Lyotropic Liquid Crystals

5 Recognition of Defects in Water-Lecithin

Downloaded by NORTH CAROLINA STATE UNIV on September 24, 2012 | http://pubs.acs.org Publication Date: September 1, 1976 | doi: 10.1021/ba-1976-0152.ch005

L

Phases

M . KLÉMAN and C. C O L L I E X Laboratoire de Physique des Solides, Université de Paris-Sud, 91405-Orsay, France M . VEYSSIÉ Laboratoire de Physique de la Matière Condensée, Collège de France, 75231 Paris Cedex 05, France The textures in homeotropic lamellar phases of lecithin are studied in lecithin—water phases by polarizing microscopy and in dried phases by electron microscopy. In the former, we observe the L phase (the chains are liquid, the polar heads disordered)—the texture displays classical Friedel's oily streaks, which we interpret as clusters of parallel dislocations whose core is split in two disclinations of opposite sign, with a transversal instability of the confocal domain type. In the latter case, the nature of the lamellar phase is less understood. However, the elementary defects (negative staining) are quenched from the L phase; they are dislocations or Grandjean terraces, where the same transversal instability can occur. We also observed dislocations with an extended core; these defects seem typical of the phase in the electron microscope.

'Ipextures

o f l y o t r o p i c mesophases h a v e b e e n t h e object o f n u m e r o u s

observations b y o p t i c a l (1,2,3)

a n d e l e c t r o n i c (4,5,6,7)

microscopy.

E x c e p t f o r t h e p i o n e e r i n g w o r k of L e h m a n n (1) a n d F r i e d e l (2) w h o i n t e n d e d t o i d e n t i f y t h e v a r i o u s k i n d s o f defects w h i c h constitute t h e textures, the p u r p o s e o f these observations w a s t o r e c o g n i z e t h e different existing phases—lamellar,

hexagonal

( o r i n t h e soaps l a n g u a g e :

neat

phase, m e d i a n phase, e t c . ) — i n c o r r e l a t i o n w i t h x-ray d a t a . A s i m i l a r a i m has p r o m p t e d o u r interest i n t h e p r o p e r t i e s o f l y o t r o p i c s i n t h e i r l a m e l l a r m o d i f i c a t i o n , i.e. i n this same structure t h a t i s 71

In Lyotropic Liquid Crystals; Friberg, S.; Advances in Chemistry; American Chemical Society: Washington, DC, 1976.


72

LYOTROPIC

Figure 1. La lecithinwater phase. The circles represent the polar heads, the wiggly lines the hydrophobic chains.

LIQUID

CRYSTALS

Water

c h a r a c t e r i s t i c of t h e r m o t r o p i c smectics, f o r w h i c h studies of defects a r e c u r r e n t l y u n d e r w a y (8). t h e s t u d y of defects.

T h e r e is c e r t a i n l y a f u n d a m e n t a l interest i n

F i r s t , let us note that the w o r d defect is n o t m e r e

t e r m i n o l o g y w h i c h hides o u r i g n o r a n c e

of c r y s t a l i m p e r f e c t i o n s , b u t

rather that defects c a n b e u n a m b i g u o u s l y d e f i n e d as t o p o l o g i c a l entities t h a t are r e l a t e d i n a specific w a y to t h e s y m m e t r i e s

of t h e p e r f e c t

m e d i u m ( 9 ) . A l s o , t h e i r presence m u s t b e t a k e n i n t o a c c o u n t i n interp r e t i n g m a n y p h y s i c a l measurements

since t h e y g e n e r a l l y create ( o r

r e l a x ) l o n g r a n g e stresses i n a w a y that is characteristic of t h e elastic p r o p e r t i e s of t h e m e d i u m . A n n e a l i n g of defects has to b e u n d e r s t o o d as a step t o w a r d o b t a i n i n g p e r f e c t samples.

T h e i r m e r e presence s t r o n g l y

affects b u l k transport p r o p e r t i e s ; o u r i n i t i a l interest i n t h e subject w a s i n d e e d i n s p i r e d b y discussions w i t h L a n g e a n d G a r y - B o b o w h o r e c e n t l y s t u d i e d (10)

d i f f u s i v i t y i n e g g - y o l k l e c i t h i n - w a t e r systems as a f u n c t i o n

of w a t e r content. I n this p a p e r w e d e s c r i b e t w o types o f observations o n e g g - y o l k l e c i t h i n . W e present t h e results of o u r s t u d y of h o m e o t r o p i c a l l y o r i e n t e d samples of L a phases b y p o l a r i z i n g o p t i c a l m i c r o s c o p y . T h i s s t u d y p r o v i d e s e v i d e n c e , a m i d a p p a r e n t l y n o n s i m i l a r aspects, o f t h e existence of a n e l e m e n t a r y t y p i c a l object w h i c h w e h a v e i n t e r p r e t e d as a d i s l o c a t i o n . W e also s t u d i e d t h i n samples o f s t a i n e d l e c i t h i n i n t h e h i g h v a c u u m o f t h e electron microscope.

I n a d d i t i o n to t h e defects t h a t a r e t y p i c a l o f this

t y p e o f s a m p l e , w e o b s e r v e d t h e same e l e m e n t a r y object as i n L a l e c i t h i n . Optical

Studies

L a w a t e r - l e c i t h i n is a l a m e l l a r structure i n w h i c h t h e p o l a r heads ( t h e p h o s p h a t i d y l c h o l i n e g r o u p of l e c i t h i n ) constitute t w o - d i m e n s i o n a l d i s o r d e r e d arrays i n contact w i t h w a t e r , whereas t h e chains a r e i n t h e m o l t e n state i n b e t w e e n w a t e r layers i n d i s o r d e r e d moieties (see 1).

Figure

( F o r a r e v i e w o f x-ray studies of lecithin—water phases, see R e f . 11.)



5.

KLEMAN ET AL.

Defects

in Water-Lecithin

Figure 2. Typical network of defects in a Φ < 24% sample (crossed polars)

La

73

Phases

Figure 3. Typical network of defects in α Φ > 24% sample (crossed polars)

ν)

ν)

W e s t u d i e d samples of La l e c i t h i n w i t h 1 6 - 2 9 % w a t e r at r o o m t e m p e r a t u r e . T h e samples w e r e p r e p a r e d b e t w e e n t w o m i c r o s c o p e glass slides that w e r e first t r e a t e d w i t h a s u l f o c h r o m i c s o l u t i o n , t h e n c a r e f u l l y r i n s e d w i t h distilled water a n d dried. polarizing microscopy.

T h e y were observed b y transmission

Just after

deposition between

t h e slides, t h e

samples present a h i g h l y d i s o r d e r e d texture w h i c h s t r o n g l y diffuses l i g h t . After compression (squeezing)

a n d / o r s h e a r i n g p a r a l l e l to t h e plates,

one obtains a n o v e r a l l h o m e o t r o p i c o r i e n t a t i o n that is p e r t u r b e d b y defects. T h e thickness o f t h e samples is i n t h e o r d e r o f 20/*. T h e texture differs s i g n i f i c a n t l y w i t h w a t e r content.

I n t h e less

h y d r a t e d phases ( 2 4 % ) , t h e same m e c h a n i c a l t r e a t m e n t

of s q u e e z i n g a n d strong s h e a r i n g is f a r less efficient i n a n n e a l i n g t h e o r i g i n a l d i s o r d e r e d texture. T h e h o m e o t r o p i c regions are o f s m a l l e r size, s e p a r a t e d b y l a r g e b u n c h e s o f defects i n a m o r e or less p o l y g o n a l a r r a n g e m e n t ( F i g u r e 3 ) . T h i s c h a n g e i n t h e aspect o f t h e mesophase is r a t h e r s h a r p f o r t h e c r i t i c a l c o n c e n t r a t i o n o f 2 4 % . I t is n o t i c e a b l e t h a t t h e effective shear v i s c o s i t y o f t h e samples b e l o w 2 4 % ( a s e v a l u a t e d b y h a n d ) is v e r y l o w , w h a t e v e r t h e i n i t i a l d e n s i t y of defects m i g h t b e , a n d



74

LYOTROPIC

LIQUID

CRYSTALS

Figure 4. Longitudinal striations in the same field as in Figure 2 (the crossed polars make an angle of 45° with the stnations)

i t decreases f u r t h e r as t h e d e n s i t y decreases w i t h subsequent

shearing.

( S i m i l a r a n n e a l i n g o f defects b y shear w a s r e p o r t e d i n t h e t h e r m o t r o p i c smectic phase of D A D B — s e e

R e f . 12).

I n contrast t o this b e h a v i o r , t h e

i n i t i a l effective v i s c o s i t y o f h i g h - w a t e r - c o n t e n t samples is v e r y l a r g e a n d does n o t decrease s i g n i f i c a n t l y w i t h s u b s e q u e n t s h e a r i n g ; s u c h b e h a v i o r is r e l a t e d to t h e o b s e r v e d s m a l l decrease i n defect d e n s i t y . T h e s e facts c o u l d b e c o r r e l a t e d to t h e a n o m a l y i n d i f f u s i v i t y m e a s u r e d b y L a n g e a n d G a r y - B o b o (10) at t h e same c r i t i c a l c o n c e n t r a t i o n o f 2 4 % , a n d w e t h e n i n f e r that b o t h t h e d i f f u s i o n a n o m a l y a n d t h e c h a n g e i n visco-elastic p r o p e r t i e s s h o u l d b e a t t r i b u t e d t o t h e same i n t r i n s i c reason. I n spite o f t h e s t r i k i n g d i f f e r e n c e i n t h e aspect o f t h e samples w i t h h i g h a n d l o w w a t e r contents, t h e t o p o l o g i c a l n a t u r e o f t h e defects f o r m i n g t h e texture r e m a i n s t h e same; their d e n s i t y a n d a r r a n g e m e n t o n l y as i n a s c a l i n g change.

change

I n p a r t i c u l a r , w e n o t i c e that t h e f o l l o w i n g

p r o p e r t i e s o f t h e arrangements

are v a l i d f o r t h e w h o l e r a n g e o f w a t e r

content. ( a ) T h o s e lines (I) w h i c h enter i n t h e f o r m a t i o n o f t h e n e t w o r k m e r g e a t nodes w h e r e t h e i r w i d t h s a d d a p p a r e n t l y as intensities o n a K i r c h o f f n e t w o r k ( c o n s e r v a t i o n l a w o f t h e w i d t h s ). T h i s is most v i s i b l e o n w e l l a n n e a l e d l o w - w a t e r - c o n t e n t samples (see F i g u r e 2 ) . ( b ) L i n e s a p p e a r to consist o f b u n c h e s o f v e r y t h i n lines (see t h e l o n g i t u d i n a l striations i n F i g u r e 4 ) w h o s e t r a n s v e r s a l d i m e n s i o n s a n d distances c a n b e as s m a l l as t h e r e s o l v i n g p o w e r o f t h e m i c r o s c o p e . T h e s e l o n g i t u d i n a l striations a r e g e n e r a l l y d i f f i c u l t t o observe b e c a u s e o f the v e r y l o w contrast, a n d s p e c i a l p o l a r i z a t i o n c o n d i t i o n s are r e q u i r e d .



5.

KLEMAN

ET AL.

Defects in Water-Lecithin

La Phases

75

Figure 5. Transversal striations in the same field as in Figure 2 (crossed polars parallel or perpendicular to the striations) ( c ) O n t h e same lines (I) a t y p i c a l t r a n s v e r s a l structure appears that is most v i s i b l e w h e n t h e l i n e is a l o n g one of t h e niçois d i r e c t i o n s ( F i g u r e 5 ). T h i s transversal structure is c l e a r l y r e m i n i s c e n t of t h e structure d e s c r i b e d b y L e h m a n n a n d F r i e d e l as a d o r n i n g t h e o i l y streaks of a l c o h o l - l e c i t h i n s a m p l e s . T h e r e l a t i o n s h i p b e t w e e n lines (I) a n d o i l y streaks is d i s c u s s e d b e l o w . ( d ) S o m e c o n f o c a l d o m a i n s (c) are c l e a r l y a p p a r e n t , either p i n n e d o n lines (I) o r (less o f t e n ) i s o l a t e d i n t h e b u l k ( F i g u r e 6 ) . B e t w e e n crossed polars, t h e y a p p e a r as b r i g h t c i r c u l a r b l o b s s e p a r a t e d i n f o u r e q u a l q u a d r a n t s b y t h e b l a c k brushes of a M a l t e s e cross. T h i s aspect is consistent w i t h t h e e x p e c t e d shape of c o n f o c a l d o m a i n s i n a n h o m e o t r o p i c s p e c i m e n . T h e a r g u m e n t is as f o l l o w s . S i n c e t h e a s y m p t o t i c d i r e c t i o n s of t h e h y p e r b o l a of c are a l o n g t h e d i r e c t o r at a l o n g d i s t a n c e of t h e

Figure 6. Some visible confocal domains. The transversal striations are clearly visible.



Figure 7. Scheme of a confocal domain in an homeotropic sample. Lamellar details are not featured. Broken line: axis of revolution. e l l i p s e a n d since the s p e c i m e n is h o m e o t r o p i c , the h y p e r b o l a is degenera t e d to a straight l i n e ; h e n c e t h e ellipse is d e g e n e r a t e d to a c i r c l e , the D u p i n c y c l i d e s to t o r i . T h i s is d e p i c t e d i n F i g u r e 7. ( F o r a r e v i e w of c o n f o c a l d o m a i n s g e o m e t r y , the best i n t r o d u c t i o n is R e f . 2. F o r details o n the d i s c o v e r y of these t o p o l o g i c a l p r o p e r t i e s , see R e f . 13. F o r a m o r e r e c e n t v i e w , t o g e t h e r w i t h a d i s c u s s i o n of the l i n k s w i t h d i s l o c a t i o n s , see R e f . 14. ) ( e ) T h e most s i n g u l a r p a r t of a c d o m a i n is c e r t a i n l y a l o n g t h e axis of r e v o l u t i o n . T h i s s i n g u l a r i t y c a n b e r e m o v e d a n d r e p l a c e d b y a less energetic core structure (see F i g u r e 8 ) . W e b e l i e v e that s u c h a c o n f i g u r a t i o n explains at best the large lines ( L ) w h i c h a p p e a r m o s t l y i n h i g h - w a t e r - c o n t e n t samples ( F i g u r e 3 ) as parts of the n e t w o r k , b u t also o n less w e l l a n n e a l e d parts of l o w - w a t e r - c o n t e n t specimens ( F i g u r e 9 ) . N o t e , h o w e v e r , that a c o n s e r v a t i o n l a w seems to a p p l y also to L lines a n d t h a t t h e y , as w e l l as I lines, h a v e a l o n g i t u d i n a l a n d a transv e r s a l texture. W e assume that the l o n g i t u d i n a l s t r u c t u r e i n L lines is of the t y p e p i c t u r e d i n F i g u r e 8, a n d w e s h a l l argue that, a p a r t f r o m some differences i n size e s p e c i a l l y a n d i n the w a y of a s s e m b l i n g defects, there s h o u l d n o t b e a f u n d a m e n t a l difference b e t w e e n I a n d L lines.

Figure 8.

Removal of the core structure of a c domain. are not featured. Broken line: axis of revolution.

Lamellar



5.

KLEMAN

ET AL.

Defects in Water-Lecithin

77

La Phases

Figure 9. L lines in lowwater-content specimen

Discussion

of Optical

F r i e d e l (2)

Studies

i n t e r p r e t e d t h e t r a n s v e r s a l striations o n o i l y streaks as

s m a l l adjacent c o n f o c a l d o m a i n s that h a v e a t e n d e n c y to gather i n lines. W e a l r e a d y n o t e d that s u c h a s i t u a t i o n exists i n D A D B

(12)

( b u t the

lines are a t t a c h e d to t h e s u r f a c e ) , a n d that c d o m a i n s p i n u p o n I l i n e s ; moreover,

oily

streaks

i n cholesterics

have

clear

confocal

domains.

H o w e v e r , t h e transversal striations o n I or L lines are n o t c o m p a t i b l e w i t h c d o m a i n s since w e d o n o t see there t h e t y p i c a l M a l t e s e cross; o n t h e c o n t r a r y , t h e h y p e r b o l i c d i r e c t i o n s w o u l d b e at a s m a l l a n g l e to t h e s a m p l e p l a n e i f t h e y exist. W e d o n o t reject F r i e d e l ' s e x p l a n a t i o n , b u t w e m u s t m a k e i t c o m p a t i b l e w i t h observations, p a r t i c u l a r l y w i t h t h e l o n g i t u d i n a l striations. A c c o r d i n g to F i g u r e 8, l o n g i t u d i n a l striations are p a r a l l e l d i s c l i n a t i o n lines. P a r a l l e l d i s c l i n a t i o n lines of o p p o s i t e s i g n p a i r i n dislocations ( F i g u r e 1 0 ) , a n d i t is m o r e c o n v e n i e n t a n d m o r e p h y s i c a l t o c o n s i d e r these latter defects as t h e e l e m e n t a r y objects, since i t i s w e l l k n o w n that the B u r g e r s ' v e c t o r f o l l o w s a c o n s e r v a t i o n l a w of t h e K i r c h k o f f t y p e at nodes. ( F o r a r e v i e w o f t h e i d e a o f d i s c l i n a t i o n , see R e f . 15. ) T h e d e f e c t i n F i g u r e 8 c a n itself b e d i v i d e d i n t o t w o d i s l o c a t i o n s o f o p p o s i t e s i g n ( F i g u r e 1 1 ) . B e c a u s e o f t h e constancy i n thickness o f t h e o b s e r v e d samples, e a c h l i n e (I or L ) is a s u m of dislocations w h o s e t o t a l B u r g e r s ' v e c t o r is z e r o or v e r y s m a l l , i n t h e o r d e r of t h e b o u n d a r y surfaces tions.

fluctua-

T h e c o n s e r v a t i o n l a w o b s e r v e d o n w i d t h s at nodes is therefore

not a necessary c o n d i t i o n , b u t r a t h e r i t i m p l i e s t h a t e a c h d i s l o c a t i o n k e e p its i n d i v i d u a l i t y at t h e n o d e .



78

LYOTROPIC

LIQUID

CRYSTALS

Figure 10. Fairing of two disclination lines of opposite signs (lamellar details are not featured) (top); a less probable model for the core of a dislocation (middle); and focal line appearing on the dislocation in order to release locally deformation energy (bottom) T h i s last c o n c l u s i o n is c e r t a i n l y i n agreement w i t h t h e core m o d e l of t h e d i s l o c a t i o n that w e p r o p o s e i n F i g u r e 10 ( t o p ) .

T h e core m o d e l

i n F i g u r e 10 ( m i d d l e ) is less r e a l i s t i c s i n c e i t w o u l d r e q u i r e t h a t some of the h y d r o p h o b i c chains b e i n contact w i t h w a t e r ; also, s u c h a d i s l o c a t i o n w o u l d i m m e d i a t e l y d i s a p p e a r o n a s i m i l a r d i s l o c a t i o n of t h e o p p o s i t e sign.

I n contrast, dislocations o f t h e first t y p e ( F i g u r e 10, t o p ) k e e p

t h e i r i n d i v i d u a l i t y easily b e c a u s e t h e i r d i s a p p e a r a n c e b y f u s i o n w i t h a d i s l o c a t i o n of t h e o p p o s i t e s i g n r e q u i r e s some k i n d of p e r m e a t i o n ( t h a t is d i f f i c u l t i n lyotropics—see R e f . 16) o r b r e a k i n g of t h e layers. C o n c e r n i n g t h e t r a n s v e r s a l striations, w e r e t u r n t o F r i e d e l ' s b a s i c i d e a that t h e easiest d e f o r m a t i o n s p o s s i b l e i n a l a m e l l a r m e d i u m a r e those w h i c h k e e p t h e thickness of the layers constant.

T h i s is t h e m a i n

p r o p e r t y of c o n f o c a l d o m a i n s — t h e y i n v o l v e o n l y s p l a y e n e r g y ( i n t h e bulk).

O n t h e c o n t r a r y , a d i s l o c a t i o n is a t t e n d e d b y a d e f o r m a t i o n i n

the thickness o f t h e layers w h i c h i n v o l v e s a n e n e r g y o f t h e same o r d e r as that of a s o l i d . T h e m o d e l i n F i g u r e 10 ( t o p ) needs n o d e f o r m a t i o n energy

i n the region

v i c i n i t y of Li

surrounding L i ( +

1/2

d i s c l i n a t i o n )^ b u t t h e

is d e f o r m e d b y a c h a n g e i n l a y e r thickness.

W e may

i m a g i n e t h a t s u c h a s i t u a t i o n c a n b e r e l a x e d at p e r i o d i c i n t e r v a l s b y f o c a l lines (see

F i g u r e 10, b o t t o m )

( a t t h e expense o f l i n e e n e r g y a n d

s p l a y e n e r g y ) w h i c h p l a y the r o l e o f the h y p e r b o l a e , w h e r e a s L p l a y s l o c a l l y t h e r o l e o f t h e e l l i p s e . T h e d i s l o c a t i o n does n o t t r a n s f o r m e n t i r e l y to w e l l b e h a v e d

c o n f o c a l d o m a i n s because that

require permeation.

would undoubtedly

H o w e v e r , let us note that i n a system i n w h i c h

p e r m e a t i o n is easier, t h e process of t r a n s f o r m a t i o n c a n b e c o m p l e t e ( f o r cholesterics, see R e f . 17; f o r t h e r m o t r o p i c smectics, see R e f . 8 ) .


5.

KLEMAN ET

79

AL.


W t

Figure 11. Two disclinations whose topological sum is zero (top); their topological équivalent: two dislocations L j L / and L L ' of opposite sign (middle); and different pairing of two disclinations of opposite sign (bottom) 2

Electron

Microscopy

S

Observations

T h e specimens are p r e p a r e d f r o m a c o l l o i d a l d i s p e r s i o n of e g g - y o l k l e c i t h i n i n excess w a t e r . I n o r d e r to o b t a i n r e a s o n a b l e contrast, the w a t e r is d o p e d w i t h l e a d acetate ( a p p r o x i m a t e l y 0.25 w t % ). H o w e v e r , w e h a v e no i d e a of the p r o p o r t i o n of l e a d i n the final p r o d u c t , w h i c h is p r e p a r e d as f o l l o w s . A m i c r o s c o p e g r i d is s o a k e d i n the s o l u t i o n a n d t h e n a l l o w e d to d r y either i n a i r or o n its e d g e o n filter p a p e r . T h e s p e c i m e n is t h e n i n t r o d u c e d i n t o the h i g h v a c u u m ( ^ 10" t o r r ) of the e l e c t r o n m i c r o s c o p e ( P h i l i p s E M 3 0 0 ) a n d o b s e r v e d at 100 k V w i t h t h e h e l p of a t i l t i n g stage. 6

T h e less w e l l g r o w n parts of the specimens ( t y p i c a l w h e n the s p e c i m e n dries i n a i r ) consist of l a y e r e d structures p e r p e n d i c u l a r to the s a m p l e surface ( F i g u r e 1 2 ) .

D i f f r a c t i o n patterns d i s p l a y o n l y r i n g s at a d i s t a n c e

c o r r e s p o n d i n g to t h e l a y e r thickness; there is n o e v i d e n c e of a n y k i n d of o r d e r i n t h e layers.

T h i s seems to b e c o n f i r m e d b y p r e l i m i n a r y x - r a y

d i f f r a c t i o n studies of the d r i e d p r o d u c t u n d e r a v a c u u m of ~ one obtains a l a y e r p a r a m e t e r r e m a i n i n a m o l t e n state ( 1 8 ) .

10'

i n the o r d e r of 45 A w h i l e t h e

4

torr— chains

T h e aspect s h o w n i n F i g u r e 12 does n o t

differ f r o m that o b t a i n e d b y c o n v e n t i o n a l e l e c t r o n m i c r o s c o p i c studies b y



80

LYOTROPIC

Figure

freeze-etching

12. Electron microscopy—the layers wound up into typical disclinations

LIQUID

CRYSTALS

are

or n e g a t i v e s t a i n i n g of l i p i d - w a t e r phases,

a n d it just

confirms the t e n d e n c y of the layers to k e e p a constant thickness. M o r e i n t e r e s t i n g are the specimens

obtained b y drying on

filter

p a p e r . I n t h e best parts are b e a u t i f u l h o m e o t r o p i c areas a p p r o x i m a t e l y 2000 A t h i c k w h i c h c a n b e o b s e r v e d w i t h o u t a n y s t r u c t u r a l c h a n g e f o r h o u r s , except f o r a s l i g h t r e c r y s t a l l i z a t i o n of P b w h i c h has n o effect o n observations.

T h e r e is n o i n d i c a t i o n w h a t e v e r of o r d e r i n g i n the layers.

W e classify the o b s e r v e d defects as ( a ) G r a n d j e a n terraces, ( b ) d i s l o c a t i o n lines, ( c ) Réf.

extended disolcation lines, a n d ( d )

other objects

(see

19). Grandjean Terraces.

F i g u r e 13 p i c t u r e s a step o n t h e surface

as

seen u n d e r different c o n d i t i o n s of tilt. T h e r e is a r e v e r s a l i n contrast f r o m one side o f the step to the other, a n d f r o m p o s i t i v e t i l t t o n e g a t i v e tilt. T h e contrast is r e a d i l y u n d e r s t o o d i f w e assume t h a t i t is a t t r i b u t a b l e m a i n l y to a b s o r p t i o n c o n t r a s t — t h e electrons are t r a n s m i t t e d b e t t e r i n the regions w h e r e t h e layers are p a r a l l e l to the b e a m

( c h a n n e l l i n g effect)

t h a n i n the r e g i o n w h e r e t h e p l a n e s are p e r p e n d i c u l a r t o t h e b e a m .

Also,

a n y s t r o n g d e f o r m a t i o n w o u l d decrease the contrast i n b r i g h t field i m a g e . W e therefore c o n c l u d e f r o m F i g u r e 13 that t h e layers of the G r a n d j e a n terraces d o not stop a b r u p t l y , b u t r a t h e r t h e y s l o p e d o w n at a n angle of approximately 4 5 ° .

T h e thickness of t h e w h i t e or d a r k b a n d s i n t h e

t i l t e d s p e c i m e n v i e w s suggests (2-5

layers).

t h a t t h e terrace is a f e w layers t h i c k

F i g u r e 14 d e p i c t s o u r c o n c e p t of t h e d i s t r i b u t i o n of t h e

layers w h i c h h a v e to s p i r a l i n t o d i s c l i n a t i o n s i n o r d e r to e x p l a i n the contrast.

W e d o n o t e x c l u d e the p o s s i b i l i t y t h a t s y m m e t r i c a l a r r a n g e -

ments k e e p t h e thickness Dislocation Lines.

constant.

F i g u r e 15 represents

a line w i t h

characteristic

t r a n s v e r s a l striations. T h e thickness of t h e s a m p l e changes r a p i d l y f r o m



5.

KLEMAN

Figure

ET AL.

13.

Defects

Grandjean

Figure 14.

in Water-Lecithin

terrace

(arrow indicates

Grandjean

Figure 15.

La

the axis of

terrace—schematic

Dislocation

81

Phases

lines


tilt)


82

LYOTROPIC

LIQUID

CRYSTALS

Figure 16. Extended dislocations. The thickness of the sample increases from right to left perpendicular to the first family, and from bottom to top past the unique transversal line. one side o f t h e striations to t h e other s i d e ; h e n c e t h e B u r g e r s ' v e c t o r o f t h e defect is large, u n d o u b t e d l y m u c h larger t h a n that o f t h e G r a n d j e a n t e r r a c e i n F i g u r e 13. I t is n o t p o s s i b l e t o ascertain w h e t h e r t h e defect i n F i g u r e 15 is a d i s l o c a t i o n close to t h e surface ( G r a n d j e a n terrace ) o r a d i s l o c a t i o n i n t h e b u l k . F r o m t h e c o m p a r i s o n o f F i g u r e s 13 a n d 15, w e c o n c l u d e that there is a c r i t i c a l size f o r dislocations a b o v e w h i c h t h e y d i s p l a y a transversal i n s t a b i l i t y o f t h e t y p e w e a n a l y z e d a b o v e 10, b o t t o m ) .

(Figure

T h e change i n contrast o f t h e streaks w i t h different t i l t

angles suggests some k i n d o f d i f f r a c t i o n contrast. Extended Dislocation Lines.

F i g u r e 16 p i c t u r e s t h e lines ( a t t i l t

a n g l e 0 = 0 ) w h i c h are r e v e a l e d as p l a n a r defects i n t h e b u l k w h e n t h e t i l t i n g is a t other angles. T h e s p e c i m e n changes i n thickness f r o m edge to edge ( t h i c k n e s s contrast is n o t t o t a l l y a p p a r e n t i n t h e figure, b u t a v a r i a t i o n i n r i b b o n w i d t h , f r o m o n e r i b b o n t o another, i s v i s i b l e ) . T h e r e f o r e , the p l a n a r defects c o r r e s p o n d t o t h e l o c a t i o n o f a n e x t e n d e d d i s l o c a t i o n w i t h a v e r y p e c u l i a r core d i s t r i b u t i o n . O n o n e side o f t h e p l a n a r d e f e c t there m u s t b e , l e t us say, 20 layers, w i t h 19 layers o n t h e other s i d e ; t h e layers o n b o t h sides fit a l o n g a c o m m o n l e n g t h . T h i s is a k i n d


5.

KLÉMAN

ET AL.

Defects

in Water-Lecithin

83

La Phases

20

19


18

17

Figure 17. Schematic fitting of regions of different thickness in Figure 16. Horizontal: first family of lines; vertical: unique transversal line.

of e p i t a x i a l contact w h i c h has t h e a d v a n t a g e of k e e p i n g t h e l a y e r t h i c k ness constant f r o m side t o side, w h i l e t h e l a m e l l a e suffer a s m a l l d i s o r i e n t a t i o n o f ~ 1 / 2 0 r a d i a n (see

F i g u r e 1 8 ) . T h i s d i s o r i e n t a t i o n is

c e r t a i n l y r e l a x e d a t a s m a l l d i s t a n c e f r o m t h e defect.

Another planar

defect o f t h e s a m e t y p e crosses t h e first f a m i l y o f p l a n a r defects a n d i n d u c e s a d i s p l a c e m e n t o f t h e first f a m i l y . A c c o r d i n g to t h e m e a s u r e d w i d t h o f t h e defects, t h e dislocations to w h i c h t h e y c o r r e s p o n d h a v e a B u r g e r s ' vector o f t w o to five parameters (assuming the parameter

e q u a l to 4 5 A ) . F i g u r e

17 d i a g r a m s t h e

r e p a r t i t i o n o f t h e lines i n t h e o b s e r v e d r e g i o n ( t h e n u m b e r s c o r r e s p o n d to a r b i t r a r y values o f t h e thickness m e a s u r e d i n p a r a m e t e r u n i t s ) . O n e notices that t h e effect of t h e jogs i n d u c e d b y t h e u n i q u e d i s l o c a t i o n is t o accommodate

thicknesses

of t h e same o r d e r o f m a g n i t u d e .

I t is also

reasonable to assert that t h e jogs are s m a l l e r f o r s m a l l e r thickness. T h e e p i t a x i a l fitting is d i a g r a m m e d i n F i g u r e 18. I t necessitates contact o f the chains w i t h t h e p o l a r heads, w h i c h is p o s s i b l e o n l y i f free w a t e r i s absent. Conclusion T h i s s t u d y h a s c o n c e n t r a t e d o n t h e defects o b s e r v e d i n l y o t r o p i c l a m e l l a r phases, a n d i t has p u t i n t o e v i d e n c e t h e specific character of the textures c o m p a r e d to classical t h e r m o t r o p i c s m e c t i c phases.

Figure 18.

I n leci-

Fitting of the epitaxial layers: planar defect (left) and local configuration of molecules along the planar defect (right)


84

LYOTROPIC LIQUID CRYSTALS

t h i n , t h e essential d e f e c t is t h e d i s l o c a t i o n w i t h a c o r e s t r u c t u r e that is r e a s o n a b l y i n t e r p r e t e d as t w o d i s c l i n a t i o n s o f o p p o s i t e s i g n . T h e transversal instabilities develop w i t h t h e size increasing w i t h t h e Burgers' vector; a l t h o u g h related to curvature elasticity, they never reach the f o r m o f a t r u e c o n f o c a l d o m a i n . T h e o v e r a l l texture is a c o m p r o m i s e b e t w e e n c u r v a t u r e e l a s t i c i t y a n d o n e - d i m e n s i o n a l s o l i d elasticity.


Literature

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Cited

Lehmann, O., "Flüssige Kristalle," Wilhelm Engelman, Leipzig, 1904. Friedel, G., Ann. Phys. (1922) 18, 273. Rosevear, F. B., J. Am. Oil Chem. Soc. (1954) 31, 628. Eins, S., Mol. Cryst. Liq. Cryst. (1970) 11, 119. Pinto de Silva, J. Microsc. (1971) 12, 185. Verkleij, A. J., Ververgaert, P. H. J., van Deenen, L. L. M., Elbers, P. F., Biochim. Biophys. Acta (1972) 288, 326. Ibid. (1973) 311, 320. Williams, C. E., Kléman, M., Proc. 4th Intern. Conf. Liquid Crystals, Stockholm, 1974, J. Phys. Paris (1975) 36, C7-375. Kléman, M., Adv. Liq. Cryst. (1974) 1, 210. Lange, Y., Gary-Bobo, C., J. Gen. Physiol. (1975) 63, 640. Ranck, J. L., Mateu, L., Sadler, D. M., Tardieu, Α., Gulik-Krzywicki, T., Luzzati, V., J. Mol. Biol. (1974) 85, 249. Steers, M., Kléman, M., Williams, C. E., J. Phys. Paris Lett. (1974) 35, L-21. Friedel, G., Grandjean, F., Bull. Soc. Fr. Mineral. (1910) 33, 409. Bouligand, Y., J. Phys. Paris (1972) 33, 525. Friedel, J., Kléman, M., "Fundamental Aspects of Disclination Theory,'' Nat. Bur. Stand. U.S. Spec. Publ. (1970) 1, 607. Brochard, F., de Gennes, P. G., Ramana, Indian J. Phys., Suppl. n1 (1975), 1. Bouligand, Y., J. Phys. Paris (1973) 34, 1011. Tardieu, Α., private communication. Colliex, C., Kléman, M., Veyssié, Intern. Cong. Electron Microsc., 8th, Canberra, 1974.

RECEIVED November 19,

1974.


Lyotropic Liquid Crystals

Recommend Documents