Micellization, kinetics

It is essential to characterize the reactant species in solution. One of the problems, for example, in interpreting the rate law for oxidation by Ce(IV) or Co(III) arises from the difficulties in characterizing these species in aqueous solution, particularly the extent of formation of hydroxy or polymeric species. We used the catalyzed decomposition of HjOj by an Fe(III) macrocycle as an example of the initial rate approach (Sec. 1.2.1). With certain conditions, the iron complex dimerizes and this would have to be allowed for, since it transpires that the dimer is catalytically inactive. In a different approach, the problems of limited solubility, dimerization and aging of iron(III) and (Il)-hemin in aqueous solution can be avoided by intercalating the porphyrin in a micelle. Kinetic study is then eased. 

The schematic shows that the transport of monomers and micelles as well as the mechanism of micelle kinetics have to be taken into account in a reasonable physical model. 

To account for the micelle effect, specific parameters of the respective surfactant micelles have to be known. Numerous papers on the determination of aggregation numbers and rate constants of micelle kinetics of many surfactants have been published (for example Aniansson et al. 1976, Hoffmann et al. 1976, Kahlweit Teubner 1980). Different micelle kinetics mechanisms exist, for example that summarised by Zana (1974). Three of these mechanisms are demonstrated in Fig. 4.12. 

Fig. 4.12 Micelle kinetics mechanisms 1- formation-dissolution, 2 - rearrangement, 3 aggregation-disintegration...

The physical model, based on the micelle kinetics mechanism 1, has the following form. The transport of monomers is given by. 

A numerical solution, based on the model presented for a formation-dissolution mechanism, was derived by Miller (1981). The following two Figs 4.13 and 4.14 demonstrate the effect of micelles on adsorption kinetics. The effect of the rate of formation and dissolution of micelles, represented by the dimensionless coefficient nkfC Tj /D, becomes remarkable for a value larger than 0.1. Under the given conditions (D /D, =1, c /c , =10, n=20) the fast micelle kinetics accelerates the adsorption kinetics by one order of magnitude. 

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 first studies of the effect of micelles on the exchange of matter to interfaces subject to harmonical disturbances of the surface area were performed by Lucassen (1976). He used an aqueous solution of hexadecyl dimethyl ammonium propanesulfonate (HOPS) below and above the CMC. The exchange of matter, shown by the effective dilational elasticity E, is affected considerably by the presence of micelles, as discussed above. The lower the frequency of disturbance, the more pronounced is the influence of micelle kinetics on the exchange of matter (cf. Fig. 6.12), the line marks the CMC of HDPS. Lucassen was able to describe the behaviour by using the theory given by Eqs (6.25), (6.26)). 

These equations can serve to estimate the influence of micellar kinetics on the adsorption process. Much more details will be given in Chapter 5 where the various micelle kinetics models and their practical relevance for interfacial studies are discussed. 

In this section, we give a brief review of important selected theories for surfactant and block copolymer micelles. First, the classical thermodynamic theories covering both mean-field and scaling approaches are briefly reviewed before discussing kinetics. Classical theories for equilibrium and near-equilibrium surfactant and block copolymer micelle kinetics will be briefly reviewed before covering nonequilibrium kinetics in the final part. 

We will briefly review the available classical theories relevant to both surfactant and block copolymer micelle kinetics. 

A brate force method for calculation of the micellization kinetics is to treat the problem as series of chemical reactions. Such an approach has been developed extensively within chemical engineering to treat complex coupled reactions. For micelles, we can write the reaction scheme on the general form ... 

Non-equilibrium kinetic processes typically involve monitoring a change in micellar structure or morphology over time, or following the formation of micelles from a molecular solution (unimers), i.e., micellization kinetics. Thus, in contrast to equilibrium processes a perturbation is required. Typically this is achieved by abruptly altering the thermodynamic conditions, which can be achieved either via extensive parameters like temperature and pressure, or by changing intensive parameters such as salt concentration or pH. 

Liu and coworkers employed this method to study the micellization kinetics of a double hydrophilic diblock poly(W-isopropyIacrylamide)-poly(2-diethylamino ethyl methacrylate) (PNIPAM-PDEA) in aqueous solution [172]. The results obtained after a temperature jump from 20°C (unimers) to different final temperatures are shown in Fig. 33. 

Fig. 35 Concentration of the slow terminal relaxation constants observed for the micellization kinetics of pH-sensitive A-B-C triblock copolymers with different amount of added salts. Reprinted with permission from [178]. Copyright (2007) American Chemical Society...

The central questions occupying theoreticians and experimentalists are the mechanism and kinetic pathways of self-assembly. To answer these questions, computer simulations are particularly useful because the coordinates of each molecule can be traced individually and pathways can be observed directly. The challenge for computer simulations is to access the relatively long time scales needed to observe micellization kinetics, which can only be dmie using coarse-grained models, relatively few particles, and/or by excessively long computation times. 

In this review, we have provided a selective overview of theoretical and experimental studies on kinetic processes in block copolymer micellar systems. We have demonstrated the strengths of time-resolved small-angle scattering techniques by highlighting recent examples from the literature. Most of the available literamre in this field is either related to equihbrium exchange kinetics or micellization kinetics. 

Flow Microreactor Polymerization, Micelles Kinetics, Polypeptide Ordering, Light Emitting Nanostructures... 

Recently, the same group has presented also the micellization kinetics of a diblock copolymer, namely PEO-PDEAEMA [59]. Several samples of this type of copolymers have been synthesized having identical PEG blocks and PDEAEMA block with varying degrees of polymerization. The block copolymers tend to create micelles with PDEAEMA cores in basic conditions. Therefore, the micellization kinetics studies were performed using a stop flow technique in order to introduce micelles upon a pH-jump from 3 to 12. The observation of two processes, i.e. a fast one attributed to the formation of quasi-equilibrium micelles and a slow one attributed to the relaxation into final equilibrium micelles, were observed, as... 

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