the nature of the counterion on the properties of anionic surfactants. 1. cmc, ionization degree at the cmc and aggregation number of micelles of sodium, cesium, tetramethylammonium, tetraethylammonium, tetrapropylammonium, and tetrabutylammonium dodecyl sulfates. J Phys Chem B 107 13432-13440... 

Section 1 deals with the formal kinetics of the photochemical reactions in micellar solutions and its application to determine the rate constants of photoprocesses, the critical concentration of micellization (CMC) and the aggregation number of micelles from experimental data. In Section 2 the correlations of the rate constants of the photochemical charge separation and mass transfer processes with its thermodynamics, and also the microviscosity and effective polarity of organized assemblies are considered. 

Thus, the plot of [M] vs. the surfactant concentration is linear with a slope equal to the reverse aggregation number and the intercept with the abscissa axis equal to the CMC. This method was widely used to determine the aggregation numbers of micelles and vesicles (liposomes) [28-39],... 

From its definition, is related to the surfactant concentration (c) and the aggregation number of micelles (N) as... 

In aqueous solution micelles are generally thought to be spherical as long as the surfactant concentration remains close to the critical micelle concentration. Rod-like micelles may form at higher surfactant concentrations [1, 2]. Addition of a third component such as neutral salt or non-electrolytes may favour longer micellar structures, for instance rod-like micelles [3-6]. An increase in temperature, on the other hand, seems to favour spherical micelles [7, 8]. The effect of pressure on the shape transition point is not known, though it appears that the aggregation number of micelles decrease with pressure at least up to about 160 MPa [9-12]. 

Table 3.2 Maximum values for the aggregation number of micelles of n-alkyl...

Figure 4.2. Solubility increase above the micelle temperature range depending on the aggregation number of micelle (n). (a) n = 25 (b) n = 50 (c) n = 100 (d) n = 150 (e) n = 200. (Reproduced with permission of Academic Press.)...

As mentioned earlier, the aggregation number of micelles is not monodisperse but polydisperse. Therefore, their distribution is a matter of some concern. Let us take the model of micelle formation expressed by Eq. (4-1), where n is not definite but diffuse. Then, if /jl and fii are the chemical potentials of the micellar species composed of n monomers and the monomer, respectively, we have for the equilibrium between the monomers and any micellar species ... 

From the above moments, the number-averaged aggregation number of micelles n and the corresponding standard deviation [Pg.72]

Figure 5.1. Arithmetic mean aggregation number of micelles (Nj) of pentaoxyethylene dodecyl ether (Ci2 s) and hexaoxyethylene dodecyl ether (C12E6) at 298.15 K as a function of total surfactant concentration (Ci) under various pressures. A, 0.1 MPa B, 20 MPa, C, 40 MPa D, 80 MPa E, 100 MPa. (Reproduced with permission of the American Chemical Society.)...

We now address the effects of a polydisperse micellar aggregation number of the thermodynamic expressions of solubilization. One strong effect is variation of the association constant Kj, We define a new association constant which is Kj of the micelles of aggregation number n. Suppose the polydispersity of the aggregation number of micelles ranges from a to p. The concentration of micelles of aggregation number n with no solubilizate association becomes... 

The Krafft point, the area occupied by a surfactant molecule at the air-water and octane-water interfaces, and the aggregation number of micelles increase with an increase in fluorocarbon and/or hydrocarbon chain length of these hybrid surfactants [209]. The cmc, surface tension, and octane-water interfacial tension at the cmc decrease with an increase in fluorocarbon and/or hydrocarbon chain length. The surfactants lower the surface tension, as well as the hydrocarbon oil-water and the water-fluorocarbon oil interfacial tension. Their solutions in water can float on hydrocarbon liquids, such as benzene, cyclohexane, and decane. The 10% solution of the surfactant with m = 6 and n = 4 chains exhibit rubberlike viscoelasticity [210]. 

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