Closed association model

One of the models best able to describe the properties of micellar colloid solutions is the closed-association model. In it, we start by assuming the colloid comprises n molecules of monomer. We approximate by saying the colloid forms during a single step ... 

So far, all of the data indicate the applicability of the closed association model (28) ... 

Tuzar and coworkers [305] studied the micellization of a poly(isoprene-g-styrene) copolymer in solvent mixtures selective either for the backbone or for the grafts. Their results from static and dynamic light scattering and sedimentation velocity experiments favor the closed association model for the description of the unimers-micelles equilibrium. The graft copolymer micelles were found to have lower aggregation numbers and to be less compact than the micelles formed by linear diblocks. 

The general principles of self-assembly of amphiphilic molecules into finite-sized aggregates (micelles) are described in a number of classic books [34-36]. In our analysis of micelle formation we apply the equilibrium close association model. That is, we assume first that only one population of micelles, with an aggregation number p (number of copolymers in one aggregate), is present in the system at any given concentration of amphiphiles in the solution, or that there are no micelles at all and second, that the free energy per molecule in a micelle, Fp, exhibits a minimum at a certain value of the aggregation number, p = po. 

Using a closed association model, micelle formation can be represented by ... 

The closed association model can accoimt for the observation of a critical micelle concentration. It is also known as the mass action model. It is assumed that there is a dynamic equilibrium between molecules and micelles containing p molecules. In practice, micelles are not monodisperse (Section 1.8), i.e. there is a range of values of association number. Usually, the dispersity in p amounts to about 20-30 % of its value, which is not large enough to change the behaviour captured by models for monodisperse micelles. In the following, we consider the equilibrium between nonionic surfactant molecules and monodisperse micelles in dilute solution ... 

The closed association model means that above the CMC, added molecules go into micelles. The fraction of unassociated molecules and of micelles are plotted together in Fig. 4.18. Further information on calculating the fraction of associated molecules can be found in Section 6.4.5, where the one-dimensional self-assembly (of cylindrical micelles for example) is considered. 

The phase separation model is restricted to micellization which produces micelles with a very large association number, p. In addition, it can only describe the association process into micelles and not the association and dissociation described by the eqnilibria, npon which closed association models are based. However, the main problem with the model is that micelles cannot rigorously be considered to constitute a separate phase, since they are not uniform and homogeneous throughout. However, it is a simple model which works quite well for micelles with large association numbers. As with the closed association model, the phase separation model can be applied to ionic surfactants, provided that allowance is made for the association of counterions with the micelle. 

The closed association model of micellization can be used to obtain the fraction of molecules in micelles as a function of total amphiphile concentration. Using concepts from Section 6.4.5 derive expressions for the fractions of associated and unassociated molecules and hence obtain plots similar to those in Fig. 4.18. 

The origin of CIDNP lies in the microscopic behaviour of radical pairs. Our discussion of this will follow fairly closely the model approach associated with the names of Gloss, Kaptein, OosterhofF, and Adrian, rather than the more formal kinetic treatments of Fischer (1970a) and Buchachenko et al. (1970b). 

In mouse models of skin inflammation induced by 12-O-tetradecanoylphorbol-13-acetate (TPA), there is a close association between elevated XO activity in the epidermis and hyperplasia (Pence and Reiners, 1987). This association is also seen in psoriasis patients (Eisen and Seegmiller, 1961 Zimmer and Demis, 1966 Kizaki et al., 1977). In the study by Kizaki etal. (1977), the epidermis was increased about five-fold in comparison to normal. It is not known whether XO-derived ROS have any role in psoriatic epidermal hyperproliferation but low levels of hydrogen peroxide added to the culture medium are well known to induce skin fibroblast proliferation in vitro, an eflfect that is greatest at low passage numbers (Murrell et al., 1990). The generation of... 

Summing up, we may say that approximation methods in quantum chemistry generally involve (either explicitly or implicitly) a model H(i)> and associated model chemistry that more or less mimics the true behavior of Eq. (1.1). Such models might be closely patterned after the well-known conceptual models of empirical... 

As outlined in the previous section, there is a hierarchy of possible representations of metabolism and no unique definition what constitutes a true model of metabolism exists. Nonetheless, mathematical modeling of metabolism is usually closely associated with changes in compound concentrations that are described in terms of rates of biochemical reactions. In this section, we outline the nomenclature and the essential steps in constructing explicit kinetic models of metabolic networks. 

A working model for dendrimer thermolysis during calcination involves the PA-MAM dendrimer backbone initially reacting with oxygen (which may or may not be activated by a nanoparticle) in a relatively facile process to generate carboxylates and other surface species. Removal of carbonaceous species closely associated with the nanoparticle is required for complete activation of the catalyst. For Pt DENs, the surface carboxylates may be strongly adsorbed to the nanoparticle surface and extended O2 treatments are required for deep oxidation of the hydrocarbon to reach reasonably volatile species. Once formed, however, it appears that they can be removed more readily with a hydrogen treatment than with further oxidation. 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

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