Modeling of micelle

L. B. Kier, C.-K. Cheng, andB. Testa, Cellular automata model of micelle formation. Pharm. Res. 1996, 13, 1419. 

Fromherz s model considers a spherical micelle where the surfactants are arranged in parallel forming a packaging without tensions and without contact with the water, in which the heads of the surfactants are as separated as possible [20], The surfactant chains, in the region of the heads, are bent to lower electrostatic repulsion as much as possible. Figure 3 shows a cross-section of this model of micelle. 

In the model of micelle proposed by Dill et al. [21], the hydrocarbon chains of the surfactants are more randomly distributed, bearing in mind statistical considerations (Fig. 4). A considerable number of hydrocarbon chains are exposed to the water at the surface. 

Phase separation model, of micellization, 24 128-129 Phase structure(s)... 

The effects of micelles of cetyltrimethylammonium bromide (CTABr), tetradecyl-trimethylammonium bromide (TTABr) and sodium dodecyl sulfate (SDS) on the rates of alkaline hydrolysis of securinine (223) were studied at a constant [HO ] (0.05 m). An increase in the total concentrations of CTABr, TTABr and SDS from 0.0 to 0.2 M causes a decrease in the observed pseudo-first-order rate constants (kobs) by factors of ca 2.5, 3, and 7, respectively. The observed data are explained in terms of pseudophase and pseudophase ion-exchange (PIE) models of micelles. Cationic micelles of CTABr speed attack of hydroxide ion upon coumarin (224) twofold owing to a concentration effect. ... 

EXAMPLE 8.1 Reaction Equilibrium and Phase Equilibrium Models of Micellization. Research in which the CMC of an ionic surfactant M+ S is studied as a function of added salt, say M+X, ... 

Reaction equilibrium and phase equilibrium models of micellization 361... 

Modeling of Micellization and Solubilization Diblock (AB) Copolymeric Micelles... 

Hurterr, P. N., J. M. H. M. Scheutjens, T. A. Hatton, and T. Alan. 1993. Molecular modeling of micelle formation and solubilization in block copolymer micelles. 1. Aself-consistent mean- eld lattice theory. Macromolecule26 5592-5601. 

The CMC has its most clear-cut interpretation within the (pseudo) phase separation model of micelle formation. Although the micelles and the surrounding solution form a single phase, the amphiphile association shows a cooperativity that makes an analogy with a phase transition useful. Within this model, the CMC is the concentration at which the system enters a two phase region the two pseudophases formed being the aqueous system and the micelles. 

In the phase separation model of micelle formation (cf. Sect. 3.1) it is also possible to include the counterions specifically. One has made the distinction between the uncharged phase and the charged micellar pseudophase295). These models can, for example, be used to predict how the CMC varies with salt concentration46, but as used they are open to the same kind of criticism as is the equilibrium model. 

This very simplified model of micellization is illustrated in scheme 4 for a cationic surfactant. At concentrations below the cmc only monomeric surfactant is present, but at higher concentration the solution contains micelle, free surfactant and counterions which escape from the micelle. It is assumed that submicellar aggregates are relatively unimportant for normal micelles in water, although, as we shall see, this assumption fails in some systems. However it is probably reasonable for relatively dilute surfactant, although at high surfactant concentration, and especially in the presence of added salt, the micelle may grow, and eventually, new organized assemblies form, for example, liquid crystals are often detected in relatively concentrated surfactant [1]. However, this discussion will focus on the relatively dUute surfactant solutions in which normal micelles are present. 

In developing any theoretical method, however, a number of decisions must be made in advance. These include, in addition to a reasonable idea of what specific descriptions and predictions will be sought from the theories or models, a decision on what level of microscopic details will be incorporated into the model. Such a decision is dictated by the current limitations of the theoretical tools (e.g., classical or statistical thermodynamic theories) or computational resources. For example, microscopic models of micellization and solubilization can, in principle, be approached at the molecular level with a detailed structural representation of the various components along with their energetic interactions. Our current understanding of molecular dynamics is sufficiently comprehensive and well established to permit such a detailed approach to the evolution of mesoscopic and macroscopic structures and phenomena in surfactant-oil-water systems. However, the... 

In the case of low concentrations of the oil molecules, it is also useful to determine the extent of solubilization in the simulations, which can be represented in terms of the partition coefficient, K. If the micelles are considered to be a separate phase (as in the phase separation model of micellization [20,21]), then the concentrations of the solute in the aqueous and micellar phases can be related as... 

Self-Consistent Field Modeling of Micelle Formation. 101... 

The thermodynamic model of micellization, presented here, describes the association of any amphiphilic molecules, including low molecular weight surfactants or polymeric amphiphiles. The physical origin of the minimum in the free energy, as a function of p, is specified by the molecular architecture and the interactions between amphiphilic molecules involved in the assembly, and will be discussed in the corresponding sections. An extension of the model for the case of a continuous distribution of micelles with respect to aggregation number (polydispersity of the aggregates) involves the value of d Fp/dp. If this quantity is small in the vicinity of p = Po, then the micelle distribution is wide, and vice versa [37]. The approximation of micelle monodispersity is essential for application of the numerical SCF model which is discussed in Sect. 9. 

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