Stepwise aggregation, micelles

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. 

In the discussion of the adsorption kinetics of micellar solutions, different micelle kinetics mechanisms are taken into account, such as formation/dissolution or stepwise aggregation/disaggregation (Dushkin Ivanov 1991). It is clear that the presence of micelles in the solution influences the adsorption rate remarkably. Under certain conditions, the aggregation number, micelle concentration, and the rate constant of micelle kinetics become the rate controlling parameters of the whole adsorption process. Models, which consider solubilisation effects in surfactant systems, do not yet exist. 

The formation or dissolution of whole micelles can only occur in a stepwise aggregation process through the distribution minimum. The concentrations of the particles in this region are usually several orders of magnitude smaller than the concentrations of the proper micelles and the process in which the number of the micelles is changed is therefore much slower than... 

Although the mass action approach could account for a number of experimental results, such as the small change in properties around the c.m.c., it has not escaped criticism. For example, the assumption that surfactants exist in solution in only two forms, namely single ions and micelles of uniform size, is debatable. Analysis of various experimental results has shown that micelles have a size distribution that is narrow and concentration dependent. Thus, the assumption of a single aggregation number is an oversimplification and, in reaUty, there is a micellar size distribution. This can be analyzed using the multiple equilibrium model, which can be best formulated as a stepwise aggregation [2],... 

The above picture shows that to describe the kinetics of adsorption, one must take into account the diffusion of monomers and micelles as well as the kinetics of micelle formation and dissolution. Several processes may take place and these are represented schematically in Fig. 4.9. Three main mechanisms may be considered, namely formation-dissolution (Fig. 4.9 (a)), rearrangement (Fig. 4.9 (b)) and stepwise aggregation-dissolution (Fig. 4.9 (c)). To describe the effect of micelles on adsorption kinetics, one should know several parameters such as micelle aggregation number and rate constants of micelle kinetics [25]. 

A more detailed kinetic model utilized in studies of micelhzation kinetics is based on the theory by Aniansson and Wall [30-32] and modified by Kahlweit and co-workers [64-66]. The theoretical model developed by Aniansson and Wall [30,31] assumes a stepwise aggregation of surfactant monomers to form micelles [36]. When a micellar solution at equilibrium is perturbed by an instant change of temperature or pressure, the size distribution of micellar aggregates is shifted. The reestablishment of the equilibrium is characterized by two relaxation times, representing a fast process and a slow process. 

Dilute micellar solutions of surfactants are characterized by two well-separated relaxation times. The molecular origin of the fast relaxation time has been related to a monomer-micelle exchange [181-184]. It was realized later that the relaxation spectra of micellar solutions really exhibit two relaxation times. The theory of Aniansson and Wall [167,185] assumes a stepwise aggregation of surfactant monomers to form micelles [186]. The fast relaxation time is attributed to the exchange of monomeric surfactants between the micelles and the intermicel-lar solution. The slow relaxation time is attributed to micelle formation and breakdown. The theory and its modifications by Kahlweit and co-workers [170-174]... 

It is interesting to note that the stepwise association model or stepwise aggregation model for micelle formation, as shown in Scheme 3.2, leads to the expression = (C, - [S])/(C , - [S]), where represents the number-average micellar aggregation number, C, is the total analytical concentration of surfactant (i.e., C, = [Surflj), C i is the total concentration of osmotically active particles (i.e., monomers + micelles or CMC + [D ]), and [S] (= CMC) is the monomer concentration." Although the stepwise association model is not exactly similar to the phase-separation model, the basis of preequilibrium kinetic model of micelle (Scheme 3.1), the expression = (Ct - [S])/(Cni - [S]) is exactly similar to assumption (5) in the PEK model. The mass action model or multiequilibrium model. Equation 3.1, which is equivalent to Equation 1.20 in Chapter 1... 

Another striking difference between aqueous and anhydrous, nonaqueous systems is the size of the aggregates that are first formed. As we have seen, n is about 50 or larger for aqueous micelles, while for many reverse micelles n is about 10 or smaller. A corollary of the small size of nonaqueous micelles and closely related to the matter of size is the blurring of the CMC and the breakdown of the phase model for micellization. Instead, the stepwise buildup of small clusters as suggested by Reaction (D) is probably a better way of describing micellization in anhydrous systems. When the clusters are extremely small, the whole picture of a polar core shielded from a nonaqueous medium by a mantle of tail groups breaks down. 

It may be expected that other, highly structured solvents with a tri-dimensional network of strong hydrogen bonds, would also permit micelle formation by surfactants, but little evidence of such occurrences has been reported. On the other hand, surfactants in non-polar solvents, aliphatic or aromatic hydrocarbons and halocarbons tend to form so-called inverted micelles, but these aggregate in a stepwise manner rather than all at once to a definite average size. In these inverted micelles, formed, e.g., by long-chain alkylammonium salts or dinonyl-naphthalene sulfonates, the hydrophilic heads are oriented towards the interior, the alkyl chains, tails, towards the exterior of the micelles (Shinoda 1978). Water and hydrophilic solutes may be solubilized in these inverted micelles in nonpolar solvents, such as hydrocarbons. 

The two-stage growth process of the pellicle is of importance to the structure and function of the pellicle. The first step has been explained by an initial adsorption of discrete proteins to the enamel surface, whereas the second step is the adsorption of salivary protein aggregates in the form of micelle-like structures that move more slowly towards the interfaces, and hence give a stepwise increase in the pellicle thickness [47]. The latter structures are believed to account for the globular surface morphology of acquired salivary pellicle. 

The mass action model describes micelle formation as an equilibrium process. The micellar aggregation number becomes an important parameter. The solubilization process can be treated as a stepwise addition of solute molecules to the micelles. However, the partition coefficient based on this model requires the aggregation number, which makes it difficult to use in practice. There are several methods of simplification. One is to define the partition coefficient as ... 

It was already mentioned above that the condition of monodispersity of micelles means that only one kind of aggregates with a fixed aggregation number nj is formed. From the point of view of chemical kinetics the reaction (5.39) is a reaction of ni order. Because typical micelles consist of some tens or hundreds molecules the probability of this elementary step is zero. Therefore, Eq. (5.39) presents only the final result of nj-l stepwise reactions of first order. The corresponding equilibrium constant is then a product of n -l constants for each step of the micellisation process. In our simplest case we can consider that all these constants are the same and we get [ 12]... 

Micelles are not frozen objects. They are in dynamic equilibrium with the free (nomnicellized) surfactant. Surfactants are constantly exchanged between micelles and the intermicellar solution (exchange process), and the residence time of a surfactant in a micelle is fmite. Besides, micelles have a finite lifetime. They constantly form and break up via two identified pathways by a series of stepwise entry/exit of one surfactant A at a time into/from a micelle (Reaction 1) or by a series of frag-mentation/coagulation reactions involving aggregates A, and Aj (Reaction... 

In reality, micelles are not monodisperse, but there is a distribution of aggregation numbers, and micelles are formed in a stepwise process. This is taken into account in the following model. 

These results and those using other methods (Shah, 1971 Clausse, 1957 Ache, 1977) agree on the following interpretation. At low water concentration the surfactant molecules associate a few water and cosurfactant molecules around its polar part forming an aggregate such as the one in Fig. 5, A. With increasing water concentration a stepwise association to inverse micelles. Fig. 6, B, takes place (Eicke and Christen, 1974). ... 

Unlike surfactant aggregation in aqueous solutions, which is often characterized by a well-defined critical micelle concentration (CMC) and monomer h-mer association (n frequently taking values of ca. 50-100), surfactants in nonpolar solvents often display indefinite self association [3-13]. In several cases, the stepwise equilibrium constants for the aggregation monomer dimer trimer < ... h-mer have been found to be equal average aggregation numbers are frequently as low as three to seven at moderate total surfactant concentrations. Mono-di- and trialkylammonium salts and many non-ionic surfactants display this aggregation behaviour. 

The first meaningfnl stndies on the kinetics of dynamic processes within micellar solutions, which looked at dissociation rates via temperature-jump (T-jump) and related techniqnes, were carried out in the 1960s. The first notable attempt at a complete theory of micellization kinetics was the work of Kresheck et al. [77], who proposed a stepwise surfactant aggregation model based on a monodisperse system, where all micelles have the same aggregation nnmber, n. However, this model found... 

Nag monomers which were surrounded by water aggregate together, above CMC, and form a micelle. In this process, the alkyl chains have transferred from water phase to a alkane-like micelle interior. This occurs because the alkyl part is at a lower energy in micelle than in the water phase. The aggregation process is stepwise (i.e., monomer to dimer to trimer to tetramer and so on). This is based on the fact that some surfactants, such as cholates, form micelles with few aggregation numbers (between 5 and 20), while SDS can form micelles varying from 100 to 1000 aggregation numbers. The micelle formation takes place when the alkyl chain of the molecule as surrounded by water (above the CMC) is transferred to a micelle phase (where alkyl chain is in contact with... 

Aside from thermodynamic control, micelle-like aggregates (MAs) of various shapes can be produced as kinetically trapped products. Kinetic trapping occurs if chains of different MAs undergo negligible chain exchange, and fusion of different MAs or fission of MAs into smaller MAs do not take place (Jain and Bates, 2004). Chain exchange occurs mainly in a stepwise fashion. Initially, a MA loses one chain at a time to the solvent phase via chain dissociation. 

As pointed out in Subsection II.A.3, the values of Tg can be used to obtain information on the premicellar aggregates Ar at the minimum s = r of the micelle size distribution curve (see Figure 3.1), provided the measurements are performed on dilute solutions, where micelle formation/breakdown proceeds via stepwise reactions (4). The data were generally analyzed under the simplif3dng assumption that the concentration of the aggregates is much smaller than that of the other species in the narrow passage and kr k Equation 3.14 then reduces to... 

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