Microemulsions lamellar

The behavior of the internal energy, heat capacity, Euler characteristic, and its variance ( x ) x) ) the microemulsion-lamellar transition is shown in Fig. 12. Both U and (x) jump at the transition, and the heat capacity, and (x ) - (x) have a peak at the transition. The relative jump in the Euler characteristic is larger than the one in the internal energy. Also, the relative height of the peak in x ) - x) is bigger than in the heat capacity. Conclude both quantities x) and x ) - can be used to locate the phase transition in systems with internal surfaces. 

Many industrial products use mixtures of both surfactant and polymer molecules or surfactant and colloid. Although the effects of polymer on the phase behavior and structure of surfactant phases have begun to be investigated in microemulsions, lamellar phases, and vesicle phases, further experimental work in mixed systems is necessary to understand how the polymer or the colloid modifies the elastic properties of the surfactant film. 

The variation with oil chain length is well studied for the fish cut by Kahlweit, Strey and Sottmann with coworkers [55, 58, 139], but apart from what was already known, the phase boundaries for the two-phase region (i.e. the microemulsion lamellar phase) were also determined in [116]. In Figure 3.7a the minimum volume fraction of surfactant, O, and the maximum volume fraction of surfactant, Osu, are shown as a function of the carbon length of the oil. The relative width of the microemulsion ((Osu - 4>s )/2) is shown as a function of oil chain length in Figure 3.7b. 

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

Lattice models for bulk mixtures have mostly been designed to describe features which are characteristic of systems with low amphiphile content. In particular, models for ternary oil/water/amphiphile systems are challenged to reproduce the reduction of the interfacial tension between water and oil in the presence of amphiphiles, and the existence of a structured disordered phase (a microemulsion) which coexists with an oil-rich and a water-rich phase. We recall that a structured phase is one in which correlation functions show oscillating behavior. Ordered lamellar phases have also been studied, but they are much more influenced by lattice artefacts here than in the case of the chain models. 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

The period of the lamellar structures or the size of the cubic cell can be as large as 1000 A and much larger than the molecular size of the surfactant (25 A). Therefore mesoscopic models like a Landau-Ginzburg model are suitable for their study. In particular, one can address the question whether the bicontinuous microemulsion can undergo a transition to ordered bicontinuous phases. 

The model has been successfully used to describe wetting behavior of the microemulsion at the oil-water interface [12,18-20], to investigate a few ordered phases such as lamellar, double diamond, simple cubic, hexagonal, or crystals of spherical micelles [21,22], and to study the mixtures containing surfactant in confined geometry [23]. 

FIG. 12 The behavior of the internal energy U (per site), heat capacity Cy (per site), the average Euler characteristic (x) and its variance (x") — (x) close to the transition line and at the transition to the lamellar phase for/o = 0. The changes are small at the transition and the transition is very weakly first-order. The weakness of the transition is related to the proliferation of the wormhole passages, which make the lamellar phase locally very similar to the microemulsion phase (Fig. 13). Note also that the values of the energy and heat capacity are not very much different from their values (i.e., 0.5 per site) in the Gaussian approximation of the model [47]. (After Ref. 49.)... 

Summarizing the detailed studies of the basic Landau-Ginzburg model presented in the preceding sections and in the present one suggest that this type of simplified model is not sufficient to describe all the effects related to the ordering in microemulsions. In particular, the only stable ordered phase in the model is the lamellar phase and all the cubic phases are only meta-... 

For diffuse and delocahzed interfaces one can still define a mathematical surface which in some way describes the film, for example by 0(r) = 0. A problem arises if one wants to compare the structure of microemulsion and of ordered phases within one formalism. The problem is caused by the topological fluctuations. As was shown, the Euler characteristic averaged over the surfaces, (x(0(r) = 0)), is different from the Euler characteristics of the average surface, x((0(r)) = 0), in the ordered phases. This difference is large in the lamellar phase, especially close to the transition to the microemulsion. x((0(r)) =0) is a natural quantity for the description of the structure of the ordered phases. For microemulsion, however, (0(r)) = 0 everywhere, and the only meaningful quantity is (x(0(r) = 0))-... 

Figure 7. Topological fluctuations of the lamellar phase at different points of the phase diagram, (a) Single fusion between the lamellae by a passage (this configuration is close to the topological disorder line), (b) Configuration close to the transition to the disordered microemulsion phase the Euler characteristic is large and negative.

Here scalar order parameter, has the interpretation of a normalized difference between the oil and water concentrations go is the strength of surfactant and /o is the parameter describing the stability of the microemulsion and is proportional to the chemical potential of the surfactant. The constant go is solely responsible for the creation of internal surfaces in the model. The microemulsion or the lamellar phase forms only when go is negative. The function/(<))) is the bulk free energy and describes the coexistence of the pure water phase (4> = —1), pure oil phase (4> = 1), and microemulsion (< ) = 0), provided that/o = 0 (in the mean-held approximation). One can easily calculate the correlation function (4>(r)(0)) — (4>(r) (4>(0)) in various bulk homogeneous phases. In the microemulsion this function oscillates, indicating local correlations between water-rich and oil-rich domains. In the pure water or oil phases it should decay monotonically to zero. This does occur, provided that g2 > 4 /TT/o — go- Because of the < ), —<(> (oil-water) symmetry of the model, the interface between the oil-rich and water-rich domains is given by... 

This equation defines the internal surfaces in the system. The model has been studied in the mean held approximation (minimization of the functional) [21-23,117] and in the computer simulations [77,117,118], The stable phases in the model are oil-rich phase, water-rich phase, microemulsion, and ordered lamellar phase. However, as was shown in Refs. 21-23 there is an infinite number of metastable solutions of the minimizahon procedure ... 

Studies of inorganic photochemistry in unusual environments has attracted considerable attention. Photochemical studies conducted in organized assemblies such as micelles, microemulsions and vesicles,217 on surfaces such as porous Vycor glass,218 in a lamellar solid,219 and in the gas phase have been reported.220... 

With increasing temperature the oil drops become larger and larger because the spontaneous curvature decreases. Accordingly, the volume of the oil phase decreases until at 23°C all oil is incorporated into relatively large oil drops in water and we reach a one-phase region (often denoted Li) of an oil-in-water microemulsion. This point is ideally suited to determine the spontaneous radius of curvature because, here, the radius of the oil drop can be calculated from the added volume fractions with Eq. (12.21). Raising the temperature decreases Co further and from 29°C on lamellar structures are formed (La). At 32°C the PIT is reached and the spontaneous curvature is zero. 

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