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Introduction to liquid crystals Denis Andrienko International Max Planck Research School Modelling of soft matter 11-15 September 2006, Bad Marienberg September 14, 2006 Contents 1 What is a liquid crystal 2 1.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Cholesterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Columnar phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Lyotropic liquid crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Long- and short-range ordering 7 2.1 Order tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Director . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Phenomenological descriptions 10 3.1 Landau-de Gennes free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Frank-Oseen free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4 Nematic-isotropic phase transition 14 4.1 Landau theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Maier-Saupe theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Onsager theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5 Response to external fields 18 5.1 Frederiks transition in nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6 Optical properties 20 6.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.2 Cholesterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 7 Defects 23 8 Computer simulation of liquid crystals 24 9 Applications 27 ǰЩÌìÔÚÕÒsoft condensed matter ÔÏȼǵÃÂÛ̳ÓÐÐֵܣ¨mengzhiyong)·¢¹ý Ö»ÊÇÁ´½ÓÏÖÔÚÓò»ÆðÀ´À² ½ñÌìÓÖ¼ûÖмäÌåÉÏ´«µ½ÁíÒ»¸öÍøÅÌ Íò·Ö¸Ðл¡£¡£¡£ лл¸÷λÐֵܡ£¡£¡£ ÂÛ̳µÄÐֵܸж¯ÁËż~~~~ żҲµÃΪ´ó¼Ò×ö¹±Ï×°¡¡£¡£¡£ [ Last edited by limingscu on 2007-5-25 at 22:37 ] |
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