Nematic-Smectic A N-SmA Transition

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...

The narrower a range of the nematic phase in a homological series of different compounds (as an example see Fig. 6.1 la) the stronger are first order features of the N-SmA transition. In some sense, the SmA phase feels the proximity of the isotropic phase. In other words, we may say that, in the isotropic phase, there are traces of both nematic and smectic A short-range order. 

Therefore we again obtain the first order transition for jAi — Ci >0 and second order for IB jA2 — Ci < 0 and a tricritical point for IB /Ai — C =0. The tricritical point (TCP) is located in the continuous phase transition line separating the nematic and smectic A phases [12], see a phase diagram schematically shown in Fig. 6.12. Such a point should not be confused with the triple point common for the isotropic, nematic and SmA phases. In Fig. 6.12, for homologues with alkyl chains shorter than l , the N-SmA transition is second order and shown by the dashed curve. With increasing chain length the nematic temperature range becomes narrower (like in Fig. 6.1) and, at TCP, the N-SmA transition becomes first order (solid curve). 

The SmA liquid crystalline phase results from the development of a one-dimensional density wave in the orientationally ordered nematic phase. The smectic wave vector q is parallel to the nematic director (along the z-axis) and the SmA order parameter i/r= i/r e is introduced by P( ) = Po[1+R6V ]- Thus the order parameter has a magnitude and a phase. This led de Gennes to point out the analogy with superfluid helium and the normal-superconductor transition in metals [7, 59]. This would than place the N-SmA transition in the three-dimensional XY universality class. However, there are two important sources of deviations from isotropic 3D-XY behavior. The first one is crossover from second-order to first-order behavior via a tricritical point due to coupling between the smectic order parameter y/ and the nematic order parameter Q. The second source of deviation from isotropic 3D-XY behavior arises from the coupling between director fluctuations and the smectic order parameter, which is intrinsically anisotropic [60-62]. 

Upon cooling a nematic phase towards a second-order N-SmA transition, the susceptibility of smectic fluctuations x di-... 

As a matter of fact, the N-SmA transition may be either second or first order. It becomes first order when a coupling exists between the smectic and the nematic ordering [17-21]. The orientational order parameter is S=Sn+6S, where 5 is the order pa-... 

Figure 7. Dependence of the transition temperatures on the number of carbon atoms, m, in the terminal chain for the CB040.m series. indicates the inter-digitated smectic A-isotropic transition, the nematic-isotropic transitions, A interdigitated smectic A-nematic transitions and intercalated smectic A-ne-matic transitions. The melting points have been omitted for the sake of clarity. SraA, interdigitated smectic A SmA ., intercalated smectic A N, nematic I, isotropic.

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

Example The following compound exhibits, as temperature decreases, an isotropic (I) phase, nematic (N), smectic A (SmA) re-entrant nematic (Nre), re-entrant smectic A (SmAre) mesophases and a crystalline (Cr) phase, with transitions at the specified temperatures. 

FIGURE 45 5,5 -Substituted 2,6-6w(l-ethyl-benzimidazol-2-yl)pyridines and their transition temperatures (in °C). Abbreviations Cr = crystalline phase, SmC = smectic C phase, SmA = smectic A phase, N = nematic phase. Col/, = hexagonal columnar phase, I = isotropic liquid. 

The precursor 6 exhibits the enantiotropic nature of chiral nematic (N ), chiral smectic C (SmC ) and chiral smectic I (SmI ) phases. The shell-printed texture of the SmC phase and the rose-like texture of the SmI phase can be clearly seen in Figure 12.6. The thiophene monomers, M2 and M3, show enantiotropic N, SmA and SmC phases. The SmC phase is characteristic of ferroelectricity. The polymers show various mesophases. The phase transition temperatures are summarized in Table 12.4. PI shows an enantiotropic SmA phase. P2 shows enantiotropic SmA, SmC and SmB phases. The fan-shaped texture of the SmA phase and the striated fan-shaped texture of the SmC phase are shown in Figure 12.7. P3 shows an SmA phase in the heating process and SmA and SmX phases in the cooling process. XRD analysis suggests that the SmX phase of P3 might be a higher order smectic phase. 

P2 (Eq. 5.11) and a (Eq. 5.16) for three different values of a is shown in Eig. 5.19. Eor large a (for example a = 1.1) d is large and smectic ordering is favoured. There is thus a first-order transition on heating from the SmA phase to the isotropic phase. However, as a is lowered, a nematic phase is formed between smectic and isotropic phases. In the case o = 0.85, the transition between SmA and N phases is first order, whereas at lower o, for example a = 0.6, it is continuous (second order), as shown by the continuous decrease of a to zero (P2 also varies continuously, but there is a change of slope with respect to temperature at the transition). The McMillan theory predicts that the crossover from a first-order to a second-order transition (called a tricritical point) occurs ata = 0.98, which corresponds in the model to a ratio of phase transition temperatures 7an/ i = 0.870. 

The studied compounds all have a terminal cyano group which means a very strong dipole. Cladis et al. [69] proposed a structural model of the bilayer smectic A phase for this kind of molecules (Fig. 3). The molecules are assumed to be associated in antiparallel pairs, which results in a weak interacting between the different polar parts of the pairs and a less dense packing of the molecules. Thus a transition of such bilayer SmA phase to a re-entrant nematic phase seems to be evident, because in this phase empty spaces of the structure are filled up more efficiently. Probably for similar reasons Pollmann et al. [70-72] found a pressure-induced re-entrant cholesteric phase behavior for ternary mixtures of cholesteryl n-alkanoates which, however, are terminally nonpolar (see Fig. 4). The mixtures of... 

The experimental results confirm the theoretical prediction that the N-I transition volume increases when the N-I transition gets closer to a SmA-N transition. This is due to short-range smectic order. This influence of the nematic range on the N-I transition volume can be very obviously seen for the ninth member of the series which exhibits a SmA-N-I triple point at 92 MPa and 103 °C. 

Note that within the SmAj phase above the SmA phase, the diffuse peak at Qq 27t//o on the meridian splits into a pair of diffuse peaks on either side of the meridian, indicating the formation of small domains with a SmA-like transverse modulation, as the SmA phase is approached. A high resolution X-ray study of the N-SmA)-SmA transition of DB7NO2 [168, 169] found that two incommensurate smectic fluctuations present in the nematic phase cross over just above the SmAj phase to a region of coexisting incommensurate... 

It is clear that the transition from a nematic (or cholesteric) to a smectic phase will result in the divergence of certain of the elastic constants. In particular, k22 and 1 33 will diverge at the N-SmA phase transition. The type of divergence observed will depend on the nature of the phase transition, which can be either first or second order [143, 144]. The transition is second order if the nematic phase is sufficiently wide, such that the nematic order parameter is saturated at the transition. Both de Gennes [145] and McMillan [146] developed theories of the SmA-N phase transition that have implications for light scattering. The form of the divergence of the twist and bend elastic constants can be written as ... 

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