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SELF CONSISTENT ELECTRON ENERGY DISTRIBUTION FUNCTIONS IN
NON-EQUILIBRIUM OXYGEN
M. Capitelli, M. Dilonardo, C. Gorse
To cite this version:
M. Capitelli, M. Dilonardo, C. Gorse. SELF CONSISTENT ELECTRON ENERGY DISTRIBUTION
FUNCTIONS IN NON-EQUILIBRIUM OXYGEN. Journal de Physique Colloques, 1979, 40 (C7),
pp.C7-13-C7-14. �10.1051/jphyscol:1979706�. �jpa-00219065�
JOURNAL DE PHYSIQUE CoZZoque C7, suppzdment au n07, Tome 40, JuiZZet 2979, page C7- 13
.SELF CONSSTENT ELECTRON ENERGY DISlRIBWION F U N C T I O N S IN NON-EQUILIBWM OXYGEN
M. Capitelli, M. Dilonardo and C. Gorse.
Centro di Studio per Za Chimica dei PZasmi deZ C.N.R., Istituto d i Cihimica Generaze deZZ'Universitd- via AmendoZa 173-70100 B m i , Italy.
E l e c t r o n energy d i s t r i b u t i o n f u n c t i o n s ( e d f ) o f mo- l e c u l a r oxygen have been c a l c u l a t e d by d i f f e r e n t authors[l] by s o l v i n g t h e Boltzmann equation i n - c l u d i n g b o t h e l a s t i c and i n e l a s t i c processes from t h e ground v i b r a t i o n a l l e v e l ( t h e s e c a l c u l a t i ' o n s w i l l be r e f e r r e d h e r e a f t e r as . t h e c o l d gas appro?
ximation).tio work on t h e c o n t r a r y e x i s t s on t h e i n f l u e n c e o f s u p e r e l a s t i c v i b r a t i o n a l c o l l i s i o n s and o f oxygen atoms on edf i n r e a c t i n g oxygen.
I n t h i s n o t e we r e p o r t t h e temporal e v o l u t i o n of edf d u r i n g t h e d i s s o c i a t i o n of m o l e c u l a r oxygen under n o n - e q u i l i b r i u m c o n d i t i o n s .
According t o t h e j o i n t v i b r o e l e c t r o n i c mechanism discussed i n refs. i2,3] ,the d i s s o c i q t i ~ n r a t e of O2 i n e l e c t r i c a l discharges can be w r i t t e n as
"A
vd' ne.$Nvk:(v) = kdjkNV 1
where Nv i s t h e number d e n s i t y o f t h e v t h v i b r a ? t i o n a l l e v e l and kz(v) i s t h ? . r a t e c o e f f i c i e n t o f t h e process
e+ O2(v)-) e+ 0 2 -m e+ 20 i
To c a l c u l a t e t h e d i s s o c i a t i o n r a t e one must know both t h e e-0 r a t e s ( i . e . t h e d i f f e r e n t k z ( v ) ' s ) and t h e p o p u l a t i o n d e n s i t i e s o f v i b r a t i o n a l l e v e l s l$.~hese l a s t q u a n t i t i e s can be obtai'ned by s o l - v i n g a system o f v l + l ( v J i s t h e number o f v i ' b r a ~ t i o n a l 1evels)master equations i n c l u d i n g .
a)electron-vibration(e4)energy
exchangesb).vi b r a t i o n - v i b r a t i on(Y-V) and v i b r a t i o n - t r a n s l a - t i o n (V-T) energy exchanges
c ) d i s s o c i a t i o n processes induced by e l e c t r o n and heavy p a r t i c l e s c o l l i s i c n s ( s e e r e f s . @,3] ) . I t should be noted t h a t e d f e n t e r i n t h e determi- n a t i o n o f Nv through t h e e-V and e-0 rates.0n t h e o t h e r hand t h e Nv populations e n t e r i n t h e B o l t z - mann equation through t h e s u p e r e l a s t i c v i b r a t i c - n a l c o l l i s i o n s
e+ 02(v) -C e+ 02(v=o) i i
and through t h e i n e l a s t i c processes i.
A t t h e time t=o we can consider a.11 molecules i n
e-0 r a t e s a r e those c a l c u l a t e d from edf i n t h e c o l d gas approximation.As t h e t i m e evolves,the po- p u l a t i o n of v i b r a t i o n a l l e v e l s achieve i m p o r t a n t values,so t h a t t h e s u p e r e l a s t i c v i b r a t i o n a l c o l l i - sions can n o t be neglected.We must use e-V and e-0 r a t e s c a l c u l a t e d from edf which take i n t o account processes i ,i i . A f u r t h e r temporal e v o l u t i o n b r i n g s t h e oxygen atoms.The Boltzmann equation must be now solved f o r a m i x t u r e o f v i b r a t i o n a l l y e x c i t e d molecules and atoms.This means t h a t t h e k i n e t i c
problem should be coupled t o t h e Boltzmann equa- t i o n . T h i s c o u p l i n g has been done i n t h e p r e s e n t work.Some o f t h e r e s u l t s have been r e p o r t e d i n f i - gures 1,2.
In
p a r t i c u l a r f i g . 1 shows e d f c a l c u l a t e d d u r i n g t h e temporal e v o l u t i o n o f v i b r a t i o n a l l e -11 -3 v e l s and oxygen a t o m s ( ~ / ~ = 5 . 1 0 - ~ 7 ~ c m 2 , n e = l ~ cm
,
T =500OK,~=5 t o r r ) .The p r o d u c t i o n o f oxygen atoms under t h e c o n d i t i o n s o f f i g . 1 i s smal1,so t h a t t h e 9 d i f f e r e n c e s i n edf shown i n f i g . 1 a r e due t o t h e increased number o f v i b r a t i o n a l l y e x c i t e d molecu- les.To c h a r a c t e r i z e t h e Nv d i s t r i b u t i o n s a t t h e d i f f e r e n t times,we can say t h a t they f o l l o w Trea- n o r ' s d i s t r i b u t i o n s w i t h v i b r a t i o n a l temperatures
'8,
=Elo/ln(No/N1) assuming t h e values o f 0,1330 and 1 8 6 5 ' ~ a t t = o , 1 0 - ~ and 3.510-*set
r e s p e c t i y e - ly.0ne can a p p r e c i a t e t h a t t h e increase o fGI
i n -creases t h e t a i l o f edf by approximately one order o f magnitude-This s i t u a t i o n propagates i n t h e e-D r a t e s o f t h e process
e + 0 2 ( v ) - + e + 0 2 ( ~ 3 ~ ~ - + e + 2 0 iii (Herzberg continuum) as can be appreciated i n Fig.l,where t h e r a t e c o e f f i c i e n t s o f process iii have been r e p o r t e d as a f u n c t i o n o f t i m e f o r d i f - f e r e n t v i b r a t i o n a l l e v e l s .
F i g u r e 2 shows t h e temporal e v o l u t i o n o f e d f f o r
E/N=9.1 =500°K and p = 5 t o r r
The p r o d u c t i o n o f oxygen atoms i s i n t h i s case ve- 9 r y important,so t h a t edf evolves from t h e c o l d
mo-
l e c u l a r gas s i t u a t i o n t o an o t h e r one composed by t h e ground v i b r a t i o n a l leve1,so t h a t t h e e-V and oxygen atoms .Once more d u r i n g t h i s e v o l u t i o n t h eArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979706
e-D rates to the Herzberg continuum(upper curves in fig.2) and to the Schumann continuum(1ower cur- ves)
e+ 02(v) -+ e+ 0 ~ ( 8 ~ 2 ; ) 3 e + 20
i i i idrastically change as can be appreciated in fig.2.
It should be noted that the dissociation degree of O2 in fig.2 is 0,0.42 and 1 at t=0,2.10-~ and 1.1 10-I sec respectively.
As for the dissociation kinetics,the present re- sults obtained with e-V and e-D rates from self- consistent edf qualitatively confirm those of ref.
[2,3] .These last results have been obtained with e-V and e-D rates from Maxwell edf (ref
. [ 2 1 )and from the cold gas approximation(ref. [3]) .In parti- cular the present results show that k for the
dj -2 conditions of fig.1 reaches at t=3.6.10 sec a value of 8.1.10-~sec-l which is three times grea- ter than k:(v=O)ne. On the contrary for the calcu- lations of fig.2 k closely follows k$(v=O)ne,
d
jsince the large concentration of oxygen atoms,be- cause of their large V-T deactivation rates,prac- tically destroy the vibrational content of the mo- lecul es. In these conditions one again observes the assisted recombination-dissociation mechanism di- scussed in ref.[3] .
References
[I] R.D.Hake and A.V.Phelps,Phys.Rev.158,70(1967);
H.Myers,J.Phys.B2,393(1969); -
K.Masek,T.Ruzicka and
L.Laska,Czech.J.Phys.827,888(1977)
[2] M.Capitel1
iand M.Dilonardo,Chem.Phys.30,95 (1978)
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