Micelles equilibrium with monomer

Highly monodisperse reversed micelles are formed by sodium bis(2-ethylhexyl) sul-fosuccinate (AOT) dissolved in hydrocarbons that are in equilibrium with monomers whose concentration (cmc) is 4 X 10 M, have a mean aggregation number of about 23, a radius of 15 A, exchange monomers with the bulk in a time scale of 10 s, and dissolve completely in a time scale of 10 s [1,2,4,14], Other very interesting surfactants able to form reversed micelles in a variety of apolar solvents have been derived from this salt by simple replacing the sodium counterion with many other cations [15,16],... 

Figure 12.2 Schematic cross-section through a spherical micelle in water. A shell of polar head groups surrounds the hydrophobic core formed by the hydrocarbon chains. The micellar structure is in equilibrium with monomers in solution. Right Inverted micelle in oil.

Critical micelle concentration. The concentration in solution at which a surface-active agent forms multimolecular aggregates which are in kinetic equilibrium with monomer. 

There are two basic approaches to modeling the thermodynamics of micelle formation. The mass action model views the micelles as reversible complexes of the monomer that are aggregating and predicts the sharp change in tendency of incremental surfactant to form micelles instead of monomer at the CMC this sharp transition is a consequence of the relatively large number of molecules forming the aggregate. The mass action model predicts that micelles are present below the CMC but at very low concentrations. The ocher major model used to describe micelle formation is the pseudophase separation model, which views micelles as a separate thermodynamic phase in equilibrium with monomer. Because micelle formation is a second-order phase transition, micelles are not a true thermodynamic phase, and this model is an approximation. However, the assumption that there are no mi-celies present below the CMC, and that the surfactant activity becomes constant above the CMC. is close to reality. and the mathematical simplicity of the pseudophase... 

Solutions of molecules with pronounced amphiphilic character exhibit unusual concentration dependent properties dilute solutions behave like normal electrolytes (if ionic surfactants are considered), at higher, rather well-defined concentrations, quasisudden changes of several physical properties are observed (see Fig. 1). This phenomenon has been successfully ascribed to the formation of organised aggregates, i.e. micelles. The concentration above which micelles exist in equilibrium with monomers (and eventually small subunits) is the so-called critical micelle concentration (cmc). 

The exclusion chromatography of surfactant solutions is a problematic method for analyses, since the micelles are only stable when in equilibrium with monomers of concentration equal to the cmc. The monomer-micelle equilibrium thus can be subjected to chromatographic investigations, under various conditions, e.g. dynamic or equilibrium. In the former case, if one applies a micellar solution with concentration greater than cmc, the surfactant front would move down the column at a speed relative to the size of micelles. However, if the dilution factor in the column is too large, such that only monomers are present, then the front moves at the same speed as the monomer. In these systems the eluant is supposed to be pure solvent. However, if concentration of the surfactant in the eluant is close to the cmc, then the micellar solution moves down the column with little perturbation of the monomer-micelle equilibrium. The surfactant front under these conditions then moves... 

As shown in Fig. 5, the value of R is constant until cmc, above which concentration R value increases rapidly. If the concentration of surfactant is greater than cmc, the front advances more rapidly than the velocity of monomers. However, micelles are in equilibrium with monomers and cannot move separately, and continuously dissociated during elution. This result in the elution of front somewhere between values found for micelle and monomer, respectively. The elution volume thus depends on the degree of di-... 

With solubilisates having significant water solubility, it is of interest to know both the distribution ratio of solubilisate between micelles and water under saturation and unsaturation conditions. To measure the distribution ratio under unsaturation conditions, a dialysis technique can be employed, using membranes that are permeable to solubilisate but not to micelles. Ultrafiltration and gel filtration techniques can be applied to obtain the above information. The data are treated using the phase-separation model of micellisation (micelles are considered to be a separate phase in equilibrium with monomers). 

Sams et al. [61] proposed a two-state kinetic model which assumed a monomeric state and an associated state consisting of aggregates in various sizes larger than the monomer. The model describes only the fast process and assumes that the rate constants for association and dissociation are independent of the micelle size. A revised version of the two-state model [62,63] assumed micelle formation to be an adsorption phenomenon, with micelles at equilibrium with monomers adsorbing and escaping from the surface of micelles. 

Experimental observations based on diverse experimental techniques show that just as micelles are in rapid equilibrium with monomers (Aj), miceUized solubi-lizate molecules are also in rapid equilibrium with solubilizate molecules in aqueous pseudophase as represented by Equation 1.26... 

Moreover, taking into account that reversed micelles coexist with surfactant monomers, in principle, further effects due to the aggregation of polar and amphiphilic so-lubihzates with surfactant monomers and the shift of the monomer/reversed micelle equilibrium must be also considered [25,26],... 

The cyclodextrins are stable bodies in aqueous solution, unlike the micelles, which are transitory and are in a state of dynamic equilibrium with the monomer surfactants. However, in many aspects the inclusion of analytes in the cyclodextrin cavity is reminiscent of the solubilization of hydrophobic molecules in micelles in aqueous solution. 

Below CMC, the detergent molecules are present as single monomers. Above CMC, they are present as monomers, Cmono, in equilibrium with micelles, Cmice. The micelle with aggregation number, Nag, is formed from monomers ... 

CMC will change if the additive has an effect on the monomer-micelle equilibrium, and also if the additive changes detergent solubility. The CMC of all ionic surfactants will decrease if coions are added. However, nonionic surfactants show very little change in CMC on the addition of salts, which is to be expected from theoretical considerations. The change of CMC with NaCl for SDS is as follows (Figure 3.10) ... 

Ideal Mixed Micelles. The Critical Micelle Concentration (CMC) is the lowest surfactant concentration at which micelles form the lower the CMC, the greater the tendency of a system to form micelles. When the total surfactant concentration equals the CMC, an infintesimal fraction of surfactant is present as micelles therefore, the CMC is equal to the total monomer concentration in equilibrium with the micellar pseudo—phase. The CMC for monomer—micelle equilibrium is analogous to the dew point in vapor—liquid equilibrium. 

The equilibrium in these systems above the cloud point then involves monomer-micelle equilibrium in the dilute phase and monomer in the dilute phase in equilibrium with the coacervate phase. Prediction o-f the distribution of surfactant component between phases involves modeling of both of these equilibrium processes (98). It should be kept in mind that the region under discussion here involves only a small fraction of the total phase space in the nonionic surfactant—water system (105). Other compositions may involve more than two equilibrium phases, liquid crystals, or other structures. As the temperature or surfactant composition or concentration is varied, these regions may be encroached upon, something that the surfactant technologist must be wary of when working with nonionic surfactant systems. 

At a speci-fic adsorption level, we can view the sur-f actant monomers as being in equilibrium with admicelles on speci-fic sur-face patches, just as the monomer is in equilibrium with the micelles at a monomeric concentration o-f the CMC. There-fore, CAC is... 

The appeareance of maxima on the adsorption isotherms and decrease in flotability can be explained by the hypothesis that in the presence of micelles no adsorption layer of the surfactant can be formed, the character of which corresponds to the equilibrium state only with monomers (sufficiently hydrophobic adsorption layer). Due to a heterogeneity of forces acting at the surfactant ion mineral interface it can be assumed that at concentrations S CMC some of the molecules will be bound much more firmly in a three-dimensional micelle than in... 

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