Isotropic phase system

The number of examples of Uquid crystalline systems is limited. A simple discotic system, hexapentyloxytriphenylene (17) (Fig. 4), has been studied for its hole mobUity (24). These molecules show a crystalline to mesophase transition at 69°C and a mesophase to isotropic phase transition at 122°C (25). 

Equations la and lb are for a simple two-phase system such as the air-bulk solid interface. Real materials aren t so simple. They have natural oxides and surface roughness, and consist of deposited or grown multilayered structures in many cases. In these cases each layer and interface can be represented by a 2 x 2 matrix (for isotropic materials), and the overall reflection properties can be calculated by matrix multiplication. The resulting algebraic equations are too complex to invert, and a major consequence is that regression analysis must be used to determine the system s physical parameters. ... 

The question arises as to how useful atomistic models may be in predicting the phase behaviour of real liquid crystal molecules. There is some evidence that atomistic models may be quite promising in this respect. For instance, in constant pressure simulations of CCH5 [25, 26] stable nematic and isotropic phases are seen at the right temperatures, even though the simulations of up to 700 ps are too short to observe spontaneous formation of the nematic phase from the isotropic liquid. However, at the present time one must conclude that atomistic models can only be expected to provide qualitative data about individual systems rather than quantitative predictions of phase transition temperatures. Such predictions must await simulations on larger systems, where the system size dependency has been eliminated, and where constant... 

Figure 8.9. The scattering curve of an isotropic ideal two-phase system after multiplication by i 4 (cf. Eq. (8.43)). The Porod region in which the oscillations are almost faded away is generally beginning after the 2nd order of the long period reflection... 

If the structural entities are lamellae, Eq. (8.80) describes an ensemble of perfectly oriented but uncorrelated layers. Inversion of the Lorentz correction yields the scattering curve of the isotropic material I (5) = I (s) / (2ns2). On the other hand, a scattering pattern of highly oriented lamellae or cylinders is readily converted into the ID scattering intensity /, (53) by ID projection onto the fiber direction (p. 136, Eq. (8.56)). The model for the ID intensity, Eq. (8.80), has three parameters Ap, dc, and <7C. For the nonlinear regression it is important to transform to a parameter set with little parameter-parameter correlation Ap, dc, and oc/dc. When applied to raw scattering data, additionally the deviation of the real from the ideal two-phase system must be considered in an extended model function (cf. p. 124). 

There are three kinds of diffusion (i) within the isotropic phase (ii) the interface (between the isotropic and the crystalline phases) and (iii) the crystalline phase. In the case of a polymer system, the topological nature of polymer chains assumes an important role in all three kinds of diffusion, which has been shown in the chain sliding diffusion theory proposed by Hikosaka [14,15]. It is obvious that any nucleus (a primary nucleus and a two-dimensional nucleus) and a crystal can not grow or thicken without chain sliding diffusion. 

An A-B diblock copolymer is a polymer consisting of a sequence of A-type monomers chemically joined to a sequence of B-type monomers. Even a small amount of incompatibility (difference in interactions) between monomers A and monomers B can induce phase transitions. However, A-homopolymer and B-homopolymer are chemically joined in a diblock therefore a system of diblocks cannot undergo a macroscopic phase separation. Instead a number of order-disorder phase transitions take place in the system between the isotropic phase and spatially ordered phases in which A-rich and B-rich domains, of the size of a diblock copolymer, are periodically arranged in lamellar, hexagonal, body-centered cubic (bcc), and the double gyroid structures. The covalent bond joining the blocks rests at the interface between A-rich and B-rich domains. 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

The term microemulsion is applied in a wide sense to different types of liquid liquid systems. In this chapter, it refers to a liquid-liquid dispersion of droplets in the size range of about 10-200 nm that is both thermodynamically stable and optically isotropic. Thus, despite being two phase systems, microemulsions look like single phases to the naked eye. There are two types of microemulsions oil in water (O/W) and water in oil (W/O). The simplest system consists of oil, water, and an amphiphilic component that aggregates in either phase, or in both, entrapping the other phase to form... 

Winsor [15] classified the phase equilibria of microemulsions into four types, now called Winsor I-IV microemulsions, illustrated in Fig. 15.5. Types I and II are two-phase systems where a surfactant rich phase, the microemulsion, is in equilibrium with an excess organic or aqueous phase, respectively. Type III is a three-phase system in which a W/O or an O/W microemulsion is in equilibrium with an excess of both the aqueous and the organic phase. Finally, type IV is a single isotropic phase. In many cases, the properties of the system components require the presence of a surfactant and a cosurfactant in the organic phase in order to achieve the formation of reverse micelles one example is the mixture of sodium dodecylsulfate and pentanol. 

Random Systems The scattering from random two-phase systems was considered by Debye(13,14) and other accounts are available (15,16) These formulations have been applied to gels of a fairly stiff polymer by Goebel, Berry and Tanner (17,18) If the system is spatially isotropic then ... 

Many reports are available where the cationic surfactant CTAB has been used to prepare gold nanoparticles [127-129]. Giustini et al. [130] have characterized the quaternary w/o micro emulsion of CTAB/n-pentanol/ n-hexane/water. Some salient features of CTAB/co-surfactant/alkane/water system are (1) formation of nearly spherical droplets in the L2 region (a liquid isotropic phase formed by disconnected aqueous domains dispersed in a continuous organic bulk) stabilized by a surfactant/co-surfactant interfacial film. (2) With an increase in water content, L2 is followed up to the water solubilization failure, without any transition to bicontinuous structure, and (3) at low Wo, the droplet radius is smaller than R° (spontaneous radius of curvature of the interfacial film) but when the droplet radius tends to become larger than R° (i.e., increasing Wo), the microemulsion phase separates into a Winsor II system. 

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