Solute micelle equilibrium

Here, S is the free solute, M is the micelle, n is the number of solute molecules per micelle, SM is the solute-micelle complex, and k is the equilibrium coefficient [39],... 

Monomer/Micelle Equilibrium Mixtures of surfactants, like any surfactant species in an aqueous solution, give rise to monomer or micelle aggregates provided that the concentration reaches a minimum value, called the critical micellar concentration (CMC). The micelles thus formed are mixed, i.e. made up of the different surfactant species in solution. 

Equations 3 and 4 are derived from Equation 5 (31) which has been Found to be invalid For the systems oF interest. However, Equations 3 and 4 have been shown to accurately describe mixture CMC values and monomer-micelle equilibrium. The resolution is that Equations 3 and 4 should be considered as valuable empirical equations to describe these nonideal systems. The Fact that they were originally derived From regular solution theory is a historical coincidence. 

Solubilization o-f dissolved organic molecules into micelles is important in detergency (2), emulsion polymerization (65). and micellar—enhanced ultra-fiItration (3), Just to name a -few applications. Solubilization also indirectly a-f-fects many other operations because it o-ften a-f-fects monomer—micelle equilibrium, in-fluencing sur-factant adsorption, wetting, etc. when solubi 1 izable, non—sur-factant species are present in solution. 

As already discussed in Chapter 1, the relative tendency of a surfactant component to adsorb on a given surface or to form micelles can vary greatly with surfactant structure. The adsorption of each component could be measured below the CMC at various concentrations of each surfactant in a mixture. A matrix could be constructed to tabulate the (hopefully unique) monomer concentration of each component in the mixture corresponding to any combination of adsorption levels for the various components present. For example, for a binary system of surfactants A and B, when adsorption of A is 0.5 mmole/g and that of B is 0.3 mmole/g, there should be only one unique combination of monomer concentrations of surfactant A and of surfactant B which would result in this adsorption (e.g., 1 mM of A and 1.5 mM of B). Uell above the CMC, where most of the surfactant in solution is present as micelles, micellar composition is approximately equal to solution composition and is, therefore, known. If individual surfactant component adsorption is also measured here, it would allow computation of each surfactant monomer concentration (from the aforementioned matrix) in equilibrium with the mixed micelles. Other processes dependent on monomer concentration or surfactant component activities only could also be used in a similar fashion to determine monomer—micelle equilibrium. 

In aqueous surfactant solutions, either by circumstance or design, non—surface active organic species may be present. Examples are oil recovery, where crude oil is present, or micellar—enhanced ultrafiltration, where micelles are being used to effect a separation of dissolved organic pollutants from water. The ability of mixed micelles to solubilize organic solutes has received relatively little study. In addition, the solubilization of these compounds by micelles may change the monomer—micelle equilibrium compositions. 

As our understanding and ability to model monomer-micelle equilibrium in the absence o-f added solutes evolves, research into the more complex systems will... 

Fig. 3. Schematic diagram of anionic surfactant solution at equilibrium above its critical micelle concentration, where M...

There have been very few studies on the kinetics of micellization in block copolymer solutions. Micellization in aqueous surfactant systems close to equilibrium occurs on a time-scale far below one second. Experimental results obtained by fast reaction techniques, such as temperature jumps or pressure jumps or steady-state methods such as ultrasonic absorption, NMR and ESR, show that at least... 

Figure 17.4 shows a surfactant sorption isotherm from low to high (>CMC) concentrations of the surfactant. It can be divided into three parts (Figure 17.5). In Region 1, individual surfactant molecules are in equilibrium with the surfactant molecules adsorbed to the solid sorbent. In Region 2, the surfactant concentration in the water has exceeded the CMC. That is equivalent to saturation of the air/water interface with surfactant molecules. Subsequent addition of surfactant molecules leads to increased sorption due to formation of sorbed surfactant aggregates (Region 2). In Region 3, the aggregates in solution (micelles) are in equilibrium with the sorbed aggregates, the so-called admicelles..

Consider a micellar solution at equilibrium that is subject to a sudden temperature change (T-jump). At the new temperature the equilibrium aggregate size distribution will be somewhat different and a redistribution of micellar sizes will occur. Aniansson and Wall now made the important observation that when scheme (5.1) represents the kinetic elementary step, and when there is a strong minimum in the micelle size distribution as in Fig. 2.23(a) the redistribution of micelle sizes is a two-step process. In the first and faster step relaxation occurs to a quasi-equilibrium state which is formed under the constraint that the total number of micelles remains constant. Thus the fast process involves reactions in scheme (5.1) for aggregates of sizes close to the maximum in the distribution. This process is characterized by an exponential relaxation with a time constant Tj equal to... 

Figure 3.18 I llustration of an anionic surfactant solution at equilibrium above its critical micelle concentration, showing the components (upper) and the locations of the components at equilibrium (lower). From Cahn and Lynn [206].

The stability of inverse micelles has been treated by Eicke (8,9) and by Muller (10) for nonaqueous systems, while Adamson (1) and later Levine (11) calculated the electric field gradient in an inverse micelle for a solution in equilibrium with an aqueous solution. Ruckenstein (5) later gave a more complete treatment of the stability of such systems taking both enthalpic (Van der Waals (VdW) interparticle potential, the first component of the interfacial free energy and the interparticle contribution of the repulsion energy from the compression of the diffuse part of the electric double layer) and entropic contributions into consideration. His calculations also were performed for the equilibrium between two liquid solutions—one aqueous, the other hydrocarbon. 

Fig. 1 Solute-micelle and solute-stationary phase interactions in hybrid micellar mobile phases (see text for meaning of equilibrium constants).

Equation (6.20) represents the formation of a cationic micelle from N surfactant ions D+ and (N-p) firmly held counterions X. Whenever the thermodynamics of a process is under consideration, it is important to define the standard states of the species. In this example, the standard states are such that the mole fractions of the ionic species are unity and the solution properties are those of the infinitely dilute solutions. The equilibrium constant may be written in the usual way... 

Surfactant molecules are in dynamic equilibrium among three possible states (monomers adsorbed at the interface of the aqueous solution with a non-polar phase, monomers molecularly dispersed in the solution, and micellar aggregates formed when the CMC is reached). From various theoretical considerations, as well as experimental results, it can be said that micelles are dynamic structures whose stability is in the range of milliseconds to seconds.2223 Thus, in an aqueous surfactant solution, micelles break and reform at a fairly rapid rate, in the range of milliseconds.24 26... 

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. 

In this type of extraction, micellar structures are retained by correctly selecting the ultrafiltration (UF) membrane (Scamehorn et al., 1988). Hydrophobic species are solubilized within the micelles, but surfactant monomers in equilibrium with the micelles can penetrate the membrane along with the free solutes in equilibrium with those solubilized in the micelles. Whereas several uses for this technique have been suggested, such as the collection of radioactive uranium and plutonium present in acid wastes during nuclear plant decommissioning, from our point of view its principal use is in enantiomeric separation (Overdevest et al., 1998). 

In our opinion these examples demonstrate the value of our way of looking at the problem. Emphasis must finally be laid on one thing. In spite of the fact that we consider the phenomena in soap solutions throughout as equilibrium phenomena, we use terms as micelle , coacervate, and so on, which on account of their colloid chemical past call forth ideas of strictly determined boundary surfaces (Freundlich s Kapillarchemie). We wish however to retain these terms without crediting the boundary surface of micelle-equilibrium liquid with a separate significance. We thus look upon a micelle in a soap solution as a formation which is in equilibrium with the rest of the solution but which through its large dimensions and its structure has properties which the soap molecule as such does not possess. It is only with this restriction that we wish to continue to speak of micelles, coacervates, etc. 

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