Micelles association constant

Linear plots of Fj/( — Fq) vs. have been obtained for a large variety of organic solutes and have been utilized for the evaluation of the substrate-micelle association constant, K, from the slope, intercept, and equation (15) (Herries et al., 1964 Dunlap and Cordes, 1968 Romsted and Cordes 1968). Fig. 5 illustrates a typical plot of this type for the elution of p-nitrophenol in sodium dodecyl sulfate solution. 

V. Gonzalez, M.A. Rodriguez-Delgado, M.J. Sanchez and F. Garcia-Montelongo, Solute-Micelle Association Constants and Correlation ofP t Coefficients with Hydrophobicity for PAHs by MLC, Chromatographia, 34 627 (1992). 

Figure 8.2 Predicted retention of a zwitterion (pK and pK are acid-base dissociation constants in water and micellar solution, respectively, and [S] is surfactant concentration), as a function of pH and micelle concentration with nonionic micelles (top) solute-micelle association constants for cation, zwitterion and anion are 3, 0.1 and 3, respectively, cmc = 2.4x10 M and with anionic micelles (bottom) solute-micelle association constants are 10,000, 10 and 0.1, respectively, cmc = 8.3x10 M. The derivatives of the sigmoidal curves at each micelle concentration are also shown to give the apparent dissociation constants. Reprinted from Ref 6 with permission of the American Chemical Society.

The extent of solubilization of the substrate to the micelle can be related with the association constant or the binding constant. Some of the important models developed to explain the micellar effect are described briefly as follows ... 

This is simply the result we would expect from the law of mass action. Thus, for the reaction N monomers 1 micelle, we can immediately write that there is an equilibrium (association) constant given by... 

The essence of the shell model is that the association constant of the first step is very much smaller than the association constants of all subsequent steps. It was assumed by de Kruif et al. (2002) that, since there is a considerable similarity in various properties of p- and K-caseins, then the k-casein micelle can also be described using the shell model. Nevertheless, Vreeman et al. (1981) had previously suggested that the structure of the... 

The determination of the association constant K values can be done either graphically or numerically (Kertes and Gutmann, 1976). The K values can be used to estimate thermodynamic quantities such as AG°, AH° and AS0. The interactions of polar substances, such as methanol, ethanol and acetone, with Aerosol OT in toluene systems were examined (Kon-no, 1993). The negative AG° value was found in the decreased order methanol > ethanol > acetone and the contribution to AG° was AH° > TAS°. This result indicates that the solubilization of three solutes with Aerosol OT micelle is an enthalpy driven process. 

Murakami and co-workers12) have carried out one of the most thorough investigations of multi-armed compounds with ion-terminated chains. In 1979 they reported the substrate-binding behavior of an azaparacyclophane (16) in which the hydro-phobic cavity was deepened by substitution of long ion-terminated chains on the macrocyclic skeleton. Salient properties of the cyclophane (16) include (1) The compound has a critical micelle concentration of 3.2 x 10 4 M. (2) (16) binds cationic and neutral dyes but not anionic ones. Thus, Rhodamine 6G and Quinaldine Red form 1 1 complexes with (16) having association constants of about 5 x 103 M 1. 

A uniform stepwise association constant kj cannot produce abrupt changes in the physical properties such as those accompanying micellization. This requires a cooperative self-association, Le., kj should increase with j in the initial stages.7... 

A cursory review of the literature reveals that the ELC technique with micellar mobile phases has proven to be very beneficial in the characterization of micellar systems (184-186,190-192,227,228). For example, microcolumn exclusion LC has been applied to the determination of the CMC value of surfactants (or micellar-forming proteins), determination of the kinetic rate and equilibrium association constants for surfactant (or protein) micellization (184,192), determination of the size or size distribution of micelles (especially those formed from block copolymers or milk casein) (185,186,191,192,225) as well as for estimation of the time required for formation of micelles (or micelle-forming macromolecules) (186) among others. The size and stability of reversed micelles has also been evaluated using ELC (195). 

Triphenylenes provided with nonionic di(ethylene oxide) side-chains (25f)132 134 or with ionic alkyl chains (25g)135 form supramolecular polymers in water.136 The arene—arene interactions of the aromatic cores allow for the formation of columnar micelles . At low concentrations the columns are relatively short, and the solutions are isotropic. At higher concentrations the longer columns interact and lyotropic mesophases are formed.133 Computer simulations showed that in the isotropic solution the polymerization of the discotics is driven by solute-solute attraction and follows the theory of isodesmic linear aggregation the association constants for dimerization, trimerization, and etc., are equal and the DP of the column thus can easily be tuned by concentration and temperature.137 138 At higher concentrations the sizes of the columns are influenced by their neighbors, the columns align, and the DP rises rapidly. 

The base hydrolyses of these substrates were enhanced by the addition of cationic polyelectrolyte and polysoap. Saturation type kinetics were observed and the values of rate constants for the uncatalyzed and catalyzed reactions are given as well as the values for the association constant. The results suggest that the hydrophobic interactions play a major role in the hydrolysis enhancements of the neutral and charged substrates, and that these polymeric micelles can provide both the characteristics of polyelectrolytes and micelles and thus give higher rate enchancements. 

The general theory of micellar electrokinetic chromatography represents a confluence of chromatographic and electrophoretic principles. The expressions for electrophoretic mobility under different separation conditions are summarized in Table 8.4 [161,162]. These relationships allow the determination of the critical micelle concentration and equilibrium distribution constants for solute-micelle association complexes under typical conditions for micellar electrokinetic chromatography [60-64,161-164]. These properties change significantly with the composition of the electrolyte solution, and are generally different to common reference values for pure water. 

M. A. Garcia, S. Vera and M.L. Marina, Determination of Micelle-Solute Association Constants of Some Benzene and Naphthalene Derivatives by MLC, Chromatographia, 32 148 (1991). 

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