General phase behavior

The polyphilic quality leads to a further ordering of the molecules in their meso-phase Fig. 34 gives a simple schematic drawing of a directed lamellar phase. The molecules have a polar orientation within the layers and long range correlations between them. This special mesophase structure causes macroscopically polar properties. With regard to this kind of molecular arrangement some polyphilic compounds have been successfully studied in respect of ferroelectric properties [161-165]. 

Other types of interesting, sometimes even curious, amphotropic materials with unusual molecular architectures have also been found. Whereas T-shaped [109] molecular structures have flexible wings, T-shaped compounds are made of rigid lipophilic units [166]. In the T-shaped case, smectic instead of columnar phases are observed. While mono-alkylated amphiphiles usually show only SmA phases, an interesting exception are so-called banana shaped amphiphiles of which 51 in Fig. 35 may be an example. This gentiobioside exhibits a bi-continuous cubic mesophase [129]. 

Hitherto, only monomeric, unimolecular compounds have been discussed in this overview article of which the amphotropic behavior is based on a balanced amphiphilic character. This is also true for polymeric materials [5, 11, 167, 168] which, however, are not included here. 

According to Fig. 3, classical thermotropic smectic phases of amphotropic liquid crystals are (SmA ), colunmar hexagonal (Col ), bicontinuous cubic (Cub, i), or discontinuous cubic (Cubjis) [169]. All these meso-phases include a disclination surface between the hydrophilic and the lipophilic parts of the unordered molecules. This surface can be uncurved (SmA), curved in one direction (columnar), curved in two directions with the same sign (discontinuous cubic), or curved in two directions with opposite sign (bicontinuous cubic). 

Whereas monophilic liquid crystals can show a high diversity of smectic phases (SmA-SmQ), the amphotropic liquid crystals normally exhibit only the SmA phase. Tilted smectic phases are only observed in a few cases. The first indication of possibly tilted phases was given in 1933 for thallium stearate [ 170]. A disordered SmC phase was also clearly deseribed for mesogens containing a classical calamitic core aside to their amphiphilic structure [171]. Monophilic liquid crystals can show various ordered tilted smectic phases, for example, smectic I, F, G, J, H, and K. In the case of lipids only one mesophase, the j8 phase, 

In this Chapter, we describe the basic thermodynamic properties of single component systems. We begin with a qualitative description of their general phase behavior. Then, we discuss the mathematical relations that govern this behavior. 

The line separating the solid and liquid phases is known as the melting or freezing curve. The line separating the solid and vapor phases is known as the sublimation curve. The point where the vapor pressure curve, the melting curve, and the sublimation curves meet is the triple point. At these conditions, the solid, liquid, and vapor phases can simultaneously coexist. 

Inside these curves, multiple phases coexist. For example, if a system is prepared at a state corresponding to point A in the diagram, it will divied into a vapor phase, with density and liquid phase, with density From the phase diagram, we can also determine the relative amounts of the coexisting phases. Let s consider a system consisting of N total moles that are separated into a liquid phase that occupies a volume F and a vapor phase that occupies a volume From a mole 

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Marques, E. F., Regev, O., Khan, A., Miguel, M. D., and Lindman, B. (1998). Vesicle formation and general phase behavior in the catanionic mixture SDS-DDAB-water. The anionic-rich side. J. Phys. Chem. B, 102, 6746-58. 

In tills section, we examine the thermodynamics of systems which contain a mixture of species. First, we generalize the thermodynamic analysis of the previous section to multicomponent systems, deriving the Gibbs phase rule. Then we describe the general phase behavior of binary and ternary mixtures. 

The general phase behavior of mono-tailed amphiphiles is shown in Fig. 6. Starting at a certain chain length of the lipophilic part of the molecule, a thermotropic smectic phase... 

General Phase Behavior in Polymer/Solvent Systems... 

General phase behavior to illustrate miscible type processes for enhanced oil recovery. 

Figure 10.8. General phase behavior of cholesterol esters used for the preparation of supercooled smectic nanojrarticles. A dotted line indicates supercooling of the transition. Abbreviations C crystalline, Sm smectic, Ch cholesteric and I isotropic liquid phase.

In general, phase behavior of three-component systems is compUcated and includes one-, two-, and three-phase regions. The analysis of the whole phase behavior of a system described by Eq. (7.1), then, is fairly complicated. Ginzburg [84], and He, Ginzburg, and Balazs [85] considered a simpler problem of detertniriing the spinodal boundaries, that is, the boundaries of stability of homogeneous (one-phase) systems. The condition of stabUity of the homogeneous phase could be written as ... 

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