Dissolution micelle formation modeling

Studies described in earlier chapters used cellular automata dynamics to model the hydrophobic effect and other solution phenomena such as dissolution, diffusion, micelle formation, and immiscible solvent demixing. In this section we describe several cellular automata models of the influence of the hydropathic state of a surface on water and on solute concentration in an aqueous solution. We first examine the effect of the surface hydropathic state on the accumulation of water near the surface. A second example models the effect of surface hydropathic state on the rate and accumulation of water flowing through a tube. A final example shows the effect of the surface on the concentration of solute molecules within an aqueous solution. 

The equilibrium and dynamics of adsorption processes from micellar surfactant solutions are considered in Chapter 5. Different approaches (quasichemical and pseudophase) used to describe the micelle formation in equilibrium conditions are analysed. From this analysis relations are derived for the description of the micelle characteristics and equilibrium surface and interfacial tension of micellar solutions. Large attention is paid to the complicated problem, the micellation in surfactant mixtures. It is shown that in the transcritical concentration region the behaviour of surface tension can be quite diverse. The adsorption process in micellar systems is accompanied by the dissolution or formation of micelles. Therefore the kinetics of micelle formation and dissociation is analysed in detail. The considered models assume a fast process of monomer exchange and a slow variation of the micelle size. Examples of experimental dynamic surface tension and interface elasticity studies of micellar solutions are presented. It is shown that from these results one can conclude about the kinetics of dissociation of micelles. The problems and goals of capillary wave spectroscopy of micellar solutions are extensively discussed. This method is very efficient in the analysis of micellar systems, because the characteristic micellisation frequency is quite close to the frequency of capillary waves. 

In the previous chapters, the dissolution and micellization of surfactants in aqueous solutions were discussed from the standpoint of the degrees of freedom as given by the phase rule. The mass-action model for micelle formation was found to be better for explaining the phenomena of surfactant solutions than the phase-separation model. Two models have similarly been used to explain the Krafft point, one postulating a phase transition at the Krafft point and the other a solubility increase up to the CMC at the Krafft point. The most recent version of the first approach is a melting-point model for a hydrated surfactant solid. The most direct approach to the second model of the Krafft point rests entirely on measurements of the solubility and CMC of surfactants with temperature. From these mesurements the concept of the Krafft point can be made clear. This chapter first reviews the concepts used to relate the dissolution of surfactants to their micellization, and then shows that the concept of a micelle temperature range (MTR) can be used to elucidate various phenomena concerning dissolution... 

The formation-dissolution mechanism assumes a total dissolution of a micelle in order to reestablish the local equilibrium monomer concentration. This model is based on an idealised distribution of only monomers and micelles with a definite aggregation number. Mechanism 2 is based on the existence of micelles of different size and therefore, a broad micelle size... 

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. 

Many modem technologies depend on the optimum use of surfactants. The applied concentrations are often above the critical micelle concentration (CMC) and special effects are direcdy related to the presence of micelles. This is tme for example in cleaning and detergency [1], encapsulation of drugs in micelles (2, 3] or microemulsions [4], and many others [5]. The important parameters of micellar solutions are the CMC and the aggregation number n. The formation and dissolution of aggregates or the release or incorporation of single molecules are controlled by the relaxation times of slow and fast processes. Their values, however, depend on the models applied. 

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