Introduction to Liquid Crystals Denis Andrienko IMPRS school, Bad - PowerPoint PPT Presentation

Liquid crystalline mesophases Short- and long-range ordering Phenomenological descriptions Literature Optical properties What are liquid crystals? Defects Simulation of liquid crystals Applications Introduction to Liquid Crystals Denis Andrienko IMPRS school, Bad Marienberg September 14, 2006 Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Phenomenological descriptions Literature Optical properties What are liquid crystals? Defects Simulation of liquid crystals Applications Frederiks transition Literature Optical properties What are liquid crystals? Nematics Liquid crystalline mesophases Colors Nematics Cholesterics Cholesterics Defects Smectics Linear defects Molecular arrangement Interaction of defects Columnar phases Nematic colloids Short- and long-range ordering Simulation of liquid crystals Order tensor Forces, torques and gorques Properties of the order tensor Gay-Berne potential Director Phase diagrams Phenomenological descriptions Nematic colloids Landau-de Gennes theory Frank-Oseen free energy Applications One elastic constant approximation Liquid Crystal Displays Nematic-isotropic transition Liquid Crystal Thermometers Response to external fields Polymer dispersed liquid crystals Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Phenomenological descriptions Literature Optical properties What are liquid crystals? Defects Simulation of liquid crystals Applications Recommended books Many excellent books/reviews have been published covering various aspects of liquid crystals. Among them: 1. The bible on liquid crystals: P. G. de Gennes and J. Prost “The Physics of Liquid Crystals”. 2. Excellent review of basic properties (many topics below are taken from this review): M. J. Stephen, J. P. Straley “Physics of liquid crystals”. 3. Symmetries, hydrodynamics, theory: P. M. Chaikin and T. C. Lubensky “Principles of Condensed Matter Physics”. 4. Defects: Oleg Lavrentovich “Defects in Liquid Crystals: Computer Simulations, Theory and Experiments”. 5. Optics: Iam-Choon Khoo, Shin-Tson Wu, “Optics and Nonlinear Optics of Liquid Crystals”. 6. Textures: Ingo Dierking “Textures of Liquid Crystals”. 7. Simulations: Michael P. Allen and Dominic J. Tildesley “Computer simulation of liquids”. 8. Phenomenological theories: Epifanio G. Virga “Variational Theories for Liquid Crystals”. Finally, the pdf file of the lecture notes can be downloaded from http://www.mpip-mainz.mpg.de:/ ∼ andrienk/lectures/IMPRS/liquid crystals.pdf . Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Phenomenological descriptions Literature Optical properties What are liquid crystals? Defects Simulation of liquid crystals Applications What are Liquid Crystals? The name suggests that it is a state of a matter in between the liquid and the crystal. ◮ Liquid - Fluidity - Inability to support shear - Formation and coalescence of droplets ◮ Solid - Anisotropy in optical, electrical, and magnetic properties - Periodic arrangement of molecules in one spatial direction Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Phenomenological descriptions Literature Optical properties What are liquid crystals? Defects Simulation of liquid crystals Applications What are Liquid Crystals? The name suggests that it is a state of a matter in between the liquid and the crystal. ◮ Liquid - Fluidity - Inability to support shear - Formation and coalescence of droplets ◮ Solid - Anisotropy in optical, electrical, and magnetic properties - Periodic arrangement of molecules in one spatial direction Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Typical textures Figure: (a) Schlieren texture. (b) Thin nematic film on isotropic surface. (c) Nematic thread-like texture. “Nematic” comes from the Greek word for “thread”. Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Typical compounds From a rough steric point of view, this is a rigid rod of length ∼ 20 ˚ A and width ∼ 5 ˚ A . Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Typical textures Figure: (a) Fingerprint texture. (b) Grandjean or standing helix texture (c) DNA mesophases Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Typical textures Figure: (a,b) Focal-conic fan texture of a chiral smectic A liquid crystal (c) Focal-conic fan texture of a chiral smectic C liquid crystal. Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Molecular arrangement Figure: The arrangement of molecules in liquid crystal phases. (a) The nematic phase. The molecules tend to have the same alignment but their positions are not correlated. (b) The cholesteric phase. The molecules tend to have the same alignment which varies regularly through the medium with a periodicity distance p / 2. (c) smectic A phase. The molecules tend to lie in the planes with no configurational order within the planes and to be oriented perpendicular to the planes. Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Molecular arrangement Figure: The arrangement of molecules in liquid crystal phases. (a) The nematic phase. The molecules tend to have the same alignment but their positions are not correlated. (b) The cholesteric phase. The molecules tend to have the same alignment which varies regularly through the medium with a periodicity distance p / 2. (c) smectic A phase. The molecules tend to lie in the planes with no configurational order within the planes and to be oriented perpendicular to the planes. Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Molecular arrangement Figure: The arrangement of molecules in liquid crystal phases. (a) The nematic phase. The molecules tend to have the same alignment but their positions are not correlated. (b) The cholesteric phase. The molecules tend to have the same alignment which varies regularly through the medium with a periodicity distance p / 2. (c) smectic A phase. The molecules tend to lie in the planes with no configurational order within the planes and to be oriented perpendicular to the planes. Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Typical textures Figure: (a) hexagonal columnar phase Col h (with typical spherulitic texture); (b) Rectangular phase of a discotic liquid crystal (c) hexagonal columnar liquid-crystalline phase. Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals

Liquid crystalline mesophases Short- and long-range ordering Nematics Phenomenological descriptions Cholesterics Optical properties Smectics Defects Molecular arrangement Simulation of liquid crystals Columnar phases Applications Typical structures Figure: Typical discotics: derivative of a hexabenzocoronene and 2,3,6,7,10,11-hexakishexyloxytriphenylene. K (70 K ) → Col h (100 K ) → I . Denis Andrienko IMPRS school, Bad Marienberg Introduction to Liquid Crystals