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An Orientational Transition of Bent-Core Molecules in an Anisotropic Matrix

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Science  23 Jun 2000:
Vol. 288, Issue 5474, pp. 2184-2187
DOI: 10.1126/science.288.5474.2184

Abstract

We report the discovery of an orientational transition of bent-core molecules in a background anisotropic medium, in this case a smectic liquid crystal made of rod-like molecules. The resulting director is apolar in nature, and the medium can be described as an orthogonal biaxial smectic. The detailed phase diagram of mixtures of the two types of compounds revealed the induction of two liquid crystalline phases that are specific to compounds with bent-core molecules. The chemical nature of the bounding surface had a marked influence on the observed textures.

Thermotropic liquid crystals are states of soft condensed matter that exhibit a large variety of orderings of molecules with shape anisotropy (1, 2). Nematics (N) exhibit a long-range orientational order of rod-like or disc-like molecules about a common axis called the director, which has apolar symmetry. They are used in practically all commercial flat panel display devices. If the molecules are rod-like, the translational symmetry can be broken along one direction, giving rise to different types of smectic liquid crystals (1, 2). Although in general the molecules are not cylindrically symmetric, both N and smectic A (SmA) liquid crystals are uniaxial, characterized by two principal refractive indices.

Orientational transition of anisotropic molecules can also occur in a background medium. For example, colloidal suspensions like those of long polymeric molecules in isotropic solvents undergo an orientational transition to the N phase as the density is increased beyond a critical value (3). The possibility of getting a biaxial nematic liquid crystal (Nb) because of a mutual orientation of rod-like and disc-like molecules has been discussed in a large number of theoretical papers (1). However, an experimental investigation of such a mixture (4) showed only a coexistence of two uniaxial nematic liquid crystals, one richer in rods than the other, in agreement with the prediction of a molecular theory that properly took into account the chemical potentials of the two species (5). Nb and biaxial SmA (SmAb) phases are characterized by three directors and three refractive indices. They can be expected to have more complex electrooptic responses compared to the uniaxial phases, thus enlarging the potential for applications. The properties of the SmAbphase have been discussed theoretically (6), and the only known example of SmAb occurs in a polymeric system (7) upon cooling from the Nb phase.

In the past few years, a new type of molecular shape, namely that with a large bent core (with a bend angle of ∼120°; see Fig. 1), has been shown to give rise to novel liquid crystalline phases (8, 9). The packing of such highly biaxial bent-core (BC) but achiral molecules in smectic layers produces a spontaneous transverse polarization (8). Such molecules have also been called banana- or bow-shaped molecules in the literature (10). Further, the molecules tilt about the “arrow” directions of the bows, breaking the achiral symmetry of the layers, as was beautifully demonstrated by Link et al. (9). Thus, chirality and polarization appear to be intimately related in liquid crystals. The different possible relative arrangements of the polarization vectors, the tilting directions, and the chiral sense of successive layers can generate many different structures (9,11), and the discovery of Link et al. has led to intense activity in this field. Several hundred compounds with BC molecules have been synthesized (12), and up to five different liquid crystalline phases specific to such compounds have been identified. These are the lamellar B2 phase (12) studied in detail by Link et al.; the B1 phase, which exhibits a two-dimensional lattice (i.e., a columnar structure); and B5, B6, and B7, whose structures are not yet established. Studies on many homologous series have shown that the lower homologs (in the case illustrated in Fig. 1, if the end alkyl chains have five to seven carbon atoms, i.e., 1b to 1d) exhibit the B6 phase, a few mid-range homologs (1e to1g) the B1 phase, and the higher homologs the lamellar B2 phase. Most often a given homolog exhibits only one of these phases, with very few known examples of polymesomorphism (12) of the B liquid crystalline phases.

Figure 1

Molecular structure of the compounds used in the binary system studied: (1i) 1,3-phenylene-bis[4-(3-methylbenzoyloxy)]-4′-n-dodecylbiphenyl-4′-carboxylate; (2) 4-biphenylyl-4"-n-undecyloxybenzoate. Phase transition temperatures are, for 1i, crystal 114°C B2 128.5°C I and, for 2, crystal 98.5°C SmA2 109.5°C N 125.0°C I.

Here, we report on a new type of orientational transition of the BC molecules in an anisotropic SmA matrix made of rod-like molecules. Both the compounds were synthesized in our laboratory (13), and their molecular structures were engineered for a close matching of both the aromatic cores and the alkyl chains (Fig. 1). We show that rod-like molecules without a highly polar end group such as2 can exhibit the bilayer SmA2 phase, and that mixtures of 2 with BC molecules of 1i exhibit B2, B1, and B6 phases, such that an increase in the concentration of the rod-like molecules is equivalent to a shortening of the length of the alkyl chains in a homologous series of the BC molecules (as in going from 1i to1b). As the concentration is reduced below ∼13 mole percent (mol%) of 1i, there is a rearrangement of the1i molecules such that their symmetry axes (i.e., “arrows”) point along the layer normal of the SmA2 structure formed by the rod-like molecules. For mixtures of 2 with ∼4 to 13 mol% of 1i, an orientational ordering transition of the BC molecules in the smectic layers occurs, with the relevant director being orthogonal to that of the rod-like molecules, which gives rise to a biaxial smectic A2 (SmA2b) phase. There is a marked influence of the boundaries of the cell on the orientation of the BC molecules in the SmA2b liquid crystal, as revealed by its textures.

The rod-like molecule 2 has an alkyl chain only at one end of the aromatic moiety, thus making it biphilic in nature. X-ray scattering studies of the smectic, using an image plate, have shown a weak scattering near q = π/l (whereq is the wave vector and l is the molecular length), hence it has a bilayer SmA2 structure (14). Obviously the aromatic cores of adjacent layers would like to be in close proximity, giving rise to the SmA2 structure, which was found earlier only in compounds with the strongly polar cyano or nitro end groups and other dipoles in the aromatic core with an orientation opposite to that of the end-group dipole (1).

The compound 1i exhibits the B2 phase and shows characteristic textures. Electrooptic studies like those reported by Link et al. show that both homochiral and racemic states coexist and the tilt angle is ∼40°, which has also been confirmed by x-ray scattering studies. As the phase diagram (Fig. 2) shows, for compositions between 37 and 85 mol% 1i, the B1 phase with a two-dimensionally periodic structure is induced (14). For compositions between 13 and 37 mol%1i, the mixtures exhibit the B6 phase, which has a typical focal conic texture and is moderately switchable. Increasing the concentration of the rod-like molecules gives rise to phases that are exhibited by compounds with pure BC molecules having shorter chains. The obvious difference in the molecular shapes of the two components is reflected in a fairly large (∼10°) depression in the transition temperature to the isotropic phase (I phase) from both ends of the phase diagram (15).

Figure 2

Phase diagram of mixtures of compounds 2and 1i. Note that the B2-B1, B1-B6, and B6-SmA2btransition lines are vertical (15). First-order transition lines involving N, SmA2, SmA2b, and B6 as well as N, B6, B1, and I phases appear to meet at two points.

For the composition range of ∼4 to 13 mol% 1i, a homeotropically aligned liquid crystal sample can be obtained by treating the glass plates with a polymer having long pendant chains [such as octadecyl triethoxysilane (ODSE)]. The uniaxial nematic presents a dark field of view between crossed polarizers. However, strong fluctuations of the director can be seen, which abruptly cease at the N-SmA2 transition point. As the temperature is further lowered below another transition point, the sample exhibits a schlieren texture [that maps the director field, see (1)] between crossed polarizers, in which dark brushes emerge from some “points” (Fig. 3). schlieren textures are normally seen in the smectic C phase and are caused by curvature distortions in the c-vector field, which is the projection of the tilted director on the plane of the layers, and the points from which dark brushes emerge are projections of disclination lines (1, 2). Because of the polar nature of the cvector, only four-brush defects (i.e., of strength ±1, the sign signifying the relative rotation of polarizers and the dark brushes) are seen in that case. In the mixture studied by us, however, we see defects with two brushes (i.e., of strength ±½). This is possible only if the vector field that has curvature distortions (i) lies in planes parallel to the surfaces, and (ii) has an apolar character (16). The texture shows that the medium is an orthogonal biaxial smectic liquid crystal. In view of the SmA2 structure of the background medium with rod-like molecules, we designate the biaxial smectic phase in the mixture studied by us as SmA2b.

Figure 3

Schlieren texture of the SmA2bphase exhibited by the binary mixture with 8 mol% of the BC compound, taken between ODSE-coated glass plates with crossed polarizers. Note the large number of defects of strength ½.

The projected “length” (along the “bow string”) of the aromatic core of the BC molecule is ∼26 Å, which is comparable to the total length of the aromatic cores of a bilayer of the SmA2 background medium. If bows orient with the “arrows” lying in the smectic planes, they are likely to pack within a bilayer to give rise to a polar rather than an apolar vector field in the smectic planes (Fig. 4A). This is a possible arrangement in the B6 phase occurring in compositions above 13 mol% 1i (16). In the SmA2b phase, which has an apolar vector field, the BC molecules should be oriented with the “arrow” direction along the layer normal (Fig. 4B). The relevant lengths of the aromatic and aliphatic parts of the bows and single rods are “matched” in this configuration also. In view of the bilayer structure of the SmA2 phase, one half of the bilayer favors the “up” while the other favors the “down” orientation of the bows, so that the medium is not longitudinally ferroelectric. Thus, the BC molecules are orientationally disordered above the SmA2b-SmA2 transition point (T ub) and become ordered below it. The orientational transition takes place in the background matrix of liquid crystalline SmA2 phase made of rod-like molecules. Differential calorimetric studies (Pyris 1D, Perkin-Elmer) show that when the range of uniaxial SmA2 phase is small, the SmA2-SmA2b transition is weakly first order in nature, with a heat of transition ∼200 J/kg for a concentration of 8 mol% BC molecules (14).

Figure 4

Schematic diagram of the proposed arrangement of rod-like and BC molecules in (A) the B6 liquid crystal, (B) the SmA2b liquid crystal, and (C) the tilt of the BC molecule in a SmA2b layer adjacent to an untreated glass plate.

If the temperature is lowered at a rate of ∼1°/min in the SmA2b phase in cells constructed as described above, one can see waves of bright and dark patches moving across the sample. The precise origin of this effect is not clear to us; it may reflect the shear-induced reorientation of the director of the BC molecules due to movements of smectic layers in the sample. The texture is markedly different if the sample is prepared between cleaned but otherwise untreated slide and coverslip. The schlieren texture now has only ±1 defects with four brushes, which remains static when the temperature is lowered. This result shows the strong influence of the boundary conditions on this rather fragile phase. In the untreated cell, the aromatic cores of the BC molecules appear to be attracted to the silicon dioxide surfaces of the glass plates, and they can tilt near the surface to maximize the attractive energy (Fig. 4C). The in-plane director corresponding to the long (or bow-string) axis of the BC molecule is still in the plane of the layer, but the director â corresponding to the “arrows” is now tilted. The director deformation in â can only give rise to ±1 defects as in smectic C liquid crystals. The attraction of the BC molecules to the glass plates presumably also leads to a higher concentration near the surfaces than at the middle of the sample, which could explain the absence of the wave-like fluctuations arising from any movement of smectic layers near the center of the cell.

The uniaxial-to-biaxial transition of the medium has also been confirmed in a conoscopic study of an oriented sample (14). The uniaxial cross clearly splits as the temperature is lowered across the transition point. In cells treated for planar alignment, the SmA2 is reasonably well aligned but with some folds occurring along the rubbing direction. As the temperature is lowered across T ub, the number of folds increases perceptibly.

The biaxial smectic phase can be characterized by three principal refractive indices, μa, μb, and μc, where the suffixes a, b, and c refer to the polarization of the incident light beam being parallel to the “arrow” director â, the “bow-string” director, and the director perpendicular to the abplane, respectively. The biaxiality order parameter is reflected in the nonzero value of μb − μc. To measure it, we used a homeotropically aligned sample taken in a cell with one wall consisting of an indium tin oxide–coated transparent conducting glass plate with a gap of ∼1 mm. An electric field (∼200 V/mm̂ at 5 kHz) applied in the gap aligned the director along the field. We measured μb – μc using a quarter-wave plate compensator as a function of temperature, which was maintained to an accuracy of 10 mK using an INSTEC hot stage (14).

The orientational order parameter of the background SmA2 liquid crystal (which is given by 〈3 cos2 θ − 1〉/2, where θ is the angle made by the long axis of the rod with the layer normal) is not expected to vary much with temperature. The biaxiality order parameter of the BC molecules can then be written asEmbedded Image(1)where φ is the azimuthal angle made by the long axis of the BC molecule with the director.

For the alignment of the BC molecules as shown in Fig. 4B, we can estimate the expected values of μb − μc using the polarizabilities of the two arms of the BC molecules and those of the background rod-like molecules, and the composition of the mixture. Assuming η to be ∼0.3, we get μb – μc ≈ 0.007 for a concentration of 4.5% of the BC molecules, a value close to that measured at T ubT ≈ 10°C. However, if the BC molecules are vertically aligned, as in Fig. 4A, the value of μa – μcwould be about one-third as great. The birefringence data in the temperature range of T ub toT ub – 0.15° were fitted to the expressionEmbedded Image(2)using a nonlinear least squares fitting procedure (where C is a proportionality constant and β is the order parameter critical index). We find that β ≈ 0.79 for the mixture with 4.5 mol% BC molecules and 0.56 for the mixture with 8 mol% BC molecules. One would have expected that the ordering transition should follow the xy model, in which case β should be ∼0.35 (17). We believe that the higher measured values reflect the fact that the phase diagram of T ubversus concentration (Fig. 2) tends to have an almost vertical slope at lower concentrations of the BC molecules. It is known from studies of systems showing re-entrant phases (18) that the critical index could then double for essentially geometric reasons. As the concentration of the BC compound increases, the index β decreases. However, the concentration range over which the SmA2b phase occurs is relatively small, and the slope of the transition line is not small enough to get the expected xy value.

It would be interesting to look for this transition in other systems with the hope of widening the range of occurrence of the biaxial smectic phase. It would then be possible to study many physical properties of the system, which has an almost ideal xycharacter. A similar transition could occur in bilayer membranes, in which the strong fluctuations of the two-dimensional system can be expected to have a bearing on the problem.

  • * To whom correspondence should be addressed. E-mail: nvmadhu{at}rri.ernet.in

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