Nematic-smectic transition point

One can find a well detailed analysis of the elastic properties of the smectics in the review article of Miyano and Ketterson [l]. The essential point is that there are two elastic quantities needed to describe the state of the sample - the density and the strain perpendicular to the layers. We note p the relative change of the density from a reference state chosen to be the nematic-smectic transition point, and Xz the second elastic variable, xz can be also seen as the relative variation of the layer thickness. 

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.)...

Depending on temperature, transitions between distinct types of LC phases can occur.3 All transitions between various liquid crystal phases with 0D, ID, or 2D periodicity (nematic, smectic, and columnar phases) and between these liquid crystal phases and the isotropic liquid state are reversible with nearly no hysteresis. However, due to the kinetic nature of crystallization, strong hysteresis can occur for the transition to solid crystalline phases (overcooling), which allows liquid crystal phases to be observed below the melting point, and these phases are termed monotropic (monotropic phases are shown in parenthesis). Some overcooling could also be found for mesophases with 3D order, namely cubic phases. The order-disorder transition from the liquid crystalline phases to the isotropic liquid state (assigned as clearing temperature) is used as a measure of the stability of the LC phase considered.4... 

Fig. 9-9. Phase diagram of ferrocenes 14. Melting point nematic/isotropic liquid transition A smectic A/isotropic liquid transition o isotropic liquid/nematic transition A isotropic liquid or nematic/smectic A transition.

Fig. 9-13. Phase diagram of ferrocenes 15. Melting point clearing point smectic C/nematic transition A nematic/smectic C transition.

There has also been a study of the flow properties of a version of the Gay-Berne fluid that can form smectic A liquid crystals [36]. It becomes flow unstable close to the nematic-smectic A (N-S ) transition point. This is in agreement with the theory by Brochard and Jahnig [37]. They predicted that the twist viscosity would diverge at this transition. Therefore the correlation function P (r) P"(0))g. i2 must also diverge. This means that the equality... 

Fig. 8 The Miesowicz viscosities, 77j (diamonds), 772 (squares) and 773 (squares) as a function of temperature for a version of the Gay-Beme fluid that forms both nematic and smectic A phases. The N - transition takes place at kgT/e=. 0. Note that 77, is undefined at the N — transition point and in the smectic phase.

Fig. 2. The dependence of the melting points (O) and the nematic-isotropic transition temperatures ( ) on the nmnher of methylene units in the flexible spacer, n, for the BCBOn series [18]. Also shown are the nematic-isotropic transition temperatures ( ) and the smectic A-isotropic transition temperatures ( ) for the nOCB series...

Fig. 7. The dependence of the transition temperatures on the number of methylene groups, n, in the flexible spacer for the 4.0n0.4 series [37]. indicates smectic A-isotropic transitions, the nematic-isotropic transitions, O the melting points, smectic A-nematic transitions and A smectic B-smectic A transition. Cr Crystal SmA smectic A N nematic I isotropic...

Fig. 14. The dependence of the transition temperatures on the number of carbon atoms, m, in the terminal alkyl chain for the CB060.m series [68]. denotes nematic-isotropic transitions, O intercalated smectic A-nematic transitions, smectic-intercalated smectic A transitions, A interdigitated smectic A-interdigitated smectic C transitions and interdigitated smectic A-nematic transitions. The melting points have been omitted for the sake of clarity. SmA Interdigitated smectic A phase SmCa interdigitated smectic C phase SmA intercalated smectic A phase S unidentified smectic phase N nematic / isotropic...

Fig. 15. The dependence of the transition temperatures on the length of the flexible spacer, n, for the laterally linked dimer series, the a,(u-his[2,5-his(4-n-octyloxy-henzoyloxy)-henz-amido]alkanes [125]. Melting points are denoted hy O, indicates nematic-isotropic transitions and smectic C-nematic transitions. N Nematic I isotropic Cr crystal SmC smectic C phase...

Fig. 2.7.3. High resolution specular reflectivity data for 80CB near the peak due to the formation of smectic-like layers near the free surface of the nematic phase. The open circles refer to the scale on the left and the filled circles to the scale on the right. The temperatures T— are (a) 0.10 °C, (Z>) 0.21 C, (c) 0.40 and (

Gahwiller discovered that nematics that undergo a transformation to the smectic phase at lower temperatures exhibit an unusual type of instability as the temperature approaches the transition point. The limiting value of the flow alignment angle 0 defined as... 

In the McMillan model, the smectic A-nematic transition can be continuous or discontinuous. If a is less than 0.7, then o decreases to zero continuously and S is continuous at the smectic A- nematic transition. If a is between 0.7 and 0.98, then a jumps to zero discontinuously and S has a small discontinuity at the smectic A-nematic transition. When a is greater than 0.98, the smectic phase transforms directly into the isotropic phase with discontinuities in both order parameters. So just as in the extended Landau-de Geimes theory for the smectic A phase, a tricritical point is predicted at a=0.7, which corresponds to a ratio in the smectic A—nematic transition temperature to the nematic-isotropic transition temperature of 0.87. A great deal of experimental work has been done on the smectic A-nematic transition, and the results seem to indicate that the tricritical point occurs when the ratio of the two transition temperatures is significantly larger than 0.87. 

There are of course many open questions and further possibilities in the field. Some specific points were emphasized in the text. It should be remarked that up to now most researchers concentrated on the nematic phase. Although there are still many important aspects to be investigated even in this phase, the study of other mesophases looks very promising as well. We called attention already to the problem of optical reorientation in the cholesteric and smectic C phases. Regarding thermal effects we remind that the interesting point about nematics is the nearly critical behaviour near the nematic - isotropic phase transition. Similar phenomena can be expected to take place at other second-order phase transitions such as the smectic A - smectic C or some of the nematic- smectic A transitions. 

The results are reproduced in Fig. 2.6 [15]. It can be seen that with a drop in temperature the difference e, — e decreases even in the nematic phase. The change in sign of the anisotropy of the molar susceptibility occurs either in the smectic A phase (homologues with n = 7 and 8) or in the nematic phase (n = 6) near the transition point to smectic A. The dielectric anisotropy decreases both because of the decrease in s, and the increase in e . The effect clearly indicates the presence of the short-range smectic order even in the nematic phase. The decrease in and the increase in e , due to the short-range smectic order in the nematic phase (and the long-range order in smectic A), occurs as a consequence of correlation in... 

When a nematic-smectic A transition occurs in a capillary tube (Fig. 8 a), smectic layers nucleate at disclination points and a singular line forms along the axis, with cylindrical layers (as shown in Fig. 8 b), but the presence of beads along the axial defect shows that the situation is less schematic [42]. 

An advantage of NMR in the investigation of phase transitions is the fact that bi-phasic regions can be detected from the superposition of two different components in the spectrum. This facilitates the distinction between discontinuous (first-order) and continuous (higher-order) transitions (see Sec. 1.3.5). The tricritical point of the smectic A to nematic phase transition for binary liquid crystal mixtures, for example, has been determined by 2D NMR [54]. 

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