Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects [chapter]

O. D. Lavrentovich
2003 Patterns of Symmetry Breaking  
This review discusses static properties of topological defects, such as line defectsdisclinations and dislocations, point defectshedgehogs (monopoles) and boojums; focal conic domains and tilt grain boundaries in basic types of liquid crystals: uniaxial and biaxial nematics, cholesterics and smectics. We present the most popular experimental techniques to study defects in soft matter, namely, polarizing microscopy and fluorescence confocal polarizing microscopy. The role of bounding surfaces
more » ... ounding surfaces and the so-called surface anchoring that lifts the degeneracy of the order parameter in stability of defects is discussed. Because of the surface anchoring, the equilibridm state of a bounded liquid crystal might contain topological defects. For example, nematic bubbles nucleating during the first-order phase transition from the isotropic melt, might contain point defects (hedgehogs and boojums) and disclination loops when their size is larger than the anchoring extrapolation length defined by the ratio of the Frank elastic constant of the director curvature and the (polar) anchoring coefficient. Depending on the strength of surface anchoring, an edge dislocation might be expelled from the system with ID positional order or be stabilized in the bulk. Furthermore, focal conic domains play the role of "surface anchoring facets" by providing the necessary orientation of the liquid crystal director at the smectic boundary. H. Arodz et al. (eds.), Patterns of Symmetry Breaking, 161-195. O 2003 Kluwer Academic Publishers. Printed in the Netherlands. polarizing microscopy are outlined in order to help those who would like to explore the word of liquid crystal defects experimentally. The discussion follows the textbook on soft matter physics [I] with an addition of some recent results. An interested reader is also referred to general reviews on liquid crystals [ 2 4 ] and defects in them [5, 6, I 1 , 121. Liquid crystals are made of strongly anisometric molecules, either elongated (calamitic molecules) or disk-like (discotic molecules). As a rule, the central part of mesogenic molecules is rigid (phenyl groups) and the outer part flexible (aliphatic chains). This double character explains the existence of steric interactions (between rod-like or disk-like cores of the molecules) yielding orientational order and the fluidity of the liquid crystalline phases. Upon heating, many substances made of strongly anisometric molecules, exhibit the following phase sequence: solid crystal with a long-range orientational and positional order@liquid crystal (or mesophase) with a long-range orientational order and partial or no positional order @isotropic fluid with no orientational nor positional long-range order. There are four basic types of liquid crystalline phases, classified according to the dimensionality of the translational correlations of building units: nematic (no translational correlations), smectic (1D correlations), columnar (2D correlations), and various 3D-correlated structures, such as cubic phases. Uniaxial nematics, noted UN, are optically uniaxial fluid phases. The unit vector along the optic axis is called the director n, n2 = 1; it indicates the average orientation of the molecular axes. Even when the building units are polar, molecular flip-flops and head-to-head overlapping establish centrosymmetric (average) arrangement in the nematic bulk. Thus, n and -n are equivalent notations. In biaxial nematics (BN), the symmetry point group is one of a prism. A BN phase is characterized by three directors, n, 1, and m = n x 1, such that n = -n, 1 = -1, and m = -m. Both LTN and BN phases are fluid: the centers of gravity of the molecules are not correlated. When the building block (molecule or aggregate) is chiral, i.e., not equal to its mirror image, the nematic phase might show helicoidal structure. It is then called a cholesteric phase N*. A rotation by an angle a about the cholesteric axis is equivalent to a translation pal2.rr; p is the pitch of the cholesteric helix, and it is twice the periodicity along the axis. An N* phase can be characterized by three directors: n along the local molecular axes, t along the axis of helicity (which is also the optic axis if the pitch is much smaller than the light wavelength), and m = n x t. Both BN and N* phases are liquid phases (no correlations in molecular positions). Smectics are layered phases with quasi-long-range 1D translational order of centers of molecules in a direction normal to the layers. This positional order is not exactly the long-range order as in normal 3D crystals: As shown by Landau and Peierls, the fluctuative displacements of layers in 1D lattice diverge Defects in Liquid Crystals
doi:10.1007/978-94-007-1029-0_6 fatcat:snu52mtocvgnjba2i7qkj3zg7q