Critical micelle concentration modeling

The basic mechanism for surfactants to enhance solubility and dissolution is the ability of surface-active molecules to aggregate and form micelles [35], While the mathematical models used to describe surfactant-enhanced dissolution may differ, they all incorporate micellar transport. The basic assumption underlying micelle-facilitated transport is that no enhanced dissolution takes place below the critical micelle concentration of the surfactant solution. This assumption is debatable, since surfactant molecules below the critical micelle concentration may improve the wetting of solids by reducing the surface energy. 

This model implies a critical micelle concentration (CMC) below which the molecules do not associate and above which the molecules in excess to the CMC form multimers of N unimers. 

For a surface active betaine ester the rate of alkaline hydrolysis shows significant concentration dependence. Due to a locally elevated concentration of hydroxyl ions at the cationic micellar surface, i.e., a locally increased pH in the micellar pseudophase, the reaction rate can be substantially higher when the substance is present at a concentration above the critical micelle concentration compared to the rate observed for a unimeric surfactant or a non-surface active betaine ester under the same conditions. This behavior, which is illustrated in Fig. 10, is an example of micellar catalysis. The decrease in reaction rate observed at higher concentrations for the C12-C18 1 compounds is a consequence of competition between the reactive hydroxyl ions and the inert surfactant counterions at the micellar surface. This effect is in line with the essential features of the pseudophase ion-exchange model of micellar catalysis [29,31]. 

In the mass action model the micellar system can be described by only one parameter, and despite this simplicity, a good qualitative description of the main physical properties is obtained, for example the onset of cmc (critical micelle concentration), as shown in Figure 9.7. Notice that the formation of micelles becomes appreciable only at the cmc, and after that, by increasing further the surfactant concentration, all added surfactant is transformed directly into micelles, so that the surfactant concentration in solution remains constant at the level of cmc. 

In Section 8.2 we are concerned with the threshold concentration of surfactants at which micellization occurs. This concentration, known as the critical micelle concentration (CMC for short), is one of the most important properties of surfactant solutions. We look at two different ways of modeling micellization and discuss briefly when they are appropriate. 

In MLC, the mobile phase consists of surfactants at concentrations above their critical micelle concentration (CMC) in an aqueous solvent with an alkyl-bonded phase (52). Retention behavior in MLC is controlled by solute partitioning from the bulk solvent into micelles and into stationary phase as well as on direct transfer from the micelles in the mobile phase into the stationary phase. Eluent strength in MLC is inversely related to micelle concentration. A linear relationship exists between the inverse of retention factor and micelle concentration. Similar to what is observed in RPLC, a linear relationship exists between retention in MLC and , the volume fraction of the organic modifier. Modeling retention in MLC is much more complicated than in RPLC. The number of parameters is important. Micelles are obviously a new domain in both liquid chromatography and electrophoresis. Readers interested in the topic will appreciate Ref. 53, a special volume on it. 

This chapter is organized as follows. The thermodynamics of the critical micelle concentration are considered in Section 3.2. Section 3.3 is concerned with a summary of experiments characterizing micellization in block copolymers, and tables are used to provide a summary of some of the studies from the vast literature. Theories for dilute block copolymer solutions are described in Section 3.4, including both scaling models and mean field theories. Computer simulations of block copolymer micelles are discussed in Section 3.5. Micellization of ionic block copolymers is described in Section 3.6. Several methods for the study of dynamics in block copolymer solutions are sketched in Section 3.7. Finally, Section 3.8 is concerned with adsorption of block copolymers at the liquid interface. 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

The experimentally derived empirical expressions used in models such as the mass-action framework have contributed greatly to the logical selection of surfactants for efLcient and effective solubilization of drugs. However, there is currently a need to develop more efLcient, less toxic surfactants for use in drug delivery. A model that is able to provide quantitative prediction of the critical micelle concentration and micelle size without the need for extensive experimental measurements would greatly accelerate the development of novel surfactant chemistries for use in pharmaceutical applications. 

Monodispersed sols containing spherical polymer particles (e.g. polystyrene latexes22"24, 135) can be prepared by emulsion polymerisation, and are particularly useful as model systems for studying various aspects of colloidal behaviour. The seed sol is prepared with the emulsifier concentration well above the critical micelle concentration then, with the emulsifier concentration below the critical micelle concentration, subsequent growth of the seed particles is achieved without the formation of further new particles. 

Surfactant molecules in solution can form association colloids (called micelles) when the concentration of the surfactant is above a critical micelle concentration. This behavior only occurs above a given temperature, called the Kraft temperature. Below this temperature, the surfactant shows normal solubility behavior. In Fig. 14, a two-dimensional cut through a micelle, according to the most popular model, is shown. 

Another study on these variegated cells depicting an amphiphile revealed a temperature effect on the critical micelle concentration (cmc) that was minimal at about PB(W) = 0.25. Experimentally, the minimal cmc value occurs at about 25 °C.64 The onset of the cmc was also modeled and shown to be dependent on a modestly polar fragment of the amphiphile. 

Certain spectroscopic techniques, such as nuclear magnetic resonance (NMR) methods, require that the membrane mimetic, i.e., the lipid aggregate is not too large, and that the lipids exhibit a high degree of motion. For such studies, the micellar membrane model is often preferred. Micelles are relatively small (Fig. 3, top), which means that they rotate rapidly, on the time-scale required for NMR. These micelles consist of detergent molecules that aggregate above the critical micelle concentration (CMC). The size of a micelle is defined by the... 

Hydrophobicity of an inhibitor and critical micelle concentrations of the inhibitor in forming micelles have been found60 to play a significant role in the case of substituted imidazoles, imidazolines and fatty amines and these correlations do not take into account the electronic interactions. This correlation is based on Hansch s model of drug-receptor interactions based on transport of drug/inhibitor to the site followed by interaction at the site. 

The similarities between non-ionic micelles and globular proteins (Nemethy, 1967 Schott, 1968 Jencks, 1969) render micelles potentially useful as models for the investigation of hydrophobic interactions. Indeed, the stability of non-ionic micelles has been treated theoretically in terms of hydrophobic interactions (Poland and Scheraga, 1965). Since the critical micelle concentration is related to the degree and nature of the hydrophobic interactions of the amphiphile, its valne in the presence of additives and at different temperatures can be nsed as a quantitative measure of the effect of these variables on the hydrophobic interactions. In spite of the similarities between proteins and micelles, considerable caution is warranted in extrapolating the results obtained from micellar models to the more complex protein systems. 

The adsorption of binary mixtures of anionic surfactants of a homologous series (sodium octyl sulfate and sodium dodecyl sulfate) on alpha aluminum oxide was measured. A thermodynamic model was developed to describe ideal mixed admicelle (adsorbed surfactant bilayer) formation, for concentrations between the critical admicelle concentration and the critical micelle concentration. Specific... 

Figure 5.16 Model for associations of telechelic polymers as a function of increasing concentration. For strong associations, isolated flower micelles form just above the critical micelle concentration (CMC), which is often around 2 to 10 ppm (Winnick and Yekta 1997). At higher concentrations, the flowers are expected to be connected by bridges. (From Winnik and Yekta 1997, with permission from Current Chemistry Ltd.) 1997 Current Opinion in Colloid -i- Interface Science.

Lewis acid catalysis in micellar systems [33] was first found in the model reaction in Table 14-6 [34]. While the reaction proceeded sluggishly in the presence of 0.2 eq. Yb(OTf)3 in water, remarkable enhancement of the reactivity was observed when the reaction was carried out in the presence of 0.2 eq. Yb(OTf)3 in an aqueous solution of sodium dodecyl sulfate (SDS, 0.2 eq., 35 mM), and the corresponding aldol adduct was obtained in 50% yield. In the absence of the Lewis acid and the surfactant (water-promoted conditions), only 20% yield of the aldol adduct was isolated after 48 h, while 33% yield of the aldol adduct was obtained after 48 h in the absence of the Lewis acid in an aqueous solution of SDS. The amount of the surfactant also influenced the reactivity, and the yield was improved when Sc(OTf)3 was used as a Lewis acid catalyst. Judging from the critical micelle concentration, micelles would be formed in these reactions, and it is noteworthy that the Lewis acid-catalyzed reactions proceeded smoothly in micellar systems [35]. It was also found that the surfactants influenced the yield, and that Triton X-100 was effective in the aldol reaction (but required long reaction time), while only a trace amount of the adduct was detected when using cetyltri-methylammonium bromide (CTAB) as a surfactant. 

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