Nematic transition

The liquid-crystal transition between smectic-A and nematic for some systems is an AT transition. Depending on the value of the MacMillan ratio, the ratio of the temperature of the smectic-A-nematic transition to that of the nematic-isotropic transition (which is Ising), the behaviour of such systems varies continuously from a k-type transition to a tricritical one (see section A2.5.91. Garland and Nounesis [34] reviewed these systems in 1994. 

Camp P J, Mason C P, Allen M P, Khare A A and Kofke D A 1996 The isotropic-nematic transition in uniaxial hard ellipsoid fluids coexistence data and the approach to the Onsager limit J. Chem. Phys. 105 2837-49... 

Disc-like particles can also undergo an Onsager transition—here tire particles fonn a discotic nematic, where tire short particle axes tend to be oriented parallel to each other. In practice, clay suspensions tend to display sol-gel transitions, witliout a clear tendency towards nematic ordering (for instance, [22]). Using sterically stabilized platelets, an isotropic-nematic transition could be observed [119]. 

We conclude that the dipolar models may exhibit many interesting features, such as the influence of the strength of the dipole moment on the nematic-isotropic and smectic-nematic transitions. Determining the structure of the various smectic phases is clearly an area which needs more investigation. However, an appropriate simulation scheme must be used to avoid misunderstanding the behaviour caused by the method rather than the model. This may be as simple as checking for system size dependence, or running... 

Many technological applications of liquid crystals, as in electro-optic display devices, are based on multicomponent mixtures. Such systems offer a route to the desired material properties which cannot be achieved simultaneously for single component systems. Mixtures also tend to exhibit a richer phase behaviour than pure systems with features such as re-entrant nematic phases [3] and nematic-nematic transitions possible. In this section, we describe simulations which have been used to study mixtures of thermotropic calamitic mesogens. 

The introduction of a second chiral atom in the system leads to a reduction in the mesogenic properties and only a monotropic chiral nematic transition is observed for compound 23. However, when this compound is cooled down from the isotropic liquid state at a cooling rate of 0.5 °Cmin , very unusual blue phases BP-III, BL-II and BP-I are observed in the range 103-88 °C. Blue phases usually require pitch values below 500 nm. Hence the pitch value of the cholesteric phase for 23 must be very short, suggesting that the packing of two chiral carbons forces a faster helical shift for successive molecules packed along the perpendicular to the director. 

Note 4 T occurs below the clearing temperature, usually by about 1 K in isotropic-to-nematic transitions and increases to at least 10 K for isotropic-to-smectic transitions. 

The complexes bearing one chiral substituent display a smectic A mesophase when the non-chiral chain is long, or an enantiotropic cholesteric and a monotropic SmA phase for shorter alkoxy chains. A TGBA phase is observed for the derivative which contains the chiral isocyanide combined with the diethyloxy, when the SmA to cholesteric transition is studied. The compound with two chiral ligands shows a monotropic chiral nematic transition. When this compound is cooled very slowly from the isotropic liquid it exhibits blue phases BP-III, BP-II, and BP-I. 

Turning to the low temperature transition of the homopolymer of PHBA at 350 °C, it is generally accepted that the phase below this temperature is orthorhombic and converts to an approximate pseudohexagonal phase with a packing closely related to the orthorhombic phase (see Fig. 6) [27-29]. The fact that a number of the diffraction maxima retain the sharp definition at room temperature pattern combined with the streaking of the 006 line suggests both vertical and horizontal displacements of the chains [29]. As mentioned earlier, Yoon et al. has opted to describe the new phase as a smectic E whereas we prefer to interpret this new phase as a one dimensional plastic crystal where rotational freedom is permitted around the chain axis. This particular question is really a matter of semantics since both interpretations are correct. Perhaps the more important issue is which of these terminologies provides a more descriptive picture as to the nature of the molecular motions of the polymer above the 350 °C transition. As will be seen shortly in the case of the aromatic copolyesters, similar motions can be identified well below the crystal-nematic transition. 

On the other hand, as opposed to the randomizing reactions which occur in the nematic melt if one anneals these copolyesters near their crystal nematic transition a completely different process appears to be operative. Thus several workers [11, 14], have reported that heating the HBA/HNA system near its melting point results in a dramatic increase in Tcn by approximately 50 °C. As... 

The distribution of chain sequence extension, calculated by using RIS models, is compared with isotropic-nematic transition characteristics for a number of thermotropic polymers comprising rigid groups connected by polymethylene spacers. The distribution depends strongly not only on the odd-even character of the number of methylene units of the spacers, but also on the specific groups (or atoms connected at the ends of polymethylene spacers. 

Values of enthalpy and entropy change at isotropic-nematic transitions... 

Fig. 11. DSC-trace of bis-(4 -n-octyloxybenzal)-l,4-phenylenediamine at 5 K/min. The lowest temperature transition is the fully ordered crystal-to-smectic transition, followed by four transitions between the five smectic polymorphs. Next is the smectic-nematic transition, followed by the nematic-to-isotropic liquid transition. Drawn after data by Petrie581...

The methyl-substituted ester model compound, shown below, also shows both smectic and nematic phases, as well as a smectic C-to-nematic transitional phase (18) from 169 to 170°C. Figure 3 shows two of the textures observed in this model. 

Figure 3. Liquid-crystal textures of the methyl-substituted model ester viewed through crossed polarizers, a, Smectic C-to-nematic transitional phase and b, smectic mosaic texture at 160 °C. Original magnification, 320x.

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

The isotropic-to-nematic transition is defined by the characteristic equation Det M = 0 (where Det represents the determinant of a matrix). If the Van der Waals interactions were turned off (W0 = 0) so that only nematic interactions are left, then M would be the denominator of X so that X would blow up for this condition (Det M = 0). Above certain critical values of Wj s the blend forms the nematic phase. As in the case of purely flexible mixtures, the spinodal condition is ... 

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,... 

Thin films of the solutions between microscope slides were sheared by applying even pressure on a coverslip while sliding it approximately one cm. The anisotropy appeared to increase as measured by increases in the birefiingence. Solutions containing 10-16% (w/w) cellulose developed a threaded texture and the mesophases were stable with time and oriented in the direction of shear. These observations, while not definitive, suggested a cholesteric to nematic transition occurred on shearing. 

---