Harald Pleiner

Polar Biaxial Liquid Crystalline Phases with Fluidity in Two and Three Spatial Dimensions

Abstract We discuss the macroscopic properties of several classes of polar liquid crystalline phases. We focus on polar biaxial liquid crystalline phases made of achiral molecules with fluidity in two and three spatial dimensions. The classes we examine include polar biaxial nematic phases, orthogonal biaxial smectic phases with anisotropic in-plane fluidity and tilted polar biaxial smectic phases with in-plane fluidity. We show that many of the phases discussed are ferroelectric. In addition, we find that in each of the three classes discussed, there is one phase which has C 1 symmetry thus allowing spontaneous helix formation. Finally we investigate in detail the properties of a tilted phase with C 2 symmetry ( C B 2 ), which is probably very important for liquid crystalline phases composed of banana-shaped molecules.

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D2d 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 nonpolar. 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 nonpolar 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 D2d 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.

Fluid Biaxial Banana Phases: Symmetry at Work

Abstract Fluid biaxial smectics made from compounds without asymmetric carbons but nevertheless with a spontaneous polarization are now known as banana smectics because of their molecular shape. Here we show that symmetry changes under parity (r ← - r) are an efficient way to summarize and differentiate their electro-optic properties. Typical of fluid biaxial smectics, there are also a large number of stacking options endowing them with opto-electric properties spanning a broad range of economically viable applications. “Value-added features” of some banana smectics include a faster electro-optic response than found in liquid crystals with a helix structure, their steric property allowing rotations about an axis in a layer plane without compromising smectic layer stability and ambidextrous chirality.

Phase Transitions in Biaxial Banana Phases

Abstract We discuss symmetry properties of various phases that can result when biaxial objects with at least one polar axis are orientationally ordered and packed on layers. The possibility of spontaneous splay, bend and twist is also investigated for biaxial nematic, smectic banana and dolphin phases. We further discuss appropriate order parameters and expressions for Ginzburg-Landau free energies for some phase transitions involving these phases.

Low symmetry tetrahedral nematic liquid crystal phases: Ambidextrous chirality and ambidextrous helicity

Abstract.We discuss the symmetry properties as well as the dynamic behavior of various non-polar nematic liquid crystal phases with tetrahedral order. We concentrate on systems that show biaxial nematic order coexisting with octupolar (tetrahedral) order. Non-polar examples are phases with D2 and S4 symmetries, which can be characterized as biaxial nematics lacking inversion symmetry. It is this combination that allows for new features in the statics and dynamics of these phases. The D2-symmetric phase is chiral, even for achiral molecules, and shows ambidextrous chirality in all three preferred directions. The achiral S4-symmetric phase allows for ambidextrous helicity, similar to the higher-symmetric D2d-symmetric phase. Such phases are candidates for nematic phases made from banana-shaped molecules.Graphical abstract

Deformable tetrahedratic phases: The effects of external fields and flows

Abstract.We discuss changes in the symmetry and physical properties of an isotropic phase which has initially tetrahedral symmetry characterized by four unit vectors. In its undeformed state, these four vectors are at the tetrahedral angle (

Selected Macroscopic Consequences of Tetrahedratic Order

109.47^circ

Tetrahedral Order in Liquid Crystals

) to each other. We find that this optically isotropic phase becomes uniaxial under the influence of an external electric field,

Polar columnar and tetrahedratic phases

{bf E}

On the influence of a network on optically isotropic fluid phases with tetrahedral/octupolar order

, resulting in a phase with C3v symmetry. For an applied simple shear flow, the system becomes biaxial and a time-dependent state with C1 symmetry arises. We discuss to what extent deformations induced by external forces and flows on this optically isotropic phase, which we call a deformable tetrahedratic phase, are consistent with observations at the isotropic-B7 transition found recently in compounds composed of banana-shaped molecules and suggest a number of experiments to test the conclusions of this model.