Molecular model of biaxial ordering in nematic liquid crystals composed of flat molecules with four mesogenic groups (original) (raw)
Related papers
Physical Review E, 2011
The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D 2h point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C 2h molecules in terms of the nine independent second rank orientational order parameters defining the C 2h biaxial nematic. In addition there is a rank one order parameter constructed from two pseudovectors which is only non-zero in the C 2h phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behaviour is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.
Physical Review E
The mean-field theory approach has been applied to the boomerang type particles from P. I. C. Teixeira, A. Masters, and B. Mulder [Mol. Cryst. Liq. Cryst. 323, 167 (1998)] but with diminished strength of the interaction coefficient responsible for the coupling between molecular uniaxial and biaxial susceptibilities. For the rodlike particles, when the apex boomerang angle is larger than 107.35 • , the stable uniaxial rodlike phase occurs. For smaller angles, beyond the point where the transition is of the second order (the Landau point) and for diminished parameter of molecular biaxial-uniaxial coupling, a biaxial phase is observed with the transition undergoing directly from the isotropic phase. According to the order parameters the character of this transition is of the first order. Such behavior is in accordance with the Sonnet-Durand-Virga model of the biaxial phases. The change in the type of the phase transition order is also illustrated by the changes in the equations of state and the changes in second and third derivatives of the free energy. The possibilities to tailor interaction coefficients of real molecules to obtain such a phase transition scenario are discussed.
Polydispersity Stabilizes Biaxial Nematic Liquid Crystals
Physical Review Letters, 2011
Inspired by the observations of a remarkably stable biaxial nematic phase [E.v.d. Pol et al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality regime in between uniaxial nematic and smectic states.
Surface ordering in nano-drops containing nematic liquid crystals
The behavior and configuration of nematic liquid crystals within nanodroplets was simulated using a molecular theory and an un-symmetric radial basis function collocation approach. liquid crystals | asymmetric radial basis functions | Landau-de-Gennes Abbreviations: RBF, Radial Basis Function; TPS, thin-plate spline I n this article we describe the free energy functional minimization of nematic liquid crystals nanodroplets. History and Motivation (LC general, LC-substrate, LC-confinement, LC-drops) Theoretical model: Liquid Crystal Liquid crystals (LCs) appear as phases which posses properties intermediate to those of crystalline solids and amorphous liquids. These phases have a certain degree of long-range order of anisotropic, crystalline solids, but deform continuously under the application of stresses, as do fluids. Systems that form these anisotropic fluids are composed molecules that present themselves a degree of structural anisotropy, such as rod-like or disk-like molecules [1, 2, 3]. In general, highly symmetric molecular systems, composed of neutral and spherical molecules, exhibit a direct transition from a highly ordered crystalline state to a disordered-isotropic liquid state [4, 5]. In contrast, LC materials can undergo several mesophase transitions according to concentration and/or temperature and external fields like electrostatics, hydrodynamics, magnetic or confinement [3, 6, 7, 8]. There are mesophases that appear as intermediate stages between the isotropic liquid and the crystalline solid. They possesses long-range orientation, yet deforms continuously under the application of stresses. These phases are characterized by a director field n. They are known to occur either by heating a solid crystal up to a critical temperature, or by varying the concentration of the molecules. The first are called thermotropic, while the second are lyotropic LCs. The liquid crystalline mesophases are classified into three types: nematic, cholesteric and smectic. The nematic LC has a long-range orientational order of the molecules along the direction of the director n, but it does not present positional order. Cholesteric liquid crystals characterize a phase similar to the nematics, except that in addition to the nematic order at small distances, it exhibits a long-range molecular structure that corresponds to the helical rotation of the direction along a neutral direction. This phase is only formed by chiral molecules, i.e. without mirror symmetry. The smectics corresponds to a mesophase which exhibits positional as well as orientation order. There are several categories each one with different positional and orientational ordering of the molecules [2, 6]. The thermodynamics of phase transitions in liquid crystals requires the introduction of an additional internal structural parameter in order to characterize the degree of alignment. The average directional cosine between a particular molecule direction u and the director n is not an appropriate option because this average will vanish for most situations (relying that n and −n are equivalent). Thus, a higher moment of the molecular orientation is used; the lower moment that gives a non-trivial answer is defined by the second moment as follows [6, 3] Q (x, t) = MII (x, t) − δ 3 , [ 1 ] where δ is the 3 × 3 identity tensor and the second moment MII is given by MII (x, t) = nnψ (n, x, t) dn, [ 2 ] where ψ (n, x, t) is the configuration distribution function of orien-tations. According to this definitions tr(Q) = 0 while tr(MII) = 1. The tensor order parameter Q, in an appropriate coordinate system, can be diagonalized in terms of its eigenvalues, i.e. Q = 2S 3 0 0 0 η−S 3 0 0 0
Materials, 2011
In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the α-(4-cyanobiphenyl-4'yloxy)-ω-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N U)-isotropic (I) phase transition is first-order in nature, whereas the N B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.
Orientational ordering of small molecules in nematic liquid crystals
2004
In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Name of Author (please print) Date (dd/mm/yyyy)
Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals
The European Physical Journal E, 2010
We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D 2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is non-polar. While this phase could resemble the classic D ∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to non-polar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D 2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.
Bulk and surface biaxiality in nematic liquid crystals
Physical Review E, 2006
Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor S = ͑١n͒͑١n͒ T possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a measure of the expected biaxiality. Furthermore, the corresponding eigenvectors indicate the directions in which the order tensor Q is induced to break the uniaxial symmetry about the director n. We apply our general considerations to some examples. In particular we show that, when we enforce homeotropic anchoring on a curved surface, the order tensor becomes biaxial along the principal directions of the surface. The effect is triggered by the difference in surface principal curvatures.
Uniaxial and biaxial nematic liquid crystals
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006
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.
Phase-ordering dynamics of the Gay-Berne nematic liquid crystal
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999
Phase-ordering dynamics in nematic liquid crystals has been the subject of much active investigation in recent years in theory, experiments, and simulations. With a rapid quench from the isotropic to nematic phase, a large number of topological defects are formed and dominate the subsequent equilibration process. Here we present the results of a molecular dynamics simulation of the Gay-Berne model of liquid crystals after such a quench in a system with 65,536 molecules. Twist disclination lines as well as type-1 lines and monopoles were observed. Evidence of dynamical scaling was found in the behavior of the spatial correlation function and the density of disclination lines. However, the behavior of the structure factor provides a more sensitive measure of scaling, and we observed a crossover from a defect dominated regime at small values of the wave vector to a thermal fluctuation dominated regime at large wave vector.