## Abstract

The unusual exhibition of a biaxial nematic phase in nonlinear thermotropic mesogens derived from the 2,5-oxadiazole biphenol (ODBP) core is placed in a general context; the uniaxial nematic phase of the prototypical rod-like mesogen *para*-quinquephenyl does not follow the classical mean-field behaviour of nematics, thus questioning the utility of such theories for quantitative predictions about biaxial nematics. The nuclear magnetic resonance spectra of labelled probe molecules dissolved in ODBP biaxial nematic phases suggest that a second critical rotation frequency, related to the differences in the transverse diamagnetic susceptibilities of the biaxial nematic, must be exceeded in order to create an aligned two-dimensional powder sample. Efforts to find higher viscosity and lower temperature biaxial nematics (with lower critical rotation rates) to confirm the above conjecture are described. Several chemical modifications of the ODBP mesogenic core are presented.

## 1. Introduction

The liquid state of molecular substances is frequently referred to as a ‘marginal state’ as its window of stability—the temperature–pressure domain that supports a condensed fluid phase—is limited relative to that of solids and gases (Barrat & Hansen 2003). In ordinary molecular liquids, fluid melts at atmospheric pressure, and there is a competition between short-range molecular packing (repulsive, excluded-volume interactions) and long-range intermolecular attraction (electrostatic interactions). The former imposes a very short-range ‘structure’ (a few molecular diameters) in the fluid (Chandler 1974; Chandler *et al*. 1983; Ziman 1979), while the latter causes the molecules to cohere and form the liquid state between the solid's melting point and the liquid's boiling point. The net result of these competitive interactions is a fluid phase with full rotational and translational symmetry, i.e. all the intensive physical attributes of the fluid (density, viscosity, thermal conductivity, dielectric or diamagnetic permittivity, refractive index, etc.) are invariant under arbitrary rotations and translations. However, in a rather esoteric subset of molecular liquids (anisotropic) attractive interactions and repulsive interactions conspire to enable varying degrees of translational and/or orientational molecular order to persist over macroscopic distances within a limited temperature range. In such ordered melts, thermotropic liquid crystals (LCs), the bulk fluid's intensive physical attributes, unlike isotropic liquids, are anisotropic exhibiting measurably different values along different directions in the LC. Such anisotropy in a fluid phase underlies the technologically important application of LCs in flat-panel displays.

The uniaxial nematic phase (N_{u}) is the simplest, translationally disordered fluid found in low molar mass LCs or mesophases. The N_{u} phase has a single director, ** n**, delineating the preferred alignment direction of the orientationally ordered molecules (mesogens). Arguably, the next simplest LC phase is the biaxial nematic phase (N

_{b}), a fluid characterized by three orthogonal directors—a primary director

**and two secondary directors**

*n***and**

*l***. In this mesophase, partial molecular orientational order is manifested in three dimensions without translational order. However, for more than three decades, the N**

*m*_{b}phase's existence in melts of ‘monomeric’ mesogens—discrete, single molecules as opposed to dimers, oligomers or polymers—was merely a hypothetical possibility inspired by a theoretical assessment of the consequences of low-symmetry, idealized, mesogen shapes by Freiser (1970). Herein, we contrast new experimental data for both the uniaxial and the biaxial nematics with a goal of gaining additional insights into those molecular characteristics that lend stability to the elusive N

_{b}phase.

## 2. Background

There are three general classes of thermotropic mesogens: (i) oblate, disc-shaped mesogens (*discotics*), (ii) prolate, rod-shaped mesogens (*calamitics*), and (iii) nonlinear, bent mesogens (colloquially termed *banana* or *boomerang* mesogens). Our focus is on the latter two classes represented by the linear calamitic mesogen, *para*-Quinquephenyl (PPPPP), and derivatives of the nonlinear boomerang mesogen derived from the heterocyclic three-ring compound 2,5-oxadiazole biphenol (ODBP). We employ deuterium nuclear magnetic resonance (^{2}H NMR) spectroscopy to characterize the mesogen orientational order in the liquid crystalline phases of PPPPP and ODBP mesogens, and thereby infer information about the symmetry of the phases. This entails relating microscopic, motionally averaged interactions—deuterium quadrupolar interactions in the form of quadrupolar splittings, Δ*ν*, observed in the ^{2}H NMR spectra—to observed macroscopic properties (Photinos 2003, ch. 12; Samulski 2003, ch. 13), and, in turn, this requires approximate mesogen structures and ensemble averages in order to derive macroscopic properties.

### (a) Uniaxial nematics

The nature of the approximations used to model LCs can be appreciated by considering a volume element of the uniaxial nematic phase idealized in figure 1. The primary director of the N_{u} phase, ** n**, is parallel to the

*z*-axis of the phase-fixed

**-frame, a principal axis system (PAS) dictated by the symmetry of the phase; the**

*XYZ***- and**

*X***-directions are equivalent in this apolar fluid with**

*Y**D*

_{∞h}symmetry. The absence of translational molecular order in the N

_{u}phase is indicated schematically by a random spatial arrangement of molecular centres (shaded circles), and the partial molecular orientational order is intimated by the quasi-parallel set of the individual mesogen principal axes, {

**}. The unit vectors**

*k***,**

*i***and**

*j***constitute a mesogen-fixed PAS. Since there is no preferential azimuthal ordering about**

*k***, the randomly distributed**

*k***- and**

*i***-axes are not shown in figure 1.**

*j*In the elementary cartoon (figure 1), there is the implicit assumption that ** k** is a well-defined indicator of mesogen orientational order. In fact,

**is not readily identified for typical calamitic mesogens, especially for those with a large number of internal degrees of freedom, i.e. mesogens with**

*k**n*conformational isomers, each specified by a unique set of bond dihedral angles {

*ϕ*

_{i}}

_{n}and a corresponding internal energy

*E*{

*ϕ*

_{i}}

_{n}. This ambiguity is apparent even for the relatively simple class of cyanobiphenyl mesogens. For example, the mesogen

*para*-Octyl-

*para*′-cyanobiphenyl (8CB) with an eight aliphatic carbon ‘tail’ appended to one end of the biphenyl ‘mesogenic core’, has

*n*≈175 distinct conformers in the rotational isomeric state description (Flory 1969) of conformers generated by setting the

*i*dihedral angles. Moreover, it is reasonable to expect that in low-symmetry conformers of 8CB, the location of the molecular director will depend on each distinct conformer's shape/polarizability, i.e. the conformer's interactions with its (average) neighbours in the uniaxial nematic. This conformation dependence is suggested in figure 2, where the location of

**will vary with each distinct 8CB aliphatic-tail conformation. In summary, the specification of**

*k***in the**

*k**n*th conformer depends on {

*ϕ*

_{i}}

_{n}and is not a static attribute of, for example, the lowest energy (

*E*{

*ϕ*

_{I}=0°}) all

*trans*conformation of 8CB. Such complications, we contend, have prevented a rigorous comparison of experiments that yield microscopic details about mesogen behaviour in the uniaxial nematic phase (e.g. NMR spectroscopy) with mean-field theory, especially theoretical predictions for the temperature dependence of mesogen orientational order.

### (b) Nematic mean field

In mean-field theoretical treatments of the N_{u} phase, molecular structural details are frequently idealized. The complement of nearest-neighbour ‘solvating’ mesogens is replaced by a generic average interaction, the so-called nematic mean field. Additionally, the detailed architecture of the ‘solute’ mesogen itself is usually disregarded. The symmetry of the mesogen is normally represented by the symmetry of its ‘statistical’ shape, and for calamitics, this shape is typically further idealized to a mere ellipsoid of revolution. Instead of considering the subtle differences in the orientational biasing of each distinct conformation of the actual flexible mesogen (Samulski 2003, ch. 13), using a conformation-dependent orientational distribution function, *f*_{n}(*Ω*), an average interaction of the idealized mesogen is formulated and a conformation-independent distribution, *f*(*Ω*), is employed. (Here, *Ω* represents the Euler angles relating the molecule-fixed ** ijk**-PAS to the macroscopic director-fixed

**-PAS.) In other words, the net result of these approximations is that the potential of mean torque acting on each conformation of the actual mesogen,**

*XYZ**V*

_{n}(

*Ω*), is replaced with a generic conformation-independent potential,

*V*(

*Ω*), acting on an idealized (cylindrically symmetric) particle. The corresponding orientational distribution,

*f*(

*Ω*), is independent of {

*ϕ*

_{i}}

_{n}, leading to a simple formal definition of the idealized mesogen's orientational order. The latter is specified with an order parameter, , the principle value of an order tensor, where the superscript ZZ refers to the symmetry axis of the uniaxial nematic's phase-fixed PAS and the subscript

*kk*specifies the principle component of the molecule-fixed PAS. For a uniaxial particle in a uniaxial phase, , and the azimuthal degeneracy (

*Ω*→

*θ*) leads to a simple expression for the orientational order parameter of the cylindrical particle Dunmur

*et al*. (2001).(2.1a)

(2.1b)As the simplified potential of mean torque *V*(*θ*) in equation (2.1*b*) is itself a function of the orientational order(2.2)where *A* specifies the strength of the potential. Equation (2.1*b*) is solved self-consistently to yield the well-known ‘Maier–Saupe’ theoretical temperature dependence of *S* (solid curve in figure 3; Dunmur *et al*. 2001). The experimental observable considered herein, the deuterium quadrupolar splitting, is related to *S* via(2.3)where 3e^{2}*qQ*/4*h* is the quadrupole coupling constant (defined for the C–D bond) and the factor *g*=*P*_{2}(cos *α*) accounts for the intramolecular geometry, namely the orientation (*α*) of the C–D bond direction (the axially symmetric principal quadrupolar interaction) relative to ** k**. (For flexible molecules,

*α*might vary with {

*ϕ*

_{i}}

_{n}, and consequently

*g*would have to be averaged over the intramolecular isomerization; Samulski 2003, ch. 13.)

NMR observations can exhibit sufficiently resolved Δ*ν* values to differentiate between models that explicitly include mesogen flexibility/shape and those that do not (Photinos *et al*. 1991). For example, some models employ a conformation-dependent coefficient *A*{*ϕ*_{i}}_{n} in equation (2.2), implying a weighted sum over *n* equations (equation (2.1*b*) weighted by a Boltzmann factor based on the internal energy *E*{*ϕ*_{i}}_{n}), and some models gloss over the conformation-dependent orientational biasing in a mean field. But a rigorous method for specifying the molecular director ** k** is lacking and limits most quantitative applications of the NMR method (Samulski 2003, ch. 13).

Finally, it should be recognized that low-symmetry solutes or mesogens in the highly symmetry uniaxial nematic phase will be subjected to different biasing forces on their molecular-fixed ** ijk**-PAS, i.e. biaxial molecular shapes in a uniaxial phase often exhibit biaxial

*molecular*order parameters (); this should not be confused with phase biaxiality ().

## 3. Results and discussion

### (a) para-Quinquephenyl

If ever there were a calamitic mesogen that corresponded to the approximations used to derive *S*, the rod-like thermotropic LC PPPPP (box 1) is one among them. This virtually cylindrically symmetric, polyaromatic molecule undergoes

ring-flips at elevated temperatures in the solid-state and then exhibits a high-temperature nematic phase that persists over a range of 37°C, and there is no ambiguity about the location of this mesogen's PAS; ** k** is coincident with the

*para*axis of PPPPP, the unique axis of this rod-like mesogen. Moreover, by exchanging the

*para*protons with deuterium, the essentially axially symmetric C–D quadrupolar interaction 3 e

^{2}

*h*is also coincident with the

*para*axis, hence

*α*=0 and

*g*(0)=1 in equation (2.3). Thus, the orientational order of

**, , can readily be obtained as a function of (reduced) temperature from the quadrupolar doublet observed in the**

*k*^{2}H NMR spectrum of the labelled PPPPP-d

_{2}. Such NMR data (Madsen

*et al*. in preparation) are shown in figure 3 and clearly are at variance with the mean-field predictions. In summary, we have an actual mesogen that closely approximates the idealized particle in the mean-field model of the uniaxial nematic phase, yet there is a significant discrepancy between experiment and theory.

### (b) Nonlinear ODBP mesogens

A decade ago, when stratified phases of nonlinear mesogens—the mischievously named ‘banana phases’—were studied intensively, we embarked on the synthesis of nonlinear LCs based on esters of 2,5-oxadiazole (box 2*a*). The results were a class of ‘boomerang-shaped’ mesogens, whose cores were nonlinear owing to the 2,5-substituted heterocycle's exocyclic bond angle (*θ*∼135°). We started with esters of oxadiazole biphenyl diacid (box 2*b*). Early conoscopic observations of freely suspended films of the smectic-A like phase of hexyloxybenzoate diester of the diacid (box 2*b*) suggested that the high-temperature orthogonal smectic phase was in fact biaxial (Semmler *et al*. 1998). (No banana phases (Pelzl *et al*. 1999) similar to those observed for bent-core mesogens with *θ*≈120° were observed.)

Lower temperature mesophases, characteristic of calamitic mesogens (nematic and tilted smectics), were obtained when the ester linkage was reversed by incorporation of the oxadiazole biphenol (box 2*c*) unit into the nonlinear core (Dingemans & Samulski 2000), and, subsequently, X-ray studies of the nematic phase of the boomerang mesogens indicated biaxiality in some of the oxadiazole biphenol (ODBP) derivatives (Acharya *et al*. 2003). NMR evidence finally provided unequivocal confirmation of the N_{b} phase in this class of nonlinear boomerang-shaped mesogens (Madsen *et al*. 2004). In the latter work, the high-symmetry (*D*_{6} _{h}), deuterium-labelled solute ‘probe’ molecule, hexamethylbenzene-d_{18} (HMB-d_{18}), exhibited a biaxial two-dimensional powder pattern in the doped nematic phase of boomerang mesogens the *para*-dodecyloxybenzoate diester of 2,5-bis(p-hydroxyphenyl)-1,3,4-oxadiazole (ODBP-Ph-OC_{12}; Box 3) and the corresponding *para*-heptylbenzoate diester (ODBP-Ph-C_{7}; Box 4). (The numbers below the phase map are the measured enthalpies (kJ mol^{−1}) from differential scanning calorimetry (DSC).)

Generally, the biaxiality can be determined if only two components of the order tensor, , are measured. By rotating the N_{b} phase rapidly about an axis perpendicular to the magnetic field ** B**, a two-dimensional powder pattern is generated. When the observed powder pattern exhibited by the probe HMB-d

_{18}in ODBP-Ph-C

_{7}is fitted quantitatively by theory that includes the effect of sidebands (Collings

*et al*. 1979; Photinos

*et al*. 1979), the fit yields a value for

*η*=0.11 (figure 4

*a*). The fit to the experimental line shape and the consideration of potential pitfalls in the simulations—non-ideal director distributions—has been described in detail elsewhere (Madsen & Samulski 2005). A quantitative fit of the powder pattern in a control experiment—the N

_{u}phase of terephthalylidene-bis-butylanilene (TBBA; Box 5) at a comparable temperature (

*T*=192°C)—shows that the phase biaxiality

*η*=0 in the uniaxial phase as expected.

The qualitatively different line shapes for the two nematic phases are attributed to differences in the response of rotating the N_{u} and the N_{b} phases in a magnetic field. In the N_{u} phase, the primary director ** n**, parallel to

**in the static sample, shows a resolved quadrupolar splitting (figure 4**

*B**b*). This simple spectrum is transformed into a powder pattern when the sample is spun about an axis perpendicular to

**. Above a critical rotation rate, locally**

*B***is distributed radially and uniformly in a plane normal to the rotation axis; the smallest (most negative) value of the phase's magnetic susceptibility, the**

*n***-component (or equivalently the**

*X***-component of the phase-fixed PAS for the uniaxial phase as**

*Y**Χ*

^{XX}=

*Χ*

^{YY}) is oriented along the rotation axis Σ. When the rotation rate is larger than the magnetic reorientation rate of the director, , both the

**- and**

*Y***-axes are radially distributed giving rise to the two-dimensional powder pattern NMR line shape, a superposition of quadrupolar splittings with magnitudes dependent on and . The ‘fine structure’ observed in the N**

*Z*_{u}phase of TBBA is a modulation of the static two-dimensional powder pattern, which occurs when the rotation rate is comparable to the magnitude of the quadrupolar splitting, and this fine structure varies with rotation rate. (Sample rotation puts an additional experimental constraint on these relatively high-temperature NMR experiments; the rotation rate, approximately 250 Hz, must be controlled to ±10 Hz during the signal acquisition, for approximately 2 h at each temperature.)

The situation is more complex in the lower symmetry N_{b} phase. The components of the transverse susceptibilities are not equivalent, *Χ*^{XX}≠*Χ*^{YY}. This implies that there should be two relaxation processes, each related to the magnetic torque(s) on the director(s) and the relevant LC phase viscosities that pertain to rotating the N_{b} phase in a magnetic field. These two relaxation processes are characterized by magnetic reorientational relaxation times *τ*_{Z}>*τ*_{Y}, corresponding to the relaxation of the primary director ** n** of the N

_{b}phase and the secondary director,

**, respectively, in the magnetic field. Qualitatively, for ‘intermediate’ rotation speeds (), the susceptibility differences between the transverse directions are not manifested; a uniform two-dimensional LC powder is not created in the rotating sample. The magnetic potential energy difference between the distinct**

*m***- and**

*X***-components of the biaxial phase may be small and there is a (weak) periodic, azimuthal magnetic torque about**

*Y***in the rotating sample, i.e. there is no steady-state preference for aligning the smallest susceptibility value**

*n**Χ*

^{XX}over that of

*Χ*

^{YY}along the rotation axis Σ. Uniform alignment (a two-dimensional powder with

**‖Σ) occurs only above a second critical rotation rate , characterizing the azimuthal magnetic relaxation rate of the secondary director**

*X***about**

*m***. We thus attribute the broad line shape in the spectrum of the rotating N**

*n*_{b}phase of ODBP-Ph-C

_{7}at intermediate rotation speeds () to the convolution of azimuthal disorder—a weighted superposition of all three of the inequivalent quadrupolar splittings proportional to , respectively—with the modulated sideband pattern. Efforts to confirm this conjecture experimentally, e.g. raising LC phase viscosities by lowering transition temperatures or sample rotation at higher rates , are underway.

### (c) More ODBP derivatives

There are multiple reasons to pursue more accessible (lower temperature) biaxial nematics. This includes the technologically important possibility of exploiting (for liquid crystal displays (LCDs)) the lower viscosities associated with E-field reorientation of the transverse directors of the N_{b} phase about a stationary primary director ** n**. The subtlety of the N

_{b}phase suggests that significant molecular structural modifications of the boomerang shape might impact deleteriously the stability of the biaxial phase. For this reason, we have pursued only those derivatives that leave the ODBP mesogenic core intact. One obvious group of ODBP derivatives to study is the homologous series. Figure 5 shows the phase transitions in the DSC traces of the symmetric homologues ODBP-Ph-O-C

_{n}. When the number of carbons,

*n*, in the mesogen's tails decreases, the stability (persistence) of the nematic phase increases; unfortunately

*T*

_{NI}also increases (to nearly 250°C for

*n*=6). Additionally, there are incompletely characterized smectic phases below the nematic phase in these homologues.

Substituting the oxazole heterocycle for the oxadiazole in ODBP mesogens lowers the *T*_{NI} transition, but the persistence of the biaxial nematic phase in such mesogens without an external field remains ambiguous (Olivares *et al*. 2003). We contrast the phase maps for the *n*=4 mesogens for both the ODBP (box 6) and the oxazole (box 7) cores, where the latter exhibits a 54°C lower *T*_{NI}.

In an another effort to lower the *T*_{NI} transition while preserving the N_{b} phase, we considered *α*-methyl-substituted tails, a structural modification that we used successfully to lower transition temperatures while preserving the subtle anticlinic smectic-C phase of 4-(1-methylheptyloxycarbonyl)-phenyl 4′-octyloxybiphenyl-4-carboxylate (MHPOBC) homologues (Thisayukta & Samulski 2004). Unfortunately, this substituted dimethyl tail completely suppressed the mesophase in the nonlinear ODBP molecules; see the simple melting transitions of the ODBP mesogens (box 8) and (box 9).

Recently, (Görtz & Goodby 2005) have reported on unsymmetrical homologues of the ODBP mesogens, but the *T*_{NI} transition was not particularly sensitive to the terminal structural modification. Increasing the size of the ODBP core by adding another aromatic ring (ODBP-OBn mesogens) suggests that the nature of the termini of the nonlinear core in this class of mesogens is a very important parameter for tuning the transition temperatures. The absence of an alkyl tail (box 10) on a terminal aromatic ring suppresses the nematic mesophase. The ODBP-Ph-OBn4 mesogens, with a butyl tail (box 11), has a very wide nematic range (132 °C), but the high nematic–isotropic temperature makes this nonlinear mesogen problematic for the NMR studies.

## 4. Concluding remarks

Understanding of the simplest ordered fluids, nematic LCs, continues to evolve. We have engaged in a search for new physical phenomena and insights via these two classes of nematics, the uniaxial and the biaxial. Observations on the temperature dependence of order in the ‘ideal’ rod-like mesogen PPPPP prompts basic theoretical questions pertinent to any orientationally ordered system. If we cannot describe such a simple system adequately, how do we confront more common situations, mesogens with much higher complexity? While some of the disparity between experiment and theory might be ascribed to the approximate statistical mechanical methods used to describe the mean field, the PPPPP data Madsen *et al*. (in preparation) should provide a minimal benchmark for evaluating models of the uniaxial nematic phase.

The discovery of the N_{b} phase in the ODBP monomeric calamitics has received considerable attention Luckhurst (2004, 2005). Relative to typical, biaxial-shaped (board-like) calamitic mesogens, the nonlinear ODBP boomerangs have, in addition to a biaxial shape and its associated anisotropic excluded-volume interactions, the added possibility of strong directional intermolecular associations originating from the oxadiazole heterocycle's large electric dipole moment (approx. 5 debye). The resulting negative dielectric anisotropy of ODBP biaxial nematics bears special importance for electro-optic switching, where reorienting a transverse director about an aligned major director ** n** might be used to control birefringence. Such sensitive rotation of the minor director

*about*the major director

**should allow higher speed and lower power consumption than conventional LCDs, which must overcome the viscous drag of reorienting**

*n***. Finally, searching for more tractable ODBP mesogens is challenging. Structural modifications routinely used to lower the transition temperatures for conventional calamitic mesogens have profound effects on the nonlinear ODBP mesogens, sometimes eliminating the mesophases altogether. Nevertheless, modest structural variations on the boomerang shape appear to uncover an increasingly rich mesomorphism in this class of polar, nonlinear mesogens.**

*n*## Discussion

S. T. Lagerwall (*The Royal Swedish Academy of Sciences, Sweden*). I am sure Ed Samulski is right that there is a biaxial short-range order in his nematics. In the same way, there is a biaxial short-range order in the smectic-A phase on top of the polar smectic-A phase of Wolfgang Weissflog's compounds. The lower-lying phase provides a hint as to the fluctuations in the higher-lying phase. The normal smectic-C phase has hexagonal short-range order. A theory explaining why biaxial long-range order is permitted once you quench translational fluctuations along one direction in space should be a good step forward in the understanding of the liquid crystalline state.

E. T. Samulski. I am suggesting that virtually *all* calamitic nematics—especially, those with statistically biaxial shapes and/or charge distributions—exhibit short-range biaxial order, even high above underlying (uniaxial or biaxial) smectic phases. However, the correlation length of such biaxial order is too small to have nematics manifest biaxiality in typical experimentally accessible properties. The ‘cylindrically symmetric’ mesogen *p*-quenquiphenyl would be an exception; its nematic phase would be uniaxial on any length-scale.

S. J. Picken (*TU Delft, The Netherlands*). You showed a homeotropic texture of your biaxial nematic compound, which appeared to be uniformly dark. I found this rather surprising, as I would expect to find a schlieren texture of the minor director if the major director is oriented along the layer normal in a homeotropic fashion.

E. T. Samulski. We refer to that texture as a ‘dark state’—a fortuitous director distribution (splay or chair-like) that appears homeotropic. This dark state appears to be stable at very specific sample thicknesses in wedge cells prepared for homeotropic textures. Generally, a schlieren texture is exhibited when we try to prepare homeotropic samples, and it presumably corresponds to a random planar distribution of the minor director. (See the discussion section in Madsen *et al*. (2004)).

A. Kornyshev (*Imperial College London, UK*). How would you call a system built of long molecules, whose rotation about a mean axis practically does not affect its interaction with electric field, but strongly affect its interaction with adjacent molecules. Would you call it biaxial?

E. T. Samulski. Calamitic nematics have a single (motionally averaged) value of the transverse component of their dielectric permittivity tensor. Even those nematics comprised of biaxial molecules having two distinguishable values of the transverse molecular polarizability do not exhibit any macroscopic dielectric anisotropy in the plane normal to the director. We call these nematics uniaxial even if there may be clusters of molecules having short-range, biased rotations about the long molecular axes (e.g. short-range biaxial ‘dynamic packing’). I would merely call these materials conventional uniaxial nematics. If, however, in such a phase with negative dielectric anisotropy, a transverse electric field coupled to the local transverse asymmetry of the locally biaxially packed clusters and caused the correlation length of such clusters to grow to mesocopic scales, one might have what could be termed a ‘field-induced biaxial nematic phase’.

C. R. Safinya (*Department of Materials, University of California at Santa Barbara, USA*). Could X-ray microdiffraction techniques be a good, quantitative way to measure biaxial correlation lengths in liquid crystalline phases of bent molecules?

E. T. Samulski. Yes. X-ray microdiffraction may possibly yield a measurement of the biaxial correlation length if the mean dimensions of the volume illuminated by the X-ray beam were comparable or smaller than the biaxial correlation length.

V. Percec (*Department of Chemistry, University of Pennsylvnia, USA*). Prior to your work, there were a lot of reports on attempts to get a biaxial nematic from combinations of disc-like and rod-like molecules. Were any of these phases biaxial nematics in your opinion?

E. T. Samulski. Simple mixtures of rod- and disc-like molecules typically phase separate although there are recent reports by Georg H. Mehl (personal communication) that he may have overcome the immiscibility problem. As for covalent rod–disc combinations, I am not aware of any reports of macroscopic evidence of biaxiality in those nematic phases.

M. A. Bates (*Department of Chemistry, University of York, UK*). Have you tried making mixtures of the original boomerang molecule and the molecular engineering one with a lower melting point?

E. T. Samulski. Martin, we are trying those experiments now. We have made lower melting, but non-mesogenic, boomerang molecules and our first attempts (1 : 1 mixtures) were not mesogenic. We need to begin more conservatively and look systematically at the phase diagram. We are also pursuing asymmetric boomerangs comprised of a mesogenic and non-mesogenic ‘tail’ in an attempt to get into more tractable temperature regimes.

## Acknowledgments

We thank Demetri Photinos for clarifying conversations and Tim Dunkin for help with the synthesis of the homologous series. This work was partially supported by NSF grants DMR-9971143 and CHE-0512495.

## Footnotes

↵† Present address: Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands.

One contribution of 18 to a Discussion Meeting Issue ‘New directions in liquid crystals’.

- © 2006 The Royal Society