Ordered Fluids and Liquid Crystals

4 Determination of Bond Angle of CH Groups by Proton Magnetic Resonance in Nematic Liquid Crystalline Solutions

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3

ALFRED

S A U P E , G E R H A R D E N G L E R T , and A N N A P O V H

Physical Institute, University of Freiburg, Freiburg, Germany, and Physical Department, F . Hoffmann-La Roche & Co., L t d . , Basel, Switzerland

The theory of NMR spectra of molecules dissolved in nematic liquids is briefly reviewed, with emphasis on the determination of H-C-H bond angles of CH groups. Measurements have been carried out with carbon-13—labeled acetonitrile and methyl iodide in 4,4'-di-n-hexyloxyazoxybenzene and with acetonitrile and methanol in 4-n-octyloxybenzoic acid. The H-C-H bond angles obtained are in good agreement with previous microwave data. In the two solvents, the H-C-H angle of acetonitrile is slightly different (6'), probably because of a partial protonation in the acidic solvent. With acetonitrile, the positive sign of the indirect scalar coupling J was confirmed. Methanol showed an abnormal temperature and concentration dependence of the orientation, which may be explained by a varying degree of association. 3

CH

I V T e m a t i c l i q u i d crystals p r o v i d e a n anisotropic l i q u i d solvent i n w h i c h h i g h l y resolved n u c l e a r m a g n e t i c resonance ( N M R ) s p e c t r a of p a r t i a l l y oriented solute molecules h a v e been observed (2-4, 10-14, 16). The f o l l o w i n g properties of n e m a t i c l i q u i d c r y s t a l s are i m p o r t a n t i n t h i s respect: N e m a t i c l i q u i d s differ f r o m n o r m a l i s o t r o p i c l i q u i d s o n l y b y t h e m o r e or less complete spontaneous p a r a l l e l o r i e n t a t i o n of t h e elongated m o l e cules. T h i s m e a n s t h a t different o r i e n t a t i o n s of t h e m o l e c u l a r axes o c c u r w i t h different s t a t i s t i c a l weights. T h e diffusion a n d r o t a r y m o t i o n of the molecules, however, are as fast as i n m a n y i s o t r o p i c l i q u i d s . N e m a t i c l i q u i d s c a n be homogeneously ordered i n t h i c k l a y e r s b y a m a g n e t i c field of o n l y a few t h o u s a n d gauss. H o m o g e n e o u s l y ordered samples behave o p t i c a l l y l i k e u n i a x i a l c r y s t a l s . T h e o p t i c a l axis coincides w i t h the preferred 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 axis. I t t u r n s p a r a l l e l to the m a g n e t i c field d i r e c t i o n . 51 Porter and Johnson; Ordered Fluids and Liquid Crystals Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

52

O R D E R E D FLUIDS A N D LIQUID CRYSTALS

A s t h e molecules r e t a i n t h e i r h i g h m o b i l i t y , t h e i n t e r m o l e c u l a r m a g netic dipole interactions are averaged t o zero. T h e molecules c a n therefore be t r e a t e d as isolated s p i n systems. A s a consequence of t h e second p r o p e r t y , t h e homogeneous o r i e n t a t i o n of the n e m a t i c sample is achieved b y the m a g n e t i c field, H , w h i c h i n t h e N M R e x p e r i m e n t is needed to i n t r o d u c e the Z e e m a n s p l i t t i n g of the n u c l e a r s p i n levels. I n s u c h homogeneously ordered samples t h e i n t r a m o l e c u l a r d i p o l e i n t e r a c t i o n s are reduced t o s h a r p average values. 0

A considerable d i s a d v a n t a g e arises because of the fact t h a t no sample s p i n n i n g a r o u n d a n axis p e r p e n d i c u l a r t o t h e H field is possible since t h i s w o u l d destroy t h e m o l e c u l a r o r i e n t a t i o n . Therefore t h e m i n i m u m l i n e w i d t h o b t a i n e d for p r o t o n signals is a p p r e c i a b l y larger t h a n t h a t o b t a i n a b l e i n isotropic solutions. T h e p a r a l l e l o r i e n t a t i o n of t h e molecules i n the n e m a t i c phase is u s u a l l y characterized b y t h e degree of order or S v a l u e of t h e l o n g m o l e c u l a r axis defined b y t h e expectation v a l u e (1, 7, 8, 15, 19, 20): 0

S = ( l / 2 ) ( 3 cos 0 -

1)

2

(D

H e r e 0 is t h e angle between t h e l o n g m o l e c u l a r axis a n d t h e o p t i c a l axis of t h e l i q u i d . I n the same w a y we c a n define a degree of order of a n y m o l e c u l a r axis, w h e t h e r we consider a molecule of t h e p u r e n e m a t i c l i q u i d or a molecule dissolved i n a n e m a t i c solvent. B y d e f i n i t i o n t h e S v a l u e s range between 1 a n d — 1 / 2 . S = 1 means t h a t t h e corresponding axis is a l w a y s p a r a l l e l to the o p t i c a l a x i s ; S = — 1 / 2 means t h a t i t is a l w a y s p e r p e n d i c u l a r to i t ; AS = 0 corresponds to a r a n d o m o r i e n t a t i o n as i n isotropic l i q u i d s . T h e S v a l u e of the l o n g m o l e c u l a r axis i n p u r e n e m a t i c l i q u i d s u s u a l l y lies between 0.4 a n d 0.7 (1, 6, 7, 8, 15, 19, 20). T h e S values of different m o l e c u l a r axes are n o t i n d e p e n d e n t of each other. I n general, t h e average o r i e n t a t i o n of a r i g i d molecule c a n be c o m p l e t e l y described b y a m a t r i x (12) t h a t contains o n l y five ( i n c e r t a i n l i m i t s ) independent p a r a m e t e r s . W e denote b y ξ, 77, a n d f t h e axes of a cartesian coordinate s y s t e m fixed t o t h e molecule (or a r i g i d p a r t of t h e molecule) a n d b y 0$, Θ , a n d 0 t h e angles of these axes t o w a r d t h e o p t i c a l axis. T h e m a t r i x elements are t h e n g i v e n b y the average values : η

f

Sij = ( l / 2 ) ( 3 cos Si cos θ j -

ôij);

i,j

=

(2)

bu = 1 for i = j; otherwise ô»y = 0. T h e m a t r i x is symmetriC., a n d i t s trace disappears. B e t w e e n the S v a l u e of a n a r b i t r a r y axis, a, w i t h t h e angles af, a , a n d af t o w a r d the coordinate axes, a n d the m a t r i x elements, Sij, the f o l l o w i n g r e l a t i o n h o l d s : a

v

S

a

= Σ

C 0 S

C 0 S

j Sij

a

a

Porter and Johnson; Ordered Fluids and Liquid Crystals Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

(3)

4.

Bond Angle of CH

SAUPE ET AL.

Z

53

Groups

T h i s e q u a t i o n m a y be used to determine the degree of order of a n y axis if the S m a t r i x is completely k n o w n or to determine the m a t r i x ele ments, Su, if sufficient S values are k n o w n . a

B y a suitable choice of t h e m o l e c u l a r coordinate s y s t e m the S m a t r i x m a y be t r a n s f o r m e d i n t o a d i a g o n a l f o r m (12) w i t h t w o independent ele ments. I n sufficiently s y m m e t r i c a l molecules these p r i n c i p a l axes are de t e r m i n e d b y s y m m e t r y . If, i n special cases, we c a n choose, for instance, the f - a x i s p a r a l l e l to a n axis of threefold or h i g h e r s y m m e t r y , the o f f - d i a g o n a l elements are zero a n d we o b t a i n : Su = S „ = - ( 1 / 2 ) S „

(4)

R e l a t i o n 3 reduces now to = (1/2) (3 cos V

S

a

-

l)S

(3')

f r

R e l a t i o n s 4 a n d 3' also a p p l y for a r i g i d p a r t of a molecule, p r o v i d e d t h a t there exists a r o t a r y m o t i o n a r o u n d its three- or more-fold s y m m e t r y axis w i t h respect to the rest of t h e molecule. T h i s a l w a y s occurs i n the case of C H groups, i n the spectra of w h i c h we are especially interested here. 3

Spin-Hamiltonian

in Nematic

Liquids

I n t h i s paper we consider d i a m a g n e t i c molecules o n l y a n d denote b y x, y, a n d ζ the axes of a C a r t e s i a n coordinate s y s t e m fixed i n space. The ζ axis is directed p a r a l l e l to the s t r o n g m a g n e t i c field, H . W e assume t h a t the screening of a nucleus ρ c a n be described b y a screening tensor (ai ) (l,k — x,y,z) a n d t h a t the s p i n - s p i n i n t e r a c t i o n c a n be described b y a c o u p l i n g tensor (A i ) [interaction energy terms hI (A ik )I ]W e further assume t h a t the m o t i o n of t h e molecules is so fast t h a t i n t e r m o l e c u l a r i n t e r actions c a n be neglected a n d t h a t i n t r a m o l e c u l a r interactions are reduced to average values. F o r n u c l e i w i t h s p i n 1/2, the effective H a m i l t o n i a n (12) is t h e n g i v e n b y 0

p

k

vq

p

k

H=

-£/J.ΣΤΡ(Ι-q

VQ

q

Ρ

+ A,J")(I IP

+

+ /-*/+')

Κ &

+ 2(A,ni* I. } P

q

(5)

H e r e t h e sums h a v e to be t a k e n over the i n t e r a c t i n g n u c l e i ρ a n d q. y is the g y r o m a g n e t i c r a t i o , 7 / is the ζ component of P , the s p i n operator of nucleus p, a n d I± = I ± il . T h e brackets ( ) i n d i c a t e t h a t average values over the m o l e c u l a r m o t i o n h a v e to be t a k e n . p

p

p

x

v

u


54

O R D E R E D FLUIDS A N D LIQUID

CRYSTALS

T h e H a m i l t o n i a n c a n also be w r i t t e n i n t h e f o l l o w i n g f o r m :

H=

Σ 7,(1 -

~£h.

σ,-«,)/*

+ h Σ

B ( 3 / / J . « - M,)

+ h Σ

-W.

(6)

M

H e r e w e use t h e f o l l o w i n g abréviations :

dpq — 3 \Άχχ

~Γ ^7/2/

^22

»

^

= J ( 2 σ / — σ / — σ^/) 2

χ

σ and J correspond t o t h e f a m i l i a r scalar screening constant a n d s p i n - s p i n c o u p l i n g constant, respectively, observable i n n o r m a l l i q u i d s . δ a n d B are a d d i t i o n a l constants t h a t appear because of n o n v a n i s h i n g S values. ρ

pq

ρ

pq

I n cases where t h e regarded m o l e c u l a r properties—e.g., the i n t e r n u c l e a r distances—do n o t change w i t h t h e o r i e n t a t i o n of t h e molecule against t h e o p t i c a l axis of t h e n e m a t i c solvent, w e c a n express t h e effective constants i n t h e H a m i l t o n i a n b y the m a t r i x elements t h a t are related t o t h e m o l e c u l a r coordinate s y s t e m : «Ρ =

+

έ

jpq = i (A,r h = f Σ

*νν

+

Ρ

+ Ar

+

v

A,n = U f )

SijaJ"

(8)

Bpq ~ § ^Σ & ijA %f

q

T h e s p i n - s p i n c o u p l i n g constants, B , c o n t a i n t h e anisotropic p a r t of t h e i n d i r e c t (electron-coupled) s p i n - s p i n i n t e r a c t i o n a n d t h e d i r e c t d i p o l e dipole i n t e r a c t i o n between t h e magnetic d i p o l e m o m e n t s of the n u c l e i . T h e l a t t e r p a r t is a l w a y s g i v e n b y pq

η pq

Here d

pq

and r

pq

k

dir

B

= -

2

p

q

γ

,

C O S dpq — l \

1 / 3

— yy

2

^

j r i

/

Q

v

(9)

is t h e angle between t h e axis t h r o u g h ρ a n d q a n d t h e o p t i c a l axis is t h e distance between ρ a n d q.

I f ρ a n d q belong t o t h e same

r i g i d p a r t of t h e molecule, w e c a n w r i t e Bq P

S

pq

dlT

= -

7^2 y y S 4t7T P

9

pq

-^3 T

(10)

pq

is t h e degree of order of t h e axis t h r o u g h ρ a n d q.

Here r

vq

means a n


4.

Bond Angle of CH

SAUPE E T AL.

55

Groups

3

average distance. I t is e q u a l t o the e q u i l i b r i u m distance between n u c l e i ρ a n d q if we neglect the influence of v i b r a t i o n a l m o t i o n s . T h e anisotropic p a r t of t h e i n d i r e c t s p i n - s p i n i n t e r a c t i o n w i l l i n g e n eral be m u c h s m a l l e r t h a n the direct c o u p l i n g . H o w e v e r , its existence has been p r o v e d b y S n y d e r a n d A n d e r s o n (16) w i t h hexafluorobenzene i n a n e m a t i c l i q u i d s o l u t i o n . I n t h e case of benzene, o n t h e other h a n d , no anisotropic c o n t r i b u t i o n of the i n d i r e c t s p i n - s p i n c o u p l i n g has been o b served (13, 16). I t s influence seems n o t t o be noticeable w i t h p r o t o n p r o t o n s p i n couplings. If, therefore, the i n d i r e c t c o n t r i b u t i o n is neglected, the e x p e r i m e n t a l values of B m a y be used to calculate S w i t h t h e a i d of E q u a t i o n 10. I n t h i s w a y i t is possible t o determine e x p e r i m e n t a l l y the complete S m a t r i x p r o v i d e d t h e i n t e r n u c l e a r distances are k n o w n . pq

pq

W i t h a C H group we c a n observe t w o anisotropic c o u p l i n g constants — o n e between t h e protons ( B H H ) a n d one between carbon-13 a n d the p r o tons ( S C H ) . F o r t h e c a l c u l a t i o n of Bun a n d Ben we neglect a l l a n i s o t r o p i c c o n t r i b u t i o n s of t h e i n d i r e c t s p i n - s p i n i n t e r a c t i o n s as w e l l as the influence of v i b r a t i o n a l m o t i o n s . W e use E q u a t i o n s 3', 10, 1 3

3

and -(l/2)Sc.

SHH =

(1/2) (3 cos β -

SCH =

l)5c.

2

H e r e Sc denotes t h e degree of order of the s y m m e t r y axis, S H H t h a t of a n axis connecting t w o protons, a n d Sen t h a t of the C H - b o n d axis, β is t h e angle between t h e l a t t e r b o n d axis a n d the s y m m e t r y a x i s . W e f i n d : z

BHH = ςΓ~2 y Sc 8. 2

P

a

run

3

1 1 ο BCH = — 7-2 y 7c 17 (3 cos β 4π Δ 2

P

1 ~ 3 rcH

l)S

Ca

F r o m the s y m m e t r y of the C H group i t follows t h a t run = 2 s i n (a/2)r H a n d (3 cos β - l ) / 2 = 1 - 2 s i n (a/2). W i t h t h i s we f i n a l l y o b t a i n : C

3

2

2

| ^

HHH

= W ^ sin 7p

3

(a/2)

(2 s i n

2

(a/2)

-

1)

(12)

y a n d y are t h e k n o w n g y r o m a g n e t i c ratios of the p r o t o n a n d of the carbon-13 nucleus. E q u a t i o n 12 c a n therefore be used to determine the H - C - H b o n d angle, a. p

c

Experimental

Results

M e a s u r e m e n t s h a v e been m a d e w i t h m e t h a n o l ( C H O H ) a n d ace tonitrile ( C H C N ) i n nematic liquid 4-n-octyloxybenzoic acid ( I I ; see T a b l e I) a n d w i t h acetonitrile a n d m e t h y l iodide ( C H I ) i n n e m a t i c l i q u i d 3

3

3


56

O R D E R E D FLUIDS A N D LIQUID CRYSTALS

4,4'-di-n-hexyloxyazoxybenzene (I). Englert and Saupe

P a r t of t h e results are m e n t i o n e d b y

(#).

T h e C H groups of t h e solute molecules c a n be t r e a t e d as i s o l a t e d s p i n 3

systems:

t h e effective couplings of t h e C H p r o t o n s w i t h t h e 3

i n acetonitrile and w i t h

1 2 7

N nucleus

1 4

I i n m e t h y l i o d i d e average t o zero, for these

Scalar Coupling Constant J H and Bond Angles of C H - Groups

Table I.

C

3

PMR Compound Ν = C-CH

Solvent J H , C P S . I II II I

3

CH OH

CH3I 3

136 136 141 151 H.3

II

C

Data

109°2' 108°56' 110°3' 111°42'

6

Microwave Data (r Structure) 0

< HCH

C

± ± ± ±

0 ^ Q - N ^

< HCH 2' 2' 8' 2' - ^

N

0

Re~f.

109°16'

(17)

109°2' ± 45' 111°25'

(18) (9)

6

C

H

I 3

H, C 0-Sc v a l u e s o b t a i n e d are below 0.006. T h e r e is also n o s t e a d y increase of Sc w i t h decreasing t e m p e r a t u r e , b u t t h e curves pass t h r o u g h a m a x i m u m . F o r t h e higher c o n c e n t r a t i o n the sign of $ c is u n c e r t a i n ; for t h e lower c o n c e n t r a t i o n it w a s d e t e r m i n e d w i t h C - l a b e l e d m e t h a n o l . 3

z

3

13


58

ORDERED FLUIDS A N D LIQUID CRYSTALS

T h i s u n u s u a l o r i e n t a t i o n b e h a v i o r of m e t h a n o l is p r o b a b l y caused b y a n association w h i c h varies w i t h t h e c o n c e n t r a t i o n a n d t h e t e m p e r a t u r e . I n the n e m a t i c phase of solvent I no interprétable s p e c t r u m of m e t h a n o l has been o b t a i n e d . W i t h acetonitrile m u c h larger s p l i t t i n g s h a v e been observed [see t h e 100 M c . p . s . s p e c t r u m , F i g u r e 4 of (#)]. m a g n i t u d e i n b o t h solvents.

comparable

H

VCH between 1200 a n d 1600 c.p.s. tween 0.08 a n d 0.10.

T h e s p l i t t i n g s are of

J/ H ranged between 2400 a n d 3100 c.p.s.; T h e corresponding ASC v a l u e s were b e 3

T h e y increased s t e a d i l y w i t h decreasing t e m p e r a t u r e .

A m i x t u r e of m e t h y l iodide a n d a c e t o n i t r i l e has been i n v e s t i g a t e d i n solvent I .

W i t h t h e f o r m e r c o m p o u n d t h e *>HH v a l u e a n d hence t h e Sc-

d

values were considerably smaller.

F o r instance, at 75 ° C . we o b t a i n e d for

m e t h y l iodide : = 1206 c.p.s. VCH =

826 c.p.s.

= 0.042 a n d for a c e t o n i t r i l e : VHH = 2752 c.p.s. VCH = 1426 c.p.s. Sc

3

= 0.089

T h e ASC v a l u e of a c e t o n i t r i l e i n d i c a t e s t h a t this m o r e elongated m o l e 3

cule is c o n s i d e r a b l y b e t t e r o r i e n t e d t h a n m e t h y l i o d i d e .

T h e Sc v a l u e s of 3

t h e l a t t e r c o m p o u n d also s t e a d i l y increased w i t h decreasing t e m p e r a t u r e f r o m 0.03 a t 8 5 ° C . t o 0.05 a t 6 8 ° C . Discussion T h e H - C - H angles c a l c u l a t e d f r o m E q u a t i o n 12 are s u m m a r i z e d i n Table I. sults.

T h e errors g i v e n are t h e root m e a n square d e v i a t i o n s of o u r r e

S y s t e m a t i c a l errors are n o t i n c l u d e d .

T h e J C H values were

de

t e r m i n e d w i t h t h e same samples used for t h e d e t e r m i n a t i o n of VKK a n d VCH.

T h e same s i g n for J H a n d B H was used i n t h e c a l c u l a t i o n s . C

C

This

leads t o reasonable v a l u e s for t h e b o n d angles w i t h o u t a n o t i c e a b l e t e m perature dependence.

T h e a s s u m p t i o n of opposite signs c a n be d i s c a r d e d :

w i t h acetonitrile opposite signs l e a d t o a t e m p e r a t u r e dependence of t h e b o n d angle—e.g., i n solvent I , a = 1 Π ° 3 8 ' a t 7 7 ° C ; a = 112°20' at 9 5 ° C . — a n d w i t h m e t h a n o l a n d m e t h y l i o d i d e v a l u e s of a h i g h e r t h a n 120° w o u l d result.

W i t h J H and B n C

C

also JCH a n d Sc

k n o w n t o be p o s i t i v e (5), a n d therefore £ c

3

3

h a v e t h e same s i g n .

J H is C

is p o s i t i v e , too.

F o r a n elongated molecule s u c h as a c e t o n i t r i l e one c a n assume w i t h c e r t a i n t y t h a t i n a n e m a t i c s o l u t i o n t h e l o n g m o l e c u l a r axis w i l l be o r i e n t e d preferably p a r a l l e l to t h e o p t i c a l axis, a n d therefore &

3

is p o s i t i v e .


The

4.

SAUPE ET AL.

Bond Angle of CH

Z

Groups

59

same preferred o r i e n t a t i o n has been e x p e r i m e n t a l l y confirmed w i t h c o m pounds of s i m i l a r s t r u c t u r e — e . g . , p r o p y n e — b y m e a s u r e m e n t of t h e a n i s o t r o p y of t h e c h e m i c a l shift (2). O u r results for a c e t o n i t r i l e c a n therefore be regarded as a d i r e c t e x p e r i m e n t a l c o n f i r m a t i o n of t h e p o s i t i v e s i g n of J C H . T h e b o n d angles o b t a i n e d b y m i c r o w a v e measurements (see T a b l e I) i n t h e gas phase agree s a t i s f a c t o r i l y w i t h o u r results o b t a i n e d b y P M R spectroscopy. T h e s m a l l differences m a y be p a r t l y caused b y t h e i n f l u ence of v i b r a t i o n a l m o t i o n s . T h e r e m a y also be a s m a l l difference be t w e e n t h e m o l e c u l a r geometry i n t h e gas phase a n d i n t h e l i q u i d s o l u t i o n . A s there is n o s y s t e m a t i c d e v i a t i o n between t h e m i c r o w a v e a n d P M R v a l ues, w e c a n conclude t h a t neglecting t h e anisotropic p a r t of t h e electroncoupled s p i n - s p i n i n t e r a c t i o n is j u s t i f i e d . These results i n d i c a t e t h a t b y P M R measurements i n n e m a t i c s o l u tions t h e b o n d angle of CH3 groups m a y be d e t e r m i n e d i n a s i m p l e a n d f a i r l y precise m a n n e r . E v e n v e r y s m a l l changes of t h e b o n d angle c a n be detected. T h i s m i g h t b e useful f o r i n v e s t i g a t i n g t h e influence of s u b s t i t uents o n t h e b o n d angle i n C H X molecules a n d f o r s t u d y i n g correlations between t h e m a g n i t u d e of J C H a n d t h e b o n d angle. 3

T h e difference of 6' observed w i t h a c e t o n i t r i l e i n solvent I I against solvent I is p r o b a b l y caused b y a s m a l l change i n m o l e c u l a r geometry. I n b o t h solvents measurements were m a d e i n t h e same t e m p e r a t u r e range, a n d t h e observed l i n e s p l i t t i n g s h a v e t h e same m a g n i t u d e . W e c o n c l u d e t h a t neglecting t h e v i b r a t i o n a l m o t i o n s has n o influence o n t h e difference. A s m a l l change of t h e b o n d angle w a s i n fact t o be expected, because acetonitrile i n solvent I I w i l l be a t least p a r t i a l l y p r o t o n i z e d . T h e C H bonds c a r r y i n general a p e r m a n e n t electrical dipole m o m e n t . T h e r e is t h e n a n electrostatic i n t e r a c t i o n between these d i p o l e m o m e n t s a n d t h e a t t a c h e d p r o t o n . A s i m p l e c a l c u l a t i o n w i t h a n assumed b o n d m o m e n t of 0.4 debye shows t h a t these electrostatic i n t e r a c t i o n s m a y change t h e H - C - H angle, a , b y a b o u t 2 0 ' . I f t h e electrostatic i n t e r a c t i o n s are r e a l l y d o m i n a n t , t h e decrease of a i n the a c i d i c solvent shows t h a t i n t h e C H group of acetonitrile t h e H a t o m s c a r r y t h e p o s i t i v e charge. 3

Ac know ledgme η t W e are g r a t e f u l t o R . M e c k e , F r e i b u r g , G e r m a n y , f o r s u p p o r t of t h i s investigation.

H . Spiesecke, I s p r a , I t a l y , k i n d l y p r o v i d e d a s a m p l e of

c a r b o n - 1 3 - e n r i c h e d a c e t o n i t r i l e a n d m e t h y l iodide.

Literature Cited (1) Chatelain, P., Bull. Soc. Franc. Mineral. Crist. 78, 262 (1955). (2) Englert, G., Saupe, Α., Molecular Crystals 1, 503 (1966). (3) Englert, G., Saupe, Α., Ζ. Naturforsch. 19a, 172 (1964). (4) Ibid., 20a, 1401 (1965). (5) Karplus, M . , J. Am. Chem. Soc. 84, 2458 (1962). (6) Lippmann, H., Ann. Phys. (Leipzig) 2, 287 (1958). (7) Maier, W., Englert, G., Z. Elektrochem. 64, 689 (1960).


60

ORDERED FLUIDS A N D LIQUID CRYSTALS

(8) Maier, W., Saupe, Α., Ζ. Naturforsch. 13a, 564 (1958); 14a, 882 (1959); 15a, 287 (1960). (9) Miller, S. L., Aamodt, L . C., Dousmanis, G., Townes, C. H., Kraitchman, J., J. Chem. Phys. 20, 1112 (1952). (10) Phillips, W. D., Rowell, J . C., Melby, C., J. Chem. Phys. 41, 2551 (1964). (11) Saupe, Α., Proceedings of XIIIth Colloque Ampère, p. 321, North Holland Publishing Co., Amsterdam, 1964. (12) Saupe, Α., Ζ. Naturforsch. 19a, 161 (1964). (13) Ibid., 20a, 572 (1965). (14) Saupe, Α., Englert, G., Phys. Rev. Letters 11, 462 (1963). (15) Saupe, Α., Maier, W., Z. Naturforsch. 16a, 816 (1961). (16) Snyder, L . C., Anderson, E. W., J. Chem. Phys. 42, 3336 (1965); J. Am. Chem. Soc. 86, 5023 (1964). (17) Thomas, L . F., Sherrard, Ε. I. S., Sheridan, J., Trans. Faraday Soc. 51, 619 (1955). (18) Venkatesvarlu, P., Gordy, W., J. Chem. Phys. 23, 1200 (1955). (19) Weber, Κ. H., Ann. Phys. (Leipzig) 3, 1 (1959); Discussions Faraday Soc. 25, 74 (1958). (20) Zwetkoff, V., Acta Physicochim. URSS 16, 132 (1942). RECEIVED March 11, 1966. Investigation sponsored in part by the Deutsche Forchungsgemeinschaft.


Ordered Fluids and Liquid Crystals

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