Micellar parameters

For crew-cut micelles, Zhulina and Birshtein demonstrated that the dependence of the micellar parameters on Nb disappears and Rc scales as yl/3N /3a and Z yNA, where y is the interfacial tension between the A and B blocks and a is the segment length [209]. 

Comparison in Micellar Parameters between 17R4 and L-64 Micelles in Water... 

Table 13.2 summarizes the effect of the chain architecture, and provides a detailed comparison of micellar parameters between 17R4 and L-64 micelles, including the thermodynamic quantities of the micellization process. 

Table 4. Micellar parameters in benzene and carbontetrachloride. BAP (butyl-), HAP (hexyl-), OAP (octyl-), DeAP(decyl-), DAP (dodecyl-) ammonium propionates. [Faraday Trans. I, 68, 280 (1973))...

TABLE I. Structure, Name, Abbreviation, and Micellar Parameters of Some Aqueous Micellar-Forming Surfactants Employed in Separation Science... 

It is important to stress that the micellar parameters presented in Tables I and II are for the indicated detergent in water at ambient atmospheric pressure and room temperature ( 25°C). The quoted values can be altered (sometimes dramatically) by changes In the experimental conditions. For instance, temperature and pressure can impact the micellization process. Typically, plots of CMC vs. temperature exhibit a minimum somewhere between 20 - 30° C for charged ionic surfactants while for nonionic surfactants, only a limiting minimum is observed at ca. 40 - 50° C 06). The micellar CMC and N can also depend upon pressure (J 6). However, at the pressures under which most separation techniques are conducted ( 3.5 MPa), the changes in micellar parameters are such that this effect can be neglected in all but the most exacting work (64). 

TABLE II. Structure and Micellar Parameters of Some Bile Saltsa... 

TABLE III. Comparison of Micellar Parameters Under Different Experimental Conditions in Aqueous Media... 

By minimizing the expressions above (Eq. 1) with respect to the independent parameters, the micellar parameters, including the cmc, for a given system can in principle be obtained. 

From this formalism, the dependence of the various micellar parameters on, for example, molecular weight, composition, interfacial tension, etc. can be estimated. The results seem to compare rather well with experimental data, see, e.g., [44,45]. For example, for intermediate and star-like micelles, the aggregation number would... 

The aggregation number P can be related to other micellar parameters assuming a compact (solvent-free) core P = nR L/iVB/Nxwo) and P = AnR /(3 Ub/A avo) for cylinders and spheres, respectively. Here Ub is the molar volume of the insoluble B-block and /Vavo is Avagadro s number. 

In terms of micellar models, the cmc value has a precise definition in the pseudo-phase separation model, in which the micelles are treated as a separate phase. The cmc value is defined, in terms of the pseudo-phase model, as the concentration of maximnm solubility of the monomer in that particular solvent. The pseudo-phase model has a number of shortcomings however, the concept of the cmc value, as it is described in terms of this model, is very useful when discussing the association of surfactants into micelles. It is for this reason that the cmc value is, perhaps, the most frequently measnred and discussed micellar parameter [39]. 

For crew-cut micelles with Aai > Ab, the micellar parameters only depend on Aaj following (18) and (19) <= ... 

The micellar parameters that we will discuss include critical micelle concentration (cmc), the micellar average aggregation number and the dependence of... 

The enthalpies of micellization, AH, , can be calculated indirectly by use of the van t Hoff treatment or directly by isothermal titration calorimetry (ITC). Except for few cases (e.g., some nonionic surfactants), the results of these methods do not agree [38]. The main reason is that there is no provision in van t Hoff equation for factors that are important for micelle formation of ionic surfactants, in particular, the dependence of micellar geometry, surface-charge density, and extent of hydration on temperature T) [38]. On the other hand, the effects of (T) on the aforementioned micellar parameters are included in the direct (i.e., calorimetric) determination of AH, . From Gibbs free energy relationship, any uncertainty introduced in the calculation of Ai7, j will be carried over to so that A5 rK > AS, Where available, therefore, we compare the thermodynamic quantities of micellization, based on experimental data of the same technique. 

Minimum (s) values range from 50 to 100 for typical ionic surfactants, average sizes are in the order of nm, and CMC are in the order of mM, decreasing with charge screening and increasing with the size of the apolar tail. Micellar parameters can be predicted from detailed theoretical approaches based on the minimization of the free energy of an isolated micelle or of a multicomponent system for both low MW surfactant and block copolymers [71]. 

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