Micelle formation theory

We may begin the examination of ionic micelle formation by reviewing the main theories already presented. First of all, the mass action law is extended to ionic micelle formation( 14---16) as... 

Nagarajan R. Theory of micelle formation quantitative approach to predicting micellar properties from surfactant molecular structure. Surface Sci Ser 1997 70 1-81. 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

Only one model to describe nonideal micelle Formation was described here. Regular solution theory in a diFFerent Form than that used here has been applied to these systems ( ). Alternative models have been proposed based on statistical mechanics (37.50). the... 

Non-ideal solution theory is used to calculate the value of a parameter, S, that measures the interaction between two surfactants in mixed monolayer or mixed micelle formation. The value of this parameter, together with the values of relevant properties of the individual, pure surfactants, determines whether synergism will exist in a mixture of two surfactants in aqueous solution. 

The nature of surface adsorption and micelle formation of various mixed FC- and HC-surfactants systems can be conveniently and well investigated by the non-ideal solution theory semi-emplrlcally applied in the surface layer and micelles. The weak "mutual phobic" interaction between FC- and HC-chains has been clearly revealed in the anionic-anionic and nonlonic-nonionic systems as Indicated by the positive values. value cannot be obtained... 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

Mixed Micelles. The CMC values -for the two pure sur-factants and well de-fined mixtures thereo-f are shown in Figure 2. The experiments were run at a high added salt level (swamping electrolyte) so the counterion contributed by the dissolved sur-factant is negligible. Predicted mixture CMC values -for ideal mixing -from Equation 1 are also shown. Ideal solution theory describes mixed micelle -formation very well, as is usually the case -for similarly structured sur-factant mixtures (12.19.21—2A) ... 

The regular solution theory may be applied to surface adsorption and micelle formation of mixed nonaethoxylated fatty alcohols with Gaussian distribution In hydrophobic chain length. Such a system can be treated as an Ideal mixture,... 

Model Development. There is vast opportunity for development of fundamentally based models to describe the thermodynamics of mixed micelle formation. As discussed in Chapter 1, regular solution theory has yielded useful relations to describe monomer—mi cel 1e equilibrium. 

The lack of certain critical data for these systems, as already discussed, has hampered development of improved theories. Models of mixed micelle formation need to be based on the fundamental forces causing nonidealities of mixing. Some of these have been discussed in Chapter 1. Chapter 2 Schechter is an example of the... 

There is a substantial body of theoretical work on micellization in block copolymers. The simplest approaches are the scaling theories, which account quite successfully for the scaling of block copolymer dimensions with length of the constituent blocks. Rather detailed mean field theories have also been developed, of which the most advanced at present is the self-consistent field theory, in its lattice and continuum guises. These theories are reviewed in depth in Chapter 3. A limited amount of work has been performed on the kinetics of micellization, although this is largely an unexplored field. Micelle formation at the liquid-air interface has been investigated experimentally, and a number of types of surface micelles have been identified. In addition, adsorption of block copolymers at liquid interfaces has attracted considerable attention. This work is also summarized in Chapter 3. 

A self-consistent field theory (SCFT) for micelle formation of block copolymers in selective solvents was developed by Yuan el at. (1992). They emphasized the importance of treating the isolated chain at the same level of theoretical approximation at the micelle, in contrast to earlier approaches. This was achieved by modifying the Edwards diffusion equation for the excluded volume of polymers in solution to the case of block copolymers, with one block in a poor solvent. The results of the continuum model were compared to experimental results for PS-PI diblocks in hexadecane, which is a selective solvent for PI and satisfactory agreement was obtained. 

A simple mean field theory for micelle formation by a diblock copolymer in a homopolymeric solvent was developed by Leibler et al. (1983). This model enables the calculation of the size and number of chains in a micelle and its free energy of formation. The fraction of copolymer chains aggregating into micelles can also be obtained. A cmc was found for low copolymer contents even for weak incompatibilities between components. Leibler et al. (1983) emphasize that fora finite aggregation number p, the cmc is a region rather than a well-defined concentration and some arbitrariness is involved in its definition. 

Micelle formation in solutions of an AB diblock in low-molecular-weight A homopolymer has been considered by Leibler et al. (1983), using Flory-Huggins theory to determine the free energy of mixing of micelles. This model is discussed in detail in Section 3.4.2. 

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. 

Since they act as surfactants, copolymers are added in only small amounts, typically from a thousandth parts to a few hundredth parts. Theoretically, Leibler [30] showed that only 2% of a diblock copolymer may thermodynamically stabilize an 80%/20% incompatible blend with an optimum morphology (submicronic droplets). However, in practice kinetic control and micelle formation interfere in this best-case scenario. To a some extent, compatibilization increases with copolymer concentration [8,31,32], Beyond a critical concentration (critical micellar concentration cmc) little or no improvement is observed (moreover, for high amounts, the copolymer can act as a plasticizer). Copolymer molecular weight influence is similar to that of the concentration effect. For example, in a PS/PDMS system [8,31,32], when the copolymer molecular weight increases, domain size decreases to a certain extent. Hu et al. [31] correlated their experimental results with theoretical prediction of the Leibler s brush theory [30]. Leibler distinguishes two regimes to characterize the behaviour of the copolymer at the interface... 

A number of statistical thermodynamic theories for the domain formation in block and graft copolymers have been formulated on the basis of this idea. The pioneering work in this area was done by Meier (43). In his original work, however, he assumed that the boundary between the two phases is sharp. Leary and Williams (43,44) were the first to recognize that the interphase must be diffuse and has finite thickness. Kawai and co-workers (31) treated the problem from the point of view of micelle formation. As the solvent evaporates from a block copolymer solution, a critical micelle concentration is reached. At this point, the domains are formed and are assumed to undergo no further change with continued solvent evaporation. Minimum free energies for an AB-type block copolymer were computed this way. 

Tanford, C. (1974),Theory of micelle formation in aqueous solutions,/. Phys. Chem., 78, 24. 

In one of our earlier applications, FCS diagnosed unanticipated micelle formation and led to the first development of confocal image microscopy for smaller focal volumes [3]. Recognizing the effective applications of fluorescent marker d mamics to understand cell membrane d mamics, we applied FCS to molecular diffusion on cell membranes, entering thereby into a long series of studies of the dynamics of membrane processes in life, which was at that time a quagmire of conflicting ideas [4]. Later, we also extended FCS theory to fluid flow analysis [9]. It has proven useful for a diversity of ultrafast chemical kinetics as well, c.f. [10-13]. 

A crucial parameter-free test of the theory is provided by its application to micelle formation from ionic surfactants in dilute solution [47]. There, if we accept that the Poisson-Boltzmann equation provides a sufficiently reasonable description of electrostatic interactions, the surface free energy of an aggregate of radius R and aggregation number N can be calculated horn the electrostatic free energy analytically. The whole surface free energy can be decomposed into two terms, one electrostatic, and another due to short-range molecular interactions that, from dimensional considerations, must be proportional to area per surfactant molecule, i.e. 

Critical micelle concentration ( >cmc is expected to decrease strongly with diminished diblock asymmetry rc as low rc values favor easier creation of highly curved micelle interfaces. Theory of micelle formation [231,260] also indicates that the overall copolymer degree of polymerization Nc, as well as the anchor -homopolymer interaction parameter %AP have to be considered to explain properly the onset of micelle segregation as observed by Shull et al. [260]. Using this theory, experimenters are able to choose systems where only individual copolymers segregate. 

Deviations from the theoretical pH-solubility profiles may be an indication of experimental error. They may also suggest other interactions not predicted by the solubility theory. Examples for the causes of such deviations include changes in solid-state properties, self-association and micelle formation of the drug in solution. Figure 1 shows an example of a compound that forms micelles at a pH above 9 (Winnike, 2005). Further addition of sodium hydroxide does not increase the pH rather it enhances solubility through micelle formation. In any of these cases, it is important to identify the causes of the deviation so that appropriate formulation decisions can be made based on the solubility data. 

The two fundamental properties of surfactants are monolayer formation at interfaces and micelle formation in solution for surfactant mixtures, the characteristic phenomena are mixed monolayer formation at interfaces (Chapter 2, Section RIG) and mixed micelle formation in solution (Chapter 3, Section VIII). The molecular interaction parameters for mixed monolayer formation by two different surfactants at an interface can be evaluated using equations 11.1 and 11.2 which are based upon the application of nonideal solution theory to the thermodynamics of the system (Rosen, 1982) ... 

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