Micellar kinetics

Two other general ways of treating micellar kinetic data should be noted. Piszkiewicz (1977) used equations similar to the Hill equation of enzyme kinetics to fit variations of rate constants and surfactant concentration. This treatment differs from that of Menger and Portnoy (1967) in that it emphasizes cooperative effects due to substrate-micelle interactions. These interactions are probably very important at surfactant concentrations close to the cmc because solutes may promote micellization or bind to submicellar aggregates. Thus, eqn (1) and others like it do not fit the data for dilute surfactant, especially when reactants are hydrophobic and can promote micellization. 

Little is known about the structures of these kinetically effective complexes, or even about the aggregates of the amphiphile. Both hydrophobic and coulombic interactions are important because these aggregates are much less effective than micelles at assisting reactions of hydrophilic nucleophilic anions. These observations are consistent with the view that the aggregates are much smaller than micelles. It is probable that the structures and aggregation numbers of these aggregates depend on the nature of the solutes which bind to them and Piszkiewicz (1977) has suggested that such interactions play a role in micellar kinetics. 

Despite the abovementioned difficulties, kinetic models reproducing typical micellar kinetics have found widespread use and typically reproduce micellar reactivity well. Whereas these models are described here in terms of micellar kinetics, they can equally be adopted for the analysis of most vesicular rate effects, as long as bilayer permeation is either slow or fast compared to the rate of reaction. The issue of bilayer permeation-dependent rates of reaction has been addressed in detail by Moss et and will not be discussed here. A brief overview of the basic kinetic... 

The most straightforward of the various models describing micellar kinetics is the Menger-Portnoy model for (pseudo) unimolecular reactions.The Menger-Portnoy model assumes rapid equilibration of the reactant of interest over bulk water and the micellar pseudophase with equilibrium constant K. The reaction then proceeds in both pseudophases with rate constants and in bulk water and the micellar pseudophase, respectively (Scheme 4). 

Z/mc plate height due to sorption/desorption micellar kinetics... 

Kinetic studies have been important in many areas of chemistry, but, to date, classic kinetic approaches have not played a major role in the area of colloidal science related to self-organisation of surfactants. Although micellar kinetics were investigated in some detail in the 1970s, related work involving other self-assembly systems, e.g., vesicles, lyotropic liquid-crystalline phases, have been limited. 

The derivation of these different retention equations is important in several respects. First, they allow for calculation of micelle-solute binding constants, parameters which are important in many areas of micellar kinetics or chemistry. There have been several reports in the literature demonstrating this chromatographic approach for determination of micelle - solute binding constants (1,8,104,105). More importantly, they allow for prediction of retention behavior as a function of surfactant concentration (or of pH at constant micelle concentration), provided that the micelle - solute binding constant (or solute ionization constant) is known (which can be determined spectroscopically or from kinetic studies) (1,96,102). Consequently, the theory allows the chromatographer to determine the optimum conditions required for a desired separation. 

The terms q, and q are source terms, determined by the mechanism of micellar kinetics. If a mechanism of the formation-dissolution type is assumed (McQueen Hermans 1972, Lucassen 1976), these terms read,... 

For small disturbances of the adsorption layer from equilibrium, Lucassen (1976) derived an analytical solution (cf Section 6.1.1). An analysis of the effect of a micellar kinetics mechanism of stepwise aggregation-disintegration and the role of polydispersity of micelles was made by Dushkin Ivanov (1991) and Dushkin et al. (1991). Although it results in analytical expressions, it is based on some restricting linearisations, for example with respect to adsorption isotherm, and therefore, it is valid only for states close to equilibrium. 

When an adsorption layer is pre-equilibrated with a micellar solution and expanded, then monomers will adsorb at the surface. As this decreases the monomer concentration locally, the monomers and micelles are out of equilibrium and micelles will disintegrate. Hence, locally the concentration of micelles decreases and micelles will diffuse too. As the result the presence of micelles in the solution bulk can be seen as extra source of matter, i.e. the micellar kinetics represents an additional relaxation mechanism to interfacia perturbations. 

The coupling of the diffusion of monomers and micelles is given by the micellar kinetics, which consists of different physical processes a fast process in the range of microseconds (exchange of monomers between the micellar and the aqueous solution phase), and a second in the range of milliseconds (total disintegration of micelles into monomers). The entire variety of micellar kinetics was discussed by Aniansson et al. [91,92,93]. 

A quantitative model must consider the diffusion of monomers and micelles, and the micellar kinetics mechanisms as it was reviewed in the paper by Dushkin [94] or in the book by Joos [16]. As example the transport equations for a continuously expanding surface can be given in the following form... 

These equations can serve to estimate the influence of micellar kinetics on the adsorption process. Much more details will be given in Chapter 5 where the various micelle kinetics models and their practical relevance for interfacial studies are discussed. 

Time resolved SAXS/SANS allow a structural observation of kinetic processes on the nanoscale (1-100 nm) on a time scale ranging from milliseconds to hours. This allows micellar kinetics to be followed in real time, giving direct structural information of the process and its evolution. Synchrotron SAXS can reach smaller time scales and exhibits better resolution compared to neutron-based methods. However, SANS offers the possibility for contrast variation via simple H/D exchange chemistry, which opens up a world of possibilities for the investigation of kinetics in soft matter systems, in particular transport and exchange processes that otherwise would be invisible in scattering experiments. As most of these techniques have become available over recent years with advancements in both instrumentation and sample environments, there is a need for an overview of the development and the possibilities that are now available in the field of soft matter in general and micellar systems in particular. 

Time-Resolved Small-Angle Scattering as a Technique for Studying Micellar Kinetics... 

The use of organic microheterogeneous systems for developing new or improving known kinetic-based determinations is progressing well. Many micellar kinetic determinations based on uncatalyzed reactions have involved aromatic nucleophilic substitutions, e.g., reactions between l-fluoro-2,2-dinitrobenzene and primary and secondary amines, phenolic compounds, and thiols. These reactions... 

The first models of micellar kinetics in spatially uniform solutions have been developed by Kresheck et al. [140] and Aniansson and Wall [141]. The existence of fast and slow processes of the micellar dynamics has been established. The fast process represents exchange of separate monomers between micelles and the surrounding solution. If the micelle releases monomers, its aggregation number could decrease to a critical value, after which a complete decomposition of the micelle to monomers takes place. This decomposition is known as the slow demicellization process [141]. 

A special Aniansson Memorial Session was arranged on the afternoon of June 4 to commemorate the late Professor Gunnar Aniansson, University of Gdteborg, Sweden. A posthumous paper by Aniansson on micellar kinetics was presented at the Symposium and it opens the present volume. 

Effective rate constants and lifetimes for reactions in which diffusion to a reactive surface must occur are shown in Table 11.4 for a range of values of r and D, The latter are a quantification of expected trends which show to increase with increasing diffusion coefficient and to decrease with increasing micellar radius. In spite of good correspondence between experiment and theory there is some caution expressed by the authors in their paper in view of the uncertainty that macroscopic equations for normal chemical kinetics apply in the reactions explored by them. The problem, they say, is that micellar kinetics is a nonequilibrium phenomenon which can only be treated by taking the geometry of the system explicitly into account in any formulation of the process. 

Most chemical processes including micellar kinetics involve several steps and are characterized by several relaxation times (relaxation spectrum). The maximum number of observable relaxation times is equal to the number of independent rate equations that can be written for the system investigated. This number is equal to that of chemical species minus the number of mass-balance equations. > ... 

This section briefly introduces two techniques that seem to have potential for the study of micellar kinetics. 

The chapter is organized as follows. Section II briefly recalls the theoretical aspects of micellar dynamics and the expressions of the relaxation times characterizing the main relaxation processes (surfactant exchange, micelle formation/breakdown). Section III reviews studies of micellar kinetics of various types of surfactants conventional surfactants with a hydrocarbon chain, surfactants with a fluorinated chain, and gemini (dimeric) surfactants. Section IV deals with mixed micellar solutions. Section V considers the d5mamics of solubilized systems. Section VI reviews the dynamics of sur-... 

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