Models, of microemulsions

In this section we characterize the minima of the functional (1) which are triply periodic structures. The essential features of these minima are described by the surface (r) = 0 and its properties. In 1976 Scriven [37] hypothesized that triply periodic minimal surfaces (Table 1) could be used for the description of physical interfaces appearing in ternary mixtures of water, oil, and surfactants. Twenty years later it has been discovered, on the basis of the simple model of microemulsion, that the interface formed by surfactants in the symmetric system (oil-water symmetry) is preferably the minimal surface [14,38,39]. 

B. Widom. Lattice model of microemulsions. J Chem Phys 54 6943-6954, 1986. 

A. Ciach. Bifurcation analysis and liquid-crystal phases in Landau-Ginzburg model of microemulsion. J Chem Phys 704 2376-2383, 1996. 

W. Gozdz, R. Hotyst. Triply periodic surfaces and multiply continuous structures from the Landau model of microemulsions. Phys Rev E 54 5012-5027, 1996. 

Th. Zemb. The doc model of microemulsions Microstructure, scattering, conductivity and phase limits imposed by sterical constraints. Colloid Surface A, 129 435, 1997. 

Structural Aspects of Microemulsions. Several investigators have studied the structure of microemulsions using various techniques such as ultracentrifugation, high resolution NMR, spin-spin relaxation time, ultrasonic absorption, p-jump, T-jump, stopped-flow, electrical resistance and viscosity measurements (56-58). The useful compilation of different studies on this subject is found in the books by Robb (68) and Shah and Schechter (69). Several structural models of microemulsions have been proposed and we will discuss only a few important studies here. 

These techniques allowed us to test some structural models of microemulsions and to study forces, exchanges and connectivity phenomena in these media. 

This is due to hydrogen-bonding of hexanol to MMA. The shifts measured in the Lj phase and microemulsions are once again intermediate between those of the model systems indicating that the carbonyl s environment is neither all aqueous nor all oily. To interpret these results we have applied our two-site model of microemulsions to MMA. We imagine that MMA may reside in the micelle core, where its chemical shift should be like that in MMA solution, as well as at the micelle surface where its shift is like aqueous MMA. Assuming rapid diffusion of the MMA, the observed shift can again be written as... 

The thermodynamic modeling of microemulsions has taken various lines and gave conflicting results in the period before the thermodynamic stability and microstructure were established. It was early realized that a maximal solubilization of oil and water simultaneously could be discussed in terms of a balance between hydrophilic and lipophilic interactions the surfactant (surfactant mixture) must be balanced. This can be expressed in terms of the HLB balance of Shinoda,Winsor s R value, and a critical packing parameter (or surfactant number), as introduced to microemulsions by Israelachvili et al. [37], Mitchell and Ninham [38], and others. The last has become very popular and useful for an understanding of surfactant aggregate structures in general. 

Probably the simplest of all lattice models of microemulsions is the Widom-Wheeler model [10,11]. In addition to its simplicity, its appeal lies in the fact that it is isomorphic to the Ising model of magnetism, a model well studied and readily simulated. 

Ginzburg-Landau models can be derived in a straightforward way from all microscopic lattice models of microemulsions. This has been done explicitly for the Widom model [43], for the three-component model [44], for vector models [45], and for the charge-frustrated Ising model [37]. In the case of the three-component model of Eqs. (2) and (3), the derivation shows, for example, that... 

Microemulsions and surfactant-stabilized (macro) emulsions are distinctively different with respect to thermodynamic stability and, therefore, while most significant for both types of systems, the role of studies of phase behavior is different in the two cases. For emulsions we are con-eemed with two- or multi-phase regions in the phase diagrams, and for microemulsions with one-phase regions. Beeause of that micro emulsion studies are closely related to studies of other thermo-dynamically stable phases, notably liquid crystalline phases and micellar solutions. Structural models of microemulsions have to a considerable extent been advanced on the basis of our understanding of other stable phases the formation and stability of a micro-emulsion phase for a certain surfactant results from the comope-tition with alternative phases. The principal differences between micro emulsions and emulsions, together with the related nomenclature, is bound to lead to considerable confusion for example, the persistence in literature of emulsion-based structural pictures of microemulsions can be traced to the related names. However, the term microemulsions is kept for historical reasons. 

Hofsass, T. and Kleinert, H., Gaussian curvature in an Ising model of microemulsions, J. Ghent. Phys., 86, 3565, 1987. 

Rieka, J., Borkovec, M. and Hofmeier, U., Coated droplet model of microemulsions optical matching and polydis-persity, J. Chem. Phys., 94, 8503-8509 (1991). 

Rieka J, Borkovec M and Hofmeier U. 1991. Coated droplet model of microemulsions - optical matching and polydispersity. Journal of Chemical Physics 8503-8509. 

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