Laser Probes for Combustion Chemistry - American Chemical Society

12 What Really Does Happen to Electronically Excited Atoms in Flames? KERMIT C. SMYTH, PETER K. SCHENCK, and W. GARY MALLARD Downloaded by EAST CAROLINA UNIV on June 4, 2018 | https://pubs.acs.org Publication Date: September 23, 1980 | doi: 10.1021/bk-1980-0134.ch012

National Bureau of Standards, Washington, D.C. 20234

In recent years numerous experiments have been reported on the fluorescence and energy transfer processes of electronically excited atoms. However, for flame studies the rates of many possible collision processes are not well known, and so the fate of these excited atoms is unclear. An interesting example concerns the ionization of alkali metals in flames. When the measured ionization rates are interpreted using simple kinetic theory, the derived ionization cross sections are orders of magnitude larger than gas kinetic (1,2,3). More detailed analyses (4,5) have yielded much lower ionization cross sections by invoking participation of highly excited electronic states. Evaluation of these models has been hampered by the lack of data on the ionization rate as a function of initial state for the alkali metals. Opto-galvanic spectroscopy detects the absorption spectra of atoms (6) and some molecules (7) in a flame by measuring current changes induced by optical irradiation at a wavelength corresponding to an electronic transition. Two steps are involved: A + hv -* A* photon a b s o r p t i o n A* + M A*"+ e~ + M collisional ionization. Thus, t h e o v e r a l l i o n i z a t i o n s t a r t i n g from a g i v e n e x c i t e d s t a t e i s monitored. Since the e f f i c i e n c y o f c o l l i s i o n a l i o n i z a t i o n i s h i g h e s t when t h e e n e r g y r e q u i r e d f o r i o n i z a t i o n i s l o w e s t , t h i s method i s p a r t i c u l a r l y s e n s i t i v e f o r d e t e c t i n g h i g h - l y i n g states. We h a v e f o u n d t h a t t w o - p h o t o n t r a n s i t i o n s a r e r e a d i l y o b s e r v a b l e f o r many a t o m i c s p e c i e s . I f o n e s e l e c t s a p a r t i c u l a r atom a n d then m o n i t o r s t h e l a s e r - i n d u c e d c u r r e n t changes f o r a s e r i e s o f e l e c t r o n i c s t a t e s , the observed s i g n a l magnitudes a r e s e n s i t i v e to t h e competing i o n i z a t i o n and quenching p r o c e s s e s . In this p a p e r we compare o u r e x p e r i m e n t a l r e s u l t s o n Na w i t h m o d e l c a l c u l a t i o n s which i n c o r p o r a t e s t a t e - s p e c i f i c i o n i z a t i o n and quenching r a t e s . E x p e r i m e n t a l R e s u l t s Two-photon t r a n s i t i o n s i n Na f r o m t h e 3 s ground s t a t e t o h i g h - l y i n g s and d s t a t e s have been observed This chapter not subject to U . S . copyright. Published 1980 American Chemical Society

Crosley; Laser Probes for Combustion Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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u s i n g s t e p w i s e e x c i t a t i o n (two l a s e r s o p e r a t i n g a t d i f f e r e n t wavelengths). T h u s , we h a v e ( 1 ) 3s + 3p a t X i and ( 2 ) 3p nd a t X w h e r e n , t;he p r i n c i p a l quantum number, i s b e t w e e n 4 and 12. The t r a n s i t i o n p r o b a b i l i t i e s f o r e a c h s t e p a r e w e l l known ( 8 ) . Two d y e l a s e r s w e r e e x c i t e d s i m u l t a n e o u s l y by a p u l s e d n i t r o g e n l a s e r ( p u l s e w i d t h - 7 n s ) , and t h e two u n f o c u s s e d beams i r r a d i a t e d t h e flame i n a c o u n t e r - p r o p a g a t i n g , c o l l i n e a r geometry. W i t h 25% o f t h e n i t r o g e n l a s e r pumping t h e d y e l a s e r o p e r a t i n g a t X i , t y p i c a l l a s e r e n e r g i e s w e r e 35-70 u J , and t h e f i r s t t r a n s i t i o n 3s 3p was o p t i c a l l y s a t u r a t e d . However, f o r t h e 3p nd t r a n s i t i o n s c a r e was t a k e n t o a v o i d o p t i c a l s a t u r a t i o n ; t y p i c a l l a s e r e n e r g i e s a t X w e r e 1-300 u J . The f l a m e was f u e l r i c h H 2 / a i r , b u r n i n g o n a 5-cm l o n g s l o t b u r n e r ; t h e e s t i m a t e d t e m p e r a t u r e was 2000 K ( 7 ) . Aqueous Na s o l u t i o n s were a s p i r a t e d i n t o t h i s f l a m e , w i t h c o n c e n t r a t i o n s o f 1 ppm f o r m e a s u r i n g t h e X i s i g n a l ( 3 s -> 3p) and 10 ppb f o r the s i g n a l u s i n g both dye l a s e r s . The l a t t e r s o l u t i o n c o r r e s p o n d s t o a Na number d e n s i t y o f ~ 1 0 cm" i n t h e f l a m e . F i g u r e 1 shows a p o r t i o n o f t h e d a t a o b t a i n e d f o r t h e s t e p w i s e e x c i t a t i o n o f Na. F i g u r e 2 p l o t s t h e o b s e r v e d s i g n a l enhancement ( d e f i n e d a s s i g n a l w i t h X i + X d i v i d e d by t h e s i g n a l with X i only) versus the absorption c o e f f i c i e n t f o r the stronger (3p3/ nd) o f t h e two c o m p o n e n t s .

Downloaded by EAST CAROLINA UNIV on June 4, 2018 | https://pubs.acs.org Publication Date: September 23, 1980 | doi: 10.1021/bk-1980-0134.ch012

2

2

9

3

2

2

M o d e l l i n g t h e D a t a The p r e s e n t m o d e l e x t e n d s a n e a r l i e r v e r s i o n H e r e we s e e k t o e v a l u a t e t h e e x p e c t e d s i g n a l f r o m a s e r i e s o f d s t a t e s i n Na by u s i n g a r a t e e q u a t i o n m o d e l w h i c h i n c l u d e s a b s o r p t i o n , s t i m u l a t e d e m i s s i o n , c o l l i s i o n a l i o n i z a t i o n , and q u e n c h i n g . The e s s e n t i a l f e a t u r e s a r e t h e f o l l o w i n g : ( a ) O n l y t h e s o - c a l l e d " n - m a n i f o l d " s t a t e s (I * 2) a r e c o n s i d e r e d , s i n c e t h e Na d s t a t e s m i x v e r y r a p i d l y w i t h s t a t e s o f h i g h e r £ ( k = 10 -10 s " ( 1 0 ) ) . T h i s m i x i n g i s assumed t o be c o m p l e t e b e f o r e i o n i z a t i o n and q u e n c h i n g o c c u r . The s and p s t a t e s a r e thus ignored. (b) Q u e n c h i n g i s assumed t o p r o c e e d v i a many s m a l l s t e p s o f An = - 1 ; i . e . nd •> ( n - l ) d ... 3d + 3p ( 1 1 , 1 2 ) . ( c ) A s t a t e - s p e c i f i c i o n i z a t i o n r a t e constant i s c a l c u l a t e d (see b e l o w ) u s i n g t h e c r o s s s e c t i o n f o r Na 3s i o n i z a t i o n d e r i v e d by H o l l a n d e r ( 4 ) . ( d ) N i s assumed t o be t h e c o l l i d e r i n t h e i o n i z a t i o n and q u e n c h i n g p r o c e s s e s (_4, 1(), 11) . A l t h o u g h c h a r g e d s p e c i e s may h a v e l a r g e q u e n c h i n g c r o s s s e c t i o n s f o r e x c i t e d N a , t h e i r c o n c e n t r a t i o n s a r e orders o f magnitude lower than that o f N and s o t h e i r c o n t r i b u t i o n i s n e g l e c t e d . ( e ) The r a d i a l i n t e n s i t y d i s t r i b u t i o n s o f t h e two l a s e r s a r e d e s c r i b e d by a Gaussian f u n c t i o n . ( f ) A Voigt l i n e a n a l y s i s i s r e q u i r e d f o r c a l c u l a t i n g the o p t i c a l t r a n s i t i o n r a t e s s i n c e t h e observed l i n e w i d t h s f o r t h e Na d s t a t e s a r e s e v e r a l t i m e s t h e n o m i n a l 0.01 nm b a n d w i d t h o f t h e l a s e r . These l a r g e l i n e w i d t h s a r i s e from t h e l a r g e ^ - c h a n g i n g ( 1 0 ) and e l a s t i c (13) c o l l i s i o n r a t e s . 1 0

n

1

2

2



12.

SMYTH ET AL.

425

Electronically

430

Excited

177

Atoms

440

435

WAVELENGTH (nm) Figure 1. Optogalvanic signal for stepwise excitation of sodium (3s -» 3p -» nd, ns) in an H -air flame. Each transition is split into two components by the fast mixing of the fine structure states, 3p 3p . The data are not normalized for the variation of laser power with wavelength. At this level of sensitivity the one-photon signal (3s —» 3p) is undetectable. 2

1/2

s/2



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Figure 2. Comparison of the stepwise excitation results (O) with the model calculation (*). The enhancement (the two-photon signal divided by the one-photon signal) normalized for laser energy is plotted against the absorption coefficient for the 3p -» nd transitions. For visual clarity a curve is drawn through the points of the model calculation and a dashed line of unit slope is drawn through the data at high principal quantum number, n.


12.

SMYTH ET AL.

Electronically

Excited

Atoms

179

The o p t i c a l t r a n s i t i o n r a t e s have b e e n c a l c u l a t e d u s i n g t h e e x p e r i m e n t a l l y m e a s u r e d l a s e r e n e r g i e s . The n e x t t a s k i s t o d e r i v e o v e r a l l g l o b a l q u e n c h i n g and i o n i z a t i o n r a t e s f o r e a c h Na n-manifold s t a t e . T h i s i s a c c o m p l i s h e d as f o l l o w s . Humphrey e t l» (11) h a v e m e a s u r e d t o t a l l o s s c r o s s s e c t i o n s f r o m s e v e r a l nm a n i f o l d s t a t e s , and t h e s e show a s t e a d y d e c r e a s e w i t h n. By d e t a i l e d b a l a n c i n g one c a n e s t i m a t e t h e f r a c t i o n o f e n e r g y t r a n s f e r c o l l i s i o n s w h i c h l e a v e t h e Na atom i n s t a t e s o f h i g h e r and l o w e r n ( t h i s c a l c u l a t i o n n e g l e c t s c h e m i c a l r e a c t i o n s ) . Once t h e s e b r a n c h i n g r a t i o s a r e e v a l u a t e d , an o v e r a l l q u e n c h i n g r a t e c a n be c a l c u l a t e d by summing a l l t h e downward r a t e s f o r nd (nl ) d -> ... 3d •> 3p. The r a t e s a t e a c h s t e p a r e g i v e n by k = o*Nv, where N i s t h e number d e n s i t y and v i s t h e a v e r a g e v e l o c i t y . Table I l i s t s the r e s u l t s of these c a l c u l a t i o n s , the l o s s cross s e c t i o n s o f Humphrey e£ a l . ( 1 1 ) , as w e l l a s t h e e s t i m a t e d l o s s c r o s s s e c t i o n s f o r h i g h e r and l o w e r n. S i m i l a r l y , t h e o v e r a l l i o n i z a t i o n r a t e s c a n be e v a l u a t e d . A t 2000 K and 1 atm, H o l l a n d e r ' s s t a t e - s p e c i f i c r a t e c o n s t a n t becomes = 1.46 x 1 0 e x p ( - A E / k T ) s " , where AE i s t h e energy r e q u i r e d f o r i o n i z a t i o n . For each n-manifold s t a t e the f r a c t i o n i o n i z e d by c o l l i s i o n s i s d e t e r m i n e d , as w e l l as t h e f r a c t i o n t r a n s f e r r e d t o n e a r b y n - m a n i f o l d s t a t e s i n s t e p s o f An = ±1. Then t h e f r a c t i o n s i o n i z e d f r o m t h e s e n e a r b y n - m a n i f o l d states are calculated. I n t h i s way a t o t a l o v e r a l l i o n i z a t i o n r a t e i s e v a l u a t e d f o r each p h o t o - e x c i t e d d s t a t e . The t o t a l i o n i z a t i o n r a t e always exceeds the s t a t e - s p e c i f i c r a t e , s i n c e some o f t h e Na atoms t r a n s f e r r e d by c o l l i s i o n s t o t h e n e a r b y n-manifold s t a t e s are subsequently i o n i z e d . T a b l e I summarizes t h e v a l u e s u s e d f o r t h e s t a t e - s p e c i f i c c r o s s s e c t i o n s and t h e d e r i v e d o v e r a l l i o n i z a t i o n and q u e n c h i n g r a t e c o n s t a n t s f o r e a c h n-manifold s t a t e . The r e q u i r e d o p t i c a l t r a n s i t i o n , i o n i z a t i o n , and q u e n c h i n g r a t e s c a n now be i n c o r p o r a t e d i n t h e r a t e e q u a t i o n m o d e l . F i g u r e 2 compares t h e r e s u l t s o f t h e m o d e l c a l c u l a t i o n w i t h the experimental v a l u e s .


a

1 0

1

Discussion (a) F o r h i g h p r i n c i p a l quantum numbers ( n > 7) i o n i z a t i o n i s much f a s t e r t h a n q u e n c h i n g ( s e e T a b l e I ) , and so the d e t a i l s of the p o s s i b l e quenching processes are unimportant. E s s e n t i a l l y a l l o f t h e atoms e x c i t e d t o a g i v e n nd s t a t e a r e i o n i z e d , and t h e o b s e r v e d s i g n a l i s s i m p l y p r o p o r t i o n a l t o t h e a b s o r p t i o n p r o b a b i l i t y of t h e second s t e p (X2)• (b) F o r n = 5 and 6 t h e r e i s k e e n c o m p e t i t i o n b e t w e e n i o n i z a t i o n and q u e n c h i n g p r o c e s s e s . I t i s h e r e t h a t the r a t e e q u a t i o n model i s most s e n s i t i v e t o t h e a c t u a l s t a t e - s p e c i f i c r a t e c o n s t a n t s employed. U s i n g H o l l a n d e r ' s v a l u e s t o d e r i v e i o n i z a t i o n r a t e s (4) and t h e r e s u l t s o f Humphrey e t a l . f o r t o t a l l o s s r a t e s ( 1 1 ) , t h e agreement b e t w e e n t h e o r y and e x p e r i m e n t i s good. I f i o n i z a t i o n r a t e s lOOx l a r g e r a r e e m p l o y e d , t h e d i r e c t p r o p o r t i o n a l i t y b e t w e e n t h e o b s e r v e d s i g n a l and t h e a b s o r p t i o n p r o b a b i l i t y i s m a i n t a i n e d down t o n = 4. C l e a r l y , t h i s does n o t a g r e e w i t h t h e e x p e r i m e n t a l



3.2(-4) 0.015 0.091 0.24 0.43 0.63 0.81 0.98 1.13 1.25

1

6

2

nm

V a l u e s f o r n = 5-8 a r e f r o m R e f . 1 1 , f o r n = 4 and > 9 a r e e s t i m a t e s , and t h e r a t i o o f n = 3 t o n = 4 i s t a k e n f r o m R e f . 12.

a t 2000 K a c r o s s s e c t i o n o f 0.148

3.6(9) 1.7(9) 1.0(9) 6.3(8) 4.2(8) 2.5(8) 1.7(8) 1.2(8) 8.5(7) 6.5(7)

2.

exp(-AE/kT).

2

2.1(6) 1.2(8) 9.0(8) 2.5(9) 4.2(9) 5.2(9) 6.3(9) 7.3(9) 8.2(9) 9.0(9)

R e f . 4, a = 2.17 nm

F o r 1 atm o f N

0.54 0.50 0.43 0.36 0.32 0.18 0.15 0.12 0.10 0.09

2

G l o b a l R a t e C o n s t a n t s ( s *) k(ionization) k ( q u e n c h i n g t o 3p)

1.

2

The n o t a t i o n 2.1(6) r e p r e s e n t s 2.1 x 1 0 . c o r r e s p o n d s t o k (= aNv) o f 1 x l O ^ s " .

3 4 5 6 7 8 9 10 11 12

2

S t a t e - S p e c i f i c C r o s s S e c t i o n s (nm ) a ( i o n i z a t i o n ) a ( l o s s ) 1

S t a t e - S p e c i f i c Cross S e c t i o n s and G l o b a l Rate C o n s t a n t s f o r I > 2 S t a t e s .

P r i n c i p a l Quantum Number n

Table I .


12.

SMYTH ET AL.

Electronically

Excited

Atoms

181

results. However, f u r t h e r w o r k i s n e e d e d t o a s c e r t a i n j u s t how s e n s i t i v e t h e model i s t o t h e s t a t e - s p e c i f i c i o n i z a t i o n r a t e s , (c) F o r n = 4 t h e model p r e d i c t s a s m a l l e r s i g n a l t h a n a c t u a l l y o b s e r v e d . Some o f t h e m o d e l ' s a s s u m p t i o n s a r e l e a s t t e n a b l e f o r low v a l u e s o f n. A t n = 4 t h e il-changing c o l l i s i o n r a t e c o n s t a n t is "lO^s" (10) a n d t h u s i s no l o n g e r much f a s t e r t h a n q u e n c h i n g . A l s o , t h e q u e n c h i n g c r o s s s e c t i o n s h a v e been assumed t o be i n d e p e n d e n t o f t e m p e r a t u r e , w h i c h may w e l l b e i n c o r r e c t ( 1 4 ) . D i f f e r e n c e s i n t h e quenching c r o s s s e c t i o n s would a f f e c t t h e m o d e l e s t i m a t e s most s t r o n g l y f o r l o w n v a l u e s . F i n a l l y , although q u e n c h i n g o f t h e 4 d s t a t e p r e d o m i n a n t l y g i v e s 3d ( 1 2 ) , i t may b e n e c e s s a r y t o c o n s i d e r energy t r a n s f e r t o o t h e r nearby s t a t e s .


1

Conclusions (1) H o l l a n d e r ' s " l o w " c r o s s s e c t i o n f o r c o l l i s i o n a l i o n i z a t i o n o f Na i s s u f f i c i e n t t o m o d e l t h e o p t o - g a l v a n i c s i g n a l magnitudes a s a f u n c t i o n o f e x c i t a t i o n energy. Abnormally h i g h cross sections are not required. (2) E s s e n t i a l l y a l l (> 90%) o f t h e Na atoms e x c i t e d t o n > 7 a r e i o n i z e d a t a f l a m e t e m p e r a t u r e o f 2000 K. F o r n = 7 t h e e n e r g y needed f o r i o n i z a t i o n i s 2249 cm"" , w h i c h i s a p p r o x i m a t e l y 2 kT (kT = 1390 cm"" ). 1

1

Literature Cited 1. Tj. Hollander, P.J. Kalff, and C.T.J. Alkemade, J. Chem. Phys. 39, 2558 (1963). 2. D.E. Jensen and P.J. Padley, Trans. Faraday Soc. 62, 2140 (1966); R. Kelly and P.J. Padley, Trans. Faraday Soc. 65, 355 (1969) and Proc. Roy. Soc. London A 327, 345 (1972). 3. A.N. Hayhurst and N.R. Telford, J. Chem. Soc. Faraday I 68, 237 (1972); A.F. Ashton and A.N. Hayhurst, Comb. & Flame 21, 69 (1973). 4. Tj. Hollander, AIAA Journal 6, 385 (1968). 5. G.N. Fowler and T.W. Preist, J. Chem. Phys. 56, 1601 (1972). 6. G.C. Turk, J.C. Travis, J.R. DeVoe, and T.C. O'Haver, Anal. Chem. 51, 1890 (1979). 7. P.K. Schenck, W.G. Mallard, J.C. Travis, and K.C. Smyth, J. Chem. Phys. 69, 5147 (1978). 8. W.L. Wiese, M.W. Smith, and B.M. Miles, NSRDS-NBS 22 (1969). 9. J.C. Travis, P.K. Schenck, G.C. Turk, and W.G. Mallard, Anal. Chem. 51, 1516 (1979). 10. T.F. Gallagher, R. E. Olson, W.E. Cooke, S.A. Edelstein, and R.M. Hill, Phys. Rev. A 16, 441 (1977). 11. L.M. Humphrey, T.F. Gallagher, W.E. Cooke, and S.A. Edelstein, Phys. Rev. A 18, 1383 (1978). 12. J.E. Allen, Jr., W.R. Anderson, D.R. Crosley and T.D. Fansler, 17th Comb. Symp. (International), 797 (1979). 13. A. Flusberg, R. Kachru, T. Mossberg, and S.R. Hartmann, Phys. Rev. A 19, 1607 (1979). 14. N.S. Ham and P. Hannaford, J.Phys. B 12, L199 (1979). RECEIVED April 11, 1980.


Laser Probes for Combustion Chemistry - American Chemical Society

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