HAL Id: jpa-00220596
https://hal.archives-ouvertes.fr/jpa-00220596
Submitted on 1 Jan 1980
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
THE ROLE OF THE TRANSLATIONAL
NONEQUILIBRIUM OF REACTING PARTICLES IN
THE HF-LASER KINETICS
G. Sholin, V. Nikerov, V. Rusanov
To cite this version:
JOURNAL DE PHYSIQUE CoZloque C 9 , suppZ6ment
au
n O 1 l , Tome 41, nouembre 1980, page C9-305THE ROLE OF THE TRANSLATIONAL NONEQUILIBRIUM OF REACTING PARTICLES
I N THE HF-LASER K I N E T I C S *
G.V. S h o l i n , V.A. Nikerov and V.D. Rusanov.
I . V. Kurchatov I n s t i t u t e of Atomic Energy, 123182, Moscow,
U.S.
S . R..
The p r o g r e s s i n t h e c h e m i c a l l a s e r s t u d i e s a t t r a c t s t h e a t t e n t i o n t o t h e c h e m i c a l p r o c e s s e s p r o v i d i n g l a s e r i n g . U s u a l l y c h e m i s t s a p r i o r y imply t h a t t h e t r a n s l a t i o n a l e n e r g y of t h e "hot" p r o d u c t s o f e x o t h e r m a l r e a c t i o n s r e l e x a t e i n s t a n t l y . However t h i s a s s u m p t i o n i s u n s u f f i c i e n t sometimes and may l e a d t o wrong r e s u l t s 11-2
(
.
T h i s r e p o r t i s c o n c e r n e d w i t h t h e t h e o r e t i c a l i n v e s t i g a t i o n of t h e t r a n s l a t i o n a l n o n e q u i l i b r i u m i n f l u e n c e on t h e c h a i n b r a n c h e d H2+F2 r e a c t i o n . Here i t w i l l b e shown t h a t i n t h e c e r t a i n c o n d i t i o n s a s m a l l num- b e r of s u p e r t h e r m a l atoms o r m o l e c u l e s p r o v i d e t h e more h i g h r e a c t i o n r a t e t h a n t h e r m a l o n e s . On t h i s b a s i s t h e o p t i m a l regimes o f t h e p u l s e d c h e m i c a l H F - l a s e r s a r e a n a l y s e d . 2.The t h e r m a l i z a r i o n p r o c e s s of t h e s u p e r - t h e r m a l p a r t i c l e s i s c o n s i d e r e d w i t h h e l p o f t h e d e g r a d a t i o n s p e c t r u m method 131
.
The e l a s t i c c r o s s s e c t i o n s o f a t o m i c and m o l e c u l a r c o l l i s i o n s a r e d e s c r i b e d i n t h e r i g i d s p h e r e s model. To s i m p l i f y t h e hydrogen atoms and m o l e c u l e s masses a r e n e g l e c - t e d w i t h r e g a r d s t o t h o s e o f f l u o r i n e . The uncom- p l e t e t h e r m a l i z a t i o n of hydrogen and f l u o r i n e atDms i s t o a c c e l e r a t e p r o n o u n c e l y t h e c h a i n r e a c t i o n H2+F2, a t t h e r e l a t i v e l y low t e m p e r a t u r e s , espe- c i a l l y a t room o n e s . As known 14-51,
t h e t r a n s l a - t i o n a l e n e r g y o f r e a g e n t s i s e f f e c t i v e m a i n l y i n t h e overcoming of t h e a c t i v a t i o n b a r r i e r of a n e x o t h e r m a l r e a c t i o n . Both c h a i n r e a c t i o n sK =KO exp (-E /T)
,
~ O = 2 . 0 . l 0 -10 cm3 s-l1 1 a 1 1
K,=KO,
exp ( - E , ~ / T ),
K;-2.7 .10-l0 cm 'S-', Ea2 = 0.069 eV a r e h i g h e x o t h e r m i c w i t h t h e e x o t h e r m i t i e s e q u a l 4.26 and 1 . 3 7 eV r e s p e c t i v e l y 16-71. The t r a n s l a - t i o n a l e n e r g y s h a r e i s a b o u t a h a l f o f t h e s e v a l u e s i n a v e r a g e . The a c c e l e r a t i o n of t h e f i r s t ( 1 ) r e a c - t i o n must b e more pronounced t h a n t h a t of t h e s e c o n d b e c a u s e t h e a v e r a g e k i n e t i c e n e r g y of t h e hydrogen atoms formed by t h e s e c o n d ( 2 ) r e a c t i o n i s e q u a l a p p r o x i m a t l y 0 . 3 6 eV and e x c e e d s c o n s i d e r a b l y t h e a c t i v a t i o n b a r r i e r E = 0 . 1 0 3 eV. The therma-a 1
l i z a t i o n problem must t a k e i n t o a c c o u n t a s t h e e l a s t i c c o l l i s i o n s p r o c e s s e s a s t h e e l e m e n t a r y c h e m i c a l a c t s i n d u c e d by t h e s u p e r t h e r m a l p a r t i c l e s t o o .
The d e g r a d a t i o n s p e c t r u m Z(E)dE f o r t h e therma- l i z a t i o n problem i s d i f i n e d a s an a v e r a g e number of t h e "hot" atoms h a v i n g w h i l e c o o l i n g t h e e n e r g y w i t h i n a n i n t e r v a l from E t o E + dE. I t f o l l o w s t h e e q u a t i o n "W pw (W-E) Z(W) dw + $ ( E ) ( 3 )
*
P o s t d e a d l i n e p a p e rC9-306 JOURNAL DE PHYSIQUE
w i t h t h e boundary c o n d i t i o n Z(m) = 0 , where p (W-E)
W i s t h e p a r t i a l p r o b a b i l i t y o f t h e W-E e n e r g y l o s s by t h e p a r t i c l e w i t h i n i t i a l e n e r g y W , $(E)- i s a p r i m a r y d i s t r i b u t i o n f u n c t i o n o f ' % o t t t p a r t i c l e s . ?he e f f e c t i v e r e a c t i o n r a t e c o n s t a n t i s d e f i - ned by K1 e f f ( 4 ) 0 where K ( E )
-
i s t h e r e a c t i o n r a t e c o e f f i c i e n t f o r t h e p a r t i c l e w i t h t h e e n e r g y E . The d i s t r i b u t i o n f u n c t i o n o f " h o t " p a r t i c l e s f ( E ) d i f f e r s from t h e Maxwell one and can be c a l c u l a t e d w i t h h e l p o ft h e d e g r a d a t i o n s p e c t r u m : t h e F i g . 1 t h e e f f e c t i v e r e a c t i o d r a t e K1 e f f exceeds i t s e q u i l i b r i u m v a l u e t o a marked d e g r e e i n t h e m i x t u r e s w i t h t h e p r o m i n e n t f l u o r i n e concen- t r a t i o n . There i s a n i m p o r t a n t i d f e r e n c e from t h i s f a c t when t h e s t e a d y
-
s t a t e c o n d i t i o n i f f u l f i I l ' e d K1 e f fI H I
IF2/ = ' K 2l ~ l
Namely t h e p a r t i a l c o n c e n t r a t i o n : o f t h e hydrogen r a d i c a l s d e c r e a s e s 4 h a r p w i t h i n c r e a - s i n g t h e p a r t i a l m o l e c u l a r f l u o r i n e c o n c e n t r a t i o n I F 2 /.
I t i s c l e a r from t h e F i g . 2 t h a t t h e IF2] + IH21 b r e a k o f t h e c h e m i c a l c h a i n i s p i o v i d e d by t h e H- atoms a t t h e low p a r t i a l f l u o r i n c o n c e n t r a t i o n s o t h e r v i s e t h e b r e a k by t h e F- atoms d o m i n a t e s . where T ( E ) i s a n a v e r a g e c o l l i s i o n a l e s l i f e t i m e of t h e p a r t i c l e w i t h t h e e n e r g y E ; C - i s a nor-F
-P?
*IF
m a l i z a t i o n c o n s t a n t .The e f f e c t i v e r e a c t i o n r a t e dependence upon t h e p a r t i a l f l u o r i n e c o n c e n t r a t i o n i n m i x t u r e I F 2 [
ITZl+lH21
i s g i v e n on F i g . l . A s i t i s s e e n fromU
0
0,2
44
46
Cf?I+f~21
F i g . 2 Dependence o f t h e p a r t i a l hydrogen atom
The t r a n s l a t i o n a l n o n e q u i l i b r i u m e f f e c t s pro- v i d e some u n i f i e d e x p l a n a t i o n o f t h e v a r i o u s gene- r a t i n g regims o f t h e c h e m i c a l HF- l a s e r s . R ~ a l l y t h e r e a r e two d i f f e r e n t o p t i m a l m i x t u r e s o f chemi- c a l r e a g e n t s 18-91
,
w i t h c o r r e s p o n d t o d i f f e r e n t g e n e r a t i n g r e g i m e s of t h e HF- l a s e r , namely : ( a ) t h e m i x t u r e w i t h t h e p r e v a i l i n g p a r t i a l c o n c e n t r a t i o n of t h e i n e r t d i l u e n t ; ( b ) t h e m i x t u r e w i t h t h e p r e v a i l i n g p a r t i a l f l u o r i n e c o n c e n t r a t i o n w i t h o u t any d i l u e n t . I n t h e f i r s t regime t h e l a s e r a r e c h a r a c t e r i - zed by t h e r e l a t i v e l y h i g h e n e r g e t i c a l p a r a m e t e r s b e c a u s e t h e more complete p a r t i a l i n v e r s i o n i s r e a l i z e d i n t h i s c a s e . I n t h e s e c o n d r e g i m e , t h e p u l s e d l a s e r a r e c h a r a c t e r i z e d by t h e h i g h e r power p a r a m e t e r s b e c a u s e t h e t r a n s l a t i o n a l n o n e q u i l i b r i u m*
i s r e a l i z e d and h e n c e t h e a c t i v e m o l e c u l e s HF p r o d u c t i n g i s more e f f e c t i v e . U s u a l l y t h e a v a i l a b l e computer codes e x p l a i n o n l y one from two regimesle,-l0-111
.
The i n c l u s i o n of t h e t h e r m a l i z a t i o n p r o c e s s e s l e a d s t o m o d i f i c a t i o n of t h e r e a c t i o n r a t e K by t h a t K1 e f f and i t a l l o w s t o g e n e r a l i z e
t h e computer codes and t o e x p l a i n b o t h regimes from t h e u n i v e r s a l p o i n t o f view 1 2
.
As i t i s shown i n t h e T a b l eI
t h e e x p e r i m e n t a l l a s e r i n g d e l a y measured from t h e e l e c t r o n beam s w i t c h i n g moment 9 i s w e l l e x p l a i n e d by t h i s t h e o r e t i c a l a p p r o a c h . T a b l e I : The d e l a y t i m e o f t h e g e n e r a k i o n T~ i n dependence o f t h e t r a n s l a t i o n a l n o n e q u i l i b r i u mi
R e s u l t of t h e c a l c u l a t i o n wheni
t r a n s l a t i o n a l n o n e q u i l i b r i u m Experiment l e x i s t s:
i s a b s e n t l 1 1 T ~ n s e c ,i
20-
25 80-
90 20-
25 I 1 1-
I * t h e d e l a y i s d e f i n e d w i t h r e s p e c t t o t h e e l e c t r o n beam s w i t c h i n g moment. Thus t h e c o r r e c t c a l c u l a t i o n s o f t h e t r a n s l a - t h e t h e o r y of t h e c h e m i c a l HF- l a s e r and t h e t i o n a l n o n e q u i l i b r i u m of t h e c h a i n H2kF2 r e a c t i o n c o r r e s p o n d i n g e x p e r i m e n t s .p r o d u c t s a l l o w s t o improve t h e agreement between
REFERENCES
( l ) V.A. NIKEROV, V . D . RUSANOV, G . V . SHOLIN, 4988 (1972) "Doklady Akad. Nauk SSSR"
218,
610 ( 1 9 7 9 ) .( 8 ) Handbook of Chemical L a s e r s . Ed. by R . Gross ( 2 ) V.A. NIKEROV, V.D. RUSANOV, G . V . SHOLIN, and J . B o t t ; J . Wiley and S o n s , N . Y . , L.
P r e p i n t IAE-3213 (1979). ( 1 9 7 6 ) .
( 3 ) V.A. NIKEROV, G.V. SHOLIN, F i s i k a Plasmy,
3,
( 9 ) R.A. GERBER, E.L. PATTERSON, J . Appl. P h y s . , 1256 ( 1 9 7 8 ) . 4 7 , 3524 ( 1 9 7 6 ) .( 4 ) J . C . POLANYI e t a l , Chem. P h y s .
3,
403 ( 1 9 7 5 ) . (10)J.M. MORENO, A.I.A.A., p a p e r N.75-36 (1975) ( 5 ) J . C . POLANYI, J . L . SCHREIBER, F a r a d . D i s c . ( 1 1 ) z . ~ . ALFASSI, M. BAER, I . E . E . E . , Jounr.QE-15,Chem. S o c . ,
