Some Aspects of Liquid Crystal Microdynamics

7 Some Aspects of Liquid Crystal

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Microdynamics JEAN CHARVOLIN 1

Laboratoire de Physique des Solides , Bât. 510, Université Paris-Sud, 91405 Orsay, France Interest in thermotropic liquid crystals has focussed mainly on macroscopic properties; studies relating these properties to the microscopic molecular order are new. Lyotropic liquid crystals, e.g. lipid-water systems, however, are better known from a microscopic point of view. We detail the descriptions of chain flexibility that were obtained from recent DMR experiments on deuterated soap molecules. Models were developed, and most chain deformations appear to result from intramolecular isomeric rotations that are compatible with intermolecular steric hindrance . The characteristic times of chain motions can be estimated from earlier proton resonance experiments. There is a possibility of collective motions in the bilayer. The biological relevance of these findings is considered briefly. Recent similar DMR studies of thermotropic liquid crystals also suggest some molecular flexibility. T n 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 studies, great effort w a s e x p e n d e d i n i n A

v e s t i g a t i n g m a c r o s c o p i c p r o p e r t i e s s u c h as o r d e r , elasticity, a n d viscos-

i t y . T h e s e p r o p e r t i e s d e p e n d , o f course, o n m i c r o s c o p i c parameters are c h a r a c t e r i s t i c o f t h e interactions b e t w e e n i n d i v i d u a l m o l e c u l e s .

that Since

m o s t m e s o g e n m o l e c u l e s a r e v e r y c o m p l e x s t r u c t u r a l l y , these i n t e r a c t i o n s are e x p e c t e d t o d e p e n d g r e a t l y o n the m o l e c u l a r c o n f o r m a t i o n . N e v e r t h e less, t h e r m o t r o p i c l i q u i d crystals h a v e b e e n a n a l y z e d m a i n l y as assemblies of r i g i d c y l i n d r i c a l r o d s . Studies that a t t e m p t t o relate m a c r o s c o p i c a n d m i c r o s c o p i c orders are just b e g i n n i n g . T h e p r e l i m i n a r y findings f r o m s u c h studies w e r e d i s c u s s e d at t h e F i f t h I n t e r n a t i o n a l L i q u i d C r y s t a l C o n f e r ence; t h e y i n d i c a t e that t h e t r a d i t i o n a l r o d p i c t u r e is n o t a d e q u a t e f o r a r e a l u n d e r s t a n d i n g o f m o s t l i q u i d c r y s t a l l i n e phases. T h i s p o i n t o f v i e w 1

Laboratoire associé au C N R S . 101

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

102

LYOTROPIC

a) lamellar

LIQUID

CRYSTALS

b) hexagonal

Figure 1. Schematic representation of two lyotropic mesophases. The lamellar phase (left) is a periodical stacking along one dimension of soap and water hmellae. In the hexagonal phase (right), the soap cylinders are organized in a two-dimensional array. is r e i n f o r c e d b y r e c e n t t h e o r e t i c a l considerations that stress t h e i m p o r t a n c e of e n d chains i n the t h e r m o d y n a m i c s of s m e c t i c ( I ) a n d n e m a t i c (2)

mesophases. It is i n t e r e s t i n g that w o r k o n t h e i n t e r n a l m o t i o n s of t h e m o l e c u l e s

that p r o d u c e l y o t r o p i c mesophases is m o r e a d v a n c e d .

T h i s is m a i n l y

because of t h e i m p o r t a n c e of t h e m i c r o s c o p i c properties of these systems i n s o l u b i l i z a t i o n a n d i n t e r f a c i a l p r o b l e m s , p r o b l e m s w h i c h are e n c o u n t e r e d i n i n d u s t r y as w e l l as i n c e l l m e m b r a n e b i o l o g y . T h e s t r u c t u r a l a n d f u n c t i o n a l roles of l i p i d m o l e c u l e s i n b i o m e m b r a n e s are m u c h d i s c u s s e d ; i n vestigations of t h e p h y s i c o c h e m i c a l properties of l i p i d m e d i a thus m i g h t p r o v i d e orientations f o r b i o l o g i c a l studies. M o r e o v e r , t h e findings o n t h e f l e x i b i l i t y of t h e p a r a f f i n i c chains i n l y o t r o p i c mesophases m i g h t also b e r e l e v a n t to s i m i l a r p r o b l e m s i n t h e r m o t r o p i c mesophases. Paraffinic Chain Flexibility in Bilayers L i p i d - w a t e r systems are t h e s i m p l e s t of l y o t r o p i c l i q u i d crystals. B e cause of t h e s t r o n g a m p h i p a t i c character

of l i p i d s , these systems

con-

stitute d i s t r i b u t i o n s of t w o m e d i a : t h e aqueous a n d t h e paraffinic. T h e m u c h d i v e r s i f i e d g e o m e t r y of t h e d i s t r i b u t i o n s w a s d e m o n s t r a t e d b y x - r a y ( 3 ) . T o s u m m a r i z e b r i e f l y , t h e m o l e c u l a r aggregates c a n b e l a m e l l a e , r i b b o n s , r o d s , o r spheres o r g a n i z e d i n l o n g r a n g e lattices w i t h p e r i o d i c i t i e s i n o n e , t w o , o r three d i m e n s i o n s .

T h e s i m p l e s t w a y to u n d e r s t a n d this

r i c h p o l y m o r p h i s m is to assume that the paraffinic chains are flexible i n o r d e r to fill u n i f o r m l y the i r r e g u l a r l y s h a p e d v o l u m e s that are a v a i l a b l e to t h e m . T h i s i d e a is c o m p a t i b l e w i t h t h e short range d i s o r d e r d e t e c t e d at t h e m o l e c u l a r l e v e l b y w i d e - a n g l e x - r a y scattering ( 3 ) . T h e s c h e m a t i c representations

of t w o l y o t r o p i c mesophases ( F i g u r e 1) d e p i c t t h e c o -

existence of a l o n g range o r d e r w i t h a short r a n g e d i s o r d e r . W e s h a l l


7.

CHARVOLIN

103

Microdynamics

focus o u r interest o n some studies o f p a r a f f i n i c c h a i n b e h a v i o r i n b i l a y e r l a m e l l a r structures. Magnetic Resonance Studies. S e v e r a l e x p e r i m e n t a l t e c h n i q u e s are sensitive t o l o c a l

fluctuations

that

h a v e b e e n u s e d . O f these, n u c l e a r m a g -

n e t i c r e s o n a n c e ( N M R ) y i e l d s , i n this p a r t i c u l a r field, t h e m o s t r e l i a b l e quantitative data.

I n t h e past, m o s t N M R studies, l y o t r o p i c as w e l l as

t h e r m o t r o p i c , w e r e of t h e protons that are n a t u r a l l y present i n t h e m o l e cules.

H o w e v e r , i n s u c h a n i s o t r o p i c systems, t h e r e s i d u a l d i p o l a r c o u -

p l i n g b e t w e e n t h e protons a r e v e r y large, a l l n u c l e a r spins a r e c o u p l e d , a n d i t is i m p o s s i b l e to resolve specific m o l e c u l a r g r o u p s ( 4 ) . A d e c i s i v e step w a s t h e N M R s t u d y o f d e u t e r a t e d m o l e c u l e s

(DMR).

Since t h e

d i p o l a r c o u p l i n g s b e t w e e n deuterons a r e n e g l i g i b l e , t h e system is o n e o f u n c o u p l e d spins. D i f f e r e n t m o l e c u l a r g r o u p s c a n b e d i s t i n g u i s h e d b y d i f ferences i n t h e m o t i o n a l a v e r a g i n g o f t h e q u a d r u p o l a r c o u p l i n g s of t h e i r C - D bonds. I n t h e presence o f a q u a d r u p o l a r c o u p l i n g , t h e N M R l i n e of a d e u t e r o n is s p l i t i n t o a s y m m e t r i c d o u b l e t . W i t h a n a x i a l e l e c t r i c field g r a d i ent ( e . f . g . ) , t h e d o u b l e t s p a c i n g i n f r e q u e n c y u n i t s is g i v e n b y : A=

l f ! ^( cos 0-l) 4 h

V

w h e r e e qÇ/h 2

(1)

2

3

is t h e static q u a d r u p o l a r c o u p l i n g constant a n d θ is t h e

angle b e t w e e n t h e e.f.g. axis a n d t h e m a g n e t i c

field.

M o t i o n s o f this axis

m o d u l a t e 0, a n d t h e y s h o u l d b e t i m e - a v e r a g e d i f t h e m o t i o n f r e q u e n c i e s are l a r g e r t h a n t h e static i n t e r a c t i o n .

I f t h e m o t i o n is a n i s o t r o p i c a n d

a d m i t s a n axis of s y m m e t r y , E q u a t i o n 1 b e c o m e s : 3 e qQ . 3cos 0' —- ~ - < 2 2

Δν=

2

1

, > (

Q

3 c o s

.

, Φ — !) Λ

. ( )

( T }

2

w h e r e θ' a n d ψ a r e t h e angles m a d e b y t h e s y m m e t r y axis w i t h t h e e.f.g. axis a n d t h e m a g n e t i c field, r e s p e c t i v e l y .

A n effective q u a d r u p o l a r c o u

p l i n g constant is m e a s u r e d w h i c h i s : e qQ 2

3cos 0' g 2

1

, 3cos 0' — 1 where< > 2

>

c a n b e d e f i n e d as t h e o r d e r p a r a m e t e r , S, o f t h e axis o f t h e e.f.g. r e l a t i v e to the axis of s y m m e t r y . A s p e c t r u m of p e r d e u t e r a t e d p o t a s s i u m laurate i n o r i e n t e d

soap-

w a t e r m u l t i l a y e r s ( 5 ) is p r e s e n t e d i n F i g u r e 2 . T h e m e a s u r e d q u a d r u p o l a r c o u p l i n g constants a r e m u c h smaller t h a n those o f a static C - D b o n d , w h i c h a r e a b o u t 167 k H z ( 6 ) ; t h e r e s i d u a l q u a d r u p o l a r s p l i t t i n g s


104

LYOTROPIC

LIQUID

CRYSTALS

d-C K,217.H 0 12

(lamellar

«

I

» I—»

I

I

0

I

2

mesophase,82°C)

I 1 1I 5

I

I 10

I

• ι

15

ι

ι

I .•

ι

20

Frequency (kHz) from 13 MHz Figure 2. A DMR spectrum obtained at 13 MHz with an oriented sample. The normal to the lamella is at π/2 from the external magnetic field. Only half the spec trum, which is symmetric about the zero central fre quency, is pictured. Each line can be attributed to a methylene, or methyl, group; the greater the shift, the closer the group to the polar head. r e v e a l t h a t a n i s o t r o p i c i n t r a m o l e c u l a r m o t i o n s take p l a c e a n d average m u c h o f t h e static c o u p l i n g . T h e m e a s u r e d splittings are thus p r o p o r t i o n a l to t h e o r d e r p a r a m e t e r s S of t h e C - D b o n d s w i t h respect t o t h e o p t i c a l axis o f t h e l i q u i d c r y s t a l .

Since t h e splittings are distinct, the

amplitudes of the motions must vary a l l along the chain. V a r i a t i o n i n the s p l i t t i n g w i t h l o c a t i o n of t h e m e t h y l e n e o n the c h a i n is p l o t t e d i n F i g u r e 3.

Seelig a n d Niederberger ( 7 ) deuterated specifically each

methylene

g r o u p of s o d i u m d e c a n o a t e a n d o b s e r v e d v e r y s i m i l a r v a r i a t i o n i n a ternary

lamellar

system

(sodium

decanoate-decanol-water).

Such

a

c u r v e c a n b e c o n s i d e r e d a n a c c u r a t e representation o f c h a i n flexibility i n the paraffinic m e d i u m . Chain Deformations. A s t r i k i n g feature of t h e splittings i n F i g u r e 3 is t h a t — e x c l u d i n g t h e first, s e c o n d , a n d last three segments o f t h e c h a i n — a l l t h e other m e t h y l e n e groups h a v e n e a r l y t h e same o r d e r

parameter.

F o r a n i s o l a t e d c h a i n , this w o u l d b e v e r y o d d b e c a u s e e a c h s e g m e n t is e x p e c t e d t o h a v e greater o r i e n t a t i o n a l f r e e d o m t h a n t h e p r e c e d i n g o n e . I n other w o r d s , t h e

flexibility

of a free c h a i n c o u l d n o t y i e l d s u c h a

p l a t e a u . H o w e v e r , f o r a c h a i n i n a b i l a y e r , t h e steric r e p u l s i o n s b e t w e e n n e i g h b o r i n g chains s h o u l d also b e c o n s i d e r e d ; t h e y r e s u l t f r o m t h e c o n straints i m p o s e d b y t h e p a c k i n g of t h e l i p i d p o l a r heads at t h e interface.


7.

CHARVOLIN

Microdynamics

0,021

1

ι

1

0 1 2 3 Λ

105

'

'

ι

ι

ι

5 6 7 8 9

ι

1 L 10 11

Carbon number (from polar head) Figure 3. Variation in the order parameter S of a C-D bond as the distance from the polar head increases. S is defined refotive to the symmetry axis of the lamella. Recently, d e Gennes considered the situation i n w h i c h the mean spacing between chains, w h e n measured n o r m a l l y to the chain elongation axis, r e m a i n s u n i f o r m i n t h e regions o f t h e b i l a y e r s w i t h o u t c h a i n ends. H e d e m o n s t r a t e d that t h e steric interactions c o n s t r a i n t h e chains i n s u c h a w a y that o r i e n t a t i o n a l d i s o r d e r c a n n o t increase a l o n g t h e c h a i n as i t w o u l d f o r a n i s o l a t e d c h a i n ( 8 ) . T h e decrease of t h e o r d e r parameters f o r t h e last f e w segments is t h e n e x p l a i n e d b y t h e presence o f m a n y c h a i n ends i n t h e c e n t r a l r e g i o n of t h e b i l a y e r w h i c h makes t h e steric h i n d r a n c e m u c h less stringent. I f this i n t e r p r e t a t i o n is correct, t h e n t h e f a c t that this d r o p i n v o l v e s t h e last three segments of t h e c h a i n i m p l i e s that t h e c h a i n ends are n o t c o n f i n e d to a p l a n e i n t h e exact center of t h e b i l a y e r , b u t r a t h e r that t h e y are d i s t r i b u t e d over a r e g i o n o f s i z e a b l e thickness.

This,

i n t u r n , i m p l i e s that t h e c h a i n d e f o r m a t i o n s a r e n o t r e s t r i c t e d t o s m a l l angle torsions o r flexions o f t h e b o n d s , b u t t h e y also i n v o l v e i s o m e r i c r o t a tions a r o u n d t h e C - C b o n d s w h i c h c a n m o v e t h e c h a i n e n d a p p r e c i a b l y . A free c h a i n w i t h η l i n k s h a s a b o u t 3

n

r o t a t i o n a l isomers ( 9 ) m a n y of

w h i c h are c e r t a i n l y s t i l l accessible i n t h e mesophase.

T o describe i n de

t a i l t h e t h e r m a l m o t i o n s b e t w e e n a l l these c o n f o r m a t i o n s w o u l d b e a n o v e r w h e l m i n g task.

H o w e v e r , a f e w v e r y specific m o d e l s c a n b e d e v e l

o p e d i f o n e considers o n l y t h e s i m p l e s t isomers. A c h a i n s u b g r o u p h a s three r o t a t i o n a l isomers b e c a u s e o f rotations a r o u n d t h e C - C b o n d ( 9 ) : o n e trans ( t ) i s o m e r w h i c h is d e p i c t e d i n t h e s t r u c t u r a l s k e t c h a n d t w o g a u c h e ( g a n d g") isomers that h a v e h i g h e r +


106

LYOTROPIC

H

Chain

LIQUID

CRYSTALS

R'

subgroup

energies t h a n the trans i s o m e r ( Δ Ε ~

500 c a l / m o l e ) .

F o r a chain, de

partures f r o m the l o w - e n e r g y all-trans state c a n b e n a m e d a c c o r d i n g to the succession of the c h a i n C - C b o n d c o n f o r m a t i o n s . A n i s o l a t e d g a u c h e c o n f o r m a t i o n has a t g t or a tg"t sequence, a n d a k i n k (10) +

as t g t g ' t or tg"tg t. +

+

can be written

T r a n s sequences o n b o t h sides of a k i n k r e m a i n

p a r a l l e l to e a c h other; t h e y are s h i f t e d o n l y l a t e r a l l y . I n r e f e r e n c e to m o d e l i n g , the o c c u r r e n c e

of i s o l a t e d g a u c h e

con

f o r m a t i o n s w i t h e q u a l p r o b a b i l i t y a l l a l o n g the c h a i n y i e l d s a n e x p o n e n t i a l decrease i n the o r d e r of the m e t h y l e n e a l o n g the c h a i n . A s w a s a b o v e , this is r u l e d o u t b y the D M R measurements.

stated

W e c o n c l u d e that this

m o d e l c o u l d represent the b e h a v i o r of a n i s o l a t e d c h a i n fixed at o n e e n d b u t not that of a c h a i n i n a b i l a y e r since i t does n o t t a k e i n t o a c c o u n t the steric r e p u l s i o n s b e t w e e n n e i g h b o r i n g chains.

Seellig and Niederberger

( 7 ) d i d c o n s i d e r this f a c t o r ; t h e y c o m b i n e d t w o g a u c h e i s o m e r i z a t i o n s of different s i g n i n t o a k i n k (10)

that migrates a l o n g the c h a i n . T h i s m o b i l e

d e f e c t decreases e q u a l l y the o r d e r of a l l m e t h y l e n e g r o u p s , l e a v i n g t h e t w o parts of t h e c h a i n o n either side of i t p a r a l l e l to the b i l a y e r n o r m a l . Q u a n t i t a t i v e a g r e e m e n t w i t h F i g u r e 3 is g o o d i f one assumes a p r o b a b i l ity p

t

~

0.8 f o r a l i n k to b e i n a trans state.

I n this o n e - c h a i n m o d e l ,

n e i g h b o r i n g m o l e c u l e s are i n t r o d u c e d i m p l i c i t l y b e c a u s e one is r e s t r i c t e d to defects w h i c h d o n o t c h a n g e the o v e r a l l d i r e c t i o n of the c h a i n . defects of this t y p e , w i t h different ranges a l o n g the c h a i n (11),

Other

c o u l d be

c o n s i d e r e d as w e l l . S u c h m o d e l s , w h i c h i n t r o d u c e i n t e r m o l e c u l a r c o o p erativity arbitrarily b y eliminating presupposed unfavorable

conforma

tions, s k i p the i n t e r e s t i n g aspect of p o s s i b l e c o l l e c t i v e d e f o r m a t i o n s

of

lipids i n bilayers. S e v e r a l a p p r o a c h e s to the m a n y - c h a i n s p r o b l e m h a v e b e e n p r o p o s e d : d e t a i l i n g t w o - c h a i n interactions (12),

s o l v i n g exact t w o - d i m e n s i o n a l lat

t i c e m o d e l s ( 1 3 ) , a n d c a l c u l a t i n g a self-consistent m o l e c u l a r field a p p r o x i m a t i o n (14).

I n this last a p p r o a c h , M a r c e l j a e x t e n d e d to l y o t r o p i c l i q u i d

crystals some of the ideas h e d e v e l o p e d f o r t h e r m o t r o p i c systems

(2).

M o r e s p e c i f i c a l l y , the p a c k i n g of t h e l i p i d p o l a r heads at the i n t e r f a c e is i n t r o d u c e d t h r o u g h a l a t e r a l pressure t e r m w h i c h is e s t i m a t e d f r o m sur f a c e pressure measurements i n m o n o l a y e r s .

S t a t i s t i c a l averages are t h e n

e v a l u a t e d b y s u m m a t i o n o v e r a l l c o n f o r m a t i o n s of a c h a i n i n the field t h a t result f r o m n e i g h b o r i n g m o l e c u l e s .

T h e c a l c u l a t e d b e h a v i o r of the o r d e r

of the c h a i n l i n k s agrees w i t h F i g u r e 3 a n d R e f . 7.

A palmitate chain

( C i ) w o u l d t h e n h a v e f o u r l i n k s i n g a u c h e c o n f o r m a t i o n s w h i c h agrees 6


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107

Microdynamics

w i t h earlier t h e r m o d y n a m i c c a l c u l a t i o n ( 1 5 ) . T h i s t h e o r y also gives g o o d a g r e e m e n t w i t h the m e a s u r e d t h e r m o d y n a m i c properties o f t h e t r a n s i t i o n w h e r e a l l the chains are i n a r i g i d , all-trans c o n f o r m a t i o n . It is i n t e r e s t i n g to note that s p i n l a b e l experiments r e v e a l a m o n o t o n i e decrease i n t h e o r d e r f r o m h e a d to t a i l ( 7 ) w h i c h contrasts p r e v i o u s l y d i s c u s s e d p l a t e a u that is o b t a i n e d b y d e u t e r o n

w i t h the

experiments.

A l t h o u g h i t is not p o s s i b l e at the m o m e n t t o e l i m i n a t e the i d e a o f p e r t u r b i n g effects f r o m the n i t r o x i d e l a b e l , i t is nevertheless i n t e r e s t i n g t o attempt t o c o m p a r e E P R a n d D M R d a t a o n l y i n terms o f l i p i d b e h a v i o r .

Recently,

G a f f n e y a n d M c C o n n e l l (16) suggested that one c o u l d r e c o n c i l e t h e t w o types o f experiments b y t a k i n g i n t o a c c o u n t t h e i r different t i m e scales. A m o t i o n is s a i d to b e fast i f its f r e q u e n c y

is l a r g e r t h a n t h e fre-

q u e n c y o f t h e i n t e r a c t i o n i t m o d u l a t e s ; this is t h e s o - c a l l e d m o t i o n a l n a r r o w i n g c o n d i t i o n . T y p i c a l values f o r t h e interactions a r e 1 0 H z i n s

E P R a n d 1 0 H z i n D M R . A m o t i o n w h i c h has a f r e q u e n c y o f 1 0 - 1 0 5

5

8

w o u l d a p p e a r as a s l o w m o t i o n i n E P R ( a d i s t r i b u t e d s p e c t r u m i s o b s e r v e d ) a n d as a fast m o t i o n i n D M R ( a n a r r o w e d s p e c t r u m is o b s e r v e d ) . I n t h e G a f f n e y a n d M c C o n n e l l m o d e l ( 1 6 ) , l o c a l fast m o t i o n s , frequencies

with

greater t h a n ~ 1 0 H z , are r e s p o n s i b l e f o r t h e m o n o t o n i e 8

decrease i n t h e s p i n l a b e l o r d e r parameters, a n d e a c h m e t h y l e n e g r o u p o c c u p i e s a larger effective v o l u m e t h a n t h e p r e c e d i n g one.

T h e region

near t h e i n t e r f a c e is t h e n a w e a k d e n s i t y r e g i o n . A p l a u s i b l e s o l u t i o n to this p a c k i n g p r o b l e m is a c o l l e c t i v e b e n d i n g o f the c h a i n s : t h e i r e l o n g a t i o n axis, w h i c h i s n o r m a l t o the b i l a y e r i n the t a i l r e g i o n , i s t i l t e d i n the v i c i n i t y of the interface ( 1 7 ) . T h i s m o d e l accounts f o r the E P R spectra i f one assumes a static b e n d i n g angle, or, t o express i t d i f f e r e n t l y , i f one assumes that t h e b i l a y e r h a s l o c a l b i a x i a l i t y at times >

10" sec; t h e f a i l u r e o f 8

D M R experiments t o detect a n y b i a x i a l i t y i n p o t a s s i u m l a u r a t e b i l a y e r s ( 5 ) c a n b e e x p l a i n e d b y the f a c t that the l i f e t i m e o f this b i a x i a l i t y i s 1 0 " 5

10"

8

sec. T h i s t i l t angle, w h i c h affects t h e first m e t h y l e n e g r o u p s , w o u l d

t h e n i n t r o d u c e a r e d u c i n g f a c t o r i n t o t h e expressions o f t h e i r D M R s p l i t tings, t h e r e b y t r a n s f o r m i n g i n t o a p l a t e a u t h e m o n o t o n i e decrease i n t h e i r o r d e r that is c a u s e d b y fast m o t i o n s . I n this m o d e l , c o n t r a r y t o t h a t o f d e G e n n e s , the m e a n l a t e r a l s p a c i n g is not constant t h r o u g h t h e b i l a y e r s . A s has b e e n stated, this a s s u m p t i o n is s u p p o r t e d m o s t l y b y t h e n e e d f o r a b e n d i n g a n g l e as a fitting p a r a m e t e r f o r the E P R spectra ( 1 7 ) . N e v e r t h e less, i t r e m a i n s a d e s c r i p t i o n o f the b e h a v i o r o f l a b e l l e d chains w h i c h , i n the absence o f d i r e c t c o n c l u s i v e experiments, c a n s t i l l b e c o n s i d e r e d somewhat

different f r o m that

of nonlabelled molecules

r e c e n t experiments i n t h e t h e r m o t r o p i c

field

demonstrated b y

(18). (Order

parameters

a n d t i l t angles d e t e r m i n e d b y s p i n l a b e l e x p e r i m e n t s i n S m C phases d e p e n d o n the l o c a t i o n of the l a b e l o n the a l k o x y c h a i n of the m o l e c u l e . ) Dynamics of the Deformations.

A c o m p l e t e d e s c r i p t i o n m u s t also


108

LYOTROPIC

LIQUID

CRYSTALS

p r o v i d e t h e c h a r a c t e r i s t i c times o f t h e m o t i o n s a n d t h e i r a c t i v a t i o n ener gies. T h i s c a n b e o b t a i n e d f r o m N M R experiments t h r o u g h t h e m o d u l a t i o n o f t h e s p i n H a m i l t o n i a n b y t h e m o t i o n s . I f / ( ω ) is t h e s p e c t r a l d e n sity associated w i t h a

fluctuating

s p i n H a m i l t o n i a n , t h e r e l a x a t i o n rate o f

the Z e e m a n energy a t f r e q u e n c y ω c a n b e a p p r o x i m a t e d b y Γ ι " oc / ( ω ) . 1

F o r e x a m p l e , t h e s p e c t r a l d e n s i t y o f a fluctuating m a g n e t i c field w i t h a n e x p o n e n t i a l c o r r e l a t i o n f u n c t i o n w o u l d b e

2T (1 + ω Λ )

2

2

c

_ 1

, where

is t h e m e a n q u a d r a t i c strength o f t h e i n t e r a c t i o n , a n d T is t h e

2

c

c o r r e l a t i o n t i m e o f its v a r i a t i o n s . M e a s u r e m e n t o f t h e r e l a x a t i o n rate as a f u n c t i o n o f f r e q u e n c y , i n t h e l a b o r a t o r y f r a m e ( Tf

1

frame

) a n d i n the rotating

( T i p " ) , provides information about the correlation functions of 1

the m o t i o n s i n a d y n a m i c range f r o m a f e w H e r t z t o 1 0 H z . 8

I n this field, t h e r e s o l u t i o n of D M R is p r o m i s i n g . H o w e v e r , e x p e r i ments o n d e u t e r a t e d m o l e c u l e s h a v e just b e g u n , a n d t h e n u c l e a r r e l a x a t i o n w a s n o t y e t a n a l y z e d . W e c a n just present here some p r e l i m i n a r y ideas that w e r e o b t a i n e d f r o m p r o t o n r e l a x a t i o n experiments

(19). B e

cause of t h e n a t u r e of d i p o l a r i n t e r a c t i o n , w e are d e a l i n g w i t h a m u l t i s p i n system; this entails some c o m p l e x p r o b l e m s o f n u c l e a r s p i n d y n a m i c s w h i c h are b e y o n d t h e scope o f this d i s c u s s i o n . T h e q u a n t i t a t i v e analysis o f p r o t o n r e l a x a t i o n d a t a is thus f a r f r o m s t r a i g h t - f o r w a r d (20). W e s h a l l l i m i t ourselves t o a q u a l i t a t i v e i n t e r p r e t a t i o n of t h e f r e q u e n c y

dependence

o f t h e r e l a x a t i o n rate t h a t is s u m m a r i z e d s c h e m a t i c a l l y i n F i g u r e 4. I m p o r t a n t r e l a x a t i o n effects a p p e a r i n b o t h h i g h a n d l o w f r e q u e n c y regions.

io L

C K,28% D 0 12

2

lamellar mesophase, · : 90 °C , 0 : 5 5 ° C

-O- · -

10

1

ι ml 10 -2

10"

10'

10'

Frequency ( MHz )

Figure 4. Schematic representation of proton relaxation rates as func tion of frequencies. No measurements were made in the 0.1 MHz range which is between the domain of the T and T techniques. ip

t


7.

CHARVOLiN

109

Microdynamics

T h e h i g h f r e q u e n c y r e l a x a t i o n is a t t r i b u t e d i n p a r t t o t h e m o d u l a t i o n of i n t e r m o l e c u l a r d i p o l a r i n t e r a c t i o n s b y t h e t r a n s l a t i o n a l d i f f u s i o n . T h e cutoff f r e q u e n c y ( 6 0 M H z at 5 5 ° C )

corresponds t o t h e l o c a l d i f f u s i v e

j u m p f r e q u e n c y that is e s t i m a t e d f r o m measurements coefficient (D ~

of t h e d i f f u s i o n

10" c m / s e c at 5 5 ° ) ( 1 9 , 2 1 ) . T h i s cutoff f r e q u e n c y 6

2

also varies i n t e m p e r a t u r e w i t h t h e same a c t i v a t i o n e n e r g y ( E

a c t

~ 0.25

e V ) as t h e d i f f u s i o n f r e q u e n c y . T h e l o w f r e q u e n c y r e l a x a t i o n c a n t h e n b e a t t r i b u t e d to t h e m o d u l a t i o n of i n t r a - a n d i n t e r m o l e c u l a r interactions b y t h e d e f o r m a t i o n s o f t h e m o l e c u l e s . I n this r e g i o n , t h e T ~ curves are n o t s i m p l e L o r e n t z i a n s as lp

x

they should b e i f only one m o t i o n were responsible f o r the relaxation. T h e y c a n b e a n a l y z e d as a s u p e r p o s i t i o n of L o r e n t z i a n c u r v e s w i t h d i f f e r ent c h a r a c t e r i s t i c f r e q u e n c i e s w h o s e l o w e r l i m i t is a b o u t 1 0 H z . T h i s 5

suggests t h a t the c h a i n d e f o r m a t i o n s r e s u l t i n t h e a p p e a r a n c e of a d i s t r i b u t i o n of m o d e s , e a c h w i t h its o w n l i f e t i m e . T h e slowest m o d e has a t e m p e r a t u r e - i n d e p e n d e n t c h a r a c t e r i s t i c t i m e of 3.5 X 10~ sec; i t c o u l d b e a 6

l o n g w a v e l e n g t h d e f o r m a t i o n of the m o l e c u l e . W e c a n n o t d e r i v e a c c u r a t e d e t e r m i n a t i o n s f o r t h e fastest l o c a l m o d e s . b y A g r e n (22),

A theoretical consideration

that d e v e l o p s a R o u s e analysis f a m i l i a r i n t h e f i e l d of

p o l y m e r p h y s i c s (23), estimates t h e i r c h a r a c t e r i s t i c times a t a b o u t 10~ o r 8

10" sec; these c o u l d i n t e r f e r e w i t h t r a n s l a t i o n a l d i f f u s i o n i n t h e h i g h fre9

q u e n c y r e l a x a t i o n range. O n e m u s t r e m a r k that, since e a c h m o t i o n m o d u lates several interactions of different o r i g i n , i t is effectively hopeless to t r y to i n t e r p r e t t h e values of t h e m o d u l a t e d interactions t h a t a r e d e r i v e d f r o m relaxation data. Consequently, rely only o n the frequency a n d temp e r a t u r e d e p e n d e n c e s o f t h e r e l a x a t i o n rates a n d n e v e r o n t h e i r absolute values. Discussion. W e c a n n o w p r o p o s e a coarse d e s c r i p t i o n of t h e p a r a f finic

m e d i u m i n a l a m e l l a r l y o t r o p i c mesophase

(potassium

laurate-

w a t e r ) . F a s t t r a n s l a t i o n a l d i f f u s i o n , w i t h D ~ 1 0 ' at 90 ° C , occurs w h i l e 6

the c h a i n c o n f o r m a t i o n changes.

T h e c h a r a c t e r i s t i c times o f t h e c h a i n

d e f o r m a t i o n s are d i s t r i b u t e d u p t o 3.10"

6

sec at 9 0 ° C .

Presence o f t h e

s o a p - w a t e r interface a n d of n e i g h b o r i n g m o l e c u l e s l i m i t s t h e n u m b e r of c o n f o r m a t i o n s accessible to t h e chains.

T h e s e findings c o n f i r m t h e c o n -

c e p t o f t h e p a r a f f i n i c m e d i u m as a n a n i s o t r o p i c l i q u i d .

O n e m u s t also

c o m p a r e t h e f r e q u e n c i e s of t h e slowest d e f o r m a t i o n m o d e ( 1 0 H z ) a n d 6

of t h e l o c a l d i f f u s i v e j u m p ( 1 0 H z ). W h e n o n e m o l e c u l e w a n t s to s l i p 9

b y t h e side o f another, the w a y has to b e free. I f t h e s w i n g i n g m o t i o n s o f the m o l e c u l e s , o r t h e i r slowest d e f o r m a t i o n m o d e s , w e r e u n c o r r e c t e d , t h e m o l e c u l e s w o u l d h a v e to w a i t a b o u t 10" sec b e t w e e n t w o d i f f u s i v e j u m p s . 6

T h e r a p i d diffusion c o u l d then be understood if the slow motions were c o l l e c t i v e m o t i o n s i n t h e l a m e l l a e . I n this respect, t h e s l o w m o t i o n s c o u l d d e p e n d o n the m a c r o s c o p i c s t r u c t u r e ( l a m e l l a r o r c y l i n d r i c a l , f o r example)


110

LYOTROPIC

LIQUID

CRYSTALS

w h e r e a s t h e fast m o t i o n s a p p e a r t o b e q u a l i t a t i v e l y i n d e p e n d e n t o f i t a n d g o v e r n e d essentially b y t h e d e n s i t y o f t h e m e d i u m ( 1 9 , 24).

Unfortu-

n a t e l y , n o other i n v e s t i g a t i o n besides ours has b e e n d o n e i n t h e l o w f r e q u e n c y r e g i o n so far. A s is r e p o r t e d i n T i d d y ' s recent, w e l l d o c u m e n t e d r e v i e w (25),

more

a n d m o r e r e l a x a t i o n experiments a r e c o n c e r n e d w i t h l i p i d s of b i o l o g i c a l significance i n v e s i c u l a r structures w h i c h a p p r o x i m a t e b i o m e m b r a n e s m o r e t h a n o u r l a m e l l a r l y o t r o p i c l i q u i d c r y s t a l c a n . B e c a u s e of t h e c o m p l e x i t y of t h e m o l e c u l e s a n d t h e s o m e w h a t u n c e r t a i n state of d e t e r m i n i n g struct u r a l parameters of vesicles, t h e i n t e r p r e t a t i o n of these d a t a is sometimes less s t r a i g h t f o r w a r d t h a n i n t h e case of s i m p l e l y o t r o p i c l i q u i d crystals. N e v e r t h e l e s s , s u c h p h y s i c a l studies r e v e a l that, i n a d d i t i o n to t h e i r r i c h p o l y m o r p h i s m , l i p i d - w a t e r systems e x h i b i t c o m p l e x d y n a m i c p r o p e r t i e s t h a t a r e associated w i t h m o l e c u l a r d e f o r m a t i o n s a n d

fluidity.

The lipid

m e d i u m thus appears c a p a b l e of fast, l o c a l , s t r u c t u r a l t r a n s f o r m a t i o n s i n response to e x t e r n a l p h y s i c o c h e m i c a l s t i m u l a t i o n . T r a n s p o r t p r o p e r t i e s i n a n d across t h e b i l a y e r , f o r e x a m p l e , are r e l a t e d to t h e c h a i n t r a n s i t i o n f r o m a n o r d e r e d to a d i s o r d e r e d state that is i n d u c e d b y t e m p e r a t u r e v a r i a t i o n . W h a t e v e r interest s u c h p h e n o m e n a m i g h t present i n t h e i n t e r p r e t a t i o n of b i o m e m b r a n e p r o p e r t i e s (26), n o t h i n g c a n y e t b e s a i d a b o u t t h e i r i m p o r t a n c e i n b i o l o g i c a l f u n c t i o n s . T h e b i l a y e r is a n extreme overs i m p l i f i c a t i o n , a f r a g m e n t a r y r e p r e s e n t a t i o n of a c t u a l m e m b r a n e s , a n d m u c h is to b e e x p e c t e d f r o m c o m p l e x l i p i d s a n d proteins as w e l l as f r o m l i p i d - p r o t e i n interactions. Alkyl Chain Behavior in Smectic Phase T h e deuteron spectrum obtained f r o m a thermotropic smectic A p h a s e is p r e s e n t e d i n F i g u r e 5. T h e b u t o x y b e n z y l i d e n e - p - o c t y l a n i l i n e m o l e c u l e ( B B O A ) w a s s y n t h e s i z e d after d e u t e r a t i o n o f t h e o c t y l a n i l i n e g r o u p . F r o m t h e center ( z e r o f r e q u e n c y ) of t h e s p e c t r u m , there a p p e a r successively: a m e t h y l line, a partially deuterated p h e n y l group doublet, i n t e r m e d i a t e m e t h y l e n e l i n e s , a n d t h e l i n e o f t h e m e t h y l e n e close t o t h e b e n z y l g r o u p . T h e s e findings a n d t h e i r r e l a t i o n to p r e v i o u s c a l c u l a t i o n (2) are p r e s e n t e d a n d d i s c u s s e d i n a p r e l i m i n a r y r e p o r t (27).

A t this t i m e ,

l i q u i d c r y s t a l studies a p p e a r t o b e at a cross-point. S t u d y o f t h e m i c r o d y n a m i c s of t h e r m o t r o p i c s c a n benefit f r o m t h e m o r e a d v a n c e d state o f this w o r k f o r l y o t r o p i c s , w h e r e a s t h e experience g a i n e d i n t h e o p t i c a l m a c r o s c o p i c studies of t h e r m o t r o p i c s is u s e f u l i n t h e l y o t r o p i c field f o r i n v e s t i g a t i n g c o l l e c t i v e m o t i o n s s u c h as those d i s c u s s e d a b o v e . Conclusion S o m e recent D M R a n d E P R experiments w i t h l y o t r o p i c l i q u i d crystals h a v e b e e n d e s c r i b e d b r i e f l y a n d i n t e r p r e t e d i n terms of t h e flexibility o f


7.

CHARVOLIN

111

Microdynamics

B.B,d.O.A

A

ο

-J—ι—ι—ι

Smectic A phase, 58.5°C

ι

I

ι

ι

ι

ι

L

10 20 30 Frequency (kHz) from 13 MHz

ι

ι I AO

Figure 5. A DMR spectrum obtained at 13 MHz with the thermotropic sample BBOA in the smectic A phase. Only half the spectrum, which is symmetric about the zero frequency, is pictured. paraffinic c h a i n s . S o m e findings a b o u t l a t e r a l d i f f u s i o n o f t h e m o l e c u l e s i n t h e b i l a y e r w e r e c i t e d . T h e c h a r a c t e r i s t i c times of these m o t i o n s w e r e d i s c u s s e d o n t h e basis o f p r e v i o u s p r o t o n r e l a x a t i o n experiments. T h i s set of d a t a p e r m i t s a p r e l i m i n a r y d e s c r i p t i o n of the l i p i d m e d i u m . C o m p a r isons w i t h l i q u i d paraffins c o u l d b e a t t e m p t e d : the densities d o n o t differ d r a s t i c a l l y ( T h e c h a i n disorders i n l y o t r o p i c l i q u i d crystals a n d i n l i q u i d paraffins a r e c h a r a c t e r i z e d b y analogous x - r a y diffuse b a n d s a t 4.5 A " . ) 1

a n d c h a i n d e f o r m a t i o n s r e s u l t i n g f r o m reorientations a r o u n d t h e C - C b o n d s a r e also present (28). H o w e v e r , a n o r i g i n a l a n d f u n d a m e n t a l d i f f e r ence is i n t r o d u c e d b y t h e p a c k i n g of the p o l a r heads a t the i n t e r f a c e : l i p i d d i f f u s i o n a l o n g t h e d i r e c t i o n n o r m a l t o t h e i n t e r f a c e is of v e r y l o w p r o b a b i l i t y , a n d c h a i n ends are l o c a l i z e d either at t h e interface o r i n t h e c e n t r a l r e g i o n of t h e b i l a y e r . T h u s , there is less free v o l u m e i n the b u l k o f e a c h h a l f b i l a y e r t h a n there is i n l i q u i d paraffins w h e r e t h e c h a i n ends are d i s t r i b u t e d u n i f o r m l y . T h i s greater l a t e r a l c o h e s i o n c o u l d b e a n i m p o r t a n t factor i n the development of long-wavelength collective modes i n l i p i d w a t e r systems, t h e existence o f w h i c h is suggested b y o u r d y n a m i c d a t a . ( A t h e o r e t i c a l a p p r o a c h t o c o l l e c t i v e m o d e s i n l i p i d - w a t e r systems w a s p r e s e n t e d at t h e F i f t h I n t e r n a t i o n a l L i q u i d C r y s t a l C o n f e r e n c e .

I n addi

t i o n t o t h e u s u a l s m e c t i c m o d e s , w h i c h d e p e n d o n t h e s y m m e t r y of t h e system, a n extra h y d r o d y n a m i c m o d e appears that is r e l a t e d t o t h e pres ence of t w o c o m p o n e n t s , i.e. t o fluctuations i n t h e r e l a t i v e concentrations of w a t e r a n d l i p i d s

(29).)


112

LYOTROPIC LIQUID CRYSTALS H o w e v e r , i f reference is m a d e to t h e r m o t r o p i c studies, c o l l e c t i v e m o -

tions i n smectic phases h a v e w a v e l e n g t h s that e x t e n d u p t o t h e o p t i c a l w a v e l e n g t h . I n this respect, t h e y w e r e i n v e s t i g a t e d better b y light-scatt e r i n g t e c h n i q u e s t h a n b y a t e c h n i q u e as l o c a l as N M R . F i n a l l y , n o t h i n g has b e e n s a i d a b o u t m o l e c u l a r r o t a t i o n a r o u n d t h e l o n g axis, a d o m a i n where local techniques c a n still b e useful. W i t h a

flexible

disordered

c h a i n , i t is d i f f i c u l t t o d i s t i n g u i s h c l e a r l y b e t w e e n t h e r e l a t i v e r e o r i e n t a tions o f its segments a n d its o v e r a l l r o t a t i o n ; o n the other h a n d , i f b i l a y e r s w i t h t i l t e d chains i n trans c o n f o r m a t i o n s a r e c o n s i d e r e d ( 3 0 ) , i t w o u l d b e o f great interest t o d e t e r m i n e i f t h e i r m a c r o s c o p i c b i a x i a l i t y p r o ceeds f r o m a n y a n i s o t r o p y i n t h e o v e r a l l r o t a t i o n o f t h e m o l e c u l e . A s i m i l a r p r o b l e m arises

i n t h e thermotropic

the b i a x i a l s m e c t i c C a n d H phases.

field

with

understanding

T h i s point w a s m u c h discussed at

the F i f t h International L i q u i d C r y s t a l Conference.

I t was demonstrated

recently f o r T B B A i n S m H phase that n o anisotropy i n the overall rotat i o n of t h e m o l e c u l e a r o u n d its l o n g axis is a p p a r e n t a t times l o n g e r t h a n about 1 0

1 0

sec ( 3 1 ) .

Acknowledgment M o s t of o u r p r o t o n N M R studies o n l i p i d - w a t e r systems w e r e m a d e i n P . Rigny's laboratory ( D i v i s i o n de C h i m i e , C . E . N . Saclay).

M a n y of

the ideas t h a t a r e expressed h e r e w e r e d i s c u s s e d u n d e r h i s c r i t i c a l a n d stimulating guidance. Literature Cited 1. McMillan, W. L., Phys. Rev. A (1971) 4, 1238. 2. Marčelja, J. Chem. Phys. (1974) 60, 3599. 3. Luzzati, V., in "Biological Membranes," D. Chapman Ed., Academic, New York, 1968. 4. Charvolin, J., Rigny, P., Nat. New. Biol. (1972) 237, 127. 5. Charvolin, J., Manneville, P., Deloche, B., Chem. Phys. Lett. (1973) 23 345. 6. Burnett, L . J., Muller, Β. M., J. Chem. Phys. (1971) 55, 5829. 7. Seelig, J., Niederberger, W., Biochemistry (1974) 13, 1585. 8. de Gennes, P. G., Phys. Lett. A (1974) 47, 123. 9. Flory, P. J., "Statistical Mechanics of Chain Molecules," Interscience, New York, 1969. 10. Pechhold, W., Kolloid Ζ. Z. Polym. (1968) 228, 1. 11. Dubois-Violette, E . , Geny, F., Monnerie, L . , Parodi, O., J. Chem. Phys. (1969) 66, 1865. 12. Bothorel, P., Belle, J., Lemaire, B., Chem. Phys. Lipids (1974) 12, 96. 13. Nagle, J. F., J. Chem. Phys. (1973) 58, 252. 14. Marčelja, S., Intern. Liquid Crystal 5th, Stockholm, 1974. 15. Nagle, J. F., Proc. Natl. Acad. Sci. U. S. A. (1973) 70, 1443. 16. Gaffney, B., McConnell, H . M., J. Magn. Reson. (1974) 16, 1. 17. Gaffney, B., McConnell, H . M., Proc. Natl. Acad. Sci. U.S.A. (1971) 68, 1274.


7.

CHARVOLIN

Microdynamics

113

18. Poldy, F., Dvolaitsky, M., Taupin, C., J. Phys. Paris Collog. (1975) 36, 1-27. 19. Charvolin, J., Rigny, P., J. Chem. Phys. (1973) 58, 3999. 20. Bloom, M., Specialized Colloque Ampère, Cracow, 1973. 21. Roberts, R. T., Nature London (1973) 242, 348. 22. Ågren, G., J. Phys. Paris (1972) 33, 887. 23. Rouse, P. E., J. Chem. Phys. (1953) 21, 1272. 24. Chapman, D., Salsbury, N. J., Trans. Faraday Soc. (1966) 62, 2607. 25. Tiddy, G. J. T., "NMR of Liquid Crystals and Micellar Solutions," Chem ical Society Annual Report on NMR, London, 1974. 26. Chapman, D., Intern. Liquid Crystal Conf., 5th, Stockholm, 1974. 27. Deloche, B., Charvolin, J., Liébert, L., Strzelecki, L., J. Phys. Paris Colloq. (1975) 36, 21. 28. Levine, Y. K., Birdsall, N. J. M., Lee, A. G., Metcalfy, J. C., Partington, P., Roberts, G. C. K., J. Chem. Phys. (1974) 60, 2890. 29. Brochard, F., de Gennes, P. G., in "Liquid Crystals," Proc. Intern. Liquid Crystal Conf. 4th, Bangalore, 1973. 30. Tardieu, Α., Luzzati, V., Reman, F. C., J. Mol. Biol. (1973) 75, 711. 31. Hervet, H., Volino, F., Dianoux, A. J., Lechner, R. E., Phys. Rev. Lett. (1975) 34, 451. RECEIVED November 19, 1974.


Some Aspects of Liquid Crystal Microdynamics

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