Enantiotropic Nematics From Cross‐Like 1,2,4,5‐Tetrakis(4′‐alkyl‐4‐ethynylbiphenyl)benzenes and Their Biaxiality Studies

The theoretically predicted optimum length/breadth/width ratio for maximizing shape biaxiality was investigated experimentally by the facile and successful synthesis of cross‐shaped compound 3 , which showed enantiomeric nematic phase behavior. This cross‐like core structure could alternatively be viewed as two fused V‐shaped mesogens, which have recently immerged as a new direction in biaxial nematic research, at the bending tips that can act as a new structure for biaxial investigations. Whilst the thermal analysis data of compound 3 did not meet the expected theoretical values for biaxial nematics, surface‐induced biaxiality was evidenced by optical studies. Cluster‐size analysis within the nematic phase of compound 3 revealed the formation of meta‐cybotactic nematics, which approached the cluster sizes of cybotactic nematics. The split small‐angle 2D X‐ray diffraction patterns of magnetic‐field‐aligned samples indicated that the nematic phase was composed of small smectic C‐like clusters with the tilting of molecules within the clusters. The wide‐temperature‐range enantiomeric nematic phase of cross‐like compound 3 enabled the molecular skeleton to serve as an alternative skeleton to bent‐rod mesogens, which exhibited nematic phases with the potential competition of transitions to higher‐order liquid‐crystalline phases and crystallization, for future biaxial investigations.     

Search for nematic biaxiality in bent-core mesogens: an X-ray diffraction perspective

ABSTRACT

Since its theoretical prediction in 1970, the search for the biaxial nematic phase in thermotropic systems has challenged generations of liquid crystal scientists. Over the last 10 years, bent-core mesogens have drawn much interest as promising candidates for nematic biaxiality. However, despite a number of disputed claims, conclusive evidence of proper (spontaneous and macroscopic) biaxial order in these materials is still missing. By contrast, it is now widely recognised that biaxiality exists on a local scale, in the form of nano-sized clusters of molecules (cybotactic groups) possessing smectic-like positional order and biaxial orientational order. This article provides a review of X-ray diffraction studies on biaxiality and cybotaxis in bent-core nematics, discussing the most relevant issues related to this research field.     

To be or not to be – nematic liquid crystals from shape-persistent V-shaped nematogens with the ‘magic angle’

The tetrahedral bending angle in V-shaped nematogens was claimed to be the optimum for finding a biaxial nematic liquid crystal phase. The benzo[1,2-b:4,3-b’]dithiophene core, recently successfully applied as a tetrahedral bending unit in mesogens with lateral flexible chains, is here embedded in a scaffold with only terminal chains, which conventionally promotes the formation of nematic phases at low temperature. A series of new mesogens has been successfully prepared, realising hockey-stick, hockey-stick dimer and V-shaped molecular topologies. Only the hockey-stick mesogens assemble in uniaxial nematic phases over a broad temperature range. Single crystal structure analysis of a hockey-stick and V-shaped compound reveal remarkable similarities with the benzodithiophene core wrapped by aliphatic chains. A model explaining the absence of nematic mesophases in the family of V-shaped, shape-persistent mesogens with terminal aliphatic chains is presented and results in the proposal of a new design for biaxial nematogens.     

Biaxial nematics: symmetries,order domains and field-induced phase transitions †

We studied the symmetry and spatial uniformity of the orientational order of the biaxial nematic phase in the light of recent experimental observations of phase biaxiality in thermotropic bent-core and calamitic-tetramer nematics. Evidence is presented supporting monoclinic symmetry, instead of the usually assumed orthorhombic symmetry. The use of deuterium nuclear magnetic resonance to differentiate between the possible symmetries is described. The spatial aspects of biaxial order are presented in the context of the cluster model, wherein macroscopic biaxiality can result from the field-induced alignment of biaxial and possibly polar domains. The implications of different symmetries on the alignment of biaxial nematics and on the measurements of biaxial order are discussed in conjunction with the microdomain structure of the biaxial phase.     

Phase diagram of the uniaxial and biaxial soft-core Gay-Berne model

Classical molecular dynamics simulations have been used to explore the phase diagrams for a family of attractive-repulsive soft-core Gay-Berne models [R. Berardi, C. Zannoni, J. S. Lintuvuori, and M. R. Wilson, J. Chem. Phys. 131, 174107 (2009)] and determine the effect of particle softness, i.e., of a moderately repulsive short-range interaction, on the order parameters and phase behaviour of model systems of uniaxial and biaxial ellipsoidal particles. We have found that isotropic, uniaxial, and biaxial nematic and smectic phases are obtained for the model. Extensive calculations of the nematic region of the phase diagram show that endowing mesogenic particles with such soft repulsive interactions affect the stability range of the nematic phases, and in the case of phase biaxiality it also shifts it to lower temperatures. For colloidal particles, stabilised by surface functionalisation, (e.g., with polymer chains), we suggest that it should be possible to tune liquid crystal behaviour to increase the range of stability of uniaxial and biaxial phases (by varying solvent quality). We calculate second virial coefficients and show that they are a useful means of characterising the change in effective softness for such systems. For thermotropic liquid crystals, the introduction of softness in the interactions between mesogens with overall biaxial shape (e.g., through appropriate conformational flexibility) could provide a pathway for the actual chemical synthesis of stable room-temperature biaxial nematics.     

Phase biaxiality in nematic liquid crystalline side-chain polymers of various chemical constitutions

In a previous deuterium NMR study conducted on a liquid crystalline (LC) polymer with laterally attached book-shaped molecules as the mesogenic moiety, we have revealed a biaxial nematic phase below the conventional uniaxial nematic phase (Phys. Rev. Lett. 2004, 92, 125501). To elucidate details of its formation, we here report on deuterium NMR experiments that have been conducted on different types of LC side-chain polymers as well as on mixtures with low-molar-mass mesogens. Different parameters that affect the formation of a biaxial nematic phase, such as the geometry of the attachment, the spacer length between the polymer backbone and the mesogenic unit, as well as the polymer dynamics, were investigated. Surprisingly, also polymers with terminally attached mesogens (end-on polymers) are capable of forming biaxial nematic phases if the flexible spacer is short and thus retains a coupling between the polymer backbone and the LC phase. Furthermore, the most important parameter for the formation of a biaxial nematic phase is the dynamics of the polymer backbone, as the addition of a small percentage of low molar mass LC to the biaxial nematic polymer from the original study served to shift both the glass transition and the appearance of detectable biaxiality in a very similar fashion. Plotting different parameters for the investigated systems as a function of T/Tg also reveals the crucial role of the dynamics of the polymer backbone and hence the glass transition.     

Addressing non-idealities in NMR experiments on rotating liquid crystals

Unequivocal evidence for a biaxial nematic phase in low-molar-mass calamitic thermotropic liquid crystals has been challenging to generate. Recently we provided NMR evidence that nonlinear calamitic mesogens based on the oxadiazole heterocycle exhibit a biaxial nematic phase (Phys. Rev. Lett., 2004, 92, 145505). Herein we probe the robustness of that claim by exploring potential variations of the director distribution from the ideal one that would apply to nematics rotated about an axis perpendicular to the spectrometer magnetic field. Moreover, we demonstrate that our methodology, when applied to the high temperature uniaxial nematic TBBA, yields a biaxial order parameter η = 0.0, thereby confirming the validity of our procedures. Our findings suggest that the original claim of biaxial order (η∼0.1) as reflected by probe molecule studies of oxadiazole mesogens is still valid.     

Biaxial nematic phases in fluids of hard board-like particles

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes σ(1) > σ(2) > σ(3). A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio κ(1) = σ(1)/σ(2) while keeping κ(2) = σ(2)/σ(3), we predict phase diagrams for various values of κ(2) which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid types are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for κ(2)? 2.5. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxiality centred at κ(1)≈κ(2) which widens as κ(2) increases. For κ(2)? 5 the region κ(2)≈κ(1) of the packing-fraction vs. κ(1) phase diagrams exhibits interesting topologies which change qualitatively with κ(2). We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric in the neighbourhood of κ(1)≈κ(2) is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.     

Long- and short-range order in the mesophases of laterally substituted calamitic mesogens and their radial octapodes

The mesomorphic behavior of a calamitic mesogen (4'-undecyloxybiphenyl-4-yl-4-octyloxy-2-(pent-4-en-1-yloxy)benzoate) and of a supermesogenic octapode formed by the side-on attachment of the mesogen to a octasilsesquioxane central core is studied by X-ray diffraction and polarizing optical microscopy. The calamitic compound is found to have a nematic phase that has biaxial domains (cybotactic clusters) of tilted layers throughout its entire temperature range. Domains of analogous structure are also found in both the nematic and the hexagonal columnar mesophases exhibited by the obctapode compound. The spacing of the layers forming the domains is found to have the same, essentially temperature independent value for the calamitic monomer and for the octapode, in both its mesophases. Comparison with compounds of analogous structure shows that this value is determined by the length of the rigid part of the mesogenic unit. Variation of the latter length is shown to have no effect on the size of the hexagonal lattice of the octapode columnar phase or on the stacking distance within the columns. The presence of the biaxial domains in the nematic phase is discussed in connection with the phase biaxiality that has been observed in structurally related tetrapode compounds and the possibility of field induced macroscopic biaxial nematic order.     

X‐ray diffraction from the uniaxial and biaxial nematic phases of bent‐core mesogens

X‐ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent‐core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X‐ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X‐ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial–biaxial phase transition, and estimate the order parameters of the nematic phase.     

X-ray diffraction from the uniaxial and biaxial nematic phases of bent-core mesogens

X-ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent-core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X-ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X-ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial-biaxial phase transition, and estimate the order parameters of the nematic phase.     

Thermotropic biaxial nematic liquid crystals: spontaneous or field stabilized?

An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematic liquid crystals. The phase is macroscopically uniaxial but has microscopic biaxial, and possibly polar, domains. Under the action of an electric field, the phase acquires macroscopic biaxial ordering resulting from the collective alignment of the domains. A phenomenological theory is developed for the molecular order in this phase and for its transitions to purely uniaxial and to spontaneously biaxial nematic phases.     

Bent-core mesogens based on semi-flexible dicyclohexylmethane spacers

New, bent-core mesogens are described in which the core of the molecule is a semiflexible, di(4-aminocyclohexyl)methane spacer. The compounds show nematic, columnar nematic and columnar phases as shown by a combination of X-ray diffraction and optical microscopy. The potential of these new mesogens as biaxial nematic candidates is considered.     

Bent‐core mesogens based on semi‐flexible dicyclohexylmethane spacers

New, bent‐core mesogens are described in which the core of the molecule is a semiflexible, di(4‐aminocyclohexyl)methane spacer. The compounds show nematic, columnar nematic and columnar phases as shown by a combination of X‐ray diffraction and optical microscopy. The potential of these new mesogens as biaxial nematic candidates is considered.     

Thermotropic biaxial nematic phases with negative optical character [1]

Two disc-shaped multialkynyl arene ethers (1 and 2) with unusual thermo-mesomorphic properties are presented. Conoscopic studies show that the nematic phases of these new low molecular weight liquid crystals are biaxial and that the sign of their biaxiality is negative. The diether 2 is the first discotic twin liquid crystal which exhibits a nematic phase.     

Textural and calorimetric investigations on a homologous series of mesogenic azocompounds complexed with palladium(II)

A comparative study of some mesogenic azobenzene compounds and their organometallic palladium(II) derivatives is reported. On the basis of the textural properties, calorimetric data and uniaxial order parameters (as deduced approximately from infrared spectroscopy), the main features induced by palladium complexation are (i) the transition temperatures increase, (ii) the number of ordered mesophases increases, (iii) the nematic uniaxial order parameter decreases, (iv) the textures are typical of highly ordered phases, and (v) an optical biaxiality appears in the nematic phase. The calorimetric data as well as the order parameters, if discussed in terms of molecular biaxiality result are interpreted at least qualitatively. Optical investigations show that macroscopical biaxial ordering can be achieved.     

Thermotropic uniaxial and biaxial nematic and smectic phases in bent-core mesogens

Two azo substituted achiral bent-core mesogens have been synthesized. Optical polarizing microscopy and synchrotron X-ray scattering studies of both compounds reveal the existence of the thermotropic uniaxial and biaxial nematic and three smectic phases at different temperatures in these single component small molecule systems. The transition from the uniaxial to biaxial nematic phase is confirmed to be second order. The transitions from the biaxial nematic to the underlying smectic phase and between the smectic phases have barely discernible heat capacity signatures and thus are also second order.     

Synthesis and properties of oxadiazole based V-shaped, shape persistent nematogens

A series of biaxial V-shaped, shape-persistent molecules has been synthesised by stepwise coupling of phenylene ethynylene arms to an oxadiazole bending unit. Studies of their thermotropic nematic phases point to phase biaxiality.     

Optically Biaxial,Re‐entrant and Frustrated Mesophases in Chiral,Non‐symmetric Liquid Crystal Dimers and Binary Mixtures

Sixteen optically active, non‐symmetric dimers, in which cyanobiphenyl and salicylaldimine mesogens are interlinked by a flexible spacer, were synthesized and characterized. While the terminal chiral tail, in the form of either (R)‐2‐octyloxy or (S)‐2‐octyloxy chain attached to salicylaldimine core, was held constant, the number of methylene units in the spacer was varied from 3 to 10 affording eight pairs of (R & S) enantiomers. They were probed for their thermal properties with the aid of orthoscopy, conoscopy, differential scanning calorimetry and X‐ray powder diffraction. In addition, the binary mixture study was carried out using chiral and achiral dimers with the intensions of stabilizing optically biaxial phase/s, re‐entrant phases and important phase sequences. Notably, one of the chiral dimers as well as some mixtures exhibited a biaxial smectic A (SmA_b) phase appearing between a uniaxial SmA and a re‐entrant uniaxial SmA phases. The mesophases such as chiral nematic (N*) and frustrated phases viz., blue phases (BPs) and twist grain boundary (TGB) phases, were also found to occur in most of the dimers and mixtures. X‐ray diffraction studies revealed that the dimers possessing oxybutoxy and oxypentoxy spacers show interdigitated (SmA_d) phase where smectic periodicity is over 1.4 times the molecular length; whereas in the intercalated SmA (SmA_c) phase formed by a dimer having oxydecoxy spacer the periodicity was found to be approximately half the molecular length. The handedness of the helical structure of the N* phases formed by two enantiomers was examined with the aid of CD measurements; as expected, these enantiomers showed optical activities of equal magnitudes but with opposite signs. Overall, it appears that the chiral dimers and mixtures presented herein may serve as model systems in design and developing novel materials exhibiting the apolar SmA_b phase possessing D_2h symmetry and nematic‐type biaxiality.     

Unusual molecular packing within the low symmetry mesophases of alkyl- and alkoxy-acylhydrazinatonickel(II) liquid crystals

Three series of novel thermotropic metallomesogens have been synthesized and characterized using microscopy and DSC. Unexpected X-ray scattering is observed within all of the observed mesophases. Diffuse in-layer reflections are observed both at angles corresponding to approximately twice the molecular width and to the side-by-side separation of molecules within the nematic, SmA and SmC mesophases. Furthermore, the tilt angles within the SmC phases are observed to decrease as the terminal chain lengths decrease. Conoscopic observations show the SmC phases to be strongly biaxial as expected, but surprisingly, weak biaxiality is also observed within both the SmA and nematic mesophases. A model to explain the results is proposed, in which the cores remain orthogonal to the layers, whilst the overall molecular tilt necessary for SmC phase formation is provided by the contribution of the terminal alkyl chains to the overall molecular shape. IR spectroscopy is used to confirm the model.