Micelle formation modeling

Mutual mixing of two ILs might show fascinating properties. Low concentration (0.3 mM) of IL-1 was found to produce a striking effect on IL-2. In the / versus log [IL-2] dependence, a CMC-like inflection of IL-2 was observed at a very low concentration of 0.1 pM at 298 K in aqueous medimn, the CMC of IL-2 was foimd to be 0.03 mM. There were reports of CMC decrease on mntnal interaction between two ILs [29] interaction in the IL-2/IL-1 combination herein fonnd was conspicuons (Fig. 10.1a, inset A). Tensiometric results of CMCs of mixed micelles were tested against Clint s ideal mixed micelle formation model. 

Mass-action model of surfactant micelle formation was used for development of the conceptual retention model in micellar liquid chromatography. The retention model is based upon the analysis of changing of the sorbat microenvironment in going from mobile phase (micellar surfactant solution, containing organic solvent-modifier) to stationary phase (the surfactant covered surface of the alkyl bonded silica gel) according to equation ... 

The reader is encouraged to run this model and collect the average cluster size of amphiphile cells. Observing the run reveals a view of the emergent property known as micelle formation. Periodic halting of the run when these micelles are prominent will be of interest. Try a screen grab of several good examples. 

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

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 results were interpreted in terms of the model proposed by Balia and co-workers (36). It is reasonable to assume that the micelle formation produces a somewhat organized pattern of the metal centers and, due to the shortened distance between the copper(II) containing head groups, the coordination of catechol to two metal centers may increase the stability of the catalyst substrate complex. Perhaps, the same principles... 

In a recent study, Jin and Kaplan (2003) demonstrate the formation of silk fibroin aggregates in the presence of polyethylene glycol, and present a step by step model for fiber formation based on the principle of micelle formation, and driven by dehydration as well as flow elongation. During this process, hydrophobic chains are exposed to the solvent, but because of the molecules high free energy, water solvation is unfavorable and phase separation followed by aggregation predominates. 

The phase separation model for nonionic micelle formation has been modified for ionic micelle formation to give an equation close to Equation 12 for Ai (26.). ... 

Hetaeric chromatography, 230, 231 effect of charge on hetaeron, 233 retention model of, 231-238 Hetaeron. 191, 230, 231, 240, 243, 249, 280 see also Complexing agent adsorption on the stationary phase, 231, 249,230 amphiphilic, 243 cetrimide, 248 decylsulfonate, 230 dodecylbenzenesulfonate, 230 formation constant of complexes, 276 lauryl sulfate, 230 metal chelating, 262 micelle formation, 230 optically active, 262 surface concentration of, 232... 

The effect of using mixtures of surfactants on micelle formation, monolayer formation, solubilization, adsorption, precipitation, and cloud point phenomena is discussed. Mechanisms of surfactant interaction and some models useful in describing these phenomena are outlined. The use of surfactant mixtures to solve technological problems is also considered. 

This overview will outline surfactant mixture properties and behavior in selected phenomena. Because of space limitations, not all of the many physical processes involving surfactant mixtures can be considered here, but some which are important and illustrative will be discussed these are micelle formation, monolayer formation, solubilization, surfactant precipitation, surfactant adsorption on solids, and cloud point Mechanisms of surfactant interaction will be as well as mathematical models which have been be useful in describing these systems,... 

Except for some anionic/cationic surfactant mixtures which form ion pairs, in a typical surfactant solution, the concentration of the surfactant components as monomeric species is so dilute that no significant interactions between surfactant monomers occur. Therefore, the monomer—mi celle equilibria is dictated by the tendency of the surfactant components to form micelles and the interaction between surfactants in the micelle. Prediction of monomer—micelle equilibria reduces to modeling of the thermodynamics of mixed micelle formation. 

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... 

This brief review has attempted to discuss some of the important phenomena in which surfactant mixtures can be involved. Mechanistic aspects of surfactant interactions and some mathematical models to describe the processes have been outlined. The application of these principles to practical problems has been considered. For example, enhancement of solubilization or surface tension depression using mixtures has been discussed. However, in many cases, the various processes in which surfactants interact generally cannot be considered by themselves, because they occur simultaneously. The surfactant technologist can use this to advantage to accomplish certain objectives. For example, the enhancement of mixed micelle formation can lead to a reduced tendency for surfactant precipitation, reduced adsorption, and a reduced tendency for coacervate formation. The solution to a particular practical problem involving surfactants is rarely obvious because often the surfactants are involved in multiple steps in a process and optimization of a number of simultaneous properties may be involved. An example of this is detergency, where adsorption, solubilization, foaming, emulsion formation, and other phenomena are all important. In enhanced oil recovery. 

The importance of entropic considerations in the formulation of a thermodynamic model for micelle formation in mixtures of ionic and nonionic surfactants has been demonstrated by the ability of the... 

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. 

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... 

The thermodynamics of micelle formation has been studied extensively. There is for example a mass action model (Wennestrdm and Lindman, 1979) that assumes that micelles can be described by an aggregate Mm with a single aggregation number m, so that the only descriptive equation is mMi Mm. A more complex form assumes the multiple equilibrium model, allowing aggregates of different sizes to be in equilibrium with each other (Tanford, 1978 Wennestrdm and Lindman, 1979 Israelachvili, 1992). 

This description of micelle formation is also called the two-state model. Thus, the solution contains p-casein micelles of about 38—40 monomer... 

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. 

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