Calamitic systems

Note 4 The situation for thermotropic calamitic systems is less clear and for some compounds claimed to form a Nb, detailed investigations have found the mesophase to be of type Nu. 

In calamitic systems it is the long axis of the molecules that is correlated in the mesophases but in discotic systems it is the short axis and different types of organization are seen, although disk-like molecules also form a nematic phase in which a unique axis is orientationally correlated (Fig. 25). However, below the nematic phase is a series of columnar phases (Col) in which the disks are stacked up into columns, which are themselves arranged according to some symmetric pattern. Typical... 

Although the cubic phase is interesting in several regards, it is particularly worth noting that while liquid crystal mesophases are fluid, cubic phases are very viscous. Furthermore, because of their high symmetry, cubic phases possess isotropic physical properties, setting them apart from other liquid-crystal mesophases. Transitions into, and out of, cubic phases tend to be rather slow. Exactly why cubic phases form in calamitic systems is tmclear at the present time. 

So what about the cubic phase In polycatenar systems, it is possible to rationalize the formation of cubic phases on the basis of surface curvature alone, which will be considered in subsequent sections. However, it can be argued that, for calamitic systems, these arguments do not hold—at least on their own—and that other factors are important. For example, if cubic-phase formation is due to surface curvature, it is not possible to explain why an Sa phase (lamellar and with no surface curvature) is seen at higher temperatures. An important factor is the presence of specific intermolecular interactions and in the case of the silver systems, these are the intermolecular electrostatic interactions resulting from the presence of formally ionic groups. This is consistent with the observation of cubic phases in the biphenylcarboxylic acids and hydrazines (Fig. 29), as well as with other materials. However, it is also evident that this is not the only factor, as no cubic phase is seen with anion chains shorter than DOS, while other studies with fluorinated alkoxystilbazoles showed that the position of fluorine substitution could determine the presence or absence of the mesophase observed in the unsubstituted derivatives (56). Thus, structural factors are clearly not negligible. 

The structure of materials forming columnar mesophases is at first sight somewhat simpler than that of calamitic systems. The disc-like core is often aromatic, and is in general surrounded by six or eight alkyl chains Figure 63 shows some representative examples of discotic materials. 

For example, the nematic phase formed by calamitic systems is optically positive and uniaxial, with the optical axis along n. In the absence of an external field, the two directions, n and —n are, however, indistinguishable. The nematic phase, formed by the disc-shaped mesogens, is denoted by ND to distinguish it from the one formed by the calamitic systems. Unlike the latter phase, the ND phase is optically and diamagnetically negative [15]. 

Figure 19. Typical trajectories of the unit orientation vector for a single ellipsoid revolution in two different systems, (a) Calamitic system GB(3,5,2,1) at four temperatures (i) T = 2.008 (in the isotropic phase), (ii) T = 1.396 (close to the I-N transition), (iii) T = 1.310 (close to the I-N transition), and (ii) T = 1.192 (in the nematic phase), (b) Binary mixture at the highest temperature (left) and the lowest (right) temperature studied. (Reproduced from Ref. 131.)...

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.)... 

Figure 22. Potential energy landscape explored by the model calamitic system GB(3, 5, 2, 1) (N = 256) as the system makes a transit through mesophases upon cooling, (a) Temperature dependence of the average inherent structure energy per particle, (< /s), along three isochors at densities p = 0.31,0.32, and 0.33. (b) Evolution of the average second-rank orientational order parameter S with temperature both for the inherent structures (filled) and for the instantaneous configurations (opaque). (Reproduced from Ref. 144.)...

Figure 26. Characterization of the inherent structures for the model calamitic system GB(3,5,2, 1) ( = 256). (a) Parallel radial distribution function g (/ ) for the inherent structures at all temperatures considered along the isochor at density p = 0.32. Note that the curves for the highest five temperatures are nearly superposed on each other. For others, the amplitude of the peaks gradually increases as the temperature drops, (b) Evolution of the 6-fold bond orientational order parameter 4>6 for the inherent stmctures with temperature at three densities. (Reproduced from Ref. 144.)...

Figure 29. Comparison of the scaled D and D data for the calamitic system GB(3, 5, 2, 1) (.N = 256), obtained from simulations [161], with those predicted by two theoretical models, (a) The Hess-Frenkel-Allen (HFA) model (b) the Chu and Moroi (CM) model. For the purpose of comparison, the scaling is done by (D) and ( >), respectively. (Reproduced from Ref. 161.)...

Figure 30. Evolution of the smectic order parameter for the inherent structures of the calamitic system GB(3, 5, 2, 1) (N = 256) with temperature at two densities. 

Figure 31. Coupling between the nematic order parameter S and the smectic order parameter 4/ for the calamitic system GB(3, 5, 2, 1) (TV = 256) at three state points along the isochor at density p = 0.32. At the nematic phase (T = 1.194 bottom), at the smectic phase (T = 0.502 top), and at the nematic-smectic transition region (T = 0.785 middle). The order parameters are for instantaneous configurations. (Reproduced from Ref. 161.)...

Some of the simplest systems reported raise a possible point of semantics as to whether these systems are, in fact, polycatenar in nature or perhaps ought to be described as discotic. The first of these 77 was based simply on the coordination of 3,4,5-trialkoxybenzonitriles to Pd(ll), following a motif for the formation of simple, calamitic systems "" described some years earlier. Only two compounds with different chain lengths were studied ( =10, 18). The ligands were themselves not mesomorphic, but on complexation, a Col), phase was observed over small temperature ranges, i.e., 73-91 °C for the complex with six tridecyloxy chains, and between 58 and 80 °C for that with six octadecyloxy chains. 

When the disks have no long-range translational order, an analog of the nematic phase, identified as N, is formed. Very few compounds exhibit an Ng phase. It is not entirely miscible with the nematic phase formed by calamitic systems. If a chiral center is incorporated into a nematic discogen, the material usually exhibits a chiral nematic discotic phase. Figure 2.12 shows disk-shaped molecules exhibiting discotic liquid crystal phases between the solid and isotropic liquid phases. 

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