Isotropic-nematic phase transition orientation

The SD is a phase separation process usually occurring in systems consisting of more than two components such as in solutions or blends. However, in the present case the system employed is composed of one component of pure PET. In this case, what triggers such an SD type phase separation Doi et al. [24, 25] proposed a dynamic theory for the isotropic-nematic phase transition for liquid crystalline polymers in which they showed that the orientation process... 

There are basically two possible scenarios for the behavioxir of this prenematic mean field force when the separation between surfaces is reduced, and both depend on the degree of the surface-induced nematic order. For low surface-induced order, the magnitude of the attractive force just increases when approaching the isotropic-nematic phase transition from above. On the other hand, if a surface induces a high degree of LC orientation, the prenematic phase can spontaneously transform into the nematic phase, when the separation is decreased below a certain value. This is the nematic capillary condensation, that is discussed further on in this Chapter. 

The type, range, and strength of this surface-induced order depend on the order parameter and the coupling of 8CB to the surface. The order parameter describes the average orientation of the molecules [1]. It increases when approaching the isotropic-nematic phase transition. De-... 

Phase transitions in condensed phases are characterized by symmetry changes, i.e. by transformations in orientational and translational ordering in the system. Many soft materials form a disordered (isotropic) phase at high temperatures but adopt ordered structures, with different degrees of translational and orientational order, at low temperatures. The transition from the isotropic phase to ordered phase is said to be a symmetry breaking transition, because the symmetry of the isotropic phase (with full rotational and translational symmetry) is broken at low temperatures. Examples of symmetry breaking transitions include the isotropic-nematic phase transition in hquid crystals (Section 5.5.2) and the isotropic-lamellar phase transition observed for amphiphiles (Section 4.10.2) or block copolymers (Section 2.11). 

For the isotropic-nematic phase transition, the appropriate order parameter quantifies the average degree of orientational order in the low-temperature phase. It is denoted P2, as defined by Eq. (5.11) (this order parameter only quantifies the first moment of the orientational distribution function higher-order parameters can also be defined, as discussed in Section 5.5.1). 

Figure 8 Isotropic-nematic phase transition, in the smectic phase (right) the molecules have orientational order but do not show any long-range translational order. In the isotropic phase (left) the orientational order is lost (Figure by M. Dijkstra)...

Fig. 10.25 Scattering angle dependence of autocorrelation function for the order parameter fluctuation in isotropic phase near isotropic-nematic phase transition temperature. Inset Dispersion relation of the order parameter fluctuation, which is independent of the wave number, together with the orientation fluctuation...

Here, 1 will show that the measurement of the dynamic heterogeneity revealed the characteristics of the random structure in the B4 phase [64]. Figure 10.30a shows the time autocorrelation function of the BX phase (at 27 °C) and the B4 phase (at 34 °C) of a mixed system of 80 wt% 5CB. Figure 10.30b shows the nematic and isotropic phases of pure 5CB for comparison. Large fluctuations are present around 0.1 ms in the Bx phase, but the corresponding fluctuation in the B4 phase has disappeared. In addition, the Bx-B4 transition temperature of the mixed system is almost the same as the phase transition temperature of pure 5CB, 34.10 °C. In the phase diagram, Bx-B4 transition temperature corresponds to the extrapolated isotropic-nematic phase transition temperature phase of 5CB. From these two experiments we reason that the fluctuations that had been observed in the Bx phase come from the orientation fluctuations of the 5CB nematic... 

The isotropic-to-nematic transition is determined by the condition [1 — (2/3)TBBWBB/k T] = 0 whereas the spinodal line is obtained when the denominator of XAA is equal to zero. These conditions are evaluated in the thermodynamic limit (Q = 0) in Fig. 7 for a Maier-Saupe interaction parameter Web/I bT = 0.4xAb and for NA = 200, N = 800, vA = vB = 1. When the volume fraction of component A(a) is low, the isotropic-to-nematic phase transition is reached first whereas at high < >A the spinodal line is reached first. In the second case, the macromolecules do not have a chance to orient themselves before the spinodal line is reached. This RPA approach is a generalization of the Doi et al. [36-38] results (that were developed for lyotropic polymer liquid crystals) to describe thermotropic polymer mixtures. Both approaches cannot, however,... 

Figure 20. (a) Orientational correlation time t in the logarithmic scale as function of the inverse of the scaled temperature, with the scaling being done by the isotropic to nematic transition temperature with Ti-N. For the insets, the horizontal and the vertical axis labels read the same as that of the main frame and are thus omitted for clarity. Along each isochor, the solid line is the Arrhenius fit to the subset of the high-temperature data and the dotted line corresponds to the fit to the data near the isotropic-nematic phase boundary with the VFT form, (b) Fragility index m as a function of density for different aspect ratios of model calamitic systems. The systems considered are GB(3, 5, 2, 1), GB(3.4, 5, 2, 1), and GB(3.8, 5, 2, 1). In each case, N = 500. (Reproduced from Ref. 136.)... 

The smectic layering transition [45] is a phenomenon, where smectic layers grow one by one, parallel to the surface, when the temperature approaches the isotropic-smectic phase transition from above. Ellipsometric observation of these steps is possible due to the coupling between the smectic order and the nematic (orientational) ordering. Consequently, the orientational order in... 

Brochard and de Gennes [67] discussed theoretically a flow-induced isotropic-mesophase transition in a polydisperse polymer system occurring through spinodal decomposition. Following Maier-Saupe s [50] theory of the nematic phase, the orientation-dependent interaction energy was taken as... 

As in low molecular systems, the nematic phase exhibits orientation order between rod-like units, but no positional order. Due to orientation of mesogenic units also spacers are oriented by stretching. Molecules are oriented with respect to director. Thus, the isotropic - nematic transition is a disorder-order transition from a phase without long range order to a phase with long range orientation order but still liquid-like. It is an equilibrium transition since there is no undercooling. This transition is characterized by = S -S <0 and < 0. We may relate it to equation of Clausius-Clapeyron. It follows ... 

It has also been noticed that within some temperature interval around the transition points and NI the two neighbouring phases are not strictly homogeneous, but each phase contains embryos of the other phase. The relative amount of the phase existing in an embryonic form remains very small up to temperatures very close to the transition point, but it is detectable by NMR. Figure 1 shows several proton NMR spectra of DDA9-L representative of (A) the isotropic phase with a small nematic fraction, (B) nematic phase with a small isotropic fraction (1-2 %), (C) pure nematic phase homogeneously oriented, (D) unoriented nematic phase, or solid phase above the cold crystallization temperature, (E) solid phase with some nematic fraction, and (F) solid phase near room temperature. It is interesting to note that the sharp peak at the centre of spectrum B, which could not be obtained in the line shape simulation procedure reported in... 

NMR is not the best method to identify thennotropic phases, because the spectmm is not directly related to the symmetry of the mesophase, and transitions between different smectic phases or between a smectic phase and the nematic phase do not usually lead to significant changes in the NMR spectmm [ ]. However, the nematic-isotropic transition is usually obvious from the discontinuous decrease in orientational order. NMR can, however,... 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

One of the primary features of the Gay-Berne potential is the presence of anisotropic attractive forces which should allow the observation of thermally driven phase transitions and this has proved to be the case. Thus using the parametrisation proposed by Gay and Berne, Adams et al. [9] showed that GB(3.0, 5.0, 2, 1) exhibits both nematic and isotropic phases on varying the temperature at constant density. This was chosen to be close to the transitional density for hard ellipsoids with the same ellipticity indeed it is generally the case that to observe a nematic-isotropic transition for Gay-Berne mesogens the density should be set in this way. The long range orientational order of the phase was established from the non-zero values of the orientational correlation coefficient, G2(r), at large separations and the translational disorder was apparent from the radial distribution function. 

---