Phase transitions microemulsion-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. 

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))-... 

Micellar aggregates are considered in chapter 3 and a critical concentration is defined on the basis of a change in the shape of the size distribution of aggregates. This is followed by the examination, via a second order perturbation theory, of the phase behavior of a sterically stabilized non-aqueous colloidal dispersion containing free polymer molecules. This chapter is also concerned with the thermodynamic stability of microemulsions, which is treated via a new thermodynamic formalism. In addition, a molecular thermodynamics approach is suggested, which can predict the structural and compositional characteristics of microemulsions. Thermodynamic approaches similar to that used for microemulsions are applied to the phase transition in monolayers of insoluble surfactants and to lamellar liquid crystals. 

Several microemulsion inkjet inks have been described in the literature. An inkjet phase transition ink in the form of a microemulsion consists of an organic vehicle phase having a colorant dispersed therein, where the vehicle phase is preferably liquid while jetting at temperatures above 70°C and solid upon keeping the substrate at room temperature (22-25°C). This formulation undergoes a phase transition from a microemulsion phase to a lamellar phase upon heating, which allows build up of several layers of inks on the surface of the paper. In a similar concept for phase transition, an ink comprised of an aqueous phase, an oil phase. 

If more and more surfactant is added to a Winsor III system, the surfactant-rich phase swells at the expense of the excess oil and water phases. From a certain point, a single surfactant-rich phase is found. Upon increasing the amount of surfactant even further, a first-order transition to a lamellar phase may be observed. In a special case, it has been shown that the coexistence region between the (bicontinuous) microemulsion phase and a lamellar phase was extended into the region where the surfactant-rich phase coexists with excess oil and water, leading to a four-phase equilibrium water-lamellar phase-microemulsion phase-oil [58]. In Ref. 46, even a three-phase equilibrium, water-lamellar phase-oil, was observed, the bicontinuous microemulsion phase apparently being absent. 

Nakamura, N., Tagawa, T., Kihara, K., Tobita, I., and Kunieda, H. (1997) Phase transition between microemulsion and lamellar liquid crystal. Langmuir, 13, 2001-2006. 

The second chapter, by D. Vollmer (Germany), brings a quantitative comparison of experimental data and theoretical predictions on thermodynamic and kinetic properties of microemulsions based on nonionic surfactants. Phase transitions between a lamellar and a droplet-phase microemulsion are discussed. The work is based on evaluation of the latent heat and the specific heat accompanying the transitions. The author focuses on the kinetics of phase separation when inducing emulsification failure by constant heating. The chapter is a comprehensive, detailed study of all the aspects related to the phase separation phenomenon in microemulsions. 

In this study we have investigated the structural and interaction parameters of ternary water/octane/CiaEs system by means of SAXS. Phase behavior of this system was studied by Kahlweit et al. [9]. This system shows interesting phase behavior (Fig. 1). One can study the structures of low-temperature microemulsion (LTM) phase, middle-temperature lamellar (MTL) phase and high-temperature microemulsion (HTM) phase by changing temperature only, provided that the sample contains approximately more than 12 wt% of surfactant at equal volume fraction of water and oil. Bodet et al. have clarified the structural evolution of this system by means of pulsed-field gradient spin-echo NMR, quasi-elastic light scattering and freeze-fracture transmission electron microscopy [10]. Local structure of the bilayer and monolayer of the same system was also studied by Strey et al. [11]. Recently, we have studied the mechanism of the phase transition [12]. 

Figure 27 Temperature - diblock concentration plane of the PB/PS blend phase diagram. The composition of the PB/PS homopolymer blend was the critical one of the binary blend. The right figure shows the Lifshitz part. Meaning of symbols (,) line of critical points with (-) the double critical point (() and (v) Lifshitz line between disordered and microemulsion phases (DpE and BpE droplet and bicontinuous microemulsion), respectively (B) transition from disordered to micro emulsion phase, ix) Lifshitz transition point LLT, (A) Ordering transition to lamellar phase. Erom Pipich, V. Schwahn, D. Willner, L. Phys. Rev. Lett. 2005, 94,117801 J. Chem. Phys. 2005, 123,124904-124916 ...

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. 

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.)... 

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.

The imposition of shear flow can have quite dramatic consequences on the structure and phase behavior of complex fluids. Steady shearing of binary amphiphilic systems can lead to a completely new phase of densely packed onionlike vesicles [140]. Shear flow also strongly affects the stability of the lamellar phase [141-145]. We want to discuss here the role of shear in the microemulsion-to-lamellar transition. 

As a result of the shear flow, order parameter fluctuations in the microemulsion phase are suppressed [142]. This destabilizes the microemulsion with respect to a lamellar phase, so that for a certain temperature range the lamellar phase can be induced by applying shear. Furthermore, fluctuations in the microemulsion become very anisotropic in shear flow. In particular, the lamellar fluctuations, which appear as the transition is approached, have wave vectors concentrated near maxCz transverse to both the flow velocity and its gradient. Therefore, a shear-induced lamellar phase is expected to occur preferentially in this orientation. A more detailed analysis [142] based on model (60) shows that for small D the shift of the transition temperature, T (D), is given by... 

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