Micellar distribution

Nissinen, M., Gylling, H., Vuoristo, M., and Miettinen, T.A. 2002. Micellar distribution of cholesterol and phytosterols after duodenal plant stanol ester infusion. Am. J. Physiol. Gastrointest. Liver Physiol. 282, G1009-G1015. 

These Vg and V volumes are used to evaluate the solute distribution between phases, the solute micellar partition coefficient, also called solute micellar distribution constant, and the solute local concentration in the micellar or aqueous phase. 

When a solute is added to a micellar solution, it distributes itself between the aqueous solvent and the micelles. To quantitate this distribution, the micellar partition coefficient or micellar distribution constant, > is defined as the ratio of the solute concentration in the micelles to the solute concentration in the nonmicellar phase. It is expressed by [30] ... 

At high concentrations where c 1, we have approximately x 1 - l/ /c. The micellar distribution takes the form... 

Two well separated relaxation times can always be observed by relaxation measurements on micellar systems. (1) The best model that can account for the two processes has been proposed by Aniansson and Wall. (2) For the derivation of the relaxation expressions, the micellar distribution curve was divided into three different regions The monomers and oligomers, the nuclei in the distribution minimum and finally the proper micelles around the distribution maximum. If the equilibrium is suddenly perturbed, the reequilibration process between the proper micelles of different size can proceed rapidly. The number of the micelles is not changed by this process. Aniansson showed that the monomer relaxation leads exactly to a single relaxation time... 

The constants a and P are estimated by the micellar distribution. This can be easily shown... 

A solution can be found fairly easily of the kinetic equations in and R, of which the quantity measured in relaxation studies is normally a linear function, in the case that the micellar distribution is doubly Gaussian... 

The width of the micellar distribution (a) is broad enough for n to be treated as a continuous variable, and is also the case. 

The fast process involves an exchange of monomeric surfactants between the micelles and the intermicellar solution. A monomer or several monomers dissociate from or associate to existing micelles. As a result, the micellar distribution curve shifts without a change in the number of micelles [61,62,67, 68]. 

The exchange of surfactant monomers between the micellar and the monomeric state is diffusion controlled for monomers with hydrophilic counterions. The exchange rate is slower for monomers with hydrophobic counterions. For lithium and substituted ammonium salts of perfluorooctanesulfonic acid [76], the values of the micellar distribution curve, a ln, increased with increasing hy-drophobicity of the counterion or with a decrease of temperature. Both the association rate constant, k /n, and dissociation rate constant, k /n, decreased with increasing counterion hydrophobicity. The increase in k /n values was larger than the decrease in cmc values, suggesting that hydrophobic counterions form a barrier to the monomer exchange process. 

Chemical relaxation techniques [21-23] have been utilized to determine the aggregation numbers for salts of perfluorooctanesulfonic acid [21,22]. The aggregation numbers have been calculated from the kinetic data, based on the assumption that the micellar distribution curve obeys a Gaussian distribution function. This procedure was validated with aggregation numbers for hydrocarbon-type surfactants, which were in agreement with those obtained from light-scattering data. 

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