Translational and orientational order

The correlation between the translational and orientational order is reflected by the mixed singlet orientational and translational distribution function P(z, cos ). The results for this are shown in Fig. 7 for the smectic A... 

In [C4CjIm]X ILs, the supposed local structures are positioned and oriented randomly, and there seems to be no translational and orientational orders at the macroscopic level. Taking into account that the [C4CiIm]X ILs are all transparent (not opaque), the dimension of those local structures must be much smaller than the wavelength of visible light (<100 A) [50,87]. 

Liquids are systems devoid of both long-range translational and orientational order whereas short-range order still remains at molecular scales resulting from the subtleties of forces acting on their constituent molecules. In turn, rotator-phase (plastic) crystals are liquid-like in the sense that molecules... 

The local translational and orientational order of atoms or molecules in a sample may be destroyed by singular points, lines or walls. The discontinuities associated with the translational order are the dislocations while the defects associated with the orientational order are the disclinations. Another kind of defect, dispirations, are related to the singularities of the chiral symmetry of a medium. The dislocations were observed long after the research on them began. The dislocations in crystals have been extensively studied because of the requirement in industry for high strength materials. On the contrary, the first disclination in liquid crystals was observed as early as when the liquid crystal was discovered in 1888, but the theoretical treatment on disclinations was quite a recent endeavor. 

The X-ray diffraction of polymeric liquid crystal systems and their low mass counterparts are the same in principle, but the diffraction results for the polymers are often less ideal and more difficult to interpret. In practice the oriented specimens are often preferred over the unoriented samples for an unambiguous determination. X-ray diffraction is nearly always used together with texture observations using a polarizing optical microscope. Miscibility tests are also used in some cases for confirmation. For smectic phases with higher translational and orientational orders, X-ray diffraction is the most useful (if not the only) technique for unmistakable characterization. A few examples are cited below. The details of each characterization of the various polymeric smectic phases were described by individual authors. 

It helps if we eategorize the anomalies discussed above into three different types (1) thermodynamie anomalies (for example, in density, Cp, Kt and Up), (2) dynamic anomalies (relaxation time or diffusion, dynamic crossover), and (3) stmctural anomalies (in translational and orientational order). 

Due to anisometric (particularly elongated) shape of molecules, these crystals possess both the translational and orientational order. The latter is determined by Euler angles 9,0 such molecules form with respect to selected coordinate frame as shown in the right part of Fig. 2.11. The third Euler angle describing rotation of a molecule about its longest axis is not shown for simplicity. The point group symmetry includes this orientational order. 

Figure 3 The stepwise breakdown in translational and orientational order in a typical melting process for a mesomorphic material that possesses rod-like molecules.

FIGURE 1.21. Field-induced changes in order parameters for a smectic A liquid crystal. S is the orientational order parameter, R is an order parameter describing the coupling of the translational and orientational order. The field increases from curve 1 to curve 3. 

The above discussion is consistent with the possible existence of two well-defined classes of liquids simple and water like. The formers interact via spherically symmetric nonsoftened potentials and do not exhibit thermodynamic or dynamic anomalies. One can calculate translational and orientational order parameters t and ( ), and project equilibrium state points onto the (f, q) plane thereby generating what is termed the Errington Debenedetti (ED) order map [24]. In water like liquids, interactions are orientation dependent these liquids exhibit dynamic and thermodynamic anomalies, and their ED order map is in general two dimensional but becomes linear (or quasi linear) when the liquid exhibits structural, dynamic, or thermodynamic anomalies. 

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). 

Figure 4. Field-induced changes in order parameters for a smectic A liquid crystal. Q, orientational order parameter curves ag, bg, and cq show the temperature dependence of Q at various fields. R, order parameter describing the coupling of translational and orientational order, curves Ug, b, and show the temperature dependence of R. The field increases from curves a to curves c and results in a change in the N-C transition from first to second order [24],...

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