First-order transitions liquid crystals

Xenopoulos A, Cheng J, Yasuniva M, Wunderlich B (1992) Mesophases of Alkyl-ammonium Salts. I. First-order Transitions. Molecular Crystals and Liquid Crystals 214 63-79. 

Different liquid crystal phase transitions will be more or less difficult to detect using DSC. If the transition is first order, meaning that the order parameter is discontinuous across the phase boundary, a significant latent heat will be measurable, and usually a clear peak can be observed. An example of a first-order phase transition in liquid crystals would be the crystalline-to-smectic or -nematic phase. The nematic-to-isotropic phase is also first order. Some liquid crystal phase transitions are much more... 

Figure 4.3b is a schematic representation of the behavior of S and V in the vicinity of T . Although both the crystal and liquid phases have the same value of G at T , this is not the case for S and V (or for the enthalpy H). Since these latter variables can be written as first derivatives of G and show discontinuities at the transition point, the fusion process is called a first-order transition. Vaporization and other familiar phase transitions are also first-order transitions. The behavior of V at Tg in Fig. 4.1 shows that the glass transition is not a first-order transition. One of the objectives of this chapter is to gain a better understanding of what else it might be. We shall return to this in Sec. 4.8. 

Note 2 The divergence occurs at the point where the isotropic phase would be expected to undergo a second-order transition to the liquid-crystal phase, were it not for the intervention of a first-order transition to the liquid-crystal phase. 

As with liquid crystals (Sect. 5.1.2), only the equilibrium transition to the fully ordered crystal and the transition to the isotropic melt have been studied extensively16c 102). Both transitions are of the first order transition type, similar to that shown in Fig. 1. A series of transition data are collected in Table 7. Plastic crystals with motifs as small as... 

Poly (diethyl siloxane) was suggested by Beatty et al. 1651 based on DSC, dielectric, NMR, and X-ray measurements to possess liquid crystalline type order between about 270 and 300 K. The macromolecule shows two large lower temperature first order transitions, one at about 200 K, the other at about 270 K166 ll,7). The transition of the possible mesophase to the isotropic liquid at 300 K is quite small and irre-producible, so that variable, partial crystallinity was proposed 165) [measured heat of transition about 150 J/mole1S8)], Very little can be said about this state which may even consist of residual crystals. It is of interest, however, to further analyze the high temperature crystal phase between 200 and 270 K. It is produced from the, most likely, fully ordered crystal with an estimated heat and entropy of transition of 5.62kJ/mol and 28J/(Kmol), respectively [calculated from calorimetric data 1S6)... 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

Raman spectra for the sample were conducted in a compression-decompression cycle. In this experiment, the crystalline diffraction began to disappear above 7-8 GPa during compression, and pressure-induced amorphization was indicated by the Raman spectra above 13 GPa (Fig. 14). The resultant HDA Si exhibits the Raman spectrum that differs from the spectrum of normal -Si (LDA Si). Rather, the characteristics of the spectrum for HDA Si resemble those of the (3-tin crystal, which indicates that HDA Si has a (locally) analogous structure to the (3-tin structure. The synthesis of the HDA form of Si by Deb et al. [263] has a strong resemblance to that of water (ice) by Mishima et al. [149, 196]. Whereas compression induced amorphization that was almost completed at 13-15 GPa, decompression induced an HDA-LDA transition below 10 GPa, which is clearly shown in the Raman spectra (Fig. 14). This is the first direct observation of an amorphous-amorphous transition in Si. The spectrum at 0 GPa after the pressure release exhibits the characteristic bands of tetrahedrally coordinated -Si (LDA Si). Based on their experimental findings Deb et al. [263] discussed the possible existence of liquid-liquid transition in Si by invoking a bond-excitation model [258, 259]. They have predicted a first-order transition between high-density liquid (HDL) and low-density liquid... 

We all know that when a liquid transforms to a crystal, there is a change in order the crystal has greater order than the liquid. The symmetry also changes in such a transition the liquid has more symmetry than a crystal since the liquid remains invariant under all rotations and translations. Landau introduced the concept of an order parameter, , which is a measure of the order resulting from a phase transition. In a first-order transition (e.g., liquid-crystal), the change in is discontinuous, but in a second-order transition where the change of state is continuous, the change in is also continuous. Landau proposed that G in a second-order (or structured) phase transition is not only a function of P and T but also of and expanded G as... 

Generally, the metastability is a phenomenon associated with the persistence of the given phase well below the stability domain, bordered by the first order transition, for instance (/) the glass transition phenomenon, (//) metastable systems studies linked to spinodals - absolute stability limits, with particular attention towards the inherently metastable negative pressure domain (///) metastability near a critical point, (/v) the quest for the liquid - liquid near-critical transition in one component liquid, (v) the issue of liquid crystals where... 

Transitions between a solid and a mesophase, or between two mesophases, or between a mesophase and an isotropic liquid, are thermodynamic events and are classified as either first or second order. In liquid crystals, transitions between phases are usually thought of as being weakly first order, although second-order transitions are not uncommon the melting transition is, however, first order. 

---