Mean aggregation number of micelle

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.]... 

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.)...

Highly monodisperse reversed micelles are formed by sodium bis(2-ethylhexyl) sul-fosuccinate (AOT) dissolved in hydrocarbons that are in equilibrium with monomers whose concentration (cmc) is 4 X 10 M, have a mean aggregation number of about 23, a radius of 15 A, exchange monomers with the bulk in a time scale of 10 s, and dissolve completely in a time scale of 10 s [1,2,4,14], Other very interesting surfactants able to form reversed micelles in a variety of apolar solvents have been derived from this salt by simple replacing the sodium counterion with many other cations [15,16],... 

Fig. 4.3. The mean aggregation number of SDS micelles according to luminescence...

Fig. 16. Correlation diagram of the mean aggregation number per micelle of AOT(n oT) and sodium di-2-ethylhexylphosphate (npQ-j-) in different solvents, 25 °C. [J. Colloid Interface Sci. 46, 417 (1974) (corrected according to new results)]...

The ratio of the slope above to the slope below the cmc provided an estimate of P [7]. The binding constant was also used to estimate the concentration of alcohol in the bulk phase. Time resolved fluorescence quenching of dimethylnaphthalene by cetylpyridinium bromide solubilized in the micelles was used to obtain estimates of the mean aggregation number of the surfactant in the mixed micelles. 

High concentrations of short hydrocarbon chain length alcohols are known to break down micelles. However, in this work the analysis of the ultrasonic relaxation data to obtain kinetic information was restricted to alcohol and surfactant concentrations where the mean aggregation number of the surfactant did not show a significant decrease [2,3]. 

Analysis of fluorescence decay curves can be used to determine the mean aggregation number of aqueous micelles. The use of 1-methylpyrene quenching by the immobile quencher... 

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. 

Static fluorescence quenching has been used to measure the mean aggregation number of surfactant-related systems [27-29]. This method was originally developed by Turro and Yekta for anionic surfactant micelles [30]. This method works well without significant errors when kjk1 and no quencher redistribution has taken place. On the other hand, fluorescence-decay experiment, namely, time-resolved fluorescence quenching (TRFQ), has been extensively used to determine the micelle aggregation number in a surfactant system. The reader is referred to the review [24] on this subject. 

Fig. 9. Comparison of results derived from neutron diffraction experiments and from the model for the distribution of terminal methyl groups in spherical dodecylsulphate micelles at 35 °C. The micelles are observed to have a mean aggregation number of 78. If the methyl group probability density is p(r) where r is the distance from the micelle center, the plot shows the volume weighted probability density P(r) = AnCr p r), where C is a normalization...

The above theory was applied for the interpretation of dynamic surface-tension data obtained with solutions of sodium dodecyl sulfate (SDS) by means of the MBP method. The empirical adsorption isotherm, Ci (F), of SDS due to Tajima [29] was used with a value m 77 of the mean aggregation number of the micelles. The best numerical fits of the data are shown in Fig. 7. Curves a and b correspond to surfactant concentrations below CMC that is the reason why the respective data are processed by means of Eqs. (41) and (42). The diffusion coefficient of the SDS monomers calculated from the curves is Dj => 5 X 10 cmVs, which is close to the value determined by other authors [135]. This value of Di has been further used to fit the data for concentrations above CMC by means of Eqs. (76)-(79) see curves c and d in Fig. 7. Thus, from the latter two curves, one determines 70 s for the rate constant of micelle decay, which in view of Eq. (69) yields kf 1400 s for the characteristic time of the fast relaxation process of micellization. 

Here k is the off rate constant for the micelle at the mean aggregation number n262- and a is the standard deviation of the assumed gaussian micelle size distribution. a is the relative amount of micellized monomer... 

This equation relates the standard deviation to the rate of change of mean aggregation number with respect to micelle concentration (S—Zj). Clearly, a rapid change of N with concentration is evidence of a large distribution of polydispersity in micelle size (at a given concentration). 

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