uniaxial and biaxial nematic liquid crystals

October 2006, published 15, doi: 10.1098/rsta.2006.1846364 2006 Phil. Trans. R. Soc. A

T.J Dingemans, L.A Madsen, N.A Zafiropoulos, Wenbin Lin and E.T Samulski Uniaxial and biaxial nematic liquid crystals

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Uniaxial and biaxial nematic liquid crystals

BY T. J. DINGEMANS†, L. A. MADSEN, N. A. ZAFIROPOULOS,

WENBIN LIN AND E. T. SAMULSKI*

Department of Chemistry, University of North Carolina, Chapel Hill,NC 27599-3290, USA

The unusual exhibition of a biaxial nematic phase in nonlinear thermotropic mesogensderived from the 2,5-oxadiazole biphenol (ODBP) core is placed in a general context; theuniaxial nematic phase of the prototypical rod-like mesogen para-quinquephenyl doesnot follow the classical mean-field behaviour of nematics, thus questioning the utility ofsuch theories for quantitative predictions about biaxial nematics. The nuclear magneticresonance spectra of labelled probe molecules dissolved in ODBP biaxial nematic phasessuggest that a second critical rotation frequency, related to the differences in thetransverse diamagnetic susceptibilities of the biaxial nematic, must be exceeded in orderto create an aligned two-dimensional powder sample. Efforts to find higher viscosity andlower temperature biaxial nematics (with lower critical rotation rates) to confirm theabove conjecture are described. Several chemical modifications of the ODBP mesogeniccore are presented.

Keywords: liquid crystal; nonlinear mesogen; nematic; NMR

On

*A†Pr1, 2

1. Introduction

The liquid state of molecular substances is frequently referred to as a‘marginal state’ as its window of stability—the temperature–pressure domainthat supports a condensed fluid phase—is limited relative to that of solids andgases (Barrat & Hansen 2003). In ordinary molecular liquids, fluid melts atatmospheric pressure, and there is a competition between short-rangemolecular packing (repulsive, excluded-volume interactions) and long-rangeintermolecular attraction (electrostatic interactions). The former imposes avery short-range ‘structure’ (a few molecular diameters) in the fluid (Chandler1974; Chandler et al. 1983; Ziman 1979), while the latter causes the moleculesto cohere and form the liquid state between the solid’s melting point and theliquid’s boiling point. The net result of these competitive interactions is a fluidphase with full rotational and translational symmetry, i.e. all the intensivephysical attributes of the fluid (density, viscosity, thermal conductivity,dielectric or diamagnetic permittivity, refractive index, etc.) are invariantunder arbitrary rotations and translations. However, in a rather esoteric

Phil. Trans. R. Soc. A (2006) 364, 2681–2696

doi:10.1098/rsta.2006.1846

Published online 21 August 2006

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

uthor for correspondence ([email protected]).esent address: Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg629 HS Delft, The Netherlands.

2681 q 2006 The Royal Society



T. J. Dingemans and others2682


subset of molecular liquids (anisotropic) attractive interactions and repulsiveinteractions conspire to enable varying degrees of translational and/ororientational molecular order to persist over macroscopic distances within alimited 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 directionsin the LC. Such anisotropy in a fluid phase underlies the technologicallyimportant application of LCs in flat-panel displays.

The uniaxial nematic phase (Nu) is the simplest, translationally disorderedfluid found in low molar mass LCs or mesophases. The Nu phase has a singledirector, n, delineating the preferred alignment direction of the orientationallyordered molecules (mesogens). Arguably, the next simplest LC phase is thebiaxial nematic phase (Nb), a fluid characterized by three orthogonaldirectors—a primary director n and two secondary directors l and m. Inthis mesophase, partial molecular orientational order is manifested in threedimensions without translational order. However, for more than three decades,the Nb phase’s existence in melts of ‘monomeric’ mesogens—discrete, singlemolecules as opposed to dimers, oligomers or polymers—was merely ahypothetical possibility inspired by a theoretical assessment of the con-sequences of low-symmetry, idealized, mesogen shapes by Freiser (1970).Herein, we contrast new experimental data for both the uniaxial and thebiaxial nematics with a goal of gaining additional insights into those molecularcharacteristics that lend stability to the elusive Nb 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 boomerangmesogens). Our focus is on the latter two classes represented by the linearcalamitic mesogen, para-Quinquephenyl (PPPPP), and derivatives of thenonlinear boomerang mesogen derived from the heterocyclic three-ringcompound 2,5-oxadiazole biphenol (ODBP). We employ deuterium nuclearmagnetic resonance (2H NMR) spectroscopy to characterize the mesogenorientational order in the liquid crystalline phases of PPPPP and ODBPmesogens, and thereby infer information about the symmetry of the phases.This entails relating microscopic, motionally averaged interactions—deuteriumquadrupolar interactions in the form of quadrupolar splittings, Dn, observed inthe 2H NMR spectra—to observed macroscopic properties (Photinos 2003, ch.12; Samulski 2003, ch. 13), and, in turn, this requires approximate mesogenstructures and ensemble averages in order to derive macroscopic properties.

(a ) Uniaxial nematics

The nature of the approximations used to model LCs can be appreciated byconsidering a volume element of the uniaxial nematic phase idealized infigure 1. The primary director of the Nu phase, n, is parallel to the z-axis ofthe phase-fixed XYZ-frame, a principal axis system (PAS) dictated by thesymmetry of the phase; the X- and Y-directions are equivalent in this apolar

Phil. Trans. R. Soc. A (2006)



Figure 1. Schematic illustration of a cubic volume element of the uniaxial nematic phase; theorientations of abstracted mesogens, with centres of mass (shaded circles), are represented by eachmesogen’s principal axis, k.

2683Uniaxial and biaxial nematics


fluid with DNh symmetry. The absence of translational molecular order in theNu phase is indicated schematically by a random spatial arrangement ofmolecular centres (shaded circles), and the partial molecular orientationalorder is intimated by the quasi-parallel set of the individual mesogen principalaxes, {k}. The unit vectors i, j and k constitute a mesogen-fixed PAS. Sincethere is no preferential azimuthal ordering about k, the randomly distributedi - and j -axes are not shown in figure 1.

In the elementary cartoon (figure 1), there is the implicit assumption that kis a well-defined indicator of mesogen orientational order. In fact, k is notreadily identified for typical calamitic mesogens, especially for those with alarge number of internal degrees of freedom, i.e. mesogens with nconformational isomers, each specified by a unique set of bond dihedral angles{fi}n and a corresponding internal energy E{fi}n. This ambiguity is apparenteven for the relatively simple class of cyanobiphenyl mesogens. For example,the mesogen para-Octyl-para0-cyanobiphenyl (8CB) with an eight aliphaticcarbon ‘tail’ appended to one end of the biphenyl ‘mesogenic core’, has nz175distinct conformers in the rotational isomeric state description (Flory 1969) ofconformers generated by setting the i dihedral angles. Moreover, it isreasonable to expect that in low-symmetry conformers of 8CB, the locationof the molecular director will depend on each distinct conformer’s shape/polarizability, i.e. the conformer’s interactions with its (average) neighbours inthe uniaxial nematic. This conformation dependence is suggested in figure 2,where the location of k will vary with each distinct 8CB aliphatic-tailconformation. In summary, the specification of k in the nth conformer dependson {fi}n and is not a static attribute of, for example, the lowest energy(E{fIZ08}) all trans conformation of 8CB. Such complications, we contend,have prevented a rigorous comparison of experiments that yield microscopic




Figure 2. An arbitrary conformation of the 8CB mesogen. (a) Ball-and-stick representation andspace-filling van der Waals surface wherein the orientation of the molecular principal axis k forthis particular conformation of 8CB is not coincident with the para axis of the biphenyl core.(b) Para-Quinquephenyl (PPPPP) mesogen ball-and-stick representation and van der Waalssurface; k is readily identified with the para axis of the ‘rigid’ quinquephenyl mesogen.



details about mesogen behaviour in the uniaxial nematic phase (e.g. NMRspectroscopy) with mean-field theory, especially theoretical predictions for thetemperature dependence of mesogen orientational order.

(b ) Nematic mean field

In mean-field theoretical treatments of the Nu phase, molecular structuraldetails are frequently idealized. The complement of nearest-neighbour‘solvating’ mesogens is replaced by a generic average interaction, the so-callednematic mean field. Additionally, the detailed architecture of the ‘solute’mesogen itself is usually disregarded. The symmetry of the mesogen isnormally represented by the symmetry of its ‘statistical’ shape, and forcalamitics, this shape is typically further idealized to a mere ellipsoid ofrevolution. Instead of considering the subtle differences in the orientationalbiasing of each distinct conformation of the actual flexible mesogen (Samulski2003, ch. 13), using a conformation-dependent orientational distributionfunction, fn(U), an average interaction of the idealized mesogen is formulatedand a conformation-independent distribution, f (U), is employed. (Here, Urepresents the Euler angles relating the molecule-fixed ijk-PAS to themacroscopic director-fixed XYZ-PAS.) In other words, the net result ofthese approximations is that the potential of mean torque acting on eachconformation of the actual mesogen, Vn(U), is replaced with a genericconformation-independent potential, V(U), acting on an idealized (cylindricallysymmetric) particle. The corresponding orientational distribution, f (U), isindependent of {fi}n, leading to a simple formal definition of the idealizedmesogen’s orientational order. The latter is specified with an order parameter,ShSk hSZZ

kk , the principle value of an order tensor, where the superscript ZZrefers to the symmetry axis of the uniaxial nematic’s phase-fixed PAS and thesubscript kk specifies the principle component of the molecule-fixed PAS. Fora uniaxial particle in a uniaxial phase, SXX

kk ZSYYkk ZKð1=2ÞSZZ

kk , and theazimuthal degeneracy (U/q) leads to a simple expression for the orientational




0

0.1

0.2

0.3

0.4

0.5

0.6

0.95 0.97 0.99T/TNI

orde

r pa

ram

eter

, S

0

40

80

120

160

quad

rupo

le s

plitt

ing

(kH

z)

Figure 3. The theoretical predictions for S versus reduced temperature (T/TNI), where TNI is thenematic–isotropic transition temperature (solid curve; Dunmur et al. 2001); experimental orderparameter (open circles) for PPPPP-d2

10.



order parameter of the cylindrical particle Dunmur et al. (2001).

S Z

ðP2ðcos qÞf ðqÞsin q dq ð2:1aÞ

Z

Ð12 ð3 cos2qK1ÞeKV ðqÞ=kBTsin q dqÐ

eKV ðqÞ=kBTsin q dq: ð2:1bÞ

As the simplified potential of mean torque V(q) in equation (2.1b) is itself afunction of the orientational order

V ðqÞZKA

2ð3 cos2qK1ÞS; ð2:2Þ

where A specifies the strength of the potential. Equation (2.1b) is solved self-consistently to yield the well-known ‘Maier–Saupe’ theoretical temperaturedependence of S (solid curve in figure 3; Dunmur et al. 2001). Theexperimental observable considered herein, the deuterium quadrupolarsplitting, is related to S via

DnZK3 e2qQ

2hgS; ð2:3Þ

where 3 e2qQ/4h is the quadrupole coupling constant (defined for the C–Dbond) and the factor gZP2(cos a) accounts for the intramolecular geometry,namely the orientation (a) of the C–D bond direction (the axially symmetricprincipal quadrupolar interaction) relative to k. (For flexible molecules, amight vary with {fi}n, and consequently g would have to be averaged over theintramolecular isomerization; Samulski 2003, ch. 13.)

NMR observations can exhibit sufficiently resolved Dn values to differentiatebetween models that explicitly include mesogen flexibility/shape and those thatdo not (Photinos et al. 1991). For example, some models employ a conformation-dependent coefficient A{fi}n in equation (2.2), implying a weighted sum over nequations (equation (2.1b) weighted by a Boltzmann factor based on the internalenergy E{fi}n), and some models gloss over the conformation-dependent






orientational biasing in a mean field. But a rigorous method for specifying themolecular director k is lacking and limits most quantitative applications of theNMR method (Samulski 2003, ch. 13).

Finally, it should be recognized that low-symmetry solutes or mesogens in thehighly symmetry uniaxial nematic phase will be subjected to different biasingforces on their molecular-fixed ijk -PAS, i.e. biaxial molecular shapes in auniaxial phase often exhibit biaxial molecular order parameters (SZZ

ii sSZZjj ); this

should not be confused with phase biaxiality (SYYkk sSXX

kk ).

3. Results and discussion

(a ) para-Quinquephenyl

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

I N ring-flips Cr427°C 390°C ~350°C

Box 1.

ring-flips at elevated temperatures in the solid-state and then exhibits a high-temperature nematic phase that persists over a range of 378C, and there is noambiguity about the location of this mesogen’s PAS; k is coincident with the paraaxis of PPPPP, the unique axis of this rod-like mesogen. Moreover, byexchanging the para protons with deuterium, the essentially axially symmetricC–D quadrupolar interaction 3 e2qQ/4h is also coincident with the para axis,hence aZ0 and g(0)Z1 in equation (2.3). Thus, the orientational order of k,SZZkk hSk hS, can readily be obtained as a function of (reduced) temperature

from the quadrupolar doublet observed in the 2H NMR spectrum of the labelledPPPPP-d2. Such NMR data (Madsen et al. in preparation) are shown in figure 3and clearly are at variance with the mean-field predictions. In summary, we havean actual mesogen that closely approximates the idealized particle in the mean-field model of the uniaxial nematic phase, yet there is a significant discrepancybetween experiment and theory.

(b ) Nonlinear ODBP mesogens

A decade ago, when stratified phases of nonlinear mesogens—the mischie-vously named ‘banana phases’—were studied intensively, we embarked on thesynthesis of nonlinear LCs based on esters of 2,5-oxadiazole (box 2a). The resultswere a class of ‘boomerang-shaped’ mesogens, whose cores were nonlinear owingto the 2,5-substituted heterocycle’s exocyclic bond angle (qw1358). We startedwith esters of oxadiazole biphenyl diacid (box 2b). Early conoscopic observations




–6000 –4000 –2000 0 2000 4000 6000

(a)

(b)

(c)

Figure 4. 2H NMR spectrum of nematics containing the probe HMB-d18. (a) ODBP-Ph-C7 inits Nb phase at TZ1748C; open circles are from a fit with hZ0.11, the sample is spinning atapproximately 230 Hz about an axis perpendicular to the spectrometer magnetic field. (b)Static spectrum of ODBP-Ph-C7 in its Nb phase. (c) TBBA in its Nu phase at TZ1928C(grey), simulation from a fit with hZ0.0 (black), the sample is spinning at approximately240 Hz. Note that the addition of HMB-d18 depresses the N–I transition temperatures byapproximately 58C.



of freely suspended films of the smectic-A like phase of hexyloxybenzoatediester of the diacid (box 2b) suggested that the high-temperature orthogonalsmectic phase was in fact biaxial (Semmler et al. 1998). (No banana phases (Pelzlet al. 1999) similar to those observed for bent-core mesogens with qz1208were observed.)

NN

O

e ~135˚

NN

O

OH

O

HO

O

NN

OOHHO

(a) (b) (c)

Box 2.






Lower temperature mesophases, characteristic of calamitic mesogens (nematicand tilted smectics), were obtained when the ester linkage was reversed byincorporation of the oxadiazole biphenol (box 2c) unit into the nonlinear core(Dingemans & Samulski 2000), and, subsequently, X-ray studies of the nematicphase of the boomerang mesogens indicated biaxiality in some of the oxadiazolebiphenol (ODBP) derivatives (Acharya et al. 2003). NMR evidence finallyprovided unequivocal confirmation of the Nb phase in this class of nonlinearboomerang-shaped mesogens (Madsen et al. 2004). In the latter work, the high-symmetry (D6 h), deuterium-labelled solute ‘probe’ molecule, hexamethyl-benzene-d18 (HMB-d18), exhibited a biaxial two-dimensional powder pattern inthe doped nematic phase of boomerang mesogens the para-dodecyloxybenzoatediester of 2,5-bis(p-hydroxyphenyl)-1,3,4-oxadiazole (ODBP-Ph-OC12; Box 3)and the corresponding para-heptylbenzoate diester (ODBP-Ph-C7; Box 4). (Thenumbers below the phase map are the measured enthalpies (kJ molK1) fromdifferential scanning calorimetry (DSC).)

NN

OOO

OO

OC12H25C12H25O

ODBP-Ph-OC12 (4)

I N SmC SmX204˚C 193˚C 184˚C 148˚C

–0.3–4.7 –25.5SmY

141˚C

–0.3SmZ Cr

104˚C

–0.9 –0.1

Box 3.

NN

OOO

OO

C7H15C7H15

ODBP-Ph-C7 (5)

I N SmX SmY Cr222˚C 173˚C 166˚C 148˚C

–0.7 –10.6 –25.3

Box 4.

Generally, the biaxiality hZSXXkk KSYY

kk can be determined if only two

components of the order tensor, SZZkk ; SYY

kk , are measured. By rotating the Nb

phase rapidly about an axis perpendicular to the magnetic field B, atwo-dimensional powder pattern is generated. When the observed powderpattern exhibited by the probe HMB-d18 in ODBP-Ph-C7 is fitted quantitatively




80

crystal

ODBP-Ph-O-Cn

isotropicsmectics

nematic6

7

8

9

10

11

12

250˚C

n

Figure 5. Transition temperatures (nematic ranges) for the homologous series ODBP-Ph-O-Cn.



by theory that includes the effect of sidebands (Collings et al. 1979; Photinoset al. 1979), the fit yields a value for hZ0.11 (figure 4a). The fit to theexperimental line shape and the consideration of potential pitfalls in thesimulations—non-ideal director distributions—has been described in detailelsewhere (Madsen & Samulski 2005). A quantitative fit of the powder patternin a control experiment—the Nu phase of terephthalylidene-bis-butylanilene(TBBA; Box 5) at a comparable temperature (TZ1928C)—shows that the phasebiaxiality hZ0 in the uniaxial phase as expected.

N

N C4H9

C4H9

TBBA (6)

I N SmA SmC235˚C 193˚C 172˚C 144˚C

G89˚C

H73˚C

Cr

Box 5.






The qualitatively different line shapes for the two nematic phases areattributed to differences in the response of rotating the Nu and the Nb phases in amagnetic field. In the Nu phase, the primary director n, parallel to B in the staticsample, shows a resolved quadrupolar splitting (figure 4b). This simple spectrumis transformed into a powder pattern when the sample is spun about an axisperpendicular to B. Above a critical rotation rate, locally n is distributedradially and uniformly in a plane normal to the rotation axis; the smallest (mostnegative) value of the phase’s magnetic susceptibility, the X-component (orequivalently the Y-component of the phase-fixed PAS for the uniaxial phase as

cXXZcYY) is oriented along the rotation axis S. When the rotation rate is largerthan the magnetic reorientation rate of the director, tK1

Z , both the Y- and Z-axesare radially distributed giving rise to the two-dimensional powder pattern NMRline shape, a superposition of quadrupolar splittings with magnitudes dependent

on SZZkk and SYY

kk ZKð1=2ÞSZZkk . The ‘fine structure’ observed in the Nu 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 thequadrupolar splitting, and this fine structure varies with rotation rate. (Samplerotation puts an additional experimental constraint on these relatively high-temperature NMR experiments; the rotation rate, approximately 250 Hz, mustbe controlled to G10 Hz during the signal acquisition, for approximately 2 h ateach temperature.)

The situation is more complex in the lower symmetry Nb phase. Thecomponents of the transverse susceptibilities are not equivalent, cXXscYY.This implies that there should be two relaxation processes, each related to themagnetic torque(s) on the director(s) and the relevant LC phase viscositiesthat pertain to rotating the Nb phase in a magnetic field. These two relaxationprocesses are characterized by magnetic reorientational relaxation times tZOtY, corresponding to the relaxation of the primary director n of the Nb phaseand the secondary director, m, respectively, in the magnetic field.Qualitatively, for ‘intermediate’ rotation speeds (tK1

Z !R!tK1Y ), the suscep-

tibility differences between the transverse directions are not manifested; auniform two-dimensional LC powder is not created in the rotating sample. Themagnetic potential energy difference between the distinct X- and Y-components of the biaxial phase may be small and there is a (weak) periodic,azimuthal magnetic torque about n in the rotating sample, i.e. there is nosteady-state preference for aligning the smallest susceptibility value cXX overthat of cYY along the rotation axis S. Uniform alignment (a two-dimensionalpowder with XkS) occurs only above a second critical rotation rate ROtK1

Y ,characterizing the azimuthal magnetic relaxation rate of the secondarydirector m about n. We thus attribute the broad line shape in the spectrumof the rotating Nb phase of ODBP-Ph-C7 at intermediate rotation speeds(tK1

Z !R!tK1Y ) to the convolution of azimuthal disorder—a weighted super-

position of all three of the inequivalent quadrupolar splittings proportional toSXXkk ; SYY

kk ;SZZkk , 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 ROtK1Y ,

are underway.






(c ) More ODBP derivatives

There are multiple reasons to pursue more accessible (lower temperature)biaxial nematics. This includes the technologically important possibility ofexploiting (for liquid crystal displays (LCDs)) the lower viscosities associatedwith E-field reorientation of the transverse directors of the Nb phase abouta stationary primary director n. The subtlety of the Nb phase suggeststhat significant molecular structural modifications of the boomerang shapemight impact deleteriously the stability of the biaxial phase. For thisreason, we have pursued only those derivatives that leave the ODBPmesogenic core intact. One obvious group of ODBP derivatives to study isthe homologous series. Figure 5 shows the phase transitions in the DSC tracesof the symmetric homologues ODBP-Ph-O-Cn. When the number of carbons,n, in the mesogen’s tails decreases, the stability (persistence) of the nematicphase increases; unfortunately TNI also increases (to nearly 2508C for nZ6).Additionally, there are incompletely characterized smectic phases below thenematic phase in these homologues.

Substituting the oxazole heterocycle for the oxadiazole in ODBP mesogenslowers the TNI transition, but the persistence of the biaxial nematic phase insuch mesogens without an external field remains ambiguous (Olivares et al.2003). We contrast the phase maps for the nZ4 mesogens for both theODBP (box 6) and the oxazole (box 7) cores, where the latter exhibits a548C lower TNI.

NN

OOO

OO

OC4H9C4H9O

ODBP-Ph-OC4 (7)

Cr N I280˚C193˚C

Box 6.

N

OOO

OO

OC4H9C4H9O

OxBP-Ph-OC4 (8)

Cr N I226˚C191˚C

Box 7.






In an another effort to lower the TNI transition while preserving the Nb phase,we considered a-methyl-substituted tails, a structural modification that we usedsuccessfully to lower transition temperatures while preserving the subtleanticlinic smectic-C phase of 4-(1-methylheptyloxycarbonyl)-phenyl 4 0-octyloxybiphenyl-4-carboxylate (MHPOBC) homologues (Thisayukta & Samulski 2004).Unfortunately, this substituted dimethyl tail completely suppressed themesophase in the nonlinear ODBP molecules; see the simple melting transitionsof the ODBP mesogens (box 8) and (box 9).

NN

OOO

OO

OO

ODBP-Ph-Odm (10)

I Cr82˚C

122˚C

Box 9.

NN

OOO

OO

OO

ODBP-Ph-Odm (9)

I Cr119˚C

126˚C

Box 8.

Recently, (Gortz & Goodby 2005) have reported on unsymmetricalhomologues of the ODBP mesogens, but the TNI transition was notparticularly sensitive to the terminal structural modification. Increasing thesize of the ODBP core by adding another aromatic ring (ODBP-OBnmesogens) suggests that the nature of the termini of the nonlinear core inthis class of mesogens is a very important parameter for tuning the transitiontemperatures. The absence of an alkyl tail (box 10) on a terminal aromaticring suppresses the nematic mesophase. The ODBP-Ph-OBn4 mesogens, witha butyl tail (box 11), has a very wide nematic range (132 8C), but the highnematic–isotropic temperature makes this nonlinear mesogen problematic forthe NMR studies.




NN

OOO

OO

OO

ODBP-Ph-OBn4 (12)

Cr N I290˚C173˚C

Box 11.

NN

OOO

OO

OO

ODBP-Ph-OBn (11)

I Cr116˚C

179˚C

Box 10.



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 thesetwo classes of nematics, the uniaxial and the biaxial. Observations on thetemperature dependence of order in the ‘ideal’ rod-like mesogen PPPPP promptsbasic theoretical questions pertinent to any orientationally ordered system. If wecannot describe such a simple system adequately, how do we confront morecommon situations, mesogens with much higher complexity? While some of thedisparity between experiment and theory might be ascribed to the approximatestatistical mechanical methods used to describe the mean field, the PPPPP dataMadsen et al. (in preparation) should provide a minimal benchmark forevaluating models of the uniaxial nematic phase.

The discovery of the Nb phase in the ODBP monomeric calamitics hasreceived considerable attention Luckhurst (2004, 2005). Relative to typical,biaxial-shaped (board-like) calamitic mesogens, the nonlinear ODBP boomer-angs have, in addition to a biaxial shape and its associated anisotropic excluded-volume interactions, the added possibility of strong directional intermolecularassociations originating from the oxadiazole heterocycle’s large electric dipolemoment (approx. 5 debye). The resulting negative dielectric anisotropy of ODBPbiaxial nematics bears special importance for electro-optic switching, wherereorienting a transverse director about an aligned major director n might be used






to control birefringence. Such sensitive rotation of the minor director about themajor director n should allow higher speed and lower power consumption thanconventional LCDs, which must overcome the viscous drag of reorienting n.Finally, searching for more tractable ODBP mesogens is challenging. Structuralmodifications routinely used to lower the transition temperatures for conven-tional calamitic mesogens have profound effects on the nonlinear ODBPmesogens, sometimes eliminating the mesophases altogether. Nevertheless,modest structural variations on the boomerang shape appear to uncover anincreasingly rich mesomorphism in this class of polar, nonlinear mesogens.

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.

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Discussion

S. T. LAGERWALL (The Royal Swedish Academy of Sciences, Sweden). I am sureEd Samulski is right that there is a biaxial short-range order in his nematics. Inthe same way, there is a biaxial short-range order in the smectic-A phase on topof 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. Thenormal smectic-C phase has hexagonal short-range order. A theory explainingwhy biaxial long-range order is permitted once you quench translationalfluctuations along one direction in space should be a good step forward in theunderstanding 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—exhibitshort-range biaxial order, even high above underlying (uniaxial or biaxial)smectic phases. However, the correlation length of such biaxial order is too smallto have nematics manifest biaxiality in typical experimentally accessibleproperties. The ‘cylindrically symmetric’ mesogen p-quenquiphenyl would bean exception; its nematic phase would be uniaxial on any length-scale.

S. J. PICKEN (TU Delft, The Netherlands). You showed a homeotropic texture ofyour biaxial nematic compound, which appeared to be uniformly dark. I found thisrather surprising, as Iwould expect tofinda schlieren texture of theminordirector ifthe 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 directordistribution (splay or chair-like) that appears homeotropic. This dark stateappears to be stable at very specific sample thicknesses in wedge cells preparedfor homeotropic textures. Generally, a schlieren texture is exhibited when we tryto prepare homeotropic samples, and it presumably corresponds to a randomplanar distribution of the minor director. (See the discussion section in Madsenet al. (2004)).


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A. KORNYSHEV (Imperial College London, UK). How would you call a systembuilt of long molecules, whose rotation about a mean axis practically does notaffect its interaction with electric field, but strongly affect its interaction withadjacent molecules. Would you call it biaxial?

E. T. SAMULSKI. Calamitic nematics have a single (motionally averaged) value ofthe transverse component of their dielectric permittivity tensor. Even thosenematics comprised of biaxial molecules having two distinguishable values of thetransverse molecular polarizability do not exhibit any macroscopic dielectricanisotropy in the plane normal to the director. We call these nematics uniaxialeven if there may be clusters of molecules having short-range, biased rotationsabout 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 fieldcoupled to the local transverse asymmetry of the locally biaxially packed clustersand 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 SantaBarbara, USA). Could X-ray microdiffraction techniques be a good, quantitativeway to measure biaxial correlation lengths in liquid crystalline phases of bentmolecules?

E. T. SAMULSKI. Yes. X-ray microdiffraction may possibly yield a measurementof the biaxial correlation length if the mean dimensions of the volumeilluminated by the X-ray beam were comparable or smaller than the biaxialcorrelation length.

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

E. T. SAMULSKI. Simple mixtures of rod- and disc-like molecules typically phaseseparate although there are recent reports by Georg H. Mehl (personalcommunication) that he may have overcome the immiscibility problem. As forcovalent rod–disc combinations, I am not aware of any reports of macroscopicevidence of biaxiality in those nematic phases.

M. A. BATES (Department of Chemistry, University of York, UK ). Have you triedmaking mixtures of the original boomerang molecule and the molecularengineering one with a lower melting point?

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




uniaxial and biaxial nematic liquid crystals

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