Formation of the liquid crystal phase

From the partition function in Equation 2.38 the free energy can be obtained as 

As cj) 4 there is a maximum Zmax with y. If Zmax is greater than Z0, the value for y = x, then Zmax gives the equilibrium state otherwise, it is the meta-equilibrium state. 

To obtain the critical value of 4 when the system starts to appear in the meta-stable state, i.e., the minimum value of j for the existence of liquid crystal state, let 

Substituting 2.42 into 2.41 Flory et al., in their 1956 approximation, obtained the critical f as the function of the axial ratio x 

If x 10, the error of the approximation in the above equation is less than 2%. It is concluded from Equation 2.44 that the larger the axial ratio of rods x, the less is j .  

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Xanthan forms lyotropic and isotropic liquid crystals in water at appropriate concentrations (53). The formation of solvent-based liquid crystals is an area of expanding interest in personal care because of their unique ability to form emulsifier-free suspensions, which is discussed in the section describing hydroxypropylcellulose (Section III.C.2.a.ii). Specifically, xanthan forms cholesteric mesophase lyotropic liquid crystals in water at concentrations as low as 3.5 wt%. Formation of the liquid crystal phase is influenced by salt concenfration the higher the salt concentration, the lower the xanthan concentration required to form the liquid crystal phase. 

Methyl cellulose is a derivative of cellulose soluble in water and widely used as a binder or thickener in pharmaceutical products, food products, in the field of ceramics, etc. Formation of the liquid crystal phase is dependent on molecular weight, concentration and temperature, as evidenced in different experimental studies employing differential scanning calorimetry, polarized light microscopy, optical rotatory dispersion [121]. This cellulose derivative has two stages of thermoreversible gelation in aqueous solution, as temperature rises, if concentration exceeds a certain critical value [117, 122]. Several studies [123] have revealed a crystal liquid phase in dilute solutions as well. 

Komori T, Shinkai S (1993) Novel columnar liquid crystals designed from cone-shaped cahx[4] arenes. the rigid bowl is essential for the formation of the liquid crystal phase. Chem Lett 22 1455-1458... 

Preliminary investigations of the liquid crystal phase behavior of these gold nanoparticles initially revealed an enantiotropic nematic phase (based on polarized light optical microscopy and thermal analysis) as well as some pattern formation of the gold nanoparticles in TEM experiments [540, 541],... 

This article deals with some topics of the statistical physics of liquid-crystalline phase in the solutions of stiff chain macromolecules. These topics include the problem of the phase diagram for the liquid-crystalline transition in die solutions of completely stiff macromolecules (rigid rods) conditions of formation of the liquid-crystalline phase in the solutions ofsemiflexible macromolecules possibility of the intramolecular liquid-crystalline ordering in semiflexible macromolecules structure of intramolecular liquid crystals and dependence of die properties of the liquid-crystalline phase on the microstructure of the polymer chain. 

The exposure of the fullerene unit is shown in Fig. 66. The mesogenic groups cluster together as they stabilize an ensemble that would support the formation of a liquid crystal phase. The exposed fullerene is then free to interact with other fullerenes, thereby potentially stabilizing the formation of a lamellar phase. 

The experimental data are from the following solutions PHIC(D = 12.5 A)/toluene, l = 750 A, PHIC/DMC, l = 370A at room temperature (Conio et at, 1984) and PHIC/toluene at 25 °C (Itou Teramoto, 1984). It can be seen that the theoretical prediction of the worm-like chain is in good agreement with experiments. The diagram illustrates the relationship of the critical volume fraction and molecular length or molecular weight to the formation of a liquid crystal phase. 

It is also interesting to mention that the compound (3.11) is the first published example that has lateral but no terminal substitutions and yet forms a liquid crystal phase. By and large, the studies on substitution effect have shown that while the terminal substitutions are favorable to the thermal stability and the formation of a liquid crystal phase, the lateral substitutions are not. The larger the lateral substitution, the more harm it can do to the thermal stability of the liquid crystalline phase. A typical and very convincing example for this idea is given by homologues of the well known para-substituted azoxyanisole (3.12) ... 

Rigid rods (a), laths (b) and disks (c) have no conformational degree of freedom. They are very convenient for theoretical discussions and computer simulations of the mesophase structure. Closer to reality are rods (or disks) with flexible tails (hydrocarbon chains) shown in Fig. 3.2a, which facilitate formation of layered liquid crystal phases. As an example of conformational degrees of freedom of flexible molecular fragments is the trans-cis isomerization. In sketch 3.2b transform is on the left, cis-form in the middle, a combination of the two on the right. The rotational isomerization is another example in sketch 3.2c the internal rotation of phenyl rings about the single bond in a biphenyl moiety is sketched. 

Fig. 13.19 Intermolecular interactions responsible for formation of different liquid crystal phases attractive anisotropic van der Waals and repulsive steric interactions for nematics (a), van der Waals (bifilic) and steric for SmA (b), steric quadrupolar interaction for SmC (c) and SmC A (d) owed to molecular biaxiality. The density is increasing in a sequence orthogonal (b), synclinic (c) and anticlinic (d) phases. An interlayer steric correlations in SmC (e) are shown by displacements of grey molecules . Note that the displacement of gray molecules may influence the next to nearest layer via a kind of relay race mechanism...

Geometrical analysis of the state equation surfaces of liquid-vapour and crystal-liquid equilibria (Equation 1.2-33, Figures 1.20 and 1.21), analysis of expcrimotilal data and computer simulation results lead to the conclusion of that there is no spinodal of the liquid crystal phase transition while the spinodal of crystal —> liquid transition does exist (Skripov, 1975 Skripov and Koverda, 1984). Consequently, the liquid crystdiization occurs only through the formation of critical nuclei (through the metastable state) and no barrierless transition is possible. 

In n-octane/aqueous systems at 27°C, TRS 10-80 has been shown to form a surfactant-rich third phase, or a thin film of liquid crystals (see Figure 1), with a sharp interfacial tension minimum of about 5x10 mN/m at 15 g/L NaCI concentration f131. Similarly, in this study the bitumen/aqueous tension behavior of TRS 10-80 and Sun Tech IV appeared not to be related to monolayer coverage at the interface (as in the case of Enordet C16 18) but rather was indicative of a surfactant-rich third phase between oil and water. The higher values for minimum interfacial tension observed for a heavy oil compared to a pure n-alkane were probably due to natural surfactants in the crude oil which somewhat hindered the formation of the surfactant-rich phase. This hypothesis needs to be tested, but the effect is not unlike that of the addition of SDS (which does not form liquid crystals) in partially solubilizing the third phase formed by TRS 10-80 or Aerosol OT at the alkane/brine interface Til.121. 

A change in the perception of their mechanism of action came in the sixties when Lawrence (7) pointed out that short chain surfactants would delay the gelling to a liquid crystalline phase which takes place at high surfactant concentrations. Friberg and Rydhag (8) showed that hydrotropes, in addition, prevent the formation of lamellar liquid crystals in combinations of surfactants with hydrophobic amphlphiles, such as long chain carboxylic acids and alcohols. The importance of this finding for laundry action was evident. 

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