Znn3bq.jpeg
±±¾©Ê¯ÓÍ»¯¹¤Ñ§Ôº2026ÄêÑо¿ÉúÕÐÉú½ÓÊÕµ÷¼Á¹«¸æ
²é¿´: 1672  |  »Ø¸´: 27
¡¾½±Àø¡¿ ±¾Ìû±»ÆÀ¼Û15´Î£¬×÷ÕßlimingscuÔö¼Ó½ð±Ò 14.5 ¸ö
µ±Ç°Ö÷ÌâÒѾ­´æµµ¡£

limingscu

Òø³æ (СÓÐÃûÆø)


[×ÊÔ´] £¨½÷Ï׸øÖмäÌåºÍmengzhiyong¼°ÂÛ̳µÄ¸÷룩ÂíÆÕ¸ß·Ö×ÓµÄÒº¾§µ¼ÂÛ½²Òå¼°¿Î¼þ

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 ]
»Ø¸´´ËÂ¥

» ²ÂÄãϲ»¶

» ±¾Ö÷ÌâÏà¹ØÉ̼ÒÍÆ¼ö: (ÎÒÒ²ÒªÔÚÕâÀïÍÆ¹ã)

ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)



¿Î¼þ¼û£¶£­£¸Â¥
½ö×÷ѧÊõ½»Á÷ʹÓà ÈçÉæ¼°°æÈ¨ÎÊÌ⣬ÎÒÁ¢¼´É¾³ý~~~~


[ Last edited by limingscu on 2007-5-25 at 22:11 ]
2Â¥2007-05-25 18:44:46
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

OoÐÜÐÜoO

Òø³æ (ÕýʽдÊÖ)


¡ï¡ï¡ï¡ï¡ï ÎåÐǼ¶,ÓÅÐãÍÆ¼ö

·Ç³£¸Ðл£¡
ÎÒÕýÐèÒªÕâ¸ö£¬Ð»Ð»ÁË£¡
3Â¥2007-05-25 20:29:46
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)


ÒýÓûØÌû:
Originally posted by OoÐÜÐÜoO at 2007-5-25 08:29 PM:
·Ç³£¸Ðл£¡
ÎÒÕýÐèÒªÕâ¸ö£¬Ð»Ð»ÁË£¡

²»ÓÃл¡£¡£¡£
¸Õ²Å°ÑÏà¹ØµÄ¿Î¼þ¸øÉÏ´«À­ ¹©²Î¿¼¡£¡£¡£
4Â¥2007-05-25 20:50:41
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)


5Â¥2007-05-25 22:08:37
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)


6Â¥2007-05-25 22:09:32
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)


¿Î¼þ
µÚÒ»´Î·¢¸½¼þ¡¡¸ø°ßÖñÌíÂé·³À­
7Â¥2007-05-25 22:10:06
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ÖмäÌå

ľ³æ (СÓÐÃûÆø)


×ÊÔ´¹²Ïí,ÎÒÃǹ²Í¬µÄÄ¿±ê!
9Â¥2007-05-26 08:46:58
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

mengzhiyong

½ð³æ (СÓÐÃûÆø)


¡ï¡ï¡ï¡ï¡ï ÎåÐǼ¶,ÓÅÐãÍÆ¼ö

ÐÖµÜÏä×ӵ׺ûõ²»ÉÙ°¡£¡·Ç³£¸Ðл£¡
10Â¥2007-05-26 09:12:40
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)


ллÖмäÌåºÍmengzhiyongÐÖ¼°ÂÛ̳µÄ¸÷λÐֵܵÄÅõ³¡¡£¡£¡£
11Â¥2007-05-26 23:31:53
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

limingscu

Òø³æ (СÓÐÃûÆø)


ÒýÓûØÌû:
Originally posted by liu123 at 2007-5-27 12:58 AM:
ллÄú

²»ÓÃл¡£¡£¡£
ÒýÓÃÖмäÌåµÄÃûÑÔ ×ÊÔ´¹²Ïí ÎÒÃǵÄÄ¿±ê¡£¡£¡£
12Â¥2007-05-28 11:41:53
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
¼òµ¥»Ø¸´
bt8Â¥
2007-05-26 01:50   »Ø¸´  
 
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ limingscu µÄÖ÷Ìâ¸üÐÂ
¡î ÎÞÐǼ¶ ¡ï Ò»ÐǼ¶ ¡ï¡ï¡ï ÈýÐǼ¶ ¡ï¡ï¡ï¡ï¡ï ÎåÐǼ¶
×î¾ßÈËÆøÈÈÌûÍÆ¼ö [²é¿´È«²¿] ×÷Õß »Ø/¿´ ×îºó·¢±í
[¿¼ÑÐ] 320·ÖÈ˹¤ÖÇÄܵ÷¼Á +9 Õñ¡ªTZ 2026-04-03 9/450 2026-04-08 16:24 by YG_hydrology
[¿¼ÑÐ] һ־Ըɽ¶«´óѧ»¯Ñ§Ó뻯¹¤Ñ§Ôº²ÄÁÏÓ뻯¹¤×¨Ë¶£¬360·ÖÇóµ÷¼Á +5 ²»Ô¸Í¸Â¶ÐÕÃûµÄË 2026-04-02 5/250 2026-04-08 15:28 by screening
[¿¼ÑÐ] Ò»Ö¾Ô¸211£¬»¯Ñ§Ñ§Ë¶£¬310·Ö£¬±¾¿ÆÖصãË«·Ç£¬Çóµ÷¼Á +10 ŬÁ¦·Ü¶·112 2026-04-07 10/500 2026-04-08 15:01 by screening
[¿¼ÑÐ] »úе¹¤³Ì264ѧ˶Çóµ÷¼Á +3 qiushangxian 2026-04-06 3/150 2026-04-08 01:53 by Linzejun
[¿¼ÑÐ] 288Çóµ÷¼Á +12 ûÓдð°¸_ 2026-04-05 12/600 2026-04-08 00:17 by T¿É¿ÉÎ÷ÀïT
[¿¼ÑÐ] Ò»Ö¾Ô¸Î÷ÄÏ090202Çóµ÷¼Á +4 ÔÚÏßÇóÓÐѧÉÏ 2026-04-07 4/200 2026-04-07 19:47 by biomichael
[¿¼ÑÐ] 318Çóµ÷¼Á +5 ÀîÇàɽɽɽ 2026-04-07 5/250 2026-04-07 18:24 by À¶ÔÆË¼Óê
[¿¼ÑÐ] ÉúÎïѧ363µ÷¼ÁÇóÖú +7 fanzhang6666 2026-04-06 9/450 2026-04-07 17:37 by lijunpoly
[¿¼ÑÐ] Ò»Ö¾Ô¸Î÷µç085401Çóµ÷¼Á +4 sunw1306 2026-04-07 4/200 2026-04-07 16:40 by à£à£à£0119
[¿¼ÑÐ] ²ÄÁϵ÷¼Á +12 Ò»ÑùYWY 2026-04-02 14/700 2026-04-07 12:52 by Sammy2
[¿¼ÑÐ] »¯¹¤µ÷¼Á303·Ö£¬¹ýËļ¶ +34 ÆÜÎà´ý·ç 2026-04-02 34/1700 2026-04-07 12:30 by 1018329917
[¿¼ÑÐ] 0855Çóµ÷¼Á²ÄÁÏ +11 ºìÌÒׯׯ 2026-04-04 12/600 2026-04-06 10:26 by À¶ÔÆË¼Óê
[¿¼ÑÐ] ²ÄÁÏÓ뻯¹¤371Çóµ÷¼Á +14 ÅãÁÕ¿´º£ 2026-04-04 15/750 2026-04-06 06:59 by houyaoxu
[¿¼ÑÐ] Ò»Ö¾Ô¸ÉϺ£º£Ñó´óѧ083200ʳƷѧ˶£¬Çóµ÷¼Á£¬½ÓÊÜÆäËûרҵ083200 +4 whatÕÅ 2026-04-04 5/250 2026-04-05 14:07 by chw1980_0
[¿¼ÑÐ] Çóµ÷¼Á +3 ffyyu 2026-04-02 3/150 2026-04-04 19:03 by À¶ÔÆË¼Óê
[¿¼ÑÐ] 368Çóµ÷¼Á +5 ½ñ»ªÏ° 2026-04-03 7/350 2026-04-04 18:47 by imissbao
[¿¼ÑÐ] ²ÄÁϵ÷¼Á +11 ÎâèùÓ±£¡ 2026-04-03 11/550 2026-04-04 09:56 by ССÊ÷2024
[¿¼ÑÐ] »¯¹¤Çóµ÷¼Á +11 ÀóÏã֥ʿҬÄÌ 2026-04-03 11/550 2026-04-03 22:06 by à£à£à£0119
[¿¼ÑÐ] 303Çóµ÷¼Á +3 һɫÇåÓð 2026-04-02 4/200 2026-04-03 10:22 by À¶ÔÆË¼Óê
[¿¼ÑÐ] ¡¾Çóµ÷¼Á¡¿ÐÂÄÜÔ´²ÄÁϱ¾¿Æ£¬Ò»Ö¾Ô¸211£¬³õÊÔ321 +6 Çóµ÷¼ÁѧУ£¬ 2026-04-02 6/300 2026-04-02 09:41 by Çç¿Õ210210
ÐÅÏ¢Ìáʾ
ÇëÌî´¦ÀíÒâ¼û