Molecule-micelle equilibrium

Indirect methods for obtaining information on the kinetics of the associa-tion/dissociation equilibrium include sedimentation velocity and GPC experiments. The application of these techniques is based on comparison of sedimentation or GPC elution curves with model curves based on theories for separation of unimers and micelles during a sedimentation velocity (Gilbert 1955) or GPC (Ackers and Thompson 1965 Coll 1971 Prochazka et at. 1988, 1989) experiment. Experiments have been performed that demonstrate several of the qualitative model predictions (Prochazka et at. 1989). The main conclusions were that GPC curves with two well-separated peaks can only result from a slow dynamic molecule micelle equilibrium, and that no simple interpretation of elution curves in terms of relative concentrations of unimer and micelles is possible (Prochazka et at. 1989). Thus no quantitative information on the kinetics of the molecule micelle equilibrium can be obtained from sedimentation velocity or GPC data. 

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. 

Except at concentrations near the CAC, the amount of surfactant adsorbed in the Henry s law region is small in comparison to the amount of surfactant present in the admicelles. This implies that nearly all of the adsorbed surfactant molecules are associated on the mineral surface in the form of admicelles. It is important to keep in mind that Equation 8 is valid only between the CAC and the CMC. Above the CMC, equations could be included to account for the formation of micelles, by including monomer-micelle equilibrium equations (1 1). ... 

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. 

Surfactant molecules can aggregate into clusters called micelles (see Figure 25.21). A typical spherical micelle may contain 60 surfactant molecules. Micelles usually have narrow size distributions, say from 55 to 65 surfactant molecules. To make the mathematics simple, let s suppose that every micelle is an n-mer that has exactly n surfactant molecules. The concentration of micelles is [An]- The rest of the surfactant molecules are isolated as individual molecules. Their concentration is [AiJ. The equilibrium is... 

At a given pH, the structures formed (free molecules, micelles, or vesicles) also depend on the concentration. Because the number of molecules required to form a micelle or vesicle is quite high, the equilibrium can be treated as a phase transitimi ... 

At low concentrations surfactant molecules adsorbed at the surface are in equilibrium with other molecules in solution. Above a threshold concentration, called the critical micelle concentration (cmc, for short), another equilibrium must be considered. This additional equilibrium is that between individual molecules in solution and clusters of emulsifier molecules known as micelles. 

In highly diluted solutions the surfactants are monodispersed and are enriched by hydrophil-hydrophobe-oriented adsorption at the surface. If a certain concentration which is characteristic for each surfactant is exceeded, the surfactant molecules congregate to micelles. The inside of a micelle consists of hydrophobic groups whereas its surface consists of hydrophilic groups. Micelles are dynamic entities that are in equilibrium with their surrounded concentration. If the solution is diluted and remains under the characteristic concentration, micelles dissociate to single molecules. The concentration at which micelle formation starts is called critical micelle concentration (cmc). Its value is characteristic for each surfactant and depends on several parameters [189-191] ... 

In a multiphase formulation, such as an oil-in-water emulsion, preservative molecules will distribute themselves in an unstable equilibrium between the bulk aqueous phase and (i) the oil phase by partition, (ii) the surfactant micelles by solubilization, (iii) polymeric suspending agents and other solutes by competitive displacement of water of solvation, (iv) particulate and container surfaces by adsorption and, (v) any microorganisms present. Generally, the overall preservative efficiency can be related to the small proportion of preservative molecules remaining unbound in the bulk aqueous phase, although as this becomes depleted some slow re-equilibration between the components can be anticipated. The loss of neutral molecules into oil and micellar phases may be favoured over ionized species, although considerable variation in distribution is found between different systems. 

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],... 

The encapsulation results in a chance collection of molecules that then form an autocatalytic cycle and a primitive metabolism but intrinsically only an isolated system of chemical reactions. There is no requirement for the reactions to reach equilibrium because they are no longer under standard conditions and the extent of reaction, f, will be composition limited (Section 8.2). Suddenly, a protocell looks promising but the encapsulation process poses lots of questions. How many molecules are required to form an organism How big does the micelle or liposome have to be How are molecules transported from outside to inside Can the system replicate Consider a simple spherical protocell of diameter 100 nm with an enclosed volume of a mere 125 fL. There is room within the cell for something like 5 billion molecules, assuming that they all have a density similar to that of water. This is a surprisingly small number and is a reasonable first guess for the number of molecules within a bacterium. 

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. 

An aqueous dispersion of a disperse dye contains an equilibrium distribution of solid dye particles of various sizes. Dyeing takes place from a saturated solution, which is maintained in this state by the presence of undissolved particles of dye. As dyeing proceeds, the smallest insoluble particles dissolve at a rate appropriate to maintain this saturated solution. Only the smallest moieties present, single molecules and dimers, are capable of becoming absorbed by cellulose acetate or polyester fibres. A recent study of three representative Cl Disperse dyes, namely the nitrodiphenylamine Yellow 42 (3.49), the monoazo Red 118 (3.50) and the anthraquinone Violet 26 (3.51), demonstrated that aggregation of dye molecules dissolved in aqueous surfactant solutions does not proceed beyond dimerisation. The proportion present as dimers reached a maximum at a surfactant dye molar ratio of 2 5 for all three dyes, implying the formation of mixed dye-surfactant micelles [52]. 

Although anation and aquation rates of vitamin B12 are not affected appreciably by aqueous micelles, the solubilized water in reversed micelles, in contrast, influences the rate and equilibrium constants for the formation and decomposition of glycine, imidazole, and sodium azide adducts of vitamin Bl2 (Fendler et al., 1974). A vitamin B12 molecule is conceivably shielded from the apolar solvent (benzene) by some 300 surfactant molecules. 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled306. The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds307, whereas the lifetime of the micellar entity is about 1-100 miliseconds307. Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

Below the Krafft Point, the surfactant dissolved in a molecularly dispersed manner until the saturation concentration is reached. At higher concentrations, a hydrated solid is in equilibrium with individual molecules. Above the Krafft Pointy the hydrated solid is in equilibrium with micelles and individual molecules. 

Freshwater mammals such as heaver may leave odors on the surface of their ponds and olfactorily sample the water or layer of air immediately above it. Lipids on water may form micelles, small blobs of molecules (from Latin mica, a grain, crumb, morsel) that enhance evaporation into the air layer by increased chemical potential. Some seahirds hunt hy odor (e.g. Hutchison and Wenzel, 1980 Nevitt, 1999). They may respond to prey volatiles (from krill, squid, or fish) that rise to the water surface and evaporate into the air. The air-water equilibrium for dilute solutions can be expressed by using partition coefficients, relative volatility, or Henry s law (Thibodeaux, 1979). 

Figure 1. Various physical states of phospholipids in aqueous solution. Note the following features (a) phospholipids residing at the air/water interface are arranged such that their polar head groups maximize contact with the aqueous environment, whereas apolar side chains extend outward toward the air (b) solitary phospholipid molecules remain in equilibrium with various monolayer and bilayer structures (c) bilayer vesicles and micelles remain in equilibrium with solitary phospholipid molecules, provided that the total lipid content exceeds the critical micelle concentration.

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