UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An EPR study of order and molecular orientation in liquid crystals MacKay, Alexander Lloyd 1971

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1971_A6_7 M34.pdf [ 2.82MB ]
Metadata
JSON: 831-1.0084849.json
JSON-LD: 831-1.0084849-ld.json
RDF/XML (Pretty): 831-1.0084849-rdf.xml
RDF/JSON: 831-1.0084849-rdf.json
Turtle: 831-1.0084849-turtle.txt
N-Triples: 831-1.0084849-rdf-ntriples.txt
Original Record: 831-1.0084849-source.json
Full Text
831-1.0084849-fulltext.txt
Citation
831-1.0084849.ris

Full Text

AN EPR STUDY OF ORDER AND MOLECULAR ORIENTATION IN LIQUID CRYSTALS " by ALEXANDER LLOYD MACKAY B . S c , D a l h o u s i e U n i v e r s i t y > 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF -THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the department of P h y s i c s We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH A p r i l , 1971 COLUMBIA In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the.Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of • P HVS/C S The University of British Columbia Vancouver 8, Canada Date A P f t l L 10, f 3-7 1 i i ABSTRACT Using EPR, the temperature dependence of the e f f e c t -i v e order parameter of the molecule vanadyl a c e t y l a c e t o n a t e i n the nematic l i q u i d c r y s t a l 4-methoxy b e n z y l i d e n e - n - b u t y l a n i l i n e was s t u d i e d . In the r e s u l t i n g data, a d i s c o n t i n u i t y i n slope' of the curve of e f f e c t i v e order parameter versus temp-e r a t u r e was found, i n d i c a t i n g a change to a more r e s t r i c t e d type o f motion at lower temperatures. S i m i l a r r e s u l t s were ob t a i n e d from NMR T x measurements on the pure l i q u i d c r y s t a l . The d i s c o n t i n u i t y cannot be i n t e r p r e t e d s o l e l y as a v i s c o s i t y e f f e c t . Two c h c l e s t e r i c l i q u i d c r y s t a l T i i x t i n ^ e s c ontalnine -vanadyl a c e t y l a c e t o n a t e were s u b j e c t e d t o a high magnetic f i e l d (~20 k i l o g a u s s ) . Prom EPR measurements, a 1 . 7 5 : 1 mixture by weight of c h o l e s t e r y l c h l o r i d e and c h o l e s t e r y l m y r i s t a t e was found t o o r i e n t i t s h e l i x a x i s p a r a l l e l t o the f i e l d d i r e c t i o n . In a.2 percent by weight mixture of c h o l e s t e r y l c h l o r i d e i n nematic 4-methoxy b e n z y l i d e n e - n - b u t y l a n i l i n e , the molecules tended t o arrange t h e i r l o n g axes p a r a l l e l t o the f i e l d thus making the h e l i x a x i s p e r p e n d i c u l a r t o the f i e l d . I i . ! I V-i i i TABLE OF CONTENTS page A b s t r a c t i i Ta b l e o f Contents i i i L i s t of F i g u r e s v L i s t o f Tables . . . . . . . . v i i Acknowledgements . . . . . . . . . . . . . v i i i CHAPTER 1 ' ' - i. ' L i q u i d C r y s t a l s . : 1 CHAPTER 2 Choice o f Vanadyl A c e t y l a c e t o n a t e 5 EPR Technique . . . . . . . . . . . . . . . 0 o . . 8 P r e p a r a t i o n of Samples 13 CHAPTER 3 The S p i n H a m i l t o n i a n ... 18 I n t e r p r e t a t i o n of The EPR S p e c t r a 21 CHAPTER 4 Order i n the Nematic Phase 32 'CHAPTER 5 | O r i e n t a t i o n of C h o l e s t e r i c L i q u i d C r y s t a l s w i t h a Magnetic F i e l d ^3 i v page CHAPTER 6 . . . . D i s c u s s i o n . . . . . . 53 APPENDIX 1 T r a n s f o r m a t i o n o f the S p i n H a m i l t o n i a n f o r A x i a l l y Symmetric Molecules 55 APPENDIX 2 The Energy E i g e n v a l u e s of the S p i n H a m i l t o n i a n f o r A x i a l l y Symmetric Molecules 58 References . 6 l V LIST OF FIGURES page F i g u r e 1 . 1 The th r e e types o f l i q u i d c r y s t a l s 4 F i g u r e 2 . 1 Schematic of the s t r u c t u r e of VAAC 7 F i g u r e 2 . 2 B l o c k diagram of the EPR spectrometer 11 F i g u r e 2 . 3 The temperature c o n t r o l apparatus 12 F i g u r e 3 . 1 The mol e c u l a r c o o r d i n a t e system f o r VAAC 25 F i g u r e 3 . 2 A b s o r p t i o n (a) and d e r i v a t i v e (b) l i n e s f o r VAAC i n a nematic sample when Y = 0 o 26 F i g u r e 3 . 3 A b s o r p t i o n (a) and d e r i v a t i v e (b) l i n e s f o r VAAC i n a nematic sample when y=90° 26 F i g u r e 3 A b s o r p t i o n (a.) and d e r i v a t i v e (b) l i n e s f o r VAAC i n a ramdom sample 27 •»-T - --, ~ ~> A h ^.r.-r^ ' ^ *~. ' " ^ ^ « - - > • ? • < - - - - - o f o r VAAC i n an i s o t r o p i c sample 27 F i g u r e 3 . 6 Spectrum f o r VAAC i n a nematic l i q u i d c r y s t a l when y - 0 o 28 F i g u r e 3 .7 Spectrum f o r VAAC i n a nematic l i q u i d c r y s t a l when y = 9 0 ° 29 F i g u r e 3 . 8 Spectrum f o r VAAC i n a random sample 30 F i g u r e 3 • 9 Spectrum f o r VAAC i n an i s o t r o p i c sample 3 1 F i g u r e -4 . 1 H y p e r f i n e s p l i t t i n g versus k i n e m a t i c v i s c o s i t y f o r VAAC i n O c t o i l 36 F i g u r e 4 . 2 E f f e c t i v e order parameter versus reduced temperature f o r VAAC i n the nematic l i q u i d c r y s t a l s : (a) b i s (-J ' - n - o c t y l -o x y b e n t a l ) - 2 - c h l o r o - l , 4 - p h e n y l -e nediamine 6, (b) MBBA, (c) 4-methoxy benzylidene - 4-amino-a-methyl cinnamic a c i d - n - p r o p y l e s t e r 8 37 F i g u r e 4 . 3 Kinematic v i s c o s i t y versus temperature f o r (a) O c t o i l , X , (b) 4-methoxy b e n z y l -idene - 4-amino-a-methy 1 cinnamic a c i d - n -p r o p y l e s t e r 8 , o , and (c) MBBA,• F i g u r e 4 . 4 L u c k h u r s t s 7 t h e o r e t i c a l curve i s compared wit h curves o f S e f f and S e f f - 1/3 ( S y i s + D ) versus temperature i n MBBA F i g u r e 4 . 5 Proton r e l a x a t i o n time T i versus r e c i p -r o c a l of the temperature at 1 8 . 2 MHz f o r MBBA F i g u r e 5 . 1 Peak i n t e n s i t i e s f o r the C-MBBA mixture "~ versus o r i e n t i n g magnetic f i e l d F i g u r e 5 . 2 Peak i n t e n s i t i e s f o r the CM mixture versus o r i e n t i n g magnetic f i e l d v i i LIST OF TABLES page Table 3.1 Parameters f o r VAAC i n a nematic l i q u i d c r y s t a l 20 v i i i ACKNOWLEDGMENTS I would l i k e t o express my s i n c e r e a p p r e c i a t i o n of the h e l p f u l guidance p r o v i d e d by my r e s e a r c h s u p e r v i s o r , Dr. C. F. Schwerdtfeger, i n a l l stages of r e s e a r c h and i n the w r i t i n g o f t h i s - - t h e s i s . I am a l s o very g r a t e f u l t o a l l the students i n the S o l i d S t a t e P h y s i c s Group f o r much i n s t r u c t i o n and a s s i s t a n c e throughout my p e r i o d of r e s e a r c h . As w e l l , the many e n l i g h t e n i n g d i s c u s s i o n s with Mr. M. Marusic have been extremely b e n e f i c i a l i n the achievement of my present l e v e l of ^3 ^ ~ 4- c: ^  *3 y. ^ 4- l-> f K O O V J T ~ J - ? ^ f i i T ( S ^ v n r q f - a 1 q m i u i - i Uu.m..^  _ w _ J. — _J -_ J i r. J_ i i The s c h o l a r s h i p s awarded by the N a t i o n a l Research C o u n c i l o f Canada d u r i n g the p e r i o d of r e s e a r c h are g r a t e f u l l y acknowledged. The r e s e a r c h f o r t h i s t h e s i s was supported by the N a t i o n a l Research C o u n c i l , grant number A - 2 2 2 8 . CHAPTER 1 I n t r o d u c t i o n to L i q u i d C r y s t a l s L i q u i d c r y s t a l s were f i r s t d i s c o v e r e d i n 1888 by an A u s t r i a n b o t a n i s t , F r e d e r i c h R e i n i t z e r , who. found t h a t the compound c h o l e s t e r y l benzoate had two m e l t i n g p o i n t s . At l45°C i t changed from a s o l i d t o a t u r b i d l i q u i d and at 179°C i t became a t r a n s p a r e n t l i q u i d . The next s i g n i f i c a n t work was done by a German p h y s i c i s t 0. Lehmann who found o t h e r s i m i l a r compounds, d e f i n e d some of t h e i r c h a r a c t e r i s t i c s , and c o i n e d the word l i q u i d c r y s t a l . The l i q u i d c r y s t a l i s a s t a t e of matter ( r e f e r r e d to as a roesophase) with p r o p e r t i e s i n t P T m p d i a t e between those of a l i q u i d and a c r y s t a l l i n e s o l i d . L i q u i d c r y s t a l s possess the p r o p e r t i e s common to l i q u i d s . o f f l u i d i t y and a b i l i t y to form d r o p l e t s . As w e l l they have the p r o p e r t y of c r y s t a l s to e x h i b i t a n i s o t r o p i c o p t i c a l c h a r a c t e r i s t i c s . F u r t h e r , they are more s u s c e p t i b l e t o e x t e r n a l i n f l u e n c e s , such as e l e c t r i c and magnetic f i e l d s , than e i t h e r c r y s t a l l i n e s o l i d s or l i q u i d s . Some l i q u i d c r y s t a l s are formed by c o o l i n g a l i q u i d through a t r a n s i t i o n temperature or h e a t i n g a s o l i d c r y s t a l . ' These are c l a s s i f i e d as t h e r m o t r o p i c . A l l the work c o n s i d e r -j | ed i n t h i s study i s on t h e r m o t r o p i c l i q u i d c r y s t a l s . Other mesophases are formed by a d d i t i o n o f a s o l v e n t to a compound. These are known as l y o t r o p i c l i q u i d c r y s t a l s . The e x i s t e n c e - 1 2 o f t h i s type o f l i q u i d c r y s t a l i s determined not by tempera-t u r e but by s o l u t e c o n c e n t r a t i o n . L i q u i d c r y s t a l s have predominantly long molecules. S l i g h t v a r i a t i o n s i n the shape of these molecules and changes i n the m o l e c u l a r order are r e s p o n s i b l e f o r the t h r e e types: s m e c t i c , nematic, and c h o l e s t e r i c . As i l l u s t r a t e d i n f i g u r e " v l . l , these t h r e e types have very d i f f e r e n t s t r u c t u r e s . In smectic l i q u i d c r y s t a l s the molecules are p a r a l l e l to each o t h e r and arranged i n l a y e r s . The l o n g axes of a l l the molecules i n a g i v e n l a y e r are p a r a l l e l t o one another and o f t e n p e r p e n d i c u l a r to the plane of the l a y e r . Smectic l i q u i d c r y s t a l s are o p t i c a l l y p o s i t i v e and u s u a l l y u n a x i a l . Nematic l i q u i d c r y s t a l s have l e s s o r d e r than smectic m a t e r i a l s . The molecules are p a r a l l e l t o each other but not d i v i d e d i n t o p l a n e s . Nematic m a t e r i a l s are u s u a l l y u n a x i a l and o p t i c a l l y p o s i t i v e . The l o n g range m o l e c u l a r s t r u -t u r e of nematic substances has not yet been s a t i s f a c t o r i l y determined. Some s c i e n t i s t s support the "swarm t h e o r y " i n which the molecules are arranged as i n f e r r o m a g n e t i c domains. The opposing view i s the "continuum t h e o r y " which claims t h e r e i s at every p o i n t i n the l i q u i d c r y s t a l a d e f i n i t e p r e f e r r e d d i r e c t i o n f o r the o r i e n t a t i o n of the l o n g m o l e c u l a r axes. T h i s p r e f e r r e d d i r e c t i o n i s assumed to vary c o n t i n u o u s l y w i t h p o s i t i o n . 3 In the t h i r d type o f l i q u i d c r y s t a l , c h o l e s t e r i c , the molecules are grouped i n l a y e r s w i t h t h e i r l o n g axes p a r a l l e l t o the l a y e r . In each l a y e r the molecular axes p o i n t i n the same d i r e c t i o n but due to the s l i g h t l y unsymmetric shape of the c h o l e s t e r i c molecules the d i r e c t i o n of the long axes i n one l a y e r i s s l i g h t l y d i f f e r e n t from the c o r r e s p o n d i n g d i r e c t i o n i n the n e i g h b o u r i n g layers.. Through many l a y e r s t h i s d i r e c t i o n w i l l change c o n t i n u o u s l y through 36O 0. The l i n e c u t t i n g normally through the planes of a c h o l e s t e r i c l i q u i d c r y s t a l i s c a l l e d the h e l i x a x i s . A very s t r o n g o p t i c a l r o t a r y power e x i s t s about t h i s a x i s . The r e s e a r c h d e s c r i b e d i n t h i s t h e s i s d e a l s w i t h nematic and c h o l e s t e r i c l i q u i d c r v ? t ; p i p. : > h e l i x a x i s -C h o l e s t e r i c F i g u r e 1.1 The t h r e e l i q u i d c r y s t a l s t r u c t u r e s . CHAPTER 2 Choice o f Vanadyl A c e t y l a c e t o n a t e The l i q u i d c r y s t a l s used i n t h i s study d i d not, themselves, e x h i b i t EPR s p e c t r a . In order to e x t r a c t i n f o r m -a t i o n about the l i q u i d c r y s t a l s i t was necessary to d i s s o l v e i n them a paramagnetic probe which d i d have an EPR s i g n a l . For t h i s study, vanadyl a c e t y l a c e t o n a t e (VAAC) was chosen as the paramagnetic probe. I t s s t r u c t u r e i s i l l u s t -r a t e d i n f i g u r e 2.1. -Being e s s e n t i a l l y p l a n a r i n shape, VAAC l o s e s some m o t i o n a l freedom when i n s o l u t i o n w i t h the el o n g a t e d molecules of a l i q u i d c r y s t a l . T h i s l o s s of freedom i n the s o l u t e leads t o u s e f u l i n f o r m a t i o n about the l i q u i d c r y s t a l i t s e l f . Vanadyl a c e t y l a c e t o n a t e was chosen f o r s e v e r a l r e a s o n s . I t i s r e a d i l y a v a i l a b l e . I t i s s t a b l e i n the r e -q u i r e d temperature range (0°C-100°C) and can be d i s s o l v e d i n " most l i q u i d c r y s t a l s . VAAC has a l a r g e a n i s o t r o p i c h y p e r f i n e s p l i t t i n g . Only one n u c l e a r moment c o n t r i b u t e s to the s p e c t r a . T h i s i s the vanadium nucleus w i t h i t s s p i n 7/2 produc i n g 8 h y p e r f i n e l i n e s . I B e f o r e d i s c u s s i n g the use o f VAAC i t i s necessary i ;to determine how w e l l i t s spectrum r e p r e s e n t s the o r i e n t a t i o n o f the l i q u i d c r y s t a l . In the l i t e r a t u r e t h e r e are s e v e r a l treatments o f t h i s problem. Glarum and M a r s h a l 1 have shown . - 5 t h a t the degree of order and i t s temperature dependence observed from the use of VAAC as a paramagnetic probe c o r r e s -ponds c l o s e l y t o t h a t o f the pure l i q u i d c r y s t a l as found by r e f r a c t i v e index measurements. Chen and L u c k h u r s t 2 have found t h a t the degree .of order of VAAC.in a l i q u i d c r y s t a l i s not a l t e r e d by changes i n the c o n c e n t r a t i o n of a second s o l u t e . A p l o t o f order a g a i n s t reduced temperature produced a common curve f o r a wide range of s o l u t e s and c o n c e n t r a t i o n s suggest-i n g t h a t the ordered s t r u c t u r e of the mesophase was not a l t e r -ed by the presence o f * a second s o l u t e . While the evidence i s not y e t c o n c l u s i v e i t appears that the use of VAAC as a paramagnetic probe i s at l e a s t q u a l i t a t i v e l y j u s t i f i e d . F i g u r e 2.1 Schematic of the s t r u c t u r e of VAAC. 8 EPR Technique The s p e c t r a used i n t h i s t h e s i s were obtained with an X-band EPR spectrometer o p e r a t i n g at 9.1 KMHz. The micro-wave power source was a V a r i a n A s s o c i a t e s r e f l e x k l y s t r o n V-153/6315. A Hewlett Packard HP716B power supply was used to operate the k l y s t r o n . Prom the k l y s t r o n the microwaves f i r s t passed through a Microwave A s s o c i a t e s f e r r i t e i s o l a t o r and then i n t o a S t a r r e t t f l a p type a t t e n u a t o r of range 0 to 50db. A f t e r a t t e n u a t i o n the microwaves entered a magic tee b r i d g e . Power from the k l y s t r o n was f e d i n t o two arms - on one s i d e a s l i d e scre'v tuner and a dummy lo a d and on the o t h e r s i d e the sample c a v i t y . The TE102 sample c a v i t y was p a t t e r n e d a f t e r one made by V a r i a n A s s o c i a t e s . The modulation c o i l s were mounted d i r e c t l y on the s i d e w a l l s of the c a v i t y . The output of the 1N23B c r y s t a l d e t e c t o r coupled the c a v i t y s i g n a l to a p r e a m p l i f i e r which had an AC c u r r e n t g a i n of 40db i n the frequency range of 1KC to IMC. A 100KC o s c i l l a t o r was used to modulate the magnetic f i e l d and to p r o v i d e the r e f e r e n c e s i g n a l f o r phase s e n s i t i v e d e t e c t i o n . The phase s e n s i t i v e d e t e c t i o n was c a r r i e d out w i t h an E l e c -t r o n i c s , . M i s s i e s , and Communications Inc model RJB Lock-In A m p l i f i e r . A Hewlett Packard Moseley 680 s t r i p c h a r t r e c o r d -er t r a c e d the output. 9 To s t a b i l i z e the k l y s t r o n frequency a 10KC modul-a t i o n was imposed on I t s r e f l e c t o r v o l t a g e by an Automatic Frequency C o n t r o l l e r (AFC). The r e s u l t i n g microwave frequency modulation produced a 20KC s i g n a l at the p r e a m p l i f i e r when the k l y s t r o n was on the c a v i t y resonance frequency. I f the k l y s t r o n was on e i t h e r s i d e of the resonance a 10KC s i g n a l of the a p p r o p i a t e phase was measured at the p r e a m p l i f i e r . T h i s s i g n a l , when a m p l i f i e d and r e c t i f i e d by phase s e n s i t i v e de-t e c t i o n i n the AFC, p r o v i d e d an e r r o r s i g n a l t o r e s t o r e the k l y s t r o n t o c a v i t y resonance. For the work on nematic l i q u i d c r y s t a l s :.a. s m a l l V a r i a n A s s o c i a t e s magnet of range from 0 to 4 k i l o g a u s s was used. Tc apply the h i g h magnetic f i e l d s n e cessary f o r o r i e n t -a t i o n of c h o l e s t e r i c l i q u i d c r y s t a l molecules i t was necessary t o use a Magnion model L 2 6 L a b o r a t o r y Electromagnet w i t h h i g h f i e l d p o l e t i p s capable of pr o d u c i n g from 0 to 2 3 k i l o g a u s s . T h i s magnet was powered by a Harvey Wells FFC - 4 power supply. The f i e l d o f the V a r i a n A s s o c i a t e s magnet co u l d be measured t o ± 0 . 1 gauss w i t h a g l y c e r i n e NMR probe. I n c o r p o r a t e d i n the Magnion magnet system was a r o t a t i n g c o i l gaussmeter which was capable of p r o v i d i n g f i e l d measurements w i t h e r r o r s l e s s than one p e r c e n t . The experiments i n t h i s t h e s i s were c a r r i e d out at temperatures between 0° and 100°C. T h i s temperature r e g i o n i s t e c h n i c a l l y d i v i d e d i n t o two. r e g i o n s : one from .C°C to room 10 temperature and the other from room temperature up to 1 0 0°C. The temperature c o n t r o l mechanism c o n s i s t e d b a s i c a l -l y o f a dry n i t r o g e n gas flow d i r e c t e d a l o n g the sample tube. To minimize thermal g r a d i e n t s due to heat l o s s t o the e n v i r o -ment, a g l a s s dewar made by V a r i a n A s s o c i a t e s was p l a c e d i n the c a v i t y around the sample. The n i t r o g e n gas passed between t h i s dewar and the sample tube. I f temperatures l e s s than room temperature were des-i r e d the n i t r o g e n gas was passed through a copper c o i l immer-sed i n l i q u i d n i t r o g e n at 7 7°K. Temperature c o n t r o l was ac h e i v e d by r e g u l a t i n g the gas flow r a t e . For temperatures g r e a t e r than room temperature the n i t r o g e n tlcvi path bypassed the "liquid n i t r o g e n c o i l but went a l o n g a h e a t e r c o i l i n s i d e the g l a s s dewar j u s t b e f o r e r e a c h -i n g the sample tube. In t h i s case.temperature c o n t r o l was ac h e i v e d e i t h e r by r e g u l a t i n g the gas flow r a t e or by v a r y i n g the c u r r e n t i n the h e a t e r c o i l . A F e n w a l l E l e c t r o n i c s Inc GA - J3P21 t h e r m i s t o r was used to measure temperature. The r e s i s t a n c e of t h i s therm-i s t o r v a r i e d from about 70 kiloohms at 5°C t o 2 kiloohms at 1 0 0°C. I t was p l a c e d i n a simple b r i d g e c i r c u i t . The therm-''I i s t o r was c a l i b r a t e d w i t h a G. H. Z e a l ( - 1 0°C to 1 1 0°C) mer-icury thermometer. k l y s t r o n TpC—;  AFC k l y s t r o n power supply dummy loa d s l i d e screw tuner 7K 3 i s o l a t o r a t t e n u a t o r magic trip II c a v i t y magnet c r y s t a l ' d e t e c t o r . 100KC m o d u l a t i o n e r r o r s i g n a l 5 p r e a m p l i f i e r phase $ s e n s i t i v e d e t e c t o r r e c o r d e r F i g u r e 2.2 Block diagram o f the EPR spectrometer, sample tube dewar -\, c a v i t y h eater ^ P S ^ s _ ir heater power supply l i q u i d n i t r o g e n dry N2 gas F i g u r e 2.3 The temperature c o n t r o l apparatus. 13 P r e p a r a t i o n o f Samples For these experiments t h r e e d i f f e r e n t samples were used. These were: (a) VAAC i n 4-methoxy b e n z y l i d e n e - n - b u t y l a n i l i n e (MBBA), (b) VAAC i n a 1.75:1 by weight mixture of c h o l -e s t e r y l c h l o r i d e and c h o l e s t e r y l m y r i s t a t e , and (c) VAAC i n a 2 percent by weight mixture of c h o l e s t e r y l c h l o r i d e i n MBBA. In order t h a t the or g a n i c r a d i c a l molecules (VAAC) i n t e r a c t e d only with l i q u i d crystal., molecules and not wit h other r a d i c a l s i t was necessary to keep the VAAC c o n c e n t r a t i o n l e s s than 1 0 " 3 molar. Owing t o the i n h e r e n t low s o l u b i l i t y of VAAC t h i s c o n d i t i o n was e a s i l y s a t i s f i e d . f o i ' o b s e r v a t i o n oy J-JPR the l i q u i d c r y s t a l samples were put i n t o pyrex tubes. ' These tubes were of i n s i d e diameter 3 m i l l i m e t e r s , w a l l t h i c k n e s s 1 m i l l i m e t e r , and l e n g t h about 16 c e n t i m e t e r s . They produced no E P R s i g n a l i n the range from 2 t o -J k i l o g a u s s and d i d not s u b s t a n t i a l l y decrease the Q o f the c a v i t y . (a) For the i n v e s t i g a t i o n o f the order parameter the nematic l i q u i d c r y s t a l MBBA was used. Unevacuated samples of MBBA have been found t o possess the p e c u l i a r p r o p e r t y t h a t t h e i r i s o t r o p i c t r a n s i t i o n temperatures are a d e c r e a s i n g f u n c t i o n of time. A f r e s h sample changes from a nematic l i q u i d c r y s t a l t o an i s o t r o p i c l i q u i d at about 47°C. Some 5 month o l d MBBA i n the lab had an i s o t r o p i c t r a n s i t i o n p o i n t at 3 7 ° C I t has been proposed t h i s d i s c r e p a n c y i s due to chemical absorp-14 t i o n o f oxygen by the l i q u i d c r y s t a l . In any case the problem was circumvented by u s i n g only f r e s h samples. The MBBA was used as obtained from V a r i L i g h t C o r p o r a t i o n . I t was found t h a t i n the presence of VAAC the i s o t r o p i c t r a n s i t i o n temp-e r a t u r e decreased t o 44°C. Because i t i s d i f f i c u l t t o d i s s o l v e VAAC i n MBBA and the s t r e n g t h of the EPR s i g n a l i s p r o p o r t i o n a l to the number of s o l u t e m o l e c u l e s , a s p e c i a l procedure was developed f o r t h i s sample. The i n i t i a l mixing was c a r r i e d out i n a 1 0 centimeter l o n g pyrex tube which had a t i n y h o l e at one end and was open at fche other end. F i r s t , a s m a l l amount (a few m i l l i g r a m s ) of VAAC was ground up i n t o a " f i n e powder and put i n t o the bottom of the tube. The MBBA was then poured i n t o the tube. When the open end of the sample tube was a t t a c h e d t o a vacuum pump, s m a l l a i r bubbles were p u l l e d through the bottom, v i g o r o u s l y s t i r r i n g the mixture. The s u c t i o n exerted by the vacuum pump was a d j u s t e d such t h a t the MBBA d i d not bubble out of the tube. A f t e r s e v e r a l minutes of t h i s , a s u f f i c i e n t amount of VAAC was d i s s o l v e d f o r s u c c e s s f u l EPR work. However, th e r e remained a great d e a l of u n d i s s o l v e d VAAC i n the sample. T h i s was removed i n two s t e p s . F i r s t , the sample was c e n t r i f u g e d u n t i l a l l u n d i s s o l v e d VAAC had s e t t l e d t o the bottom. Then, u s i n g a drawn-out eyedropper, the r e q u i r e d amount of sample was t r a n s f e r r e d t o a c l e a n pyrex tube. To e l i m i n a t e d i s s o l v e d a i r from the sample, the vacuum pump was ag a i n a p p l i e d f o r 15 s e v e r a l minutes. At t h i s p o i n t the.sample was ready f o r exp-eriment . I f an order measurement i s to be ac c u r a t e i t i s es-s e n t i a l t h a t any thermal g r a d i e n t s i n the l i q u i d c r y s t a l be minimized. For MBBA i t was found t h a t a thermal g r a d i e n t along the sample tube was i n e v i t a b l e because o f the experimental arrangement. The best way to reduce t h i s g r a d i e n t was to make the volume of l i q u i d c r y s t a l s m a l l e r . For t h i s reason only a s m a l l amount of MBBA was used and the sample tube was arranged such t h a t the e n t i r e volume of sample was i n s i d e the c a v i t y . To achieve t h i s i t was. necessary to put the t h e r m i s t o r i n s i d e the c a v i t y . F o r t u n a t e l y , i t was found t h a t the t h e r m i s t o r d i d not have an EPR s i g n a l i n the 2 to 4 k i l o g a u s s range -(b) C h o l e s t e r y l c h l o r i d e i s a c h o l e s t e r i c l i q u i d c r y s t a l w i t h a l e f t - h a n d e d o p t i c a l r o t a r y power. C h o l e s t e r y l m y r i s t a t e , on the other hand, possesses a righ t - h a n d e d o p t i c a l power. I f the a p p r o p i a t e p r o p o r t i o n s of these l i q u i d c r y s t a l s are mixed t o g e t h e r t h e r e should be zero o p t i c a l r o t a r y power 9; T h i s s i t u a t i o n i s s i m i l a r t o a nematic l i q u i d c r y s t a l . In mix-t u r e s which d e v i a t e s l i g h t l y from the proper nematic c o n d i t i o n s the l i q u i d c r y s t a l Is weakly c h o l e s t e r i c . In t h i s c o n d i t i o n the molecules are more r e s p o n s i v e t o e x t e r n a l i n f l u e n c e s such as e l e c t r i c and magnetic f i e l d s whereas i n a pure c h o l e s t e r i c the i n t e r m o l e c u l a r f o r c e s are dominant. The c h o l e s t e r y l c h l o r i d e and c h o l e s t e r y l m y r i s t a t e 16 l i q u i d c r y s t a l s were ob t a i n e d i n powder form from V a r i L i g h t C o r p o r a t i o n . To produce a mesophase i t was necessary t o heat the powders t o the i s o t r o p i c t r a n s i t i o n p o i n t . Upon c o o l i n g they formed c h o l e s t e r i c l i q u i d c r y s t a l s . In p r e p a r i n g the l i q u i d c r y s t a l mixture the c o r r e c t amounts of c h o l e s t e r y l c h l o r i d e , c h o l e s t e r y l m y r i s t a t e , and VAAC were weighed and then s t i r r e d i n t o a homogeneous mixture w h i l e s t i l l i n powder form. A f t e r b e i n g poured i n t o a sample tube, the powder mixture was heated above i t s t r a n s i t i o n p o i n t . Then i t was f u r t h e r mixed by b e i n g shaken v i g o r o u s l y f o r sev-e r a l minutes. Since the l i q u i d c r y s t a l mixture was r e l a t i v e l y v i s c o u s when i n the c h o l e s t e r i c s t a t e , the mixing was c a r r i e d out In the i s o t r o p i c s t a t e . When enough VAAC had been d i s -s o l v e d and the sample appeared homogeneous i t was c e n t r i f u g e d u n t i l a l l u n d i s s o l v e d VAAC had s e t t l e d t o the bottom. R e l a t i v e l y l a r g e samples o f the c h o l e s t e r i c mixture were used s i n c e f o r the experiments b e i n g performed on them the presence o f a moderate thermal g r a d i e n t was a c c e p t a b l e . The sample tube was p l a c e d so t h a t the u n d i s s o l v e d VAAC i n the bottom was o u t s i d e the EPR c a v i t y w h i l e the b u l k o f the l i q u i d c r y s t a l was i n s i d e the 'cavity. (c) The presence o f a s m a l l amount of an o p t i c a l l y a c t i v e s o l u t e i n ,a nematic l i q u i d c r y s t a l i s i n some cases s u f f i c i e n t to produce a c h o l e s t e r i c mesophase 1 1. I f about 2 percent by weight of c h o l e s t e r y l c h l o r i d e i s added to MBBA the r e s u l t i n g mixture i s weakly c h o l e s t e r i c . In f a c t , i n s t r o n g f i e l d s the h e l i c a l s t r u c t u r e w i l l untwist to a nematic o n e 1 1 . The p r e p a r a t i o n of the above sample was very simple The r e q u i r e d amount of c h o l e s t e r y l c h l o r i d e was added to a s o l u t i o n of MBBA and" VAAC. The mixture was heated u n t i l the c h o l e s t e r y l c h l o r i d e became i s o t r o p i c and then shaken u n t i l the sample was homogeneous. I t was suggested t h a t VAAC r e a c t e d c h e m i c a l l y with the above samples. T h i s was e s p e c i a l l y e v i d e n t with MBBA. For t h i s r e a s on sample p r e p a r a t i o n was always c a r r i e d out w i t h i n a few hours b e f o r e an EPR r u n . No runs v/ere made w i t h samples more than 2k hours o l d or a f t e r any s u s p i c i o n o f contam i n a t i o n or d e t e r i o r a t i o n . CHAPTER 3 The S p i n H a m i l t o n i a n An EPR spectrum i s d e r i v e d from microwave induced t r a n s i t i o n s between the e l e c t r o n i c energy l e v e l s of a para-magnetic i o n . The e n e r g i e s o f these l e v e l s are determined by the p r o p e r t i e s of the i o n , the a p p l i e d magnetic f i e l d , the l o c a l f i e l d about the i o n , the i n t e r a c t i o n of e l e c t r i c and n u c l e a r moments, and s e v e r a l other mechanisms. In order t h a t e x p e r i m e n t a l data maybe compared w i t h t h e o r y , the s p i n H a m i l t o n i a n has been c r e a t e d t o express a l l r e l a v e n t i n f o r m -a t i o n c o n c i s e l y w i t h a s m a l l number of parameters. The pro-cedure c f an E^R expe^ir ^ e^t i Q a R f 1^"^  o u r^ - "First - the e x p -e r i m e n t a l d a t a i s accumulated. Then t h i s data i s f i t t e d to an a p p r o p i a t e s p i n H a m i l t o n i a n . From.the magnitude of the terms of the s p i n H a m i l t o n i a n c o n c l u s i o n s are made about the exp-e r i m e n t a l system. VAAC i s an almost a x i a l l y symmetric paramagnetic probe. I t s p r i n c i p l e "g" and "A" valu e s are l i s t e d i n t a b l e 3.1. g i s the gyromagnetic r a t i o and A i s the h y p e r f i n e c o u p l i n g t e n s o r . By f a r the l a r g e s t term i n the s p i n H a m i l t o n i a n j f o r VAAC i n a l i q u i d c r y s t a l i s the e l e c t r o n i c Zeeman term. T h i s term d e s c r i b e s the i n t e r a c t i o n o f the e l e c t r o n s p i n S w i t h the a p p l i e d e x t e r n a l f i e l d H and has the form: - - - - -H Z=3H.£.S 18 1 9 The g-tensor f o r an a x i a l l y symmetric molecule can be w r i t t e n i n terms of two components, g ( ( and g x , r e s u l t i n g i n the f o l l o w i n g e x p r e s s i o n : H i = 3 ( g ( ( H z S z + g A ( H x S x + HySy)) The i n t e r a c t i o n between the e f f e c t i v e s p i n of the e l e c t r o n S and the a c t u a l s p i n o f the nucleus I_, known as the h y p e r f i n e i n t e r a c t i o n i s w r i t t e n : H„=S.A.I A g a i n i n the case of an a x i a l l y symmetric molecule the h y p e r f i n e s p l i t t i n g constant can be d i v i d e d Into two comp-onents A(l and AJL . The s i g n i f i c a n t terms of the s p i n H a milt-onian d e s c r i b i n g VAAC a r e : ^ 5 - M \.&nAiz'-,2 ' e-i-^ •'•Lx^ x • "y-'y'' + A H S Z I Z + A X ( S X I X + S y l y ) By l i m i t i n g H t o the x-z plane and changing the axes of q u a n t l t i z a t i o n o f the e l e c t r o n s p i n and the n u c l e a r s p i n , the H a m i l t o n i a n may be w r i t t e n i n the f o l l o w i n g form (Appendix 1 ) : H 5=g3HS z' + A S Z - I Z ' + (A , , A A / A ) S X ' I X ' + AxSy'Iy' + 1 ( A „ 2 - A x 2 ) g „ g x s i n ( 2 e ) S x " I x " 3.1 2 A where g 2 = g „ 2 c o s 2 0 + g x 2 s i n 2 8 and A 2 g 2 = A 1 1 2 g „ 2 c o s 2 0 + A x 2 g x 2 s i n 2 6 0 i s the angle between H and the V-0 bond of the 20 VAAC molec u l e . The primes denote transformed q u a n t i t i e s . A c a l c u l a t i o n c a r r i e d t o second order p e r t u r b a t i o n theory y i e l d s the energy d i f f e r e n c e f o r the t r a n s i t i o n (M,m)-(M-l,m) f o r an e l e c t r o n o f s p i n 1/2. T h i s i s giv e n by the f o l l o w i n g e q u a t i o n . M and m denote the components of the e l e c t r o n s p i n and the n u c l e a r s p i n along the a x i s o f q u a n t i t -i z a t i o n . AE=gBH + Am + ( A n 2 + A 2)Ax 2(I(I+D-m 2) "Wgp -" " s i n 2 (2G)m 2 3*.'2 + ( A , , 2 - A^2)2(g„gJ8A^g3H T h i s r e l a t i o n i s d e r i v e d i n Appendix 2 . TABLE 3 . 1 Parameters f o r VAAC i n a Nematic L i q u i d C r y s t a l S x x = 1 - 9 8 5 A x x = 5 2 5 gauss . g y y = 1 . 9 7 9 A y y = 4 9 5 gauss g z z = 1 . 9 4 3 A z z = 1 2 5 7 gauss 21 I n t e r p r e t a t i o n of the EPR S p e c t r a S i n c e , as p r e v i o u s l y e x p l a i n e d , the EPR s i g n a l Is from the VAAC molecule and not d i r e c t l y from the l i q u i d c r y s t a l the shape of the VAAC molecule must be c o n s i d e r e d . VAAC i s p l a n a r and approximately square. The V=0 bond pro-j e c t s normally from the c e n t e r of the plane and along w i t h the magnetic f i e l d d e f i n e s the angle 6. The V=0 d i r e c t i o n i s . c a l l e d the Z r a x i s and the X r and Y r axes are i n the p l a n e . S i n c e the molecule has a x i a l symmetry i t i s not necessary t o d i s t i n g u i s h the X r and Y r axes. VAAC molecules are f o r c e d t o arrange t h e i r p l a n a r s i d e s p a r a l l e l to the l o n g axes o f the ne i g h b o u r i n g l i q u i d c r y s t a l m o l e c u l e s . They are f r e e t o r o -t a t e around the l i q u i d c r y s t a l molecule or about an a x i s through the V=0 bond. In a nematic mesophase the VAAC molecules a l i g n p a r a l l e l t o the l i q u i d c r y s t a l m o l e c u l e s . "Meier and Saupe 3 have used an angular d i s t r i b u t i o n f u n c t i o n of the f o l l o w i n g form: f (a)=exp(-Ccos 2a) where C i s a constant t o be determined and a i s the angle between the l o n g m o l e c u l a r axes and the o r i e n t a t i o n a x i s (e. g. magnetic f i e l d ) . E i t h e r by imposing a s t r o n g e l e c t r i c f i e l d 1 * or s u p e r c o o l i n g 5 i t i s . p o s s i b l e t o have a nematic l i q u i d c r y s t a l sample whose molecules are o r i e n t e d about a d i r e c t i o n 22 Y,<J> from the magnetic f i e l d ( f i g u r e 3 . 1 ) . Some understanding of the angular d i s t r i b u t i o n of long m o l e c u l a r axes i n nematic l i q u i d c r y s t a l s can be obt a i n e d by t a k i n g EPR s p e c t r a . f o r d i f -f e r e n t y's1*'5. In t h i s study only the two endpoints y=0° and y=90° w i l l be d i s c u s s e d . When Y = 0 ° the l i q u i d c r y s t a l molecules are o r i e n t e d about the magnetic f i e l d i n a d i s t r i b u t i o n : f ( a ) = e x p ( - C c o s 2 a ) . For the VAAC molecule t h i s may be w r i t t e n : f (-6)=exp(-Csin2e) . The p r e f e r r e d d i r e c t i o n i s that which makes the Z r a x i s per-p e n d i c u l a r t o the magnetic f i e l d . Then, t h e r e should be a l a r g e and equal number of Xp and Y r axes and a sm a l l number of Z r axes a l o n g the magnetic f i e l d . A s i n g l e a b s o r p t i o n l i n e f o r Y = U ° has the shape i l l u s t r a t e d i n f i g u r e 3 . 2 ( a ) . H H and H j . are ob t a i n e d by s e t t i n g 9 = 0° and 6=90° i n eq u a t i o n 3.2 and s o l v i n g f o r H . X r and Y r energy a b s o r p t i o n s occur at Ho. and Z r a b s o r p t i o n s occur at H„. When the f i e l d i s not along one of the p r i n c i p l e axes o f the VAAC molecule (6?-0° or 9 0 ° ) , the energy a b s o r p t i o n occurs at an i n t e r m e d i a t e f i e l d v a l u e . The d e r i v a t i v e o f the a b s o r p t i o n l i n e f o r Y = ° ° i s shown i n f i g u r e ' " '3.2(b). The EPR spectrum f o r Y=0° c o n s i s t s o f 8 of these sep-arated by a d i s t a n c e approximately equal t o A A. T h i s spectrum has been c a l c u l a t e d by computer and i s i l l u s t r a t e d i n f i g u r e 3.'1. 23 A procedure f o r c a l c u l a t i n g EPR s p e c t r a f o r d i f -f e r e n t y has been developed by James and L u c k h u r s t 5 . However, the computing r o u t i n e a v a i l a b l e f o r t h i s study enabled only the r e p r o d u c t i o n of the two endpoints: 0° and 9 0 ° . A r e -w r i t i n g of the program would have been a major u n d e r t a k i n g . Now i n the case where the l i q u i d c r y s t a l molecules are d i s t r i b u t e d around an a x i s 90° to the magnetic f i e l d ( Y = 9 0 ° ) , the number of Z r a b s o r p t i o n s w i l l be approximately equal to the sum of the X R and Y r a b s o r p t i o n s . There w i l l be more Z r a b s o r p t i o n s and fewer X r and Y r a b s o r p t i o n s than i n the Y = 0 ° case. The a b s o r p t i o n and d e r i v a t i v e curves f o r a s i n g l e l i n e are shown i n f i g u r e s 3 . 3 ( a ) and 3 . 3 ( b ) . The EPR spectrum f c r Y — 9 0 ° c o n s i s t s of 8 d e r i v a t i v e Xrnes in. wbicb the peaks c o r r e s p o n d i n g to Z r a b s o r p t i o n s are separated by An. Another s i t u a t i o n t o be c o n s i d e r e d i s where the l i q u i d c r y s t a l molecules are f i x e d randomly i n a l l d i r e c t i o n s . Then, i n an EPR experiment t h e r e w i l l be an equal number of X R , Y r, and Z R energy a b s o r p t i o n s . The a b s o r p t i o n and der-i v a t i v e curves f o r a s i n g l e l i n e are shown i n f i g u r e 3 . 6 ( a ) and 3 . 6 ( b ) . The EPR spectrum- i s i l l u s t r a t e d i n f i g u r e 3 . 8 . I t c o n s i s t s of 8 l i n e s s eparated by Aj_ and 8 peaks separated by A„. In the examples d e s c r i b e d above, the VAAC molecules were assumed to have undergone a n e g l i g i b l e change of d i r e c t -i o n i n the time c o r r e s p o n d i n g t o one Larmour p r e c e s s i o n of 2k t h e i r s p i n s . With t h i s c o n d i t i o n i t i s meaningful t o r e f e r t o the l i q u i d c r y s t a l as b e i n g o r i e n t e d i n a p a r t i c u l a r d i r -e c t i o n . The remaining case i s t h a t where the VAAC molecules undergo many r e v o l u t i o n s d u r i n g one Larmoui* p r e c e s s i o n . When a l i q u i d c r y s t a l i s i n i t s i s o t r o p i c s t a t e , t h i s c o n d i t i o n i s u s u a l l y s a t i s f i e d . For the i s o t r o p i c case, t h e r e i s an av e r a g i n g o f the angular p a r t s of the s p i n h a m i l t o n i a n . E q u a t i o n 3.2 i s r e p l a c e d b y 5 : AE=g3H + am + l a 2 ( I ( I + l ) - m 2 ) 2 g3H where g=l(g« + 2Sx) 3 and a=l(A« + 2 A X ) . 3 The i s o t r o p i c EPR spectrum c o n s i s t s o f 8 symmetric l i n e s s e p a r a t e d by the d i s t a n c e a. F i g u r e 3.1 The m o l e c u l a r c o o r d i n a t e system f o r VAAC 26 F i g u r e 3'..3 A b s o r p t i o n (a) and d e r i v a t i v e (b) l i n e s f o r VAAC i n a nematic sample when y = 90° . F i g u r e 3 . 5 A b s o r p t i o n (a) and d e r i v a t i v e (b) l i n e s f o r VAAC i n an i s o t r o p i c sample. -^2.5 67.9 -J 84.2 F i g u r e 3.6 Spectrum f o r VAAC m a nematic l i q u i d c r y s t a l when Y 7 0 . On the x-axis f i e l d v a l u e s - ( i n gauss) are give n r e l a t i v e to the resonant f i e l d of the e l e c t r o n ro co F i g u r e 3.8 Spectrum f o r VAAC i n a: r a n d o m - s a m p l e . The x - a x i s i s r e p resented as i n f i g u r e 3.6. The numbered peaks and l i n e s are r e f e r r e d t o i n f i g u r e s - 5 - 1 and 5.2. uo o F i g u r e 3.9 Spectrum f o r VAAC i n an i s o t r o p i c sample. The x - a x i s i s r e p resented as i n f i g u r e 3 - 6 . U) CHAPTER 4 Order i n the Nematic Phase F o r the nematic mesophase the molecular order par-ameter S i s d e f i n e d by the f o l l o w i n g e x p r e s s i o n 2 o . S=l<3cos 26 - 1> 2 tfhere 0 i s the angle between the long axes of the l i q u i d c r y s t a l molecules and the magnetic f i e l d and < > i n d i c a t e s a thermodynamic average. I f t h e r e i s complete order <cos 26>=l and S=l. For complete d i s o r d e r <cos 26>=l/3 and S=0. Because VAAC has i t s symmetry a x i s p e r p e n d i c u l a r to the l i q u i d c r y s t a l m o l e c u l a r a x i s , values of the order parameter c a l c u l a t e d f o r i t d i f f e r , from those of the l i q u i d c r y s t a l by the f a c t o r -1/2. Then S=-l/2 i n d i c a t e s p e r f e c t o r d e r i n g and S=0 denotes t o t a l d i s o r d e r . In nematic l i q u i d c r y s t a l s , S i s i n t e r m e d i a t e between these two v a l u e s . S measures the extent t o which the. l i q u i d c r y s t a l i s d i s o r d e r e d due_to thermal f l u c t u a t i o n s . i n which the degree of order of a s o l u t e i n a nematic meso-phase i s a u n i v e r s a l f u n c t i o n o f the reduced temperature T.. (eT/Tk where Tk i s the i s o t r o p i c - n e m a t i c t r a n s i t i o n tempera-t u r e ) . They have used the f o l l o w i n g e x p r e s s i o n t o c a l c u l a t e the temperature dependence of S. Chen, James, and L u c k h u r s t 7 have i n t r o d u c e d a model exp(U/KT)dcos6 - 1 2 33 U i s the o r i e n t a t i o n a l p o t e n t i a l energy o f the s o l u t e m o l e c u l e s . I f i t i s assumed the nematic order i s mainly due t o d i s p e r s i o n f o r c e s ( f o r c e s between i n s t a n t e o u s d i p o l e moments of the m o l e c u l e s ) , U w i l l have the f o l l o w i n g form: U=-lAS(3cos 2G-l) 2V 2 V i s the molar volume of the l i q u i d c r y s t a l and A i s a constant c h a r a c t e r i s t i c o f the l i q u i d c r y s t a l . The t h e o r e t i c a l depend-ence o f S can be found n u m e r i c a l l y from the above e x p r e s s i o n s . An EPR study o f l i q u i d c r y s t a l s i s com p l i c a t e d by the concept o f mo l e c u l a r tumbling time. In the pr e v i o u s c h a p t e r the two extremes i n tumbling time were i n v e s t i g a t e d . I f the molecules make a n e g l i g i b l y s m a l l angular change i n the time o f one Larmour p r e c e s s i o n of t h e i r s p i n s ( 1 0 ~1 0 s e c ) , they are e s s e n t i a l l y f i x e d and depending on the experimental c o n d i t i o n s they . y i e l d an o r i e n t e d or a random EPR spectrum. There w i l l be 8 l i n e s s eparated by A4, and u s u a l l y 8 peaks s e p a r a t e d by A u. On the other hand, i f the molecules undergo many r e v o l u t i o n s d u r i n g a Larmour p r e c e s s i o n an i s o t r o p i c EPR spectrum o f 8 l i n e s s eparated by "a" i s produced. The slow tumbling c o n d i t i o n has been i n v e s t i g a t e d by Schwerdtfeger and Diehl 1* and James and L u c k h u r s t 5 . The c a l c u l a t i o n of m o l e c u l a r order i s c a r r i e d out i n two s t e p s . F i r s t , an ang u l a r d i s t r i b u t i o n f u n c t i o n i s found experiment-a l l y f o r the l i q u i d c r y s t a l m o l e c u l e s . As d i s c u s s e d i n the 34 p r e v i o u s chapter t h i s has the form f ( 8 ) = e x p ( - C c o s 2 6 ) . Then t h i s d i s t r i b u t i o n f u n c t i o n i s used to c a l c u l a t e the average <3cos26 - 1>. In p r a c t i c e t h i s i s a l o n g and t e d i o u s pro-cedure because i n order to f i n d an angular d i s t r i b u t i o n f u n c t i o n at a g i v e n temperature, the l i q u i d c r y s t a l must be examined i n a range of o r i e n t a t i o n s between 0° and 90° to the magnetic f i e l d . The f a s t tumbling c o n d i t i o n i s d e s c r i b e d by Pryburg and G e l e r i n t e r 6 and Chen, James and L u c k h u r s t 7 . The order parameter may be d e r i v e d from the H a m i l t o n i a n f o r i s o t r o p i c l i q u i d s . S=l<3cos26 - l>=l(<a> - a) 2 2 (a - A i . ) <a> i s the measured h y p e r f i n e s p l i t t i n g . I t i s r e l a t i v e l y easy to f i n d the temperature dependence of S with t h i s r e l a t i o n . The p r e c e e d i n g paragraphs d e s c r i b e the two extremes i n tumbling time. U n f o r t u n a t e l y , the experimental s i t u a t i o n d i s c u s s e d i n t h i s t h e s i s i n v o l v e s i n t e r m e d i a t e tumbling times f o r which n e i t h e r of the above methods are t r u l y a p p l i c a b l e . The m o l e c u l a r tumbling time i s l a r g e l y a f u n c t i o n of v i s c o s i t y . In the temperature range through which the nematic mesophase e x i s t s , l i q u i d c r y s t a l s u s u a l l y undergo l a r g e changes i n v i s c o s i t y . Hence a r i g o r o u s c a l c u l a t i o n of the order parameter i s not s t r a i g h t f o r w a r d . For t h i s study, 35 the assumption o f f a s t tumbling was made i n so f a r as the e x p r e s s i o n (<a> - a ) / 2 * ( a - Ax) was used f o r order c a l c u l -a t i o n s . F u r t h e r c o n s i d e r a t i o n was made f o r changes i n v i s c o s i t y . The h y p e r f i n e s p l i t t i n g o f VAAC i n " O c t o i l " , a vacuum pump o i l , was obt a i n e d as a f u n c t i o n o f kinematic v i s c o s i t y ( f i g u r e 4.1). T h i s o i l was chosen because i t s v i s c o s i t y covers the range of the v i s c o s i t i e s o f the l i q u i d c r y s t a l s used i n t h i s study i n a s i m i l a r . t e m p e r a t u r e range. The h y p e r f i n e s p l i t t i n g i n the l i q u i d c r y s t a l s was expected t o have a s i m i l a r dependence on v i s c o s i t y . S c h w e r d t f e g e r 8 has suggested the measured S i s an e f f e c t i v e o r d e r parameter and the q u a n t i t i e s o f v i s c o u s order and t r u e o r d e r may be c o n s i d e r e d to be a d d i t i v e . Then Seff= s t r u e + s v i s * ^v±s m a v b e estimated by c a l c u l a t i n g (<a> - a ) / 2 * ( a - Aj.) from the VAAC i n O c t o i l curve at the a p p r o p i a t e v i s c o s i t y . The e f f e c t i v e order parameter c a l c u l a t e d as a f u n c t -i o n o f temperature f o r s e v e r a l l i q u i d c r y s t a l s i s i l l u s t r a t e d i n f i g u r e 4.2. The kinematic v i s c o s i t i e s f o r the same l i q u i d c r y s t a l s are p l o t t e d a g a i n s t temperature i n f i g u r e 4.3. The i n t e r e s t i n g f e a t u r e o f these curves i s t h a t w h i l e the v i s c o s -i t i e s are continuous throughout the nematic range, f o r a l l the l i q u i d c r y s t a l s the e f f e c t i v e order parameter has a d i s c o n t -i n u i t y at an i n t e r m e d i a t e temperature i n the nematic range. 37 <d- ro C V J A T ro CM <T ro co o" o o" d d d o " d d ~ s e f f F i g u r e k ,2 E f f e c t i v e order parameter versus reduced temperature f o r VAAC i n the nematic l i q u i d c r y s t a l s : (a) b i s ( 4 ' - n - o c t y l o x y b e n z a l ) - 2 - c h l o r o - l , 4 - p h e n y l e n e d i a -mine 6, (b) MBBA, and (c) 4-methoxy b e n z y l i d e n e - 4 -amino-a-methyl cinnamic a c i d - n - p r o p y l e s t e r 8 38 X TEMPERATURE (°C) F i g u r e 4.3 Kinematic v i s c o s i t y versus temperature f o r (a) O c t o i l , X, (b) 4-methoxy benzylidene-4-amino-a-methy1 c i n - • namic a c i d - n - p r o p y l e s t e r 8 , 6 , and (c) MBBA,* F i g u r e Luckhursts t h e o r e t i c a l curve i s compared wi t h curves of S e f f and S e f f - l / 3 ( S v i s + D) versus temperature i n MBBA. The dashed curve i s S e f f - l / 3 ( S y i s + D) and the bottom curve i s Luckhursts curve. vo 40 l / T ' 1 0 3 ( ° K ) _ 1 Figure 4.5 Proton r e l a x a t i o n time T versus r e c i p r o c a l of the temperature at 18 .2 MHz f o r MBBA 41 The dashed l i n e s i n f i g u r e 4.2 correspond to the u n i v e r s a l t h e o r e t i c a l o r d e r curve c a l c u l a t e d by L u c k h u r s t 7 . In each case the experimental s l o p e i s g r e a t e r than the t h e o r e t i c a l s l o p e . In f i g u r e 4.4 the temperature dependence o f the e f f e c t i v e order parameter f o r VAAC i n MBBA i s compared w i t h L u c k h u r s t s curve. Luckhurst has suggested the d i f f e r e n c e between the two curves may be accounted f o r by i n t r o d u c i n g o t h e r terms i n the o r i e n t a t i o n a l p o t e n t i a l energy f u n c t i o n U. The dashed curve i n f i g u r e 4.4 i s S e f f - l / 3 ( S v i s + D) where S vj_s i s c a l c u l a t e d as d e s c r i b e d p r e v i o u s l y and D i s a c o n s t a n t . The f a c t o r 1/3 may be an i n d i c a t i o n t h a t the VAAC molecules are r e s t r i c t e d i n only one of the t h r e e p o s s i b l e d i r e c t i o n s of angular motion. That t h i s curve i s p a r a l l e l t o the t h e o r e t i c a l curve i s an i n d i c a t i o n t h a t the d e v i a t i o n i n S e f f from S t r u e may be due to v i s c o s i t y e f f e c t s a l o n e . NMR s p i n r e l a x a t i o n s t u d i e s on two l i q u i d c r y s t a l s 8 show a change i n the dominant r e l a x a t i o n mechanism at the same temperature as the s l o p e d i s c o n t i n u i t y i n the e f f e c t i v e o r d e r c u r v e s . T h i s suggests the d i s c o n t i n u i t y may be due to some p h y s i c a l change i n the l i q u i d c r y s t a l . Both v i s c o s i t y and t h e o r e t i c a l o r d e r are smoothly v a r y i n g f u n c t i o n s of temp-e r a t u r e so i t i s u n l i k e l y they c o u l d e f f e c t the observed change i n s l o p e . .. In c o n c l u s i o n , i t appears the e f f e c t i v e order curves are c o n s i d e r a b l y a f f e c t e d by the v i s c o s i t y of the l i q u i d 42 c r y s t a l . But the sl o p e d i s c o n t i n u i t y i n the i n t e r m e d i a t e temperature range cannot be due to v i s c o s i t y and must t h e r e -f o r e i n d i c a t e some p h y s i c a l change i n the l i q u i d c r y s t a l i t s e l f . The mechanism of t h i s change i s not apparent from the dat a a v a i l a b l e at the present time. • At t h i s stage i t should be noted t h a t EPR i s not an i d e a l t o o l f o r order d e t e r m i n a t i o n i n l i q u i d c r y s t a l s . F i r s t l y , the order o b t a i n e d i s of the s o l u t e , i n t h i s case VAAC, and.not t h a t o f the l i q u i d c r y s t a l . Secondly, f o r the l i q u i d c r y s t a l s used i n t h i s study the mol e c u l a r tumbling times were i n an i n t e r m e d i a t e range where n e i t h e r the theory f o r f i x e d s p i n s or f a s t tumbling was a c c u r a t e l y a p p l i c a b l e . T h i r d l y , i n the range of v i s c o s i t y where the measurements were taken, t h e r e was c o n s i d e r a b l e l i n e broadening and o v e r l a p p i n g o f adjacent l i n e s which made i t d i f f i c u l t to determine the h y p e r f i n e s p l i t t i n g w i t h p r e c i s i o n . CHAPTER 5 O r i e n t a t i o n of C h o l e s t e r i c L i q u i d C r y s t a l s by a Magnetic F i e l d The l i q u i d c r y s t a l molecules used i n t h i s study have approximately a x i a l symmetry. Two values of diamagnetic s u s c e p t i b i l i t y may be a s c r i b e d t o them: one i n the d i r e c t i o n o f the m o l e c u l a r a x i s , X ( ( J a n ( i one i n the t r a n s v e r s e d i r e c -t i o n , Xx • The d i f f e r e n c e between these two v a l u e s , X=Xt» - Xx determines how a f r e e l i q u i d c r y s t a l molecule behaves i n an e x t e r n a l magnetic f i e l d . The f r e e energy i n v o l v e d in„the i n t e r a c t i o n w i t h a magnetic f i e l d H may be expressed by the f o l l o w i n g p r o p o r t i o n a l i t y . Fmag ' - x C n-H) 2 n i s a u n i t v e c t o r i n the d i r e c t i o n of the long m o l e c u l a r a x i s . In order t o minimize i t s f r e e energy a molecule with p o s i t i v e x w i l l o r i e n t w i t h i t s symmetry a x i s p a r a l l e l t o the magnetic f i e l d and a molecule with n e g a t i v e x w i l l o r i e n t w i t h i t s symmetry a x i s p e r p e n d i c u l a r to the f i e l d . Now, i n the case of a l i q u i d c r y s t a l sample with molecules of p o s i t i v e XJ a magnetic f i e l d e x e r t s a torque on the s t r u c t u r e t e n d i n g to a l i g n the l o c a l symmetry a x i s p a r a l l e l t o the f i e l d . For a nematic mesophase with x p o s i t i v e the b e h a v i o r i n an e x t e r n a l magnetic f i e l d i s s i m p l e . The mole-c u l e s tend t o a l i g n i n the magnetic f i e l d d i r e c t i o n . Since a s i t u a t i o n w i t h a l l the molecules a l i g n e d or n e a r l y a l i g n e d 43 44 i s compatible with the nematic s t r u c t u r e , t h i s i s the f i n a l arrangement of the l i q u i d c r y s t a l . As d e s c r i b e d i n the f i r s t c h apter, the c h o l e s t e r i c mesophase i s made up of s u c c e s s i v e planes i n which the l i q u i d c r y s t a l molecules are s i t u a t e d with t h e i r symmetry axes p a r a l l e l t o the p l a n e s . The d i r e c t i o n normal to these planes i s c a l l e d the h e l i x a x i s . In each plane the molecules are a l i g n e d i n the same d i r e c t i o n but i n s u c c e s s i v e planes the symmetry axes change d i r e c t i o n by a s m a l l angle making up the c h a r a c t e r i s t i c h e l i c a l s t r u c t u r e . I t has been shown 9 1 1 0' 1 1 that i n h i g h e x t e r n a l mag-n e t i c f i e l d s a c h o l e s t e r i c s t r u c t u r e breaks down to a nematic s t r u c t u r e w i t h a l l the molecules p o i n t i n g i n the same d i r -e c t i o n . However, f o r i n t e r m e d i a t e f i e l d s the b e h a v i o r of the c h o l e s t e r i c s t r u c t u r e i s not t r i v i a l . The h e l i c a l sym-metry of the c h o l e s t e r i c mesophase d e f i n e s two d i r e c t i o n s : one along the h e l i x a x i s and the other i n the plane perpend-i c u l a r to the h e l i x a x i s . The molecules are arranged t r a n s -v e r s e to the h e l i x a x i s d i r e c t i o n . P e r p e n d i c u l a r to the h e l i x a x i s , they are p o i n t i n g i n a l l a n g l e s , 0° through 360°,in the p l a n e . I t i s assumed t h a t a magnetic f i e l d would o r i e n t a c h o l e s t e r i c l i q u i d c r y s t a l along one of these two d i r e c t i o n s . M e y e r 1 0 reasons t h a t a c h o l e s t e r i c l i q u i d c r y s t a l whose molecules have p o s i t i v e x should o r i e n t w i t h i t s h e l i x a x i s p e r p e n d i c u l a r to a magnetic f i e l d . His q u a l i t a t i v e 45 argument i s based on the assumption the c h o l e s t e r i c mesophase behaves as a u n i t w i t h s u s c e p t i b i l i t i e s of Xx along the h e l i x a x i s and (x„ + Xx)/2 p e r p e n d i c u l a r to the h e l i x a x i s . S i n c e , f o r p o s i t i v e X J ( X « + Xx)/2 i s g r e a t e r than x x t h e s t r u c t u r e s h ould have l e s s f r e e energy when i t s h e l i x a x i s i s perpend-i c u l a r to the f i e l d . In t h i s case as the f i e l d i n t e n s i t y i s i n c r e a s e d , more and more molecules are turned toward the f i e l d d i r e c t i o n c a u s i n g an u n t w i s t i n g o f the l i q u i d c r y s t a l about the h e l i x a x i s . At h i g h e r f i e l d s the s t r u c t u r e becomes nematic. A second p o s s i b i l i t y i s f o r the c h o l e s t e r i c l i q u i d c r y s t a l to have i t s h e l i x a x i s p a r a l l e l to the f i e l d . For n e g a t i v e x t h i s o r i e n t a t i o n would f o l l o w from Meyer* "s theory In t h i s case an i n c r e a s e i n f i e l d s t r e n g t h should not cause the s t r u c t u r e to become nematic. I f x i s p o s i t i v e , B a e s s l e r and L a b e s 1 2 suggest, f o r the analogous e l e c t r i c f i e l d case, t h a t the h e l i x a x i s can be a l i g n e d i n the f i e l d d i r e c t i o n i f a c o n i c a l p e r t u r b a t i o n o c c u r s . T h i s c o n i c a l p e r t u r b a t i o n i s a t i l t i n g of the l i q u i d c r y s t a l molecules out of t h e i r planes due to the torque e x e r t e d on them by the magnetic f i e l d . Each l i q u i d c r y s t a l molecule i s at a s m a l l angle to the d i r e c t i o n p e r p e n d i c u l a r to the f i e l d . As the magnetic f i e l d s t r e n g t h i n c r e a s e s t h i s angle gets l a r g e r and as w e l l the h e l i c a l s t r u c t u r e begins to u n w i n d 1 3 . When the angle of p e r t u r b a t i o n reaches 4 ° 1 2 , the c h o l e s t e r i c s t r u c t u r e breaks down and a 46 nematic s t r u c t u r e i s produced. The f i e l d s r e q u i r e d t o o r i e n t c h o l e s t e r i c l i q u i d c r y s t a l s are i n g e n e r a l much h i g h e r than those necessary to o r i e n t nematic l i q u i d c r y s t a l s 1 1 . Thus f a r , c h o l e s t e r i c o r i e n t a t i o n has been produced only i n s p e c i a l p r e p a r a t i o n s which are weakly c h o l e s t e r i c ( i . e., the angle between suc-c e s s i v e planes i s l a r g e and o r i e n t a t i o n i s more r e a d i l y a c h i e v a b l e ) . In t h i s study, the magnetic b e h a v i o r o f two types o f weak c h o l e s t e r i c s i s examined. I f a s m a l l amount of an o p t i c a l l y a c t i v e m a t e r i a l i s added to a nematic l i q u i d c r y s t a l , the r e s u l t i n g mixture i s o f t e n weakly c h o l e s t e r i c . When 2 percent by weight of c h o l e s t e r y l c h l o r i d e (C) i s added t o MBBA, a c h o l e s t e r i c mixture r e s u l t s . Since MBBA arranges i t s molecules p a r a l l e l t o a magnetic f i e l d i t must have a p o s i t i v e x - Then the mixture d e s c r i b e d above i s an example of a weak c h o l e s t e r i c w i t h p o s i t i v e x« I t was b e l i e v e d on the b a s i s of other e x p e r i m e n t s 1 0 ' 1 1 t h a t the C-MBBA mixture would o r i e n t with i t s h e l i x a x i s p e r p e n d i c u l a r to a magnetic f i e l d . The ob j e c t o f the f o l l o w -i n g experiment was to demonstrate t h i s u s i n g EPR. An o r i e n t -i n g f i e l d was imposed on the C-MBBA sample f o r a p e r i o d of 7 minutes. Then an EPR spectrum was taken by sweeping the f i e l d between 2 and 4 k i l o g a u s s . The sample was r o t a t e d 9 0 ° and another spectrum was taken. Then the sample was r o t a t e d 47 back to 0 ° , the o r i e n t i n g f i e l d was incremented by 5 k i l o g a u s s , and the procedure r e p e a t e d . T h i s was c a r r i e d out f o r o r i e n t i n g f i e l d i n t e n s i t i e s between 0 and 20 k i l o g a u s s . A l l measurements were made at room temperature. The r e l a x -a t i o n time o f the l i q u i d c r y s t a l from the o r i e n t e d s t a t e to the random s t a t e was found, by measuring peak i n t e n s i t i e s as a f u n c t i o n o f time, to be about 30 minutes. Since 8 minutes were r e q u i r e d t o o b t a i n EPR s p e c t r a between each o r i e n t a t i o n the experiment was e s s e n t i a l l y q u a l i t a t i v e . In order to ana l y s e the EPR data i t i s u s e f u l t o p r e d i c t the c h a r a c t e r i s t i c s of the s p e c t r a obtained at 0° and 90° to the f i e l d as a f u n c t i o n of f i e l d s t r e n g t h . A sample which has not undergone any o r d e r i n g can be expected t o produce a random EPR spectrum. As the o r i e n t i n g f i e l d i n c r e a s e s the h e l i x a x i s w i l l move p e r p e n d i c u l a r t o the f i e l d d i r e c t i o n . Since the h e l i x a x i s can be anywhere i n a plane p e r p e n d i c u l a r t o the f i e l d , the spectrum at 90° should s t i l l be random. However, along the f i e l d d i r e c t i o n , the s p e c t r a w i l l not remain random. As the f i e l d i n t e n s i t y i n -creases the h e l i c a l s t r u c t u r e w i l l unwind such t h a t more and more molecules are p a r a l l e l to the f i e l d . In the l i m i t of very h i g h f i e l d s the s t r u c t u r e becomes nematic and the s p e c t -rum w i l l be t h a t of a nematic at 0°. Then, the EPR s p e c t r a w i l l have the f o l l o w i n g p r o p e r t i e s . A l l the s p e c t r a at 90° w i l l be s i m i l a r and w i l l be r e p r e s e n t a t i v e of randomly 48 arranged m o l e c u l e s . The spectra, at 0° w i l l be random at zero f i e l d but as f i e l d s t r e n g t h i n c r e a s e s the p a r a l l e l comp-onents become l a r g e r and the p e r p e n d i c u l a r components s m a l l e r . F i g u r e 5.1 shows the h e i g h t s o f some of the p e r p e n d i c u l a r peaks and the h e i g h t s of one of the p a r a l l e l l i n e s as a f u n c t i o n o f magnetic f i e l d f o r sample o r i e n t a t i o n s of 0° and 90°. I t i s i n t e r e s t i n g to note t h a t i n the 0° data the l i n e s c o r r e s p o n d i n g t o VAAC molecules o r i e n t e d along the f i e l d do i n c r e a s e as the f i e l d s t r e n g t h i n c r e a s e s and the l i n e s c o r -responding to VAAC molecules o r i e n t e d t r a n s v e r s e t o the f i e l d decrease as f i e l d s t r e n g t h i n c r e a s e s . " The peak h e i g h t s are e s s e n t i a l l y constant f o r the 90° da t a . On the b a s i s o f t h i s d ata i t i s a s s e r t e d t h a t the C-MBBA mixture o r i e n t s w i t h i t s h e l i x a x i s p e r p e n d i c u l a r t o the f i e l d . T h i s i s i n agreement with Meyer's theory f o r l i q u i d c r y s t a l s w i t h p o s i t i v e x v a l u e s . C h o l e s t e r y l c h l o r i d e (C) possesses a l e f t handed o p t i c a l r o t a r y power. C h o l e s t e r y l m y r i s t a t e (M) has a r i g h t handed o p t i c a l r o t a r y power. I f these two are mixed i n the ap p r o p i a t e p r o p o r t i o n s the r o t a r y powers have a c a n c e l l i n g e f f e c t p r o d u c i n g a weak c h o l e s t e r i c or i n some circumstances. a nematic s t r u c t u r e . A 1.75:1 by weight c h o l e s t e r y l c h l o r i d e -c h o l e s t e r y l m y r i s t a t e mixture (CM) i s weakly c h o l e s t e r i c at room temperature. The experiment w i t h C-MBBA was repeated with the 1.75:1 CM mixture. On the b a s i s of other work 9' 1 2 t h i s mixture 4 9 F i g u r e 5 .1 Peak i n t e n s i t i e s f o r the C-MBBA mixture versus o r i e n t i n g magnetic f i e l d . The numbers r e f e r to the c o r r e s p o n d i n g peaks and l i n e s i n f i g u r e 3.8. 50 was expected to o r i e n t with i t s h e l i x a x i s p a r a l l e l to the magnetic f i e l d . As b e f o r e , a sample which has not undergone any o r d e r i n g can be expected to g i v e a random EPR spectrum. Now, as the o r i e n t i n g f i e l d i s i n c r e a s e d the l i q u i d c r y s t a l molecules w i l l tend to o r i e n t themselves t r a n s v e r s e to the magnetic f i e l d . Then, f o r the 0° s p e c t r a the p e r p e n d i c u l a r components should i n c r e a s e and the p a r a l l e l components de-c r e a s e . On the other hand,.for the 90° s p e c t r a t h e r e should be an i n c r e a s e i n the p a r a l l e l components and a decrease i n the p e r p e n d i c u l a r components. A c o n i c a l p e r t u r b a t i o n , i f i t e x i s t e d , would be l e s s than 4°12 and t h e r e f o r e not obser-vab l e . w i t h i n the accuracy of the experiment. The data i s p r e s e n t e d i n f i g u r e 5.2. The h i g h e s t magnetic f i e l d used, 20 k i l o g a u s s , was not i n t e n s e enough to produce h e l i c a l breakdown t o a nematic s t r u c t u r e . T h i s data i s b e l e i v e d t o r e i n f o r c e the a s s e r t i o n t h a t the CM mixture o r i e n t s w i t h i t s h e l i x a x i s p a r a l l e l t o a magnetic f i e l d . The above evidence on the CM mixture may be i n t e r -p r e t e d i n two ways. I f the molecules i n the CM mixture have n e g a t i v e x v a l u e s , the h e l i x a x i s would be expected t o o r i e n t p a r a l l e l t o the f i e l d 1 " 1 . However, t h i s p o s s i b i l i t y i s not f e a s i b l e because i t has been shown 9 t h a t under h i g h magnetic f i e l d s the CM mixture may be made nematic with the l i q u i d c r y s t a l molecules p a r a l l e l to the f i e l d d i r e c t i o n . The second i n t e r p r e t a t i o n i s t h a t the CM mixture takes on a c o n i c a l I I I I : 1 0 5 10 15 20 . ORIENTING FIELD (KILOGAUSS) F i g u r e 5.2 Peak i n t e n s i t i e s f o r the CM mixture versus o r i e n t i n g magnetic f i e l d . The numbers r e f e r t o the c o r r e s p o n d i n g peaks and l i n e s i n f i g u r e 3-8. 52 p e r t u r b a t i o n 1 2 ' 1 5 . Although experimental^ v e r i f i c a t i o n of the e x i s t e n c e o f t h i s p e r t u r b a t i o n was not p o s s i b l e , the second i n t e r p r e t a t i o n seems to be the most reasonable mechanism. However,.more experimental evidence i s necessary b e f o r e a complete d e s c r i p t i o n o f the problem can be made. CHAPTER 6 D i s c u s s i o n T h i s t h e s i s p r e s e n t s the a p p l i c a t i o n of EPR techniques to two important problems i n l i q u i d c r y s t a l s : the d e t e r m i n a t i o n o f m o l e c u l a r order i n nematics and the b e h a v i o r of c h o l e s t e r i c s i n a high magnetic f i e l d . The s t a t e of understanding of the theory o f mol-e c u l a r order i s f a r from complete. One of the p r i n c i p l e d i f f i c u l t i e s i s t h a t no method has been d e v i s e d t o c a l c u l a t e t r u e order from EPR s p e c t r a i n the i n t e r m e d i a t e tumbling time r e g i o n where the time f o r one r e v o l u t i o n of the l i q u i d c r y s t a l molecules i s of the order of one Larmour p r e c e s s i o n . U n f o r t -u n a t e l y , the most i n t e r e s t i n g p a r t of the order curve, the s l o p e d i s c o n t i n u i t y , occurs i n t h i s r e g i o n . P o s s i b l y the answer i s t o determine order w i t h another technique. I n f r a r e d d i c h r o i s m , u l t r a v i o l e t d i c h r o i s m , NMR, X-ray s c a t t e r i n g , measurement of p r i n c i p l e r e f r a c t i v e i n d i c e s , and measurement o f p r i n c i p l e diamagnetic s u s c e p t i b i l i t i e s are a l t e r n a t e methods of c a l c u l a t i n g the order p a r a m e t e r 1 6 . Since these techniques g i v e i n f o r m a t i o n d i r e c t l y on the l i q u i d c r y s t a l i t s e l f and not on a s o l u t e i n the l i q u i d c r y s t a l , i t would be f r u i t f u l t o compare them w i t h EPR The knowlege of magnetic b e h a v i o r of c h o l e s t e r i c s i s r e l a t i v e l y c o n s i s t e n t but more experimental evidence and 53 54 t h e o r e t i c a l background are r e q u i r e d . I f more a c c u r a t e EPR data c o u l d be ob t a i n e d i t would be u s e f u l to do an e x t e n s i v e computer a n a l y s i s of the o r i e n t a t i o n of c h o l e s t e r i c molecules. T h i s might v e r i f y the e x i s t e n c e of a c o n i c a l p e r t u r b a t i o n i n the CM mixture. Although EPR i s perhaps one of the most con-v e n i e n t and p r o d u c t i v e methods of de t e r m i n i n g o r i e n t a t i o n i n l i q u i d c r y s t a l s , many other u s e f u l techniques are a v a i l a b l e . These i n c l u d e measurement of l i g h t a b s o r p t i o n by d i s s o l v e d r a d i c a l s 1 7 , measurement of . d i e l e c t r i c c o n s t a n t s 1 2 , measurement o f o p t i c a l r o t a r y p o w e r 1 8 , and NMR9. The value of EPR i n the study of l i q u i d c r y s t a l s may be i n c r e a s e d i f more convenient paramagnetic probes can be found. An i n t e r e s t i n g r a d i c a l was used by F e r r u t t i et a l 1 9 i n an EPR d e t e r m i n a t i o n of o r d e r . T h i s r a d i c a l , 2 , 2 , 6 - t e t r a -m e t h y l - 4 - ( p - a c t l o x y ) - b e n z o y l o m i n o - p i p e r d i n e - l - a x y l i s c i g a r shaped and has an approximately a x i a l "g" t e n s o r and an a x i a l A t e n s o r . The s p e c t r a l i n e s from i t are w e l l s e p a r a t e d . Due to i t s c i g a r shape t h i s molecule w i l l be more r e s t r i c t e d by the l i q u i d c r y s t a l molecules than the p l a n a r VAAC. For t h i s r eason, i t should g i v e a more d i r e c t r e p r e s e n t a t i o n of order and o r i e n t a t i o n than VAAC. The i d e a l way to use EPR i n l i q u i d c r y s t a l s would be to a t t a c h s p i n l a b e l s to the l i q u i d c r y s t a l molecules them-s e l v e s . As yet no c o n v i n c i n g treatment of t h i s problem has been found i n the l i t e r a t u r e . APPENDIX 1 T r a n s f o r m a t i o n o f the S p i n H a m i l t o n i a n f o r A x i a l l y Symmetric  Ions In the case o f a x i a l symmetry i t i s convenient to choose the x- a x i s such t h a t the e x t e r n a l f i e l d H i s i n the x-z p l a n e . Then Hy=0 w i t h no l o s s o f g e n e r a l i t y . H i s at angle 0 to the -z-axis. The H a m i l t o n i a n may be w r i t t e n as: H s=3H(g l lS zcos0 + g x S x s i n 0 ) + A „ S Z I Z + A X ( S X I X + S y l y ) Using the t r a n s f o r m a t i o n : S z = Sz''cos(J) - Sx^sincf) Sx=Sz^sin<|) + Sx""cos(j> s y = s y " the e l e c t r o n s p i n s may be changed to a set of axes r o t a t e d about the y - a x i s by an angle <J>.. T h i s y i e l d s the f o l l o w i n g e x p r e s s i o n f o r the Zeeman term. H 4=3H[S Z^ (gxsin0sin<|> + g„cos0cost|>) + S x" (g^sinecostj) - g„cos0sin(|>) ] The term i n S x" i s zero i f : g^sinOcosc}) - g(l cos0sincj)=O o r : tan(j>=gxtan0 D e f i n e : g 2 = g „ 2 c o s 2 0 + g x 2 s i n 2 0 55 56 Then: sin<j)=g_isin0 and cos<j)=gnCos8 g g Upon s u b s t i t u t i n g these back i n t o the Ha m i l t o n i a n the r e s u l t i s : H a=gSHS z' I f the transformed S z^, Sx"*, and Sy"* are put i n t o the h y p e r f i n e p a r t o f the H a m i l t o n i a n , terms e x i s t i n S X ' I X , S y ' l y , S X ' I Z , and S Z " I X . The f i r s t t h r e e , which connect energy s t a t e s separated by g3H, may be t r e a t e d by second .order p e r t u r b a t i o n theory i n f i n d i n g the energy e i g e n v a l u e s s i n c e |A j <<g3H f o r VAAC. However, because S Z ' I X connects s t a t e s t h a t d i f f e r i n energy only by A i t cannot be handled i n t h i s way. But S Z-*I X may be e l i m i n a t e d by choosing a new set of axes f o r I t h a t are r o t a t e d about the y - a x i s at an angle \p. Then: I z = I z ' c o s ^ - I x ^ s i n i j j I x = I z ^ s i n i | j + I x"cos^ T =1 " With t h i s t r a n s f o r m a t i o n the h y p e r f i n e p a r t of the Ha m i l t o n i a n may be w r i t t e n : H =S Z'I z^.( Aj.sincj)sini|J + A« cos<J>cosip) + . S z -*I x"(AiSin<{>cosif) - A» coscj)sin^) + Sx^I^CAxcos^cos^ -. An sincj)sin^) + S X ^ I Z " ( A x c o s t j j s i n ^ - Ansincj>cosip) t ' S y ' I y ' A x 57 Now S Z " * I X ^ i s e l i m i n a t e d i f : A A sincj>cosiJ; - A(,cos<J>sin^=0 D e f i n e : A 2 g 2 = A „ 2g„ 2cos 29 + A x 2 g j . 2 s i n 2 6 Then: sin^=Axgj. sin6 and cos^=A»gn cos9 Ag Ag By s u b s t i t u t i n g the above e x p r e s s i o n s f o r \p and cf) i n terms o f 6 the f o l l o w i n g s p i n H a m i l t o n i a n i s ach i e v e d . H 5=g3HS z- + A S Z ' I Z ' + A M A X S X ' I x " + A j . S Y " I Y ' + (A,>2 - A x 2 ) g „ g x s i n ( 2 6 ) S Y - ' I 7 / 2A T h i s i s e x p r e s s i o n 3.1. , APPENDIX 2 The Energy E i g e n v a l u e s of the S p i n H a m i l t o n i a n f o r A x i a l l y  Symmetric Ions I t i s r e q u i r e d to f i n d the energy o f the s t a t e |M,m> f o r the H a m i l t o n i a n 3.1. Hj.=g!3HSz- + A S Z * I Z ' + A„Ai.S Y'I v" + A i S ' I ' ' — ^ X X y y + (An 2 - A i. 2)g„gxsin(2e)S v"I f 7" 2A gr To f i r s t order the eigenvalues of H are: E1=<M,m|Hs|M,m>=g3HM + AMm Ap p l y i n g second order p e r t u r b a t i o n t h e o r y : E 2=E* + E l<M",m"|H?|M,m>|2 M*,mVM,m E u - E u i where E° i s the z e r o t h order energy ggHM. Then the s o l u t i o n t o the problem l i e s i n c a l c u l a t i n g the f o l l o w i n g matrix elements. <M",m'|Hy|M,m> The values of these elements are: ( u s i n g S x= S+ + S_; Sy=S + - S_; and s i m i l a r r e l a t i o n s f o r I x and l y <M+lim|Hs |MJm> = (A„ 2 - Aa, 2 )g„ g ^ s i n ( 29 )m[S (S + l ) -M (M+l) ] ^ <M - l , m | H 5 | M J m > = ( A „ 2 - Ai 2)g„g xsin(29)m[S(S+1)-M(M-1)V 4A " i 2 -58 59 <M,m+l|Hs|M,m>=0 <M,m-l |H s |M ,m>=0 <M+l,m-l| Hs |M,m>= (A„ A x : + 4A A A O [ S ( S + l ) -M(M+1)]*[I(I+1) i -m(m-l)]* <M-l,m+l| H S |M,m>= (An Ao. + HA AAJ. ) [S(S+1) -M(M-l)]*[1(1+1) -m(m+l) <M+l,m+l| H S |M,m>= ( A T L A X AAJL)[S ( S+1) -M(M+1)]'[I(I+1) -m(m+l)]* 4A <M-l,m-l| H 5 |M,m>= ( A „ Ax A A A ) [ S ( S + 1 ) -M(M-l)]*[I(I+1) -m(m-l)]* .Then the second order energy ei g e n v a l u e s are: E=g$HM + AMm . + l<M+l,m|HslM,m>|2 + [<M-1,m1H41M,m>|2 -ggH +g6H + 1<M+l,m-l|Hs |M,m> j 2 + j <M-1,m+l|Hy [M,m>| -g3H +g3H + l<M+l,m+llH 3|M,m>| 2 + |<M-l,m-l|H5|Mfm>12 -g3H +ggH On m u l t i p l y i n g t h i s out and c o l l e c t i n g terms the f o l l o w i n g r e s u l t i s o b t a i n e d . E=g3HM + AMm + A „ A x 2 m [ M 2 - S ( S + l ] + ( A u 2 + A 2 ) A x 2 M [ I ( I + l ) - m 2 ] 2AggH 4A zggH - (Au 2 - A x 2 ) 2 8A zg3H g„gxl 2 s i n (20)Mm5 The energy absorbed by the microwave f i e l d i n a t r a n s i t i o n between e l e c t r o n energy l e v e l s i s ob t a i n e d by s o l v i n g the above e q u a t i o n f o r (M,m) and (M-l,m) and t a k i n g the d i f f e r e n c e . The f o l l o w i n g r e s u l t i s o b t a i n e d . 60 AE=g3H + Am + (A t > 2 + A z ) A x 2 ( I ( I + l ) - m 2 ) 4A^ggH + (A,,2 - A x 2 ) 2 8A zg3H I S ; s i n 2 ( 2 0 ) m : T h i s i s e x p r e s s i o n 3-2. ( 61 REFERENCES 1. Glarum, S. H. and M a r s h a l l , J . H., J . Chem. Phys. 16_» 55, (1967). 2. Chen, D. H. and L u c k h u r s t , G. R., T r a n s . Faraday Soc. 65, 6 5 6 , (1969). 3. Meier, G. and Saupe, A., Mol. C r y s t . 1, 515, (1966). 4. Schwerdtfeger, C. F. and D i e h l , P., Mol. Phys. 17, 417, (1969). 5. James, P. G. and Luck h u r s t , G. R., Mol. Phys. 19, 489, (1970). 6 . F r y b u r g , G. C. and G e l e r i n t e r , E. J . , J . Chem Phys. 52, 3378, (1970). 7 . Chen, D. H., James, P. G., and L u c k h u r s t , G. R., Mol. C r y s t 8, 789, (1969). 8 . Schwerdtfeger, C. F., Ma r u s i c , M., Mackay, A. L,, '.arid Dong, R. Y., to be p u b l i s h e d i n Mol. C r y s t . 9. Sachman, E., Meiboom, S., and Snyder, L. C , J . Am. Chem. Soc. 8 9 , 5981, (1968). 1 0 . Meyer, R. B., A p p l i e d Phys. L e t t . 1_4, 2 0 8 , (1969). 11. Durand, G., Leger, L., Rondelez, F., and V e y s s i e , M., Phys. Rev. L e t t . 2_2, 2 2 7 , (1969). 1 2 . B a e s s l e r , H., Laronge, T. M., and Labes, M. M., J . Chem. Phys.. 5 1 , 3 2 1 3 , (1969). 1 3 . B a e s s l e r , H., Laronge, T. M., and Labes, M. M., J . Chem. Phys. 5 2 , 6453, (1970). 14. K e s s l e r , J . 0., i n " L i q u i d C r y s t a l s and Ordered F l u i d s " e d i t e d by Johnson, R. F. and P o r t e r , R. S., Plenum P r e s s , New York (1970) p . 3 6 1 15. De Gennes, P. G., Mol. C r y s t . 8_, 531, ( 1 9 6 9 ) . 1 6 . Saupe, A., Angew. Chem. I n t e r n a t . E d i t . 7, 97, (1969). 1 7 . Sachman, E., Chem. Phys. L e t t . 3, 253, (1969). 62 18. Wysocki, J . J . , Adams, J . , and Haas, W., Phys. Rev. L e t t . 2p_, 1 0 2 4 , ( 1 9 6 8 ) . 1 9 . F e r r u t t i , P., G i l l , D., Harpold, M. A., and K l e i n , M. P., J . Chem. Phys. 5 0 , 4 5 4 5 , ( 1 9 6 9 ) . 2 0 . Saupe, A., Z. N a t u r f . A 1 9 , l 6 l , ( 1 9 6 4 ) . 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0084849/manifest

Comment

Related Items