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Depolarized Rayleigh scattering in gases as a new probe of intermolecular forces
Volume 27A, n u m b e r 1
PHYSICS
n e g a t i v e i s e x p o s e d i n t h e l i n e a r p a r t of t h e H - D c u r v e [8] a n d d e v e l o p e d s u c h t h a t V = 2. (We u s e d p r e - e x p o s e d A g f a - G e v a e r t S c i e n t i a 8 E 70 p l a t e s d e v e l o p e d 5 m i n i n 1:3 d i l u t e d V a r i t o l n o r m a l . ) In fig. 2 t h e p h o t o m u l t i p l i e r s c a n of t h e c e n t r a l v e r t i c a l l i n e i n the a u t o c o r r e l a t i o n f u n c t i o n of the letter H shows that there is a considerable l i g h t i n t e n s i t y o u t s i d e t h e c e n t e r ( c u r v e a). T h e transformation into a 5-function is demonstrated i n c u r v e b w h i c h i s o b t a i n e d if t h e f i l t e r (OO*) ~1 i s i n s e r t e d a d d i t i o n a l l y i n f r o n t of t h e h o l o g r a m . We t h a n k P r o f e s s o r D r . W. M a r t i e n s s e n stimulating discussions.
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References 1. G.W. Stroke and R. G. Zech. Phys. L e t t e r s 25A (1967) 89. 2. A.W. Lohmann and H. W. Werlich, Phys. L e t t e r s 25A (1967) 570. 3. F, Lanzl, H.J. Mager and W. Waidelich, Z . A n g e wandte Phys. 24, n r . 3 (1968). 4. A. V a n d e r Lugt, IEEE T r a n s . I n f o r m . Theory 10 (1964) 139. 5. S. Lowenthal and Y. Belvaux, Revue d'Optique 46 (1967) 1. 6. J . V i e n o t and J . B u l a b o i s , Optica Acta 14 (1967) 57. 7. E . M a r o m and R. K. Mueller, Nondestructive early fatique detection. P r e p r i n t Bendix R e s e a r c h Labor a t i e s . Southfield. Michigan (1967). 8. G.W. Stroke, An introduction to coherent optics and holography (Academic P r e s s , New York 1966) p. 107,
DEPOLARIZED RAYLEIGH SCATTERING A NEW PROBE OF INTERMOLECULAR V. G. C O O P E R ,
20 May 1968
IN GASES FORCES
AS
A . D . M A Y , E . H . H A R A a n d H. F. P. E N A A P *
Department of Physics, University of Toronto, Toronto, Canada Received 17 April 1968
The widths of the depolarized Rayleigh line for CO 2, N 2 and H 2 a r e m e a s u r e d and used to calculate r e orientation c r o s s sections. The r e o r i e n t a t i o n a r i s e s only f r o m anisotropic i n t e r m o l e c u l a r interactions.
It i s t h e p u r p o s e of t h i s n o t e to r e p o r t on t h e m e a s u r e m e n t of the p r o f i l e of t h e d e p o l a r i z e d R a y l e i g h l i n e in s e v e r a l g a s e s . T h e w i d t h of t h e d e p o l a r i z e d R a y l e i g h l i n e m e a s u r e s t h e e f f e c t of c o l l i s i o n s on the o r i e n t a t i o n [1] of e a c h individual scattering molecule and unlike Raman or infrared lines is unaffected by phase shifts or inelastic coll i s i o n s . T h e r e o r i e n t a t i o n of m o l e c u l e s a r i s e s only from collisions involving anisotropic interm o l e c u l a r f o r c e s a n d t h e m e a s u r e m e n t of t h e c r o s s s e c t i o n c a n s e r v e a s a p r o b e of s u c h f o r c e s . T h e S e n f t l e b e n e f f e c t ( i n f l u e n c e of a m a g n e t i c f i e l d on v i s c o s i t y ) a n d N M R r e l a x a t i o n in g a s e s also involve the reorientation crosssection [2, 3]. H o w e v e r i n the S e n f t l e b e n e f f e c t i t i s a m a j o r b u t n o t the o n l y c r o s s s e c t i o n c o n t r i b u t i n g to t h e e f f e c t . In t h e N M R the c r o s s s e c t i o n c a n o n l y b e determined for the molecules whose nuclei have a quadrupole moment and the quadrupole coupling constant must be known. T h e e x p e r i m e n t a l a r r a n g e m e n t c o n s i s t e d of a 100 m W H e - N e l a s e r , a h i g h p r e s s u r e c e l l of 90 ° 52
s c a t t e r i n g , a N i c o l p r i s m to e l i m i n a t e the s t r o n g p o l a r i z e d c o m p o n e n t of t h e R a y l e i g h l i n e a n d s o m e f i l t e r i n g a r r a n g e m e n t to b l o c k t h e r o t a t i o n a l R a m a n l i n e s . T h e s p e c t r u m of t h e d e p o l a r i z e d Rayleigh light was then analysed with a FabryPerot interferometer, photon counting equipment a n d x-y r e c o r d e r . C u r v e s w e r e o b t a i n e d f o r N 2 a n d O2 b e t w e e n 1 a n d 10 a r m a n d f o r H 2 b e t w e e n 20 a n d 120 a r m , a l l a t r o o m t e m p e r a t u r e . F i g . 1 s h o w s t h e f u l l h a l f - w i d t h s f o r the t h r e e g a s e s a s a f u n c t i o n of p r e s s u r e . T h e h a l f - w i d t h s , w h i c h h a v e b e e n c o r r e c t e d f o r the i n s t r u m e n t a l width, vary linearly with density over the entire r a n g e . T h e s l o p e s of t h e l i n e s a r e 3.4 + 0.2, 1.5 ± 0.2 a n d 0.15 ± 0.03 G H z / a t m f o r CO2, N2, and H 2 respectively. For comparison the broade n i n g c o e f f i c i e n t s f o r the r o t a t i o n a l R a m a n l i n e s of N 2 a n d CO 2 [4] a r e a b o u t t w i c e t h a t f o r the d e p o l a r i z e d R a y l e i g h l i n e . F o r H 2 [5] the two * P r e s e n t a d d r e s s : Kamerlingh Onnes Laboratory, Leiden, The Netherlands.
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Fig. 1. The full half-width of the depolarized Rayleigh line as a function of p r e s s u r e for CO2, N2 and H2.
20 May 1968
a p p e a r s in the e x p r e s s i o n f o r v i s c o s i t y v e r s u s m a g n e t i c f i e l d [2] and in the e x p r e s s i o n f o r T 1 [3], two o t h e r v a l u e s of the r e o r i e n t a t i o n c r o s s s e c t i o n can be e s t i m a t e d and c o m p a r e d with that d e t e r m i n e d f r o m the R a y l e i g h l i n e . F r o m the S e n f t l e b e n e f f e c t [6, 71 the c o m p u t e d c r o s s s e c t i o n s a r e 53, 24 and 1.1 A 2 f o r CO 2, N 2 and H 2 r e s p e c t i v e l y . C o n s i d e r i n g the a p p r o x i m a t e n a t u r e of the t h e o r i e s u s e d to m a k e the c o m p a r i s o n the a g r e e m e n t is s a t i s f a c t o r y . P e r h a p s a l o g i c a l s t e p w o u l d be to u s e the c r o s s s e c t i o n d e t e r m i n e d f r o m the d e p o l a r i z e d s p e c t r u m to aid in the i n t e r p r e t a t i o n of the e x p e r i mental viscosity versus magnetic field curve. Only the T 1 v a l u e f o r N 2 can be u s e d to c o m p u t e a r e o r i e n t a t i o n c r o s s s e c t i o n . The v a l u e obt a i n e d [8, 9] is 12 ~,2, and h a s a l a r g e e r r o r a s s o c i a t e d with it due to the e x t r e m e e x p e r i m e n t a l d i f f i c u l t i e s i n v o l v e d , p a r t i c u l a r l y in m e a s u r i n g the q u a d r u p o l e c o u p l i n g c o n s t a n t . O b v i o u s l y one c o u l d r e v e r s e the c a l c u l a t i o n to obtain a v a l u e f o r this m o l e c u l a r p a r a m e t e r . H o w e v e r f u r t h e r e x p e r i m e n t a l and t h e o r e t i c a l w o r k i s r e q u i r e d b e f o r e a m e a s u r e m e n t of T 1 and the width of the d e p o l a r i z e d R a y l e i g h l i n e can be c o m b i n e d to y i e l d a m e a n i n g f u l v a l u e f o r this c o n s t a n t .
coefficients are nearly equal. T h e s l o p e s of the l i n e s of fig. 1 c a n be u s e d to d e t e r m i n e the r e o r i e n t a t i o n c r o s s s e c t i o n a. G o r d o n [1] in a s e m i - c l a s s i c a l c a l c u l a t i o n h a s s h o w n that the (full) h a l f - w i d t h A v ! is g i v e n by 2
oo
2,~u!
Z
= 2n (V) a = n
(v f
6 , ( s i n 2 a ) b rib)
O
References
w h e r e n is the n u m b e r d e n s i t y , V the r e l a t i v e v e l o c i t y of the two c o l l i d i n g m o l e c u l e s , b the i m p a c t p a r a m e t e r and a the a n g l e t h r o u g h w h i c h one m o l e c u l e i s t u r n e d by a c o l l i s i o n . T h e b r a c k e t s d e n o t e a s t a t i s t i c a l a v e r a g e . F o r the m o m e n t we n e e d only the r e l a t i o n s h i p b e t w e e n (r and AV~; the • 2 e x t r e m e m g h t hand s i d e of t h i s e q u a t i o n s h o w s that a is i n d e e d a r e o r i e n t a t i o n c r o s s s e c t i o n . T h e e x p e r i m e n t a l v a l u e s of a f o r CO2, N2, and H 2 a r e 81, 28 and 0.77 ~,2 r e s p e c t i v e l y . U n f o r t u n a t e l y no t h e o r e t i c a l c a l c u l a t i o n s f o r a a r e p r e s e n t l y a v a i l a b l e with w h i c h to c o m p a r e t h e s e v a l u e s . H o w e v e r a s the s a m e i n t e g r a l , f O
1. R.G.Gordon, a. Chem. Phys.44 (1966) 3083. 2. a. Korving, H . F . P . Knaap, R.G.Gordon and J. a. M. Beenakker, Phys. Letters 24A (1967) 755. The Y of this reference equals (n(g)o~)-l. 3. R.G.Gordon, J . C h e m . Phys. 44 (1966) 228. 4. K . S . J a m m u , G . E . S t . J o h n a n d H . L.Welsh, Can. J. Phys. 44 (1966) 797. 5. A. D. May, V. Degen, J . C . Stryland and H. L. Welsh, Can. J. Phys. 39 (1961) 1769. 6. J. Korving, H. Hulsman, G. Scoles, H . F . P . Knaap a n d J. J. M. Beenakker, Physica 36 (1967) 177. 7. Private communication, J . K o r v i n g (viscosity r e suits for CO2). 8 . P . J . Haigh, T.A.Scott, J . C h e m . Phys.38 (1963) 117 (Quadrupole coupling constant for N2). 9 . Private communication, P . A . SpeigHt and R. L . A r m strong (T 1 for N2).
6~ ( s i n 2 a ) b db , *****
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n e g a t i v e i s e x p o s e d i n t h e l i n e a r p a r t of t h e H - D c u r v e [8] a n d d e v e l o p e d s u c h t h a t V = 2. (We u s e d p r e - e x p o s e d A g f a - G e v a e r t S c i e n t i a 8 E 70 p l a t e s d e v e l o p e d 5 m i n i n 1:3 d i l u t e d V a r i t o l n o r m a l . ) In fig. 2 t h e p h o t o m u l t i p l i e r s c a n of t h e c e n t r a l v e r t i c a l l i n e i n the a u t o c o r r e l a t i o n f u n c t i o n of the letter H shows that there is a considerable l i g h t i n t e n s i t y o u t s i d e t h e c e n t e r ( c u r v e a). T h e transformation into a 5-function is demonstrated i n c u r v e b w h i c h i s o b t a i n e d if t h e f i l t e r (OO*) ~1 i s i n s e r t e d a d d i t i o n a l l y i n f r o n t of t h e h o l o g r a m . We t h a n k P r o f e s s o r D r . W. M a r t i e n s s e n stimulating discussions.
for
LETTERS
References 1. G.W. Stroke and R. G. Zech. Phys. L e t t e r s 25A (1967) 89. 2. A.W. Lohmann and H. W. Werlich, Phys. L e t t e r s 25A (1967) 570. 3. F, Lanzl, H.J. Mager and W. Waidelich, Z . A n g e wandte Phys. 24, n r . 3 (1968). 4. A. V a n d e r Lugt, IEEE T r a n s . I n f o r m . Theory 10 (1964) 139. 5. S. Lowenthal and Y. Belvaux, Revue d'Optique 46 (1967) 1. 6. J . V i e n o t and J . B u l a b o i s , Optica Acta 14 (1967) 57. 7. E . M a r o m and R. K. Mueller, Nondestructive early fatique detection. P r e p r i n t Bendix R e s e a r c h Labor a t i e s . Southfield. Michigan (1967). 8. G.W. Stroke, An introduction to coherent optics and holography (Academic P r e s s , New York 1966) p. 107,
DEPOLARIZED RAYLEIGH SCATTERING A NEW PROBE OF INTERMOLECULAR V. G. C O O P E R ,
20 May 1968
IN GASES FORCES
AS
A . D . M A Y , E . H . H A R A a n d H. F. P. E N A A P *
Department of Physics, University of Toronto, Toronto, Canada Received 17 April 1968
The widths of the depolarized Rayleigh line for CO 2, N 2 and H 2 a r e m e a s u r e d and used to calculate r e orientation c r o s s sections. The r e o r i e n t a t i o n a r i s e s only f r o m anisotropic i n t e r m o l e c u l a r interactions.
It i s t h e p u r p o s e of t h i s n o t e to r e p o r t on t h e m e a s u r e m e n t of the p r o f i l e of t h e d e p o l a r i z e d R a y l e i g h l i n e in s e v e r a l g a s e s . T h e w i d t h of t h e d e p o l a r i z e d R a y l e i g h l i n e m e a s u r e s t h e e f f e c t of c o l l i s i o n s on the o r i e n t a t i o n [1] of e a c h individual scattering molecule and unlike Raman or infrared lines is unaffected by phase shifts or inelastic coll i s i o n s . T h e r e o r i e n t a t i o n of m o l e c u l e s a r i s e s only from collisions involving anisotropic interm o l e c u l a r f o r c e s a n d t h e m e a s u r e m e n t of t h e c r o s s s e c t i o n c a n s e r v e a s a p r o b e of s u c h f o r c e s . T h e S e n f t l e b e n e f f e c t ( i n f l u e n c e of a m a g n e t i c f i e l d on v i s c o s i t y ) a n d N M R r e l a x a t i o n in g a s e s also involve the reorientation crosssection [2, 3]. H o w e v e r i n the S e n f t l e b e n e f f e c t i t i s a m a j o r b u t n o t the o n l y c r o s s s e c t i o n c o n t r i b u t i n g to t h e e f f e c t . In t h e N M R the c r o s s s e c t i o n c a n o n l y b e determined for the molecules whose nuclei have a quadrupole moment and the quadrupole coupling constant must be known. T h e e x p e r i m e n t a l a r r a n g e m e n t c o n s i s t e d of a 100 m W H e - N e l a s e r , a h i g h p r e s s u r e c e l l of 90 ° 52
s c a t t e r i n g , a N i c o l p r i s m to e l i m i n a t e the s t r o n g p o l a r i z e d c o m p o n e n t of t h e R a y l e i g h l i n e a n d s o m e f i l t e r i n g a r r a n g e m e n t to b l o c k t h e r o t a t i o n a l R a m a n l i n e s . T h e s p e c t r u m of t h e d e p o l a r i z e d Rayleigh light was then analysed with a FabryPerot interferometer, photon counting equipment a n d x-y r e c o r d e r . C u r v e s w e r e o b t a i n e d f o r N 2 a n d O2 b e t w e e n 1 a n d 10 a r m a n d f o r H 2 b e t w e e n 20 a n d 120 a r m , a l l a t r o o m t e m p e r a t u r e . F i g . 1 s h o w s t h e f u l l h a l f - w i d t h s f o r the t h r e e g a s e s a s a f u n c t i o n of p r e s s u r e . T h e h a l f - w i d t h s , w h i c h h a v e b e e n c o r r e c t e d f o r the i n s t r u m e n t a l width, vary linearly with density over the entire r a n g e . T h e s l o p e s of t h e l i n e s a r e 3.4 + 0.2, 1.5 ± 0.2 a n d 0.15 ± 0.03 G H z / a t m f o r CO2, N2, and H 2 respectively. For comparison the broade n i n g c o e f f i c i e n t s f o r the r o t a t i o n a l R a m a n l i n e s of N 2 a n d CO 2 [4] a r e a b o u t t w i c e t h a t f o r the d e p o l a r i z e d R a y l e i g h l i n e . F o r H 2 [5] the two * P r e s e n t a d d r e s s : Kamerlingh Onnes Laboratory, Leiden, The Netherlands.
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Fig. 1. The full half-width of the depolarized Rayleigh line as a function of p r e s s u r e for CO2, N2 and H2.
20 May 1968
a p p e a r s in the e x p r e s s i o n f o r v i s c o s i t y v e r s u s m a g n e t i c f i e l d [2] and in the e x p r e s s i o n f o r T 1 [3], two o t h e r v a l u e s of the r e o r i e n t a t i o n c r o s s s e c t i o n can be e s t i m a t e d and c o m p a r e d with that d e t e r m i n e d f r o m the R a y l e i g h l i n e . F r o m the S e n f t l e b e n e f f e c t [6, 71 the c o m p u t e d c r o s s s e c t i o n s a r e 53, 24 and 1.1 A 2 f o r CO 2, N 2 and H 2 r e s p e c t i v e l y . C o n s i d e r i n g the a p p r o x i m a t e n a t u r e of the t h e o r i e s u s e d to m a k e the c o m p a r i s o n the a g r e e m e n t is s a t i s f a c t o r y . P e r h a p s a l o g i c a l s t e p w o u l d be to u s e the c r o s s s e c t i o n d e t e r m i n e d f r o m the d e p o l a r i z e d s p e c t r u m to aid in the i n t e r p r e t a t i o n of the e x p e r i mental viscosity versus magnetic field curve. Only the T 1 v a l u e f o r N 2 can be u s e d to c o m p u t e a r e o r i e n t a t i o n c r o s s s e c t i o n . The v a l u e obt a i n e d [8, 9] is 12 ~,2, and h a s a l a r g e e r r o r a s s o c i a t e d with it due to the e x t r e m e e x p e r i m e n t a l d i f f i c u l t i e s i n v o l v e d , p a r t i c u l a r l y in m e a s u r i n g the q u a d r u p o l e c o u p l i n g c o n s t a n t . O b v i o u s l y one c o u l d r e v e r s e the c a l c u l a t i o n to obtain a v a l u e f o r this m o l e c u l a r p a r a m e t e r . H o w e v e r f u r t h e r e x p e r i m e n t a l and t h e o r e t i c a l w o r k i s r e q u i r e d b e f o r e a m e a s u r e m e n t of T 1 and the width of the d e p o l a r i z e d R a y l e i g h l i n e can be c o m b i n e d to y i e l d a m e a n i n g f u l v a l u e f o r this c o n s t a n t .
coefficients are nearly equal. T h e s l o p e s of the l i n e s of fig. 1 c a n be u s e d to d e t e r m i n e the r e o r i e n t a t i o n c r o s s s e c t i o n a. G o r d o n [1] in a s e m i - c l a s s i c a l c a l c u l a t i o n h a s s h o w n that the (full) h a l f - w i d t h A v ! is g i v e n by 2
oo
2,~u!
Z
= 2n (V) a = n
(v f
6 , ( s i n 2 a ) b rib)
O
References
w h e r e n is the n u m b e r d e n s i t y , V the r e l a t i v e v e l o c i t y of the two c o l l i d i n g m o l e c u l e s , b the i m p a c t p a r a m e t e r and a the a n g l e t h r o u g h w h i c h one m o l e c u l e i s t u r n e d by a c o l l i s i o n . T h e b r a c k e t s d e n o t e a s t a t i s t i c a l a v e r a g e . F o r the m o m e n t we n e e d only the r e l a t i o n s h i p b e t w e e n (r and AV~; the • 2 e x t r e m e m g h t hand s i d e of t h i s e q u a t i o n s h o w s that a is i n d e e d a r e o r i e n t a t i o n c r o s s s e c t i o n . T h e e x p e r i m e n t a l v a l u e s of a f o r CO2, N2, and H 2 a r e 81, 28 and 0.77 ~,2 r e s p e c t i v e l y . U n f o r t u n a t e l y no t h e o r e t i c a l c a l c u l a t i o n s f o r a a r e p r e s e n t l y a v a i l a b l e with w h i c h to c o m p a r e t h e s e v a l u e s . H o w e v e r a s the s a m e i n t e g r a l , f O
1. R.G.Gordon, a. Chem. Phys.44 (1966) 3083. 2. a. Korving, H . F . P . Knaap, R.G.Gordon and J. a. M. Beenakker, Phys. Letters 24A (1967) 755. The Y of this reference equals (n(g)o~)-l. 3. R.G.Gordon, J . C h e m . Phys. 44 (1966) 228. 4. K . S . J a m m u , G . E . S t . J o h n a n d H . L.Welsh, Can. J. Phys. 44 (1966) 797. 5. A. D. May, V. Degen, J . C . Stryland and H. L. Welsh, Can. J. Phys. 39 (1961) 1769. 6. J. Korving, H. Hulsman, G. Scoles, H . F . P . Knaap a n d J. J. M. Beenakker, Physica 36 (1967) 177. 7. Private communication, J . K o r v i n g (viscosity r e suits for CO2). 8 . P . J . Haigh, T.A.Scott, J . C h e m . Phys.38 (1963) 117 (Quadrupole coupling constant for N2). 9 . Private communication, P . A . SpeigHt and R. L . A r m strong (T 1 for N2).
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