Modulated Smectics

Note 1 The recommended mark to designate a modulated smectic mesophase is a superior tilde ( ). 

Due to the rigidity of Rp-chains, in fluorinated LCs the transition from smectic to columnar organization often takes place via modulated smectic phases (ribbon phases, c2mm, p2gg, and Colob see Fig. 20, left) which completely or partly replace the bicontinuous cubic phases at the Sm-to-Col cross-over. Similarly, in columnar phases the circular columns can be deformed to an elliptic, rectangular, or square... 

Coleman DA et al (2003) Polarization-modulated smectic liquid crystal phases. Science 301 1204-1211... 

Coleman DA, Femsler J, Chattham N, Nakata M, Takanishi Y, Korblova E, Link DR, Shao R-F, Jang WG, Maclennan JE, Mondainn-Monval O, Boyer C, Weissflog W, Pelzl G, Chien L-C, Zasadzinski J, Watanahe J, Walba DM, Takezoe H, Clark NA (2003) Polarization-modulated smectic liquid crystal phases. Science 301 1204—1211... 

Keywords Liquid crystal dimers. Structure-property relationships. Modulated smectic phase. Intercalated smectic phase... 

In contrast the even members of this chiral series do not exhibit modulated smectic phases. 

I. 1. Smalyukh, N.A. Clark, Organization of the polarization splay modulated smectic liquid crystal phase by topographic confinement. Proc. Nat. Acad. Sci. USA 107, 21311-21315 (2010)... 

As described above, the kink in the molecular shape and the requirement to fill the space as effectively as possible are not compatible with a three-dimensional fluid order. In other words, when translating a bent-core molecule in the melt of the neighbouring bent-core molecules, it experiences a periodic potential with its periodicity determined by the length I of the molecules. To allow for fluidity at the macroscopic level, one needs to frustrate the bent-core structure so that they do not lock into smectic layers easily. Such a frustration can be introduced by some steric or electrostatic disturbance of the bare bent-core (or peeled banana ) shape, which has been seen in some modulated smectic phases.As discussed by Bailey and Jdkli,a steric or electrostatic inclusion in the core of the molecules leads to layer modulation, an SmCc structure and broken smectic layers that effectively correspond to a columnar phase, as the inclusions increase. Following this picture, here we postulate that bent-core nematics are probably more frustrated than the electrically unswitchable B7 (columnar) phases, in which the broken smectic ribbons are separated by melted fluid nematic regions. Such over-frustrated B7 materials are characterized... 

D.A. Coleman, J. Fernsler, N. Chattham, M. Nakata, Y. Takanishi, E. Korblova, D.R. Link, R.-F. Shao, W.G. Jang, J.E. Maclennan, O. Mondainn-Monval, C. Boyer, W. Weissflog, G. Pelzl, L.-C. Chien, J. Zasadzinski, J. Watanabe, D.M. Walba, H. Takezoe and N.A. Clark, Polarization-modulated smectic liqnid crystal phases. Science 301(568), 1204-1211, (2003). doi 10.1126/science.l084956... 

Polar Columnar (ColP) Phases In calamitic rod-shaped LCs, the frustration occurring in the layer organization of molecules due to steric and/or polar effects leads to form a variety of 2D density structures such as undulated layers, modulated layers (ribbons), and Cols. The situation for bent-core molecules with an ability to form macroscopic polar order is much more complex, and different types of modulated smectic and Col phases form. Since their 2D X-ray patterns, structural models, and nomenclature have been in great detail described in the two previous reviews [29, 32], in this section, the field-induced switching properties of polar columnar (ColP) phases are focused on. 

Reddy, R. A. Baumeister, U. Tschierske, C. Self-assembly of bent-core liquid crystals formation of a modulated smectic phase with p2gg lattice to escape anticlinic tilt. Chem. Commun. 2009, 28, 4236-4238. 

Fig. 3.7 Sketch of the modulated smectic phases. For the sake of clarity, the sinusoidal modulations are drawn in an exaggerated way. a Shows the SmA phase, which is described with a centered rectangular lattice and b shows the SmC phase in which the mesogens are found on an oblique lattice...

Another example shows the smectic A polymorphism. Fig. 1.17 [43]. In mixtures of 80CB (l.xv) and 4-n-heptyloxyphenyl-4 -cyanobenzoyloxyben-zoate (DB70CN), in addition to the bilayer 5a,2 and the partially bilayer 5a,d phases, a novel incommensurate phase 5a,ic appears. Its X-ray diffraction pattern consists of both 5a,u and 5a,2 periodicities which are incommensurate. The SA2 SAd transition line (for x < 0.24) corresponds to a continuous transition between the two phases. Other examples of the incommensurate and modulated smectic A phases are given in [4, 44]. 

A phenomenological model for frustrated smectics proposed that 2-D modulated smectic phases might arise as an escape from underlying incommensurability in the system [22,161,162]. The role of polar and steric molecular assymetry in smectic polymorphism has been comprehensively reviewed [23, 163]. The forms of the X-ray diffraction patterns from modulated and incommensurate smectic phases have been extensively discussed [20-23] and these papers should be consulted for earlier references and for details which will not be covered here. 

Modulated smectic phases are just one of a number of classes of frustrated smectic phases, all of which arise from the competition between different characteristic length scales but differ in the manner by which this frustration is relieved. In the incommensurate SmA phases the competing periodicities coexist along the layer normal and the first example of such a phase was observed for a nonsymmetric dimer, KI5 (see Fig. 1 g). In this phase the larger periodicity appears to correspond to the molec-... 

Note The phase was identified as polar tilted smectic (SMCP) phase. Originally only one By phase was proposed, but it turned out that they correspond to at least two different phases (Byj and By.n, where Byj is basically a columnar phase, and Byjj has modulated smectic layer structure. 

Figure 4.16. A helically modulated smectic-C liquid crystal the directions of both n and p vary spatially in a helical manner.

The most well-known and extensively studied noncentrosymmetric liquid crystalline phase is the smectic—C phase. The helically modulated smectic C system, with a spatially varying spontaneous polarization, is locally characterized by a C2 symmetry the average polarization of the bulk is still vanishing. By unwinding such a helical stmeture, the system behaves as a crystal with C2 point symmetry. Such unwound SmC phases possess sizable second-order nonlinear polarizabilities,with (2) ranging from 8 X 10 m/V for DOBAMBC to about 0.2 X 10 mA for o-nitroalkoxyphenyl-biphenyl-carboxylate. ... 

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