The Mechanism of Ozone Formation in Electrical Discharges

The Mechanism of Ozone Formation in Electrical Discharges R. W. LUNT

Downloaded by AUBURN UNIV on September 12, 2017 | http://pubs.acs.org Publication Date: January 1, 1959 | doi: 10.1021/ba-1959-0021.ch039

University College,

London, England

M a n y investigations have provided data on the dependence of the rate of ozone formation on the gross characteristics of the discharge, the current carried, a n d the energy absorbed, yet the nature of the reaction is imperfectly understood. Some of the simpler aspects of ozone formation are considered in relation to other phenomena, in order to outline the nature of the problems that arise in attempting to trace the identity a n d extent of the reactions concerned.

Two p r i n c i p a l r e q u i r e m e n t s m u s t b e satisfied i n o r d e r t o i n t e r p r e t e x p e r i m e n t a l d a t a o n t h e s y n t h e s i s of ozone i n gaseous discharges i n t e r m s of a d e t a i l e d r e a c t i o n m e c h a n i s m : d a t a o n t h e a b s o l u t e r a t e of r e a c t i o n as a f u n c t i o n of t h e p a r a m e t e r s t h a t describe t h a t s t a t e of a p a r t i a l l y i o n i z e d gas w h i c h i s c a l l e d a d i s c h a r g e ; a n d a n a d e q u a t e q u a n t i t a t i v e t h e o r y p r e d i c t i n g t h e a b s o l u t e r a t e of a n y one of t h e m a n y r e a c t i o n s b y w h i c h t h e s y n t h e s i s of ozone m a y o c c u r . A k n o w l e d g e of t h e r e a c t i o n m e c h a n i s m i s i m p o r t a n t to b o t h science a n d t e c h n o l o g y : I t w o u l d b u i l d y e t a n o t h e r b r i d g e b e t w e e n c h e m i s t r y a n d p h y s i c s , in p a r t i c u l a r b e t w e e n p h o t o c h e m i s t r y a n d t h e p h y s i c s of d i s c h a r g e s a n d of t h e u p p e r a t m o s p h e r e ; a n d it w o u l d i l l u m i n a t e t h e c h e m i c a l e n g i n e e r i n g p r o b l e m of g e n e r a t i n g ozone o n a n i n d u s t r i a l scale m o r e e c o n o m i c a l l y t h a n h i t h e r t o . T h e t a s k of i d e n t i f y i n g w h i c h of t h e possible r e a c t i o n s c o n t r i b u t e to t h e o b s e r v e d s y n t h e s i s , a n d of d e d u c i n g t h e i r r e l a t i v e c o n t r i b u t i o n s t o t h e o b s e r v e d r a t e of s y n t h e s i s , is a n a l o g o u s t o t h e t a s k of i n t e r p r e t i n g t h e d a t a f o r t h e p h o t o c h e m i c a l s y n t h e s i s of ozone. I t i s , h o w e v e r , m u c h m o r e c o m p l e x . T h e first s t e p i n m o s t p h o t o c h e m i c a l r e a c t i o n s i n v o l v e s a t r a n s i t i o n of h i g h p r o b a b i l i t y ( a n o p t i c a l l y a l l o w e d t r a n s i t i o n ) f r o m t h e g r o u n d s t a t e to an e l e c t r o n i c a l l y e x c i t e d s t a t e of a r e a c t a n t species ; t h e e x c i t e d s t a t e e i t h e r i n i t i a t e s t h e o b s e r v e d c h e m i c a l c h a n g e o r s p o n t a n e o u s l y dissociates i n t o f r a g m e n t s w h i c h i n i t i a t e those c h e m i c a l changes. A n y a l l o w e d t r a n s i t i o n effected b y p h o t o n s c a n also b e effected b y e l e c t r o n i m p a c t , t h e cross s e c t i o n f o r t h e l a t t e r process p a s s i n g t h r o u g h a m a x i m u m f o r a n e l e c t r o n e n e r g y u s u a l l y t h r e e t o five t i m e s t h e v e r t i c a l e x c i t a t i o n e n e r g y . A l l o p t i c a l l y d i s a l l o w e d t r a n s i t i o n s , h o w e v e r , c a n also b e effected b y e l e c t r o n i m p a c t ; a n d t h e m a x i m u m cross s e c t i o n f o r t h e process o f t e n o c c u r s f o r a n e l e c t r o n e n e r g y o n l y s l i g h t l y i n excess of t h e vertical excitation energy. I n m o s t f o r m s of gaseous d i s c h a r g e t h e electrons p r e s e n t h a v e a d i s t r i b u t i o n i n energy, a n d consequently, i n general, a n d certainly i n molecular oxygen, the p r i m a r y g e n e r a t i o n of m o l e c u l e s i n e l e c t r o n i c a l l y e x c i t e d states i n c l u d e s those states c o r r e s p o n d i n g n o t m e r e l y t o a l l o w e d t r a n s i t i o n s b u t also those a s s o c i a t e d w i t h d i s a l l o w e d t r a n s i 286

OZONE CHEMISTRY AND TECHNOLOGY Advances in Chemistry; American Chemical Society: Washington, DC, 1959.

LUNT—FORMATION IN ELECTRIC DISCHARGE

287


t i o n s , f o r w h i c h l a t t e r t h e cross sections f o r e x c i t a t i o n b y p h o t o n a b s o r p t i o n a r e t o o s m a l l t o be a s s o c i a t e d w i t h a r e a d i l y d e t e c t a b l e r a t e of r e a c t i o n . A n o t h e r m a j o r c o n s i d e r a t i o n is associated w i t h t h e c o m p l e x i t y of t h e p r o b l e m o f i d e n t i f y i n g t h e r e a c t i o n m e c h a n i s m i n discharges i n r e l a t i o n t o those f o r t h e same r e a c t a n t s y s t e m b u t i n i t i a t e d b y t h e a b s o r p t i o n of p h o t o n s . T h e techniques for measur i n g t h e n u m b e r of p h o t o n s a b s o r b e d b y a g i v e n m a s s of r e a c t a n t gas a r e w e l l e s t a b l i s h e d . O n t h e o t h e r h a n d , those f o r d e r i v i n g i n a gaseous d i s c h a r g e t h e c o r r e s p o n d i n g n u m b e r of e l e c t r o n i m p a c t s l e a d i n g t o a p a r t i c u l a r p r o d u c t — f o r e x a m p l e , a p a r t i c u l a r e l e c t r o n i c a l l y e x c i t e d s t a t e — a r e m u c h less w e l l d e v e l o p e d . T h e techniques for meas u r i n g t h e c o n c e n t r a t i o n of electrons, a n d t h e i r e n e r g y d i s t r i b u t i o n f u n c t i o n , a r e s t i l l s o m e w h a t c o n t r o v e r s i a l (43) ; f o r m o l e c u l a r gases d a t a f o r t h e a b s o l u t e m a g n i t u d e of t h e cross sections f o r e l e c t r o n i c e x c i t a t i o n b y electrons r e m a i n a l m o s t n o n e x i s t e n t , e x c e p t f o r some a l l o w e d t r a n s i t i o n s t h a t r e s u l t i n i o n i z a t i o n of t h e m o l e c u l e (55). D i v e r s e a p p r o a c h e s h a v e been m a d e i n a t t e m p t i n g t o describe t h e k i n e t i c s o f d i s c h a r g e r e a c t i o n . S o m e e a r l i e r i n v e s t i g a t o r s e x a m i n e d t h e s t a t i o n a r y state of a s y s t e m i n respect of t h e species r e c o g n i z a b l e c h e m i c a l l y , a n d u n d e r s t a n d a b l y a p p e a r t o h a v e been i n f l u e n c e d b y t h e c l a s s i c a l a n a l y s i s of a s y s t e m i n t h e r m o d y n a m i c e q u i l i b r i u m w h i l e f a i l i n g t o recognize t h a t t h e f i n a l s t a t e i n a c o n t i n u o u s l y m a i n t a i n e d d i s c h a r g e i s a s t a t i o n a r y state. W a r b u r g (76) w a s p e r h a p s t h e f i r s t t o recognize t h a t u s e f u l i n f o r m a t i o n c o u l d b e gained b y s t u d y i n g t h e l i m i t i n g behavior of a reactant system reached w h e n t h e c o n c e n t r a t i o n o f t h e r e s u l t a n t s is i n d e f i n i t e l y decreased. A p p a r e n t l y independently, a n d u s i n g a different k i n d o f t e c h n i q u e , K i r k b y w o r k i n g i n T o w n s e n d ' s l a b o r a t o r y (38) r e c o g n i z e d t h e same a d v a n t a g e . A n d o t h e r s , n o t a b l y B r e w e r (8) a n d F i n c h (27), p u r s u e d t h e p r o b l e m i n t h e same w a y b y e m p l o y i n g a t e c h n i q u e t h a t m a i n t a i n e d a n e g l i g i b l y s m a l l c o n c e n t r a t i o n of r e s u l t a n t s . W a r b u r g , h o w e v e r , l i n k e d t h e d a t a f o r t h e r a t e of r e a c t i o n i n ozone w i t h those f o r t h e s t a t i o n a r y state (81); a n d n e a r l y h a l f a c e n t u r y e l a p s e d b e f o r e a r e t u r n w a s m a d e , b y D e v i n s (18), t o t h e a n a l y s i s o f t h e s t a t i o n a r y s t a t e . Y e t a l t h o u g h D e v i n s ' s a p p r o a c h seeks t o l i n k t h e d a t a f o r o z o n i z e r d i s charges i n o x y g e n w i t h those of t h e p h o t o c h e m i s t s , h e does n o t discuss h i s a n a l y sis of t h e s t a t i o n a r y s t a t e i n a d i s c h a r g e i n r e l a t i o n t o t h e e a r l i e r one of W a r b u r g (81 ) ; n o r does h e c o m p a r e t h e r a t e of ozone s y n t h e s i s , e i t h e r p e r u n i t c h a r g e t r a n s p o r t e d b y , o r p e r u n i t e n e r g y u s e d t o m a i n t a i n t h e d i s c h a r g e , w i t h t h e d a t a of o t h e r i n v e s t i g a t o r s , a n d r e l a t e h i s a n a l y s i s w i t h t h a t of D e e g a n a n d Emeléus (17). A n d u n t i l t h i s t a s k of critically reviewing a l l relevant d a t a is accepted, n o coherent a n d convincing p i c t u r e of t h e m e c h a n i s m of ozone s y n t h e s i s i n discharges i s l i k e l y t o emerge.

Experimental

D a t a o n Kinetics o f O z o n e S y n t h e s i s in G a s e o u s

Discharges

T h e k i n e t i c s of d i s c h a r g e r e a c t i o n resemble those of p h o t o c h e m i s t r y i n t h a t t h e r a t e coefficient i s r e f e r r e d t o a p h y s i c a l c h a r a c t e r i s t i c of t h e e n v i r o n m e n t o t h e r t h a n pressure a n d temperature. I n photochemistry t h e relevant parameters have long been seen t o b e t h e d e n s i t y of t h e p h o t o n flux t r a v e r s i n g t h e r e a c t a n t s , a n d t h e e x t e n t of i t s a b s o r p t i o n . I n dealing w i t h discharge reactions somewhat analogous parameters have been u s e d i n d e f i n i n g a c o n v e n i e n t r e a c t i o n r a t e coefficient. T h e i n t e n s i t y of t h e elec t r o n f l u x t h r o u g h t h e gas, w h i c h i s f a i r l y s i m p l y r e l a t e d t o t h e d e n s i t y of t h e c u r r e n t c a r r i e d b y t h e gas, h a s a t t r a c t e d m a n y a n d t h e c o r r e s p o n d i n g r a t e coefficient i s o f t e n d e s c r i b e d as t h e " c u r r e n t efficiency." Others have preferred the energy supplied per u n i t t i m e t o m a i n t a i n t h e d i s c h a r g e , w h i c h , i f n o t m e a s u r e d c a l o r i m e t r i c a l l y , also r e q u i r e s a k n o w l e d g e of t h e e l e c t r i c field m a i n t a i n i n g t h e flow of c h a r g e d p a r t i c l e s . T h u s t w o v a r i e t i e s o f r a t e coefficient h a v e been e x t e n s i v e l y u s e d . O n e i s t h e n u m b e r of r e a c t a n t m o l e c u l e s c h e m i c a l l y c h a n g e d ( o r a l t e r n a t i v e l y t h e n u m b e r of p r o d u c t m o l e c u l e s f o r m e d ) p e r u n i t ( e l e c t r o n i c ) c h a r g e t r a n s p o r t e d , β, w h i c h is f o r m a l l y , b u t n o t p h y s i c a l l y , analogous to the electrochemical equivalent i n electrolysis. T h i s c o n c e p t w a s r e f i n e d b y K i r k b y i n t o t h e " a c t i v i t y " o f a d i s c h a r g e , Ρ = άβ/dz, the


A D V A N C E S IN CHEMISTRY SERIES

288

d i f f e r e n t i a l of t h e c u r r e n t efficiency w i t h respect t o t h e d i s t a n c e , z, b e t w e e n t h e elec t r o d e s ( o r t h e n u m b e r o f m o l e c u l e s c h e m i c a l l y c h a n g e d p e r c m . of u n i t c h a r g e t r a n s p o r t ) . K i r k b y h a d adduced experimental evidence t h a t t h e a c t i v i t y m a y v a r y w i t h position i n a g i v e n d i s c h a r g e (39).

T h e s e c o n d coefficient, η, o f t e n c a l l e d t h e " e n e r g y e f f i c i e n c y , "

is t h e n u m b e r of r e a c t a n t m o l e c u l e s c h e m i c a l l y c h a n g e d p e r u n i t e n e r g y s u p p l i e d t o m a i n t a i n t h e d i s c h a r g e , a n d i s of d i r e c t r e l e v a n c e t o t h e e c o n o m i c s of a n y d i s c h a r g e r e a c t i o n s u c h as t h e c o n v e r s i o n of o x y g e n i n t o o z o n e . A l t e r n a t i v e l y these r a t e coefficients m a y b e e x p r e s s e d i n t e r m s of t h e n u m b e r of m o l e c u l e s of

final

p r o d u c t , w h i c h is the procedure u s u a l l y adopted i n describing the

s y n t h e s i s of o z o n e ; i n t h i s case t h e v a l u e s d e r i v e d f r o m e x p e r i m e n t w h e n a d j u s t e d f o r t h e s t o i c h i o m e t r i c f a c t o r set l o w e r l i m i t s t o t h e coefficients r e f e r r e d t o r e a c t a n t m o l e cules. T h e r e l a t i o n b e t w e e n t h e t w o e m p i r i c a l r a t e coefficients f o r d i s c h a r g e r e a c t i o n , β


a n d 77, c a n b e t r a c e d i n t e r m s o f t h e gas p r e s s u r e , p, t h e e l e c t r o d e s p a c i n g , z, a n d t h e c o r r e s p o n d i n g p o t e n t i a l difference b e t w e e n t h e electrodes m a i n t a i n i n g t h e d i s c h a r g e . Kirkby parent

(38) w a s t h e first t o s h o w t h a t β m a y b e a f u n c t i o n of pz, a n d i t i s a p

(39) t h a t t h e v a r i a t i o n of ζ a t c o n s t a n t p r e s s u r e a n d c u r r e n t i s m u c h

more

l i k e l y t o l e a d t o d a t a a m e n a b l e t o i n t e r p r e t a t i o n t h a n s t u d i e s of t h e d e p e n d e n c e of β on ρ at constant electrode spacing.

L a t e r (40) h e s h o w e d t h a t Ρ/ρ

is a

— (1/ρ)άβ/άζ

r e a c t i o n r a t e coefficient of a f o r m s u i t a b l e f o r c o m p a r i s o n w i t h t h e o r y . The

field,

X, a t a n y p o i n t , z , i n t h e d i r e c t i o n of c u r r e n t f l o w , is g i v e n b y X =

w h e r e V i s t h e p o t e n t i a l a t t h e p l a n e , z, r e l a t i v e t o a n e l e c t r o d e ,

dV/dz,

the cathode.

T o w n s e n d h a d s h o w n t h a t P/p

i m p a c t i s i n m a n y cases a f u n c t i o n of X/p

conveniently

f o r t h e g e n e r a t i o n of ions b y e l e c t r o n

(72, 73), a n d K i r k b y d e m o n s t r a t e d t h a t t h i s

also h o l d s f o r t h e s y n t h e s i s of w a t e r f r o m e l e c t r o l y t i c gas

(40).

T h e s e c o n d e m p i r i c a l r a t e coefficient, t h e e n e r g y efficiency, η, is t h e q u o t i e n t of t h e r e d u c e d a c t i v i t y , P/p,

a n d the

field-to-pressure

r a t i o , X/p,

b o t h quantities relating to

some g i v e n p l a n e p e r p e n d i c u l a r t o t h e d i r e c t i o n of c u r r e n t f l o w ; o r η = = P/X.

I f a n y r e g i o n of a d i s c h a r g e is u n i f o r m , P/p,

η, a n d X/p

(P/p)/(X/p)

are characteristics

of t h e w h o l e r e g i o n . T h e f o l l o w i n g c o n s i d e r a t i o n s p r o v i d e a g u i d e t o w h a t m a y be e x p e c t e d

for the

u p p e r l i m i t t o t h e v a l u e of η f o r ozone g e n e r a t i o n i n d i s c h a r g e s a t t r i b u t a b l e t o e l e c t r o n r e a c t a n t c o l l i s i o n s w i t h o u t m a k i n g reference

to the detailed theory

outlined

below.

I f , i n a c c o r d a n c e w i t h t h e p h o t o c h e m i c a l d a t a , t h e p r i m a r y s t e p of t h e r e a c t i o n m e c h a n i s m i s t h e d i s s o c i a t i o n of t h e o x y g e n m o l e c u l e , a n d i f t h i s s t e p a b s o r b s Ε e.v., i t f o l l o w s t h a t t h e e n e r g y a b s o r b e d p e r o z o n e m o l e c u l e t h a t c o u l d be f o r m e d i s 0.5 Ε e.v. T h e h y p o t h e t i c a l l i m i t i n g case i s t h a t a l l t h e e l e c t r o n e n e r g y i s a b s o r b e d i n t h i s w a y , a n d i t f o l l o w s t h a t t h e u p p e r l i m i t t o η i s 1 / ( 0 . 5 E) ozone m o l e c u l e s p e r e l e c t r o n v o l t supplied to m a i n t a i n the discharge.

Spectroscopic

d a t a s h o w t h a t Ε m u s t exceed t h e

d i s s o c i a t i o n e n e r g y of t h e g r o u n d s t a t e , 5.11 e.v., a n d p r o b a b l y lies close t o t h e v e r t i c a l e x c i t a t i o n e n e r g y of t h e 2 ~ s t a t e , a b o u t 8 e.v. 3

10~

2

C o n s e q u e n t l y η cannot exceed 40 X

ozone molecule p e r electron v o l t , a n d a p r o b a b l e u p p e r l i m i t is 25 Χ 1 0

-

2

. But

because o t h e r e l e c t r o n i m p a c t processes t h a t d o n o t c o n t r i b u t e t o ozone f o r m a t i o n c a n o c c u r s i m u l t a n e o u s l y , t h e m a x i m u m a t t a i n a b l e v a l u e of η m u s t be less t h a n t h e u p p e r limiting value. A n i n d i c a t i o n of t h e f r a c t i o n o f t h e e n e r g y s u p p l i e d t o a l o w - p r e s s u r e

positive

c o l u m n d i s c h a r g e w h i c h c a n b e a b s o r b e d i n effecting a n y g r o u p of e l e c t r o n - r e a c t a n t c o l lisions g i v i n g a " s i n g l e " p r o d u c t is afforded b y the data for t h e r a d i a t i o n e m i t t e d .

For

t h e r a d i a t i o n t r a n s m i t t e d b y glass a n d e m i t t e d f r o m h y d r o g e n o r n i t r o g e n , A n g s t r o m f o u n d t h i s f r a c t i o n t o be a b o u t 0.05 (1), illumination practice

n o t m u c h s m a l l e r t h a n is a t t a i n e d i n m o d e r n

(74) ; f o r a w i d e range of c o n d i t i o n s , a t c o n s t a n t p r e s s u r e , t h e

i n t e n s i t y of r a d i a t i o n p e r u n i t v o l u m e v a r i e s l i n e a r l y w i t h t h e c u r r e n t , a n e x a m p l e o f P/p

f o r r a d i a t i o n b e i n g c o n s t a n t w h e n X/p

is c o n s t a n t .

F o r t h e processes t h a t l e a d

t o t h e e m i s s i o n of 2537 A . r a d i a t i o n f r o m m e r c u r y , B a r n e s a n d T h a y e r h a v e r e p o r t e d t h a t u p t o 0.6 of t h e i n p u t e n e r g y m a y be a c c o u n t e d f o r i n t h a t w a y

(4).


289


A p l a u s i b l e e s t i m a t e f o r m a x i m u m a t t a i n a b l e v a l u e of η f o r ozone f o r m a t i o n i n t h e p o s i t i v e c o l u m n i n o x y g e n i s t h u s 20 X 1 0 ~ m o l e c u l e p e r e . v . ; h o w e v e r , a h i g h e r v a l u e m a y h o l d f o r o t h e r f o r m s of t h e d i s c h a r g e , i n c l u d i n g t h a t r e a l i z e d i n o z o n i z e r s . I n p r i n c i p l e these m o r e e l a b o r a t e d e f i n i t i o n s of t h e e m p i r i c a l r a t e coefficients m i g h t be e x p e c t e d t o s i m p l i f y a n y r e v i e w of t h e e x i s t i n g d a t a f o r t h e s y n t h e s i s of ozone f r o m oxygen. B u t i n m a n y i n v e s t i g a t i o n s one o r m o r e o f t h e r e l e v a n t d i s c h a r g e p a r a m e t e r s has been e i t h e r n o t m e a s u r e d o r n o t r e c o r d e d . A n d a l t h o u g h t h e o z o n i z e r d i s c h a r g e has l o n g b e e n c o m m e r c i a l l y a t t r a c t i v e , i t h a s n o t b e e n s t u d i e d m u c h i n r e l a t i o n t o w h a t a p p e a r t o be t h e r e l e v a n t p a r a m e t e r s , n o r h a s i t s r e l a t i o n t o t h e w e l l - c h a r a c t e r i z e d c o l d c a t h o d e g l o w d i s c h a r g e b e e n t h e s u b j e c t of m u c h i n v e s t i g a t i o n . Y e t i t is these t w o f o r m s of d i s c h a r g e f o r w h i c h t h e m o s t e x t e n s i v e a n d r e l i a b l e e x p e r i m e n t a l d a t a o n ozone s y n t h e s i s a r e a v a i l a b l e .


2

T h e i n f o r m a t i o n h i t h e r t o a v a i l a b l e r e l a t i n g these t w o f o r m s of d i s c h a r g e is m e a g e r . T h a t t h e c o l d c a t h o d e g l o w d i s c h a r g e c a n be r e a l i z e d i n m o l e c u l a r gases a t pressures a b o v e a b o u t 5 m m . of m e r c u r y a n d u p t o a t m o s p h e r i c p r e s s u r e h a s l o n g b e e n k n o w n (24) ; b u t t h e c u r r e n t densities a r e v e r y m a n y o r d e r s o f m a g n i t u d e l a r g e r t h a n i n o z o n i z e r discharges a t c o m p a r a b l e p r e s s u r e s . O n t h e o t h e r h a n d , i f t h e c u r r e n t d e n s i t y is r e d u c e d t o t h e o r d e r of m a g n i t u d e c h a r a c t e r i s t i c of o z o n i z e r discharges a t a t m o s p h e r i c p r e s s u r e , t h e n a t u r e of t h e d i s c h a r g e i n o x y g e n a n d i n o t h e r gases m a y b e p r o f o u n d l y c h a n g e d (18). N e v e r t h e l e s s t h e r e a r e i n d i c a t i o n s t h a t a n o z o n i z e r d i s c h a r g e m a y be r e g a r d e d t o a first a p p r o x i m a t i o n as a p e r i o d i c a l l y r e v e r s e d g l o w d i s c h a r g e of r e l a t i v e l y v e r y l o w c u r r e n t d e n s i t y (49,51), a t least f o r l o w pressures. L u n t a n d M e e k (49) a n d l a t e r L u n t a n d S w i n d e l l (51) s t u d i e d o z o n i z e r discharges i n n i t r o g e n , ρ = c a . 1 m m . H g a n d ζ — c a . 1 c m . ; t h e s p e c t r a of t h e l u m i n o u s zones closely r e s e m b l e d those of a g l o w d i s c h a r g e i n n i t r o g e n f o r t h e same p r e s s u r e a n d f o r a c u r r e n t d e n s i t y of a b o u t 0.5 m a . c m . , a b o u t f o u r o r d e r s of m a g n i t u d e g r e a t e r t h a n i n the ozonizer discharge. - 2

D e v i n s (18) a s s u m e d t h a t t h e o z o n i z e r discharges i n o x y g e n s t u d i e d b y h i m m a y be r e g a r d e d as s i m i l a r t o t h e m o r e o r less i d e a l p l a s m a of t h e u n i f o r m p o s i t i v e c o l u m n of a g l o w d i s c h a r g e because, i n o t h e r e x p e r i m e n t s , M a n l e y (52) f o u n d t h a t , a t a t m o s p h e r i c p r e s s u r e , X/p is n e a r l y i n d e p e n d e n t of t h e a l t e r n a t i n g p o t e n t i a l a p p l i e d t o t h e electrodes. Some investigations have been made o n the r a d i a t i o n f r o m ozonizer a n d other d i s charges i n w h i c h ozone is g e n e r a t e d f r o m o x y g e n . M o s t of these a r e q u a l i t a t i v e , i n t h e sense t h a t t h e n a t u r e of t h e r a d i a t i o n w a s n o t i d e n t i f i e d s p e c t r o s c o p i c a l l y a n d n o d e t e r m i n a t i o n s were m a d e of t h e i n t e n s i t y of r a d i a t i o n p e r u n i t c u r r e n t d e n s i t y , o r p e r u n i t e n e r g y c o n s u m e d i n m a i n t a i n i n g t h e d i s c h a r g e (63, 71, 77). Other investigations o n o z o n i z e r discharges i n n i t r o g e n i n d i c a t e t h a t t h e r e a r e n o serious p r o b l e m s i n s t u d y i n g t h e n a t u r e a n d i n t e n s i t y of t h e r a d i a t i o n (35, 56). T h e c o m p l i c a t e d n a t u r e of t h e w a v e f o r m of t h e c u r r e n t flowing t h r o u g h a n o z o n i z e r w h e n a ( n e a r l y ) s i n u s o i d a l a l t e r n a t i n g p o t e n t i a l i s a p p l i e d across t h e electrodes a p p e a r s t o h a v e been r e c o g n i z e d first b y D e c o m b e (16) a n d b y E r l i c h a n d R u s s (20) l o n g before W a r b u r g (79) m a d e o s c i l l o g r a p h i c s t u d i e s . R u m m e l (64) describes s t u d i e s of t h e w a v e f o r m of t h e t o t a l c u r r e n t c a r r i e d b y a n o z o n i z e r , b u t does n o t a p p e a r t o h a v e discussed t h e f r a c t i o n of t h a t c u r r e n t w h i c h i s c a r r i e d b y t h e p a r t l y i o n i z e d gas. T h e p a r t l y c o n d u c t i n g gas is e q u i v a l e n t e l e c t r i c a l l y t o a n i m p e d a n c e , Z , t h a t does n o t c o n f o r m w i t h O h m ' s l a w a n d w h i c h shunts the capacitance, C , associated w i t h t h e d i s c h a r g e space. T h a t c o m b i n a t i o n of Ζ a n d C is i n series w i t h t h e c a p a c i t a n c e s 0 a n d C associated w i t h t h e i n n e r a n d o u t e r w a l l s , r e s p e c t i v e l y . T h e p r o b l e m of m e a s u r e m e n t i n o z o n i z e r discharges is t h u s t o d e t e r m i n e , f r o m m e a s u r e m e n t s of t h e applied potential a n d t o t a l current, or otherwise, t h e current carried b y Z a n d the p o t e n t i a l across i t . 2

2

Ί

3

a

I t i s e v i d e n t t h a t t h e t h e o r y of p o w e r a n d c u r r e n t m e a s u r e m e n t f o r a l t e r n a t i n g p o t e n t i a l s a p p l i e d t o a l o a d c o n s i s t i n g of a n y c o m b i n a t i o n of p u r e c a p a c i t a n c e , i n d u c t ance, a n d ( o h m i c ) resistance c a n n o t b e a p p l i e d t o a n o z o n i z e r i n w h i c h d i s c h a r g e s


290


o c c u r . T h e f a i l u r e of m a n y i n v e s t i g a t o r s t o recognize t h i s h a s c a u s e d m u c h c o n f u s i o n , a n d has i n t r o d u c e d m a n y errors difficult t o estimate i n their derivations- of the current carried b y Z f r o m measurements of the root m e a n square values of potentials a n d currents. a


A r e l a t e d p r o b l e m arises i n t h e c h a r a c t e r i z a t i o n of t h e d i s c h a r g e c u r r e n t s o c c u r r i n g i n gas p o c k e t s i n t h e i n s u l a t i o n of h i g h v o l t a g e a l t e r n a t i n g c u r r e n t p o w e r t r a n s m i s s i o n cables, b u t t h e e m p h a s i s i n those i n v e s t i g a t i o n s i s n o l o n g e r o n t h e k i n e t i c s of c h e m i c a l c h a n g e , i n t h i s case t h e d e g e n e r a t i o n of t h e d i e l e c t r i c . C o n s i d e r a b l e a t t e n t i o n h a s b e e n p a i d t o t h e e l e c t r i c a l c h a r a c t e r i z a t i o n of t h e d i s c h a r g e , a l t h o u g h t h e significance of these i n v e s t i g a t i o n s f o r o z o n i z e r discharges h a s n o t been s t u d i e d . T h e r e i s , h o w e v e r , a n e x t e n s i v e l i t e r a t u r e w i t h m a n y cross references (2, 8, 68, 61, 62, 70). W a r b u r g g a v e a t h e o r y of o z o n i z e r discharges i n 1903 w h i c h a p p e a r s n e v e r t o h a v e b e e n r e c o n s i d e r e d o r r e f u t e d (78) ; h i s a n a l y s i s l e d t o t h e i d e n t i f i c a t i o n of t h e m a x i m u m p o t e n t i a l across t h e electrodes, t h e f r e q u e n c y of r e v e r s a l , a n d t h e t o t a l flow of c h a r g e t r a n s p o r t e d b y t h e i o n i z e d gas, as t h e r e l e v a n t p a r a m e t e r s . F o r a l t e r n a t i n g c u r r e n t operation this means t h a t the relevant quantities to measure are the peak voltage a n d t h e m e a n c u r r e n t ; s u c h m e a s u r e m e n t s were first c a r r i e d o u t b y G r a y i n 1904 w o r k i n g I n W a r b u r g ' s l a b o r a t o r y (30). G r a y u s e d p e r i o d i c a l l y r e v e r s e d s t e a d y p o t e n t i a l s ( d i rect c u r r e n t ) a n d m e a s u r e d t h e flow of c h a r g e p e r c y c l e b a l l i s t i c a l l y . M u c h l a t e r , W a r b u r g (79) a p p e a r s t o h a v e l a r g e l y a b a n d o n e d h i s 1903 t h e o r y , a n d , a l t h o u g h p r o v i d i n g e x p e r i m e n t a l evidence f r o m o s c i l l o g r a m s t h a t t h e c u r r e n t i n a n o z o n i z e r m a y be f a r f r o m s i n u s o i d a l i n f o r m , u s e d t h e rules f o r s i n u s o i d a l c u r r e n t s t o c o m p u t e t h e m e a n c u r r e n t f r o m t h e r . m . s . v a l u e of t h e c u r r e n t . W h i l e t h e r a t i o of t h e m e a n v a l u e t o t h e r . m . s . v a l u e of t h e c u r r e n t c a r r i e d b y a n o z o n i z e r m a y r e m a i n n e a r l y c o n s t a n t o v e r a w i d e range of electrode v o l t a g e (45), t h e a b s o l u t e v a l u e of t h e m e a n c u r r e n t c a n n o t be i n f e r r e d w i t h c e r t a i n t y f r o m r . m . s . v a l u e s . B u t e v e n w h e n t h e r e f i n e m e n t of m e a s u r i n g t h e m e a n c u r r e n t as a f u n c t i o n of t h e p e a k v o l t a g e is a d o p t e d , t h e r e r e m a i n s t h e p r o b l e m w h i c h n o one o t h e r t h a n W a r b u r g i n 1903 seems t o h a v e been i n t e r e s t e d t o solve ; t h e d e t e r m i n a t i o n o f t h e f r a c t i o n of t h e t o t a l m e a s u r e d m e a n c u r r e n t associated w i t h t h e t r a n s p o r t of c h a r g e b y t h e i o n i z e d gas, as d i s t i n c t f r o m t h e f r a c t i o n associated w i t h dielectric displacement. A n o t h e r g r o u p o f c o m p l i c a t i o n s t h a t h a s a t t r a c t e d l i t t l e a t t e n t i o n relates t o t h e d i v e r s e devices u s e d t o o b t a i n r a t e coefficients r e l a t i n g t o o x y g e n ( o r a i r ) u n c o n t a m i n a t e d b y ozone. W a r b u r g a d o p t e d t h e m e t h o d o f p r o g r e s s i v e l y i n c r e a s i n g t h e v e l o c i t y o f t h e gas t h r o u g h t h e d i s c h a r g e t o d e r i v e t h e l i m i t i n g v a l u e of β, w h i c h he also t r e a t e d a n a l y t i c a l l y , t a k i n g i n t o a c c o u n t t h e p r o g r e s s i v e increase i n t h e c o n c e n t r a t i o n o f ozone as t h e gas m o v e s t h r o u g h t h e d i s c h a r g e . A n i n g e n i o u s b u t e m p i r i c a l t r e a t m e n t of t h e v a l u e s f o r η w a s g i v e n l a t e r b y B e c k e r (6). B u t w h a t does n o t a p p e a r t o h a v e been s t u d i e d is t h e change i n t h e n a t u r e of t h e d i s c h a r g e as t h e v e l o c i t y of t h e gas t h r o u g h i t i s v a r i e d , a n d t h e a d d i t i o n a l effects a s s o c i a t e d w i t h t h e p r o g r e s s i v e increase i n t h e c o n c e n t r a t i o n of ozone i n t h e d i r e c t i o n of &ow. T h e choice of a n o t h e r g r o u p of i n v e s t i g a t o r s h a s been t o use s t a t i o n a r y gas, a n d t o r e m o v e t h e ozone f o r m e d b y r e f r i g e r a t i n g t h e w a l l s of t h e d i s c h a r g e t u b e . Inevitably t h e r e i s t h e n a c o n c e n t r a t i o n g r a d i e n t , a n d t h e a n a l y s i s of t h a t v a r i a t i o n i n c o n c e n t r a t i o n h a s n o t been a t t e m p t e d , a l t h o u g h Emeléus a n d B e c k (21, 50) h a v e d e v e l o p e d t h e f o r m a l t h e o r y o f s u c h d i f f u s i o n . I t m a y be t h a t w h e n l i q u i d a i r o r n i t r o g e n is u s e d as t h e r e f r i g e r a n t t h e c h a r a c t e r i s t i c s of t h e d i s c h a r g e a r e c h a n g e d f r o m those a t r o o m t e n i p e r a t u r e . A s B r o i d a a n d h i s colleagues h a v e s h o w n r e c e n t l y (5, 11, 12, 37), i f l i q u i d h e l i u m i s u s e d as t h e r e f r i g e r a n t , a n e w c h e m i s t r y of f r o z e n free r a d i c a l s a p p e a r s . I n o x y g e n discharges, i n p l a c e of l i q u i d ozone o r a s o l u t i o n o f o x y g e n i n ozone, t h e r e is deposited o n t h e walls of the discharge tube a glassy solid w h i c h evaporates t o a violet solid (5,11,12). T h u s b o t h e x p e r i m e n t a l m e t h o d s give d a t a f o r t h e r a t e coefficients

of ozone s y n -


291


thesis t h a t r e l a t e t o averages o v e r i m p e r f e c t l y d e t e r m i n e d ranges of c o n d i t i o n s . A n d n o one h a s y e t a t t e m p t e d t o s h o w h o w f a r these t w o m e t h o d s a p p l i e d t o t h e same f o r m of d i s c h a r g e l e a d t o c o n s i s t e n t d a t a .


I n v i e w of a l l these u n c e r t a i n t i e s i t i s t h e m o r e i n t e r e s t i n g t o e n q u i r e w h a t m e a s u r e of c o n s i s t e n c y c a n b e t r a c e d b y r e v i e w i n g t h e m o r e s i g n i f i c a n t i n v e s t i g a t i o n s i n oxygen. F o r o n l y w h e n t h a t i s k n o w n is i t possible t o c o n s i d e r w h a t p h e n o m e n a m u s t be e x p l i c a b l e b y a n y t h e o r y of t h e m e c h a n i s m o f ozone s y n t h e s i s i n discharges. I d e a l l y , m a n y d a t a r e l a t i n g t o ozone s y n t h e s i s b y discharges i n m i x t u r e s of o x y g e n w i t h o t h e r gases, e s p e c i a l l y n i t r o g e n , w a t e r v a p o r , c a r b o n m o n o x i d e , c a r b o n d i o x i d e , a r g o n , h e l i u m , a n d n e o n (15) s h o u l d also b e t a k e n i n t o a c c o u n t . O z o n i z e r Investigations i n O x y g e n . G r a y i n 1904 a p p e a r s t o h a v e been t h e first t o i n v e s t i g a t e β f o r ozone f o r m a t i o n i n o z o n i z e r d i s c h a r g e s ; u s i n g p e r i o d i c a l l y r e v e r s e d s t e a d y p o t e n t i a l s a n d o x y g e n a t a t m o s p h e r i c p r e s s u r e , G r a y f o u n d β = 540 f o r a w i d e range of v a l u e s of t h e c h a r g e t r a n s p o r t e d (30). L a t e r (31) h e f o u n d t h a t β i n c r e a s e d f r o m 2 8 0 t o 4 5 0 , c o r r e s p o n d i n g t o a p r o g r e s s i v e i n c r e a s e i n t h e electrode p o t e n t i a l . A r e s t a t e m e n t of G r a y ' s l a t e r d a t a i n t e r m s of β, P/p, X , a n d η, i s g i v e n i n T a b l e I . T h e v a l u e s of X , t h e m e a n field across t h e gas space, a r e b a s e d o n t h e v a l u e s f o u n d b y G r a y , u s i n g W a r b u r g ' s 1903 t h e o r y , f o r t h e e x t i n c t i o n v o l t a g e of t h e d i s c h a r g e ; these v a l u e s of X m a y b e less t h a n t h e t r u e v a l u e s , a n d c o n s e q u e n t l y l e a d t o v a l u e s of η w h i c h m a y b e c o r r e s p o n d i n g l y t o o h i g h . T h e d a t a s h o w t h a t X /p increases o n l y s l i g h t l y as t h e p o t e n t i a l a p p l i e d t o t h e electrodes i s i n c r e a s e d , b u t P/p a n d η i n crease b y a f a c t o r of a b o u t 1.5. T h e s e d a t a a r e p r o b a b l y t h e earliest e s t a b l i s h i n g t h e a p p r o x i m a t e m a g n i t u d e o f P/p a n d η f o r ozone s y n t h e s i s i n o z o n i z e r discharges f r o m purely electrical measurements. m

m

m

m

I n T a b l e I a n d t h e s u b s e q u e n t t e x t β, Ρ, a n d η refer t o t h e n u m b e r of ozone m o l e cules f o r m e d , a n d n o t t o t h e n u m b e r of r e a c t a n t m o l e c u l e s c h a n g e d , b y t h e d i s c h a r g e ; ρ is i n m i l l i m e t e r s of m e r c u r y ; ζ i s t h e w i d t h of t h e gas space i n ozonizers, o r t h e r e l e v a n t p a r t of t h e i n t e r e l e c t r o d e d i s t a n c e , i n c e n t i m e t e r s ; V is t h e electrode p o t e n t i a l , in volts; X a n d X a r e i n v o l t s c m . - ; a n d X /p a n d X/p a r e i n v o l t s c m . mm. H g . 1

m

-

-

m

1

1

Table I. V

Restatement of the Data of G r a y (31) Xm/p

7,960 8,590 9,220 9,010 10,400 11,000 11,700 12,200

35.4 35.6 36.6 36.8 37.7 38.0 39.3 39.3

β

280 306 318 352 368 394 416 450

P/P

5.8 6.3 6.6 7.3 7.6 8.1 8.6 9.3

77

X 10 * 16.4 17.7 18.1 20.0 20.2 21.3 21.9 23.7 2

Conversion to practical units is given very closely by: 180 grams per kw.-hr. = 10 Χ 10 " molecule per e.v. a

-

2

I n v e s t i g a t i o n s a t a b o u t t h e s a m e t i m e b y P o h l (60) l e d t o P/p v a l u e s of a b o u t 1.6; b u t h e m e a s u r e d t h e r . m . s . v a l u e of t h e o z o n i z e r c u r r e n t , w h i c h m a y b e c o n s i d e r a b l y i n excess of t h e m e a n v a l u e , a n d t h i s m a y e x p l a i n w h y h i s v a l u e s o f P/p a r e m u c h less t h a n those f o u n d b y G r a y . W a r b u r g , P o h l , a n d L i n d (Ιβ) w e r e i m p r e s s e d b y t h e a n a l o g y b e t w e e n β a n d t h e e l e c t r o c h e m i c a l e q u i v a l e n t i n e l e c t r o l y s i s , b u t o n l y K i r k b y a t t h i s t i m e (39) seems t o have perceived t h a t t h e n u m e r i c a l values of β f o r discharge reaction m a y be expected t o be m u c h t h e l a r g e r because, as h e c l e a r l y d e m o n s t r a t e d f o r t h e s y n t h e s i s of w a t e r f r o m e l e c t r o l y t i c gas, β increases as t h e electrode s e p a r a t i o n i s i n c r e a s e d , c u r r e n t a n d gas p r e s s u r e b e i n g k e p t c o n s t a n t . A b o u t 2 0 y e a r s l a t e r W a r b u r g (82), a p p a r e n t l y u n a w a r e of K i r k b y ' s p i o n e e r w o r k , i n v e s t i g a t e d t h e d e p e n d e n c e of β f o r t h e s y n t h e s i s of ozone o n t h e w i d t h o f t h e d i s c h a r g e s p a c e z, a n d o n t h e p r e s s u r e , i n c o n c e n t r i c a l l - g l a s s ozonizers u s i n g l o w f r e q u e n c y a l t e r n a t i n g p o t e n t i a l s t o e x c i t e t h e d i s c h a r g e . H i s



292

measurements were based on a modification of his 1 9 0 3 theory by St. Sachs (65), and, although not free from uncertainties, attempted to derive values of the mean discharge current and the corresponding mean field across the gas space X from measurements of r.m.s. values. A restatement of his data i n terms of P/p, X /p, and η, considered as functions of pz and j , the mean current density, is given in Table II. T h e values of m

m

m

Table II.

Restatement of the Data of W a r b u r g and Rump

(82)

Frequency of electrode potential: 50 cycles per second jm = mean current density. μ&. per sq. cm. pz = mm. Hg X cm. X = apparent mean field strength, volts c m . - 1


m

3.6 3.8 4.0 4.0

74 51 42 39

η X 10« 4.9 7.4 9.5 10.1

3.5 5.0 7.2

3.6 4.0 4.2

29 29 29

12.3 13.7 14 2

2.7 3.8 5.1 7.9 24» 53*

3.8 3.8 4.2 4.2 3.1 3.1

32 32 32 32

12.2 12.2 13.5 13.1

17

22 21

Ρ 52 101 152 198

pz

5.2 10.1 15.2 19.8

jm 7.6 7.4 7.1 6.9

760

76

14

760

760

117

3.8 6.6 7.2

3.2 3.2 3.3

760

226

4.7 8.0

3.8 3.7

a

Xm/P

P/P

— — — — — 17

— —

— —

Frequency of electrode potential: 500 cycles per second.

P/p for atmospheric pressure i n Table II are about half those found by G r a y (Table I) ; the apparent discrepancy is probably attributable to erroneously large values of the mean current, which were derived from measurements of the r.m.s. values. Never theless, the use of the parameter pz appears to coordinate the data relating to widely different conditions in terms of P/p. Warburg's choice of r.m.s. values for measure ment of voltage probably also largely accounts for the differences between the values of η derived from his data and those of G r a y as given in Table I ; nevertheless for atmospheric pressure the two sets of values of η are of about the same magnitude. O z o n i z e r P o w e r M e a s u r e m e n t . W a r b u r g and Leithâuser (80) sought to measure the power consumed in the discharge by using the electrometer wattmeter method. Although in principle this method may be used when the current (and voltage) wave form is far from sinusoidal, these investigators did not recognize that large errors are likely to occur when, as in their procedure, the voltage applied to the electrometer needle is only a small fraction (ca. 0 . 0 1 ) of the potential across the electrodes and is derived from a resistance shunting the ozonizer. Consequently their values for η (for high streaming velocities) ranging up to about 9 Χ 1 0 are suspect; they are somewhat smaller than the values that can be derived from Gray's data (Table I) and those of Warburg and R u m p (Table II) for atmospheric pressure. Stark (68) appears to have been the first to prefer calorimetry to avoid the pitfalls of measuring the power consumed in the discharge by electrical methods. H i s data for low concentrations of ozone correspond to η = 7.85 Χ 10~~ , irrespective of the fre quency of the potential applied to the ozonizer electrodes in the range 5 0 to 1 0 cycles per second. -

2

2

4

A calorimetric method was also used by Susz (69), but was so tedious that he abandoned it for the three ammeter method without, however, citing data to compare the results of the two methods. T h e data he cites for ozone synthesis appear to relate to power measured by the latter method, which gives erroneous values for any load of variable impedance such as an ozonizer discharge; for the most part they relate to


293


r o o m t e m p e r a t u r e a n d a t m o s p h e r i c p r e s s u r e , a n d c o r r e s p o n d t o v a l u e s of η l y i n g i n t h e range of 4 X 1 0 - t o 10 X 1 0 ~ , b u t one o b s e r v a t i o n f o r a n o z o n i z e r r e f r i g e r a t e d t o —180° a n d f o r ρ = 2 0 0 g a v e η — 13.8 X 1 0 ~ . L a t e r c a l o r i m e t r i c d e t e r m i n a t i o n s of t h e o z o n i z e r p o w e r b y t h e G e n e v a s c h o o l of B r i n e r (9) h a v e g i v e n y i e l d s c o r r e s p o n d i n g t o v a l u e s of η of a b o u t 16 Χ 1 0 ; t h e t r u e v a l u e s a r e p r o b a b l y h i g h e r , because n o a l l o w a n c e a p p e a r s t o h a v e b e e n m a d e f o r losses b y l e a k a g e a n d i n t h e glass d i e l e c t r i c . 2

2

2


-

2

T h e s e c a l o r i m e t r i c d e t e r m i n a t i o n s l e a d i n g t o v a l u e s of η p r o v i d e n o u s e f u l d a t a a b o u t t h e d i s c h a r g e unless t h e y a r e c o m b i n e d w i t h m e a s u r e m e n t s of t h e p e a k electrode v o l t a g e a n d t h e m e a n c u r r e n t ; c o n s e q u e n t l y t h e d a t a f o r η c a n n o t b e r e l a t e d t o those f o r β a n d P/p p r o v i d e d b y G r a y , W a r b u r g , a n d D e v i n s . T h e t e c h n i q u e is t e d i o u s a n d i t i s m o r e c o n v e n i e n t t o use e i t h e r t h e e l e c t r o s t a t i c w a t t m e t e r m e t h o d i n w h i c h t h e needle i s o p e r a t e d a t t h e l i n e v o l t a g e , o r d i r e c t e v a l u a t i o n of J VI dt b y t h e o s c i l l o g r a p h i c m e t h o d . T h e e r r o r s i n t h i s v a r i a n t of t h e e l e c t r o m e t e r m e t h o d w h e n u s e d o n o z o n i z e r discharges e x c i t e d b y a l t e r n a t i n g p o t e n t i a l s of frequencies f r o m 50 t o 4 0 0 cycles per second is n o t more t h a n ± 2 % , a n d the errors i n the oscillographic m e t h o d m a y be c o m p a r a b l e (44)· T h e r e c e n t i n v e s t i g a t i o n s of D e v i n s (18) o n o z o n i z e r discharges i n o x y g e n a r e p a r t i c u l a r l y i n t e r e s t i n g because a n a t t e m p t is m a d e t o l i n k t h e d a t a w i t h those f o r t h e k i n e t i c s of t h e p h o t o s y n t h e s i s of ozone. T h e m e a n c u r r e n t m e t e r u s e d t o m e a s u r e t h e o z o n i z e r c u r r e n t w a s s h u n t e d b y a l a r g e c a p a c i t a n c e , so t h a t u n c e r t a i n e r r o r s a r e p r e s ent i n t h e m e a s u r e m e n t s ; a n d n o a l l o w a n c e w a s m a d e f o r t h e d i s p l a c e m e n t c u r r e n t . D a t a w h i c h a r e g i v e n i n d i a g r a m s t h a t a r e difficult t o scale a c c u r a t e l y a r e c i t e d t o s h o w t h a t t h e reaction rate is p r o p o r t i o n a l t o the current at a given pressure, b u t a careful s c r u t i n y suggests t h a t t h e p h e n o m e n a a r e m o r e c o m p l i c a t e d ; a r e s t a t e m e n t o f t h e d a t a i n t e r m s of β, P/p, a n d η i s g i v e n i n T a b l e I I I a f t e r a l l o w i n g f o r t h e f a c t s t h a t

Table III. Mm. 69 ICO 200 300 300 300 300 300 300 300 500

Restatement of the Data of Devins's Figures 1, 2, and 6 (7 8)

dpoz/dt,

I,

M m . Sec.-i 0.368 0.56 1.08 0.45 0.952 2.04 0.40 0.80 1.69 1.87 2.54

j

Ma. 0.3 0.3 0.30 0.06 0.14 0.30 0.06 0.14 0.30 0.30 0.30

β

3.0 3.0 3.0 0.6 1.4 3.0 0.6 1.4 3.0 3.0 3.0

51.5 78.5 151 158 143 143 280 240 237 262 356

Ρ

P/p

257 392 755 1580 1430 1430 1400 1200 1185 1310 1780 Av.

η

Χ 102

3.73 3.92 3.78 5.27 4.77 4.77 4.67 4.00 3.98 4.28 3.56

18.7 19.6 18.9 26.4 23.8 23.8 23.4 20.0 19.9 21.4 17.8

4.14

20.7

Fig. No. 1 1 1 6 6 6 2 2 2 1 1

dpoz/dt = initial rate derived by scaling graphs. / = current, ma. jm = mean current density, /za. c m . " . Xm/p assumed to be 20 volt c m . mm. H g . . 2

- 1

- 1

D e v i n s ' s F i g u r e 6 relates t o 301 m m . of m e r c u r y a n d t h a t t h e scale f o r dp /dt should be d o u b l e d (19). D e v i n s ' s v i e w , h o w e v e r , is t h a t a l l h i s e x p e r i m e n t a l d a t a f o r t h e i n i t i a l r a t e of r e a c t i o n a r e c o n s i s t e n t w i t h h i s F i g u r e 4, c o r r e s p o n d i n g t o w h i c h P/p — 4.55 (19), t h e d e r i v a t i o n b e i n g g i v e n b e l o w . B e c a u s e D e v i n s cites n o m e a s u r e m e n t s of t h e electrode p o t e n t i a l o r f r e q u e n c y , t o d e r i v e v a l u e s of η f r o m h i s d a t a i t is necessary t o e s t i m a t e t h e v a l u e of X i n the dis c h a r g e space f o r w h i c h ζ = 02 c m . R e c e n t d a t a f o r t h e electric s t r e n g t h of o x y g e n a p p e a r t o be l a c k i n g . A t l o w pressures i t is o n l y s l i g h t l y g r e a t e r t h a n t h a t of a i r (14, 23) a n d f o r a i r ( u n i f o r m field) i n t h e r a n g e of p r e s e n t i n t e r e s t , pz = 20 t o 2 0 0 m m . H g X c m . , i t i s g i v e n a p p r o x i m a t e l y b y X /p = 50 + l(fi/pz (66) ; a n d i t i s p r o b a b l e t h a t v a l u e s of X /p c o m p u t e d i n t h i s w a y a r e a n u p p e r l i m i t t o t h e v a l u e s X /p i n Devins's experiments, because t h e v o l t a g e n e c e s s a r y t o s t a r t a d i s c h a r g e is o f t e n c o n s i d e r a b l y g r e a t e r t h a n t o s u s t a i n i t . F r o m d e t e r m i n a t i o n s f o r o x y g e n of t h e r a t i o of t h e o z o n i z e r p o w e r t o t h e oz

m

b

h

m


A D V A N C E S IN

294

CHEMISTRY SERIES

m e a n c u r r e n t i n ozonizers c o m p a r a b l e i n size t o t h a t of D e v i n s , X /p is a b o u t 20 v o l t cm. mm. H g (46), a n d this value has therefore been used i n T a b l e I I I i n c o n j u n c t i o n w i t h D e v i n s ' s d a t a t o d e r i v e v a l u e s of η = (P/p)/(X /p). Devins's F i g u r e 4 corresponds to the relation m

- 1

-

1

m

dp„/dt

= 0.65 Χ ΙΟ" ρ 2

where p is t h e p a r t i a l p r e s s u r e of ozone a n d ρ is t h e i n i t i a l o x y g e n p r e s s u r e . F r o m t h e v o l u m e of t h e d i s c h a r g e space, 8.07 c m . , a n d t h e t e m p e r a t u r e 298° K , i t f o l l o w s t h a t , w h e n / = 0.31 m a . oz

3

β = 1.40 Χ 10

(dp Jdt)

2

0

since ζ = 0.2 c m . , i t f o l l o w s t h a t , i r r e s p e c t i v e of t h e c u r r e n t ,


P/p

= 5 β/ρ

=

4.55

F o r X /p = 20, t h e c o r r e s p o n d i n g c o n s t a n t v a l u e f o r η is a b o u t 23 Χ 1 0 ; alter n a t i v e l y , i f t h e d a t a f o r t h e e l e c t r i c s t r e n g t h a r e u s e d , η rises f r o m a b o u t 3.8 X 1 0 t o a b o u t 4.1 X 1 0 - as the t o t a l p r e s s u r e is i n c r e a s e d f r o m 70 t o 500 m m . of H g . F o r t h e same o z o n i z e r i t w a s f o u n d l a t e r t h a t , a t a t m o s p h e r i c p r e s s u r e , t h e i n i t i a l r a t e of ozone f o r m a t i o n c o r r e s p o n d s t o a v a l u e η = 14.7 X 1 0 ~ (19) ; t h i s w o u l d c o r r e s p o n d t o a v a l u e of Xm/p = 31, s o m e w h a t h i g h e r t h a n has b e e n a s s u m e d . - 2

m

_ 2

2

2

D e v i n s ' s i n t e r p r e t a t i o n of h i s i n i t i a l r e a c t i o n rates (dp /dt) is t h a t t h e y r e l a t e t o a n e g l i g i b l y s m a l l , o r zero, c o n c e n t r a t i o n of ozone. H i s v a l u e P/p = 4.55 i s , h o w e v e r , considerably lower t h a n any found b y G r a y (Table I ) , although the corresponding v a l u e η = 23 X 1 0 ~ is close t o t h e highest v a l u e s f o u n d b y G r a y . T h e a p p a r e n t d i s c r e p a n c y i n t h e v a l u e s f o r P/p o b v i o u s l y c a n n o t be a t t r i b u t a b l e t o t h e f a c t t h a t D e v i n s m e a s u r e d o n l y p a r t of t h e t o t a l c u r r e n t . U n t i l a l l s u c h d i s c r e p a n c i e s i n t h e d a t a f o r o z o n i z e r d i s c h a r g e s are r e s o l v e d , i t seems d o u b t f u l w h e t h e r a n y d e t a i l e d i n t e r p r e t a t i o n c a n be a t t e m p t e d . oz

2

G l o w Discharge Investigations i n Oxygen. I t is n e x t of i n t e r e s t t o c o n s i d e r d a t a f o r ozone s y n t h e s i s i n d i r e c t c u r r e n t g l o w discharges a t l o w pressures, r e f r i g e r a t i o n of t h e d i s c h a r g e t u b e t o —180° C . b e i n g u s e d t o ensure t h a t t h e p a r t i a l p r e s s u r e of ozone was r e l a t i v e l y l o w . T h e d a t a of H e n r y (34) a r e t h e s i m p l e s t t o a n a l y z e : t h e y r e l a t e t o i n i t i a l rates of ozone s y n t h e s i s a t ρ = 2.4 m m . H g a n d m a i n l y t o p o s i t i v e c o l u m n r e a c t i o n because t h e r a t e of s y n t h e s i s i n t h e n e g a t i v e zones ( c a t h o d e s u r f a c e t o F a r a d a y d a r k s p a c e - p o s i t i v e c o l u m n b o u n d a r y ) w a s r e l a t i v e l y n e g l i g i b l e . T h e cross s e c t i o n of t h e t u b e w a s a b o u t 0.8 c m . , a n d hence t h e c u r r e n t d e n s i t y was a b o u t 1.25 / m a . c m . . J u d g e d b y t h e r o u g h s k e t c h g i v e n , t h e p o s i t i v e c o l u m n w a s a b o u t 10 c m . l o n g . 2

- 2

H e n r y ' s d a t a are r e s t a t e d i n T a b l e I V i n t e r m s of β, P/p, X/p, a n d η. T h e v a l u e s of Ρ a n d X reflect t h e u n c e r t a i n t i e s i n t h e l e n g t h of t h e p o s i t i v e c o l u m n , b u t t h e v a l u e s of η are u n a f f e c t e d . T h e v a l u e f o r V , t h e v o l t a g e a l o n g t h e p o s i t i v e c o l u m n , has b e e n t a k e n t o be the t o t a l v o l t a g e d i m i n i s h e d b y t h e c a t h o d e f a l l , a s s u m e d t o be 400 v o l t s . T h e v a l u e of ρ w a s t a k e n t o be t h a t r e c o r d e d , b u t P/p a n d X/p s h o u l d i n v o l v e v a l u e s of t h e r e d u c e d p r e s s u r e , t h a t e q u i v a l e n t t o t h e gas d e n s i t y ; t h u s i f t h e a v e r a g e gas t e m p e r a t u r e were n o t m u c h g r e a t e r t h a n t h a t of t h e r e f r i g e r a t i n g l i q u i d a i r , t h e t r u e v a l u e s of P/p a n d X/p w o u l d be s m a l l e r t h a n those l i s t e d i n T a b l e I V b y a f a c t o r of a b o u t 3. T h e p o w e r s u p p l i e d p e r u n i t l e n g t h of t h e p o s i t i v e c o l u m n W = XI m w . p e r c m . , increases p r o g r e s s i v e l y a n d r a p i d l y . T h i s s t r o n g l y suggests t h a t i f f o r / = 0.1 m a . t h e e q u i v a l e n t p r e s s u r e s h o u l d be t a k e n t o be a b o u t t h r e e t i m e s t h e a c t u a l p r e s s u r e , f o r / = 4.0 m a . w h e n W is a b o u t 13 t i m e s l a r g e r , t h e e q u i v a l e n t p r e s s u r e m a y be m u c h closer t o t h e a c t u a l p r e s s u r e because of t h e m u c h g r e a t e r h e a t i n g of t h e gas. A p l a u s i b l e e s t i m a t e is t h a t X/p f a l l s f r o m a b o u t 17 t o a b o u t 10 as W increases f r o m 120 t o 1600 m w . p e r c m . S u c h a t r e n d i n X/p w o u l d n o t be i n c o n s i s t e n t w i t h o t h e r d a t a (25) i n respect of t h e t u b e r a d i u s a n d t h e e s t i m a t e d v a l u e s of t h e r e d u c e d pressure. PC

a

a

a


LUNT—FORMATION

295

IN ELECTRIC DISCHARGE

Table IV.

Restatement of the Data of Henry (34)

Reaction assumed to occur only in positive column of estimated length ζ = 10 cm. I = total current, ma. pz = 24 mm. Hg X cm. Vpc = voltage across positive column assuming cathode fall to be 400 volts W = power supplied to positive column = XI mw. per cm. a

I

Ρ

β

0.1 0.25 » 0.50 0.75 1.0 2.0 3.0 4.0

144 70 82 73 69 63 44 40

1

P/P

14.4 7.0 8.2 7.3 6.9 6.3 4.4 4.0

VPC

6.0» 2.9 3.4 3.0 2.9ο 2.6 1.8 1.7*

1200 1100 800 700 600 500 450 400

X

Wa

120 110 80 70 60 50 45 40

120 280 400 530 600 1000 1350 1600

* Estimated corrected values after allowing for temperature not much above X/p = ca. 17. Values of β, hence of P/p and η, are anomalously small, probably because Estimated corrected values after allowing for gas temperature of about X/p = 11. Estimated corrected values after allowing for gas temperature of about X/p = 10. b


c

X/p

77

50» 46 33 29 25° 21 19 l d 7

X 10« 12.0 6.4 10.3 10.4 11.5 12.6 10.0 10.0

—180°: pz = 74, P/p = ca. 2.0, of adventitious error. —160° C : pz = 55, P/p — 1.25, —120° C : pz = 40, P/p = 1.0

d

I f some s u c h a d j u s t m e n t w e r e a d m i t t e d , i t i s p l a u s i b l e t o i n f e r t h a t t h e c o r r e s p o n d i n g t r e n d i n P/p i s f r o m a b o u t 2.0 t o 1.0; t h a t w o u l d be r o u g h l y c o n s i s t e n t w i t h t h e r e l a t i v e l y s m a l l decrease o b s e r v e d i n η f r o m a b o u t 12 χ 1 0 t o 10 Χ 1 0 . S u c h t r e n d s i n P/p a n d i n η w o u l d b e e x p e c t e d i f t h e m e a n e l e c t r o n e n e r g y were t o f a l l c o r r e s p o n d i n g l y w i t h X/p, as i t i s k n o w n t o d o a t m u c h l o w e r c u r r e n t densities (33). -

2

- 2

T h e d a t a w o u l d also t h e n be a p p a r e n t l y c o n s i s t e n t i n t e r m s of X/p w i t h t h e s o m e w h a t h i g h e r v a l u e s of P/p a n d η i n T a b l e I I I a n d w i t h t h e e s t i m a t e d v a l u e X /p — 2 0 , f o r w h i c h i n o t h e r o z o n i z e r discharges v a l u e s of η a b o u t 11.5 X 10 were f o u n d f o r high streaming velocities at r o o m temperature a n d atmospheric pressure (47). m

2

T h e s l i g h t l y e a r l i e r i n v e s t i g a t i o n of B r e w e r a n d W e s t h a v e r (8) relates t o a glow d i s c h a r g e b e t w e e n m e t a l electrodes i n a t u b e 3.5 c m . i n d i a m e t e r a n d i m m e r s e d i n l i q u i d a i r f o r a d i s t a n c e of 13.5 c m . f r o m t h e a n o d e ; f r o m t h e cross s e c t i o n of t h e t u b e , t h e m e a n c u r r e n t d e n s i t y i s a b o u t 0.1 / m a . p e r s q . c m . N o s y n t h e s i s w a s o b s e r v e d e x c e p t i n t h e p o s i t i v e c o l u m n , a n d as i n H e n r y ' s e x p e r i m e n t s , t h e r e a r e n o d a t a f o r t h e effect of v a r y i n g t h e electrode s p a c i n g a t c o n s t a n t p r e s s u r e . T h e d a t a f r o m B r e w e r a n d W e s t h a v e r ' s T a b l e I a n d others d e r i v e d f r o m t h e i r F i g u r e s 1 a n d 2 a r e r e s t a t e d i n t e r m s of P/p, X/p, a n d i n T a b l e V . v

Table V .

Restatement of the Data of Brewer and Westhaver (8)

ζ = 13.5 cm., extension of refrigerated positive column. W = power input to the positive column = 10~ X I watt c m . 3

a

- 1

pz

β

6.0

4.45

8.9

Vpc 215

15.9

31.8

η X 102 Wa 0.32 2.8

1.0 1.0 1.0

13.5 13.5 13.5

62.9 33.8 20.2

4.66 2.50 1.50

4.66 2.50 1.50

750 400 315

55.5 29.7 23.4

55.5 29.7 23.4

8.4 8.4 6.4

0.11 0.45 0.47

Fig. 2 Fig. 2 Tab. 1

55 20 50

3.5 3.5 3.5

47.3 47.3 47.3

23.6 20.3 4.9

1.76 1.50 0.36

0.50 0.43 0.10

540

40

11.4

6.4

0.20

230

16

2.1

0.80

Fig. 2 Fig. 1 Fig. 2

20

5.0

19.9

1.48

0.30

350

25.9

5.18

5.7

0.52

Tab. 1

20

9.0

122.

18.3

1.37

0.15

420

31.1

3.46

4.4

0.62

Tab. 1

10 20 40

12.0 12.0 12.0

162 162 162

18.2 16.9 6.2

1.35 1.25 0.46

0.11 0.10 0.04

570 430 310

42.0 31.8 23.0

3.5 2.5 1.9

3.2 3.9 2.0

0.42 0.64 0.92

Fig. 2 Fig. 1 Fig. 2

20

13

175

16.4

1.22

0.09

440

32.6

2.52

3.7

0.65

Tab. 1

J,Ma. 20

0.5

2 15 20

Ρ

6.75

67.5

Ρ

P/P

X

X/P

4.57

Ref. (5) Tab. 1

A s i n H e n r y ' s e x p e r i m e n t s , t h e r e is c o n s i d e r a b l e u n c e r t a i n t y a b o u t t h e m e a n t e m p e r a t u r e of t h e gas. T h e r a n g e of p o w e r i n p u t p e r c e n t i m e t e r of p o s i t i v e c o l u m n o v e r laps t h a t i n H e n r y ' s experiments, b u t a l t h o u g h i t is d i s t r i b u t e d over a larger cross-


296

A D V A N C E S IN

CHEMISTRY SERIES

s e c t i o n a l a r e a , t h e c o o l i n g a r e a p e r u n i t v o l u m e is s m a l l e r . H e n c e i t is p l a u s i b l e t o assume t h a t t h e l o w e s t a n d h i g h e s t v a l u e s of W i n T a b l e V are a s s o c i a t e d w i t h a v e r a g e gas t e m p e r a t u r e s n o t g r e a t l y different f r o m t h e lowest a n d h i g h e s t , r e s p e c t i v e l y , e s t i m a t e d f o r H e n r y ' s e x p e r i m e n t s (see footnotes t o T a b l e I V ) . W h i l e t h e v a l u e s of η r e m a i n u n c h a n g e d , these r o u g h e s t i m a t e s w o u l d change t h e h i g h e s t v a l u e of X/p to a b o u t 18.5, a n d t h e associated v a l u e of P/p t o a b o u t 1.55; a n d t h e y w o u l d change t h e c o r r e s p o n d i n g d a t a associated w i t h t h e highest v a l u e s of W t o P/p = 0.06 f o r X/p = 2.7 (/ = 50) a n d t o P/p = 0.025 f o r X/p = 1.2 (/ = 4 0 ) . a

a

A l t h o u g h no g r e a t r e l i a n c e c a n be p l a c e d o n these a d j u s t e d v a l u e s , some a d j u s t m e n t i n t h e sense m a d e is i n e v i t a b l y r e q u i r e d . T h e p r i n c i p a l c o n c l u s i o n s t h a t emerge f r o m these a d j u s t e d v a l u e s are t h e f o l l o w i n g . F i r s t , the value = 8Αχ 1 0 ~ f o r X/p = 18.5 lies close t o t h e v a l u e s d e r i v e d f r o m o t h e r i n v e s t i g a t i o n s ; a n d as t h i s v a l u e relates t o a gas i n w h i c h ozone ( v a p o r p r e s s u r e a b o u t 0.11 m m . H g a t —180° C . ) f o r m s a b o u t one t e n t h of t h e t o t a l c o n c e n t r a t i o n , i t m a y be r e g a r d e d as n o t i n c o n s i s t e n t w i t h t h e h i g h e r v a l u e s a l r e a d y c i t e d , w h i c h relate t o v e r y m u c h l o w e r f r a c t i o n a l c o n c e n t r a t i o n s of ozone. Secondly, η has t h e r e l a t i v e l y h i g h v a l u e of a b o u t 2 X 10 ~ w h e n X/p lies i n t h e r a n g e 1 t o 2. 2


η

2

Q u i t e a p a r t f r o m these a d j u s t e d v a l u e s , t h e d a t a s h o w c l e a r l y t h a t , a t c o n s t a n t p r e s s u r e i n t h e range 1 t o 2 m m . of m e r c u r y , b o t h P/p a n d η f a l l m o r e o r less r a p i d l y as t h e c u r r e n t o r c u r r e n t d e n s i t y is i n c r e a s e d ; o n l y f o r ρ = 1 m m . a n d / = 2 t o 15 m a . is η c o n s t a n t (8, F i g u r e 2 ) , a n d i n no case was t h e r e a c t i o n r a t e p r o p o r t i o n a l t o t h e c u r r e n t , b u t i n c r e a s e d m o r e s l o w l y . T h i s seems t o be a n i n d i c a t i o n of some d e s t r u c t i v e m e c h a n i s m , t h e t o t a l r a t e of w h i c h increases w i t h t h e c u r r e n t . T h e c o r r e s p o n d i n g increase of t h e m e a n gas t e m p e r a t u r e does n o t a p p e a r to a c c o u n t f o r t h e w h o l e effect, f o r a t ρ = 1 m m . , P/p a n d η d i m i n i s h m a r k e d l y as / is i n c r e a s e d f r o m 15 t o 20 m a . , a l t h o u g h W is p r a c t i c a l l y u n c h a n g e d . a

T h e r e seems t o be l i t t l e d i r e c t e x p e r i m e n t a l evidence o n t h e r a t e coefficient f o r t h e d e c o m p o s i t i o n of ozone i n a d i s c h a r g e , β . I n t h e W a r b u r g - L e i t h â u s e r t h e o r y of 1909 (81), t h e r a t e coefficient, β , f o r ozone d e c o m p o s i t i o n was a s s u m e d t o be i n d e p e n d e n t of t h e c u r r e n t ( a t c o n s t a n t p r e s s u r e ) , as is ( a p p r o x i m a t e l y ) β f o r ozone s y n t h e s i s . H o w e v e r , M o e l l e r (58, p . 112) w h e n d e s c r i b i n g t h e W a r b u r g - L e i t h â u s e r t h e o r y m a k e s t h e f o l l o w i n g u n d o c u m e n t e d s t a t e m e n t : T h e ozone y i e l d , βΐ, f o r zero ozone c o n c e n t r a t i o n increases m o r e r a p i d l y t h a n t h e c u r r e n t , a n d t h e same h o l d s i n a m o r e m a r k e d degree f o r t h e c o r r e s p o n d i n g y i e l d of o x y g e n f r o m ozone, β Ι. α

α

α

B r e w e r a n d W e s t h a v e r suggest t h a t β m a y be c o n s i d e r a b l y l a r g e r t h a n β i n t h e s a m e a p p a r a t u s . O n t h e o t h e r h a n d H e n r y describes t h e d e c o m p o s i t i o n as n o t oc c u r r i n g i n t h e gas, a n d o n l y o n t h e r e f r i g e r a t e d t u b e surfaces w h e n t h e p r e s s u r e is close t o t h e s t e a d y - s t a t e p r e s s u r e . H e f o u n d t h a t t h e r a t e d e c o m p o s i t i o n of ozone o n t h e w a l l of a d i s c h a r g e t u b e is v e r y s e n s i t i v e to t h e s t a t e of t h e s u r f a c e ; his o b s e r v a t i o n s a r e c o n s i s t e n t w i t h those of o t h e r i n v e s t i g a t o r s w o r k i n g w i t h u n - i o n i z e d gas (57). C o n c e r n i n g t h e s t a t i o n a r y state i n a d i s c h a r g e , t h e r e is also l i t t l e u n a m b i g u o u s evidence a b o u t t h e c o n d i t i o n s i n t h e d i s c h a r g e r e l a t i v e t o those a t t a i n e d w h e n t h e ozone c o n c e n t r a t i o n is n e g l i g i b l e . W a r b u r g a n d L e i t h a u s e r c l a i m e d t o h a v e s h o w n t h a t t h e ozone c o n c e n t r a t i o n i n t h e s t a t i o n a r y s t a t e of a n o z o n i z e r d i s c h a r g e decreases s l o w l y as t h e c u r r e n t is i n c r e a s e d ; t h i s a p p e a r s t o be at v a r i a n c e w i t h t h e d a t a r e p r e s e n t e d i n D e v i n s ' s F i g u r e 2. W a r b u r g seems t o h a v e t h o u g h t t h a t h i s d e m o n s t r a t i o n t h a t t h e c h a r a c t e r i s t i c s of a p o i n t - t o - p l a n e d i s c h a r g e i n o x y g e n depends o n t h e ozone c o n c e n t r a t i o n (75) i m p l i e s t h a t t h e s a m e h o l d s f o r o z o n i z e r d i s c h a r g e s ; evidence f o r t h e l a t t e r was p r o v i d e d b y t h e i n v e s t i g a t i o n s of S t . S a c h s (65). α

F o r —73° C . , t h e d a t a of B e i l l (7) a t a t m o s p h e r i c pressure c o r r e s p o n d to a v a l u e of 780 f o r t h e r a t i o p /p u s e d b y D e v i n s i n his a n a l y s i s of t h e k i n e t i c s , w h i l e f o r 20° C . t h e v a l u e is a b o u t 8 3 0 0 ; these v a l u e s are t w o a n d t h r e e orders of m a g n i t u d e l a r g e r t h a n those c i t e d b y D e v i n s i n h i s T a b l e I f o r t h e pressure range 70 to 400 m m . H g . T h e e a r l y d a t a of B r i n e r a n d D u r a n d (10) s h o w t h a t a t —180° C , t h e r a t i o m u s t h a v e been of t h e o r d e r u n i t y i n a n o z o n i z e r d i s c h a r g e , a n d t h e s a m e h o l d s 2

0e>

0z


297


f o r a g l o w d i s c h a r g e a t —180° C , as i s s h o w n b y t h e d a t a of H e n r y a n d of B r e w e r a n d Westhaver.


Formal Theory of Discharge Reaction a n d M e c h a n i s m s of O z o n e Synthesis T h e s t a t e of affairs i n a p p r o a c h i n g t h e i d e n t i f i c a t i o n of t h e m e c h a n i s m of ozone s y n t h e s i s i n discharges i s p e r h a p s t i d i e r t h a n t h e e x p e r i m e n t a l r e s u l t s r e v i e w e d a b o v e , b u t m o r e f r u s t r a t i n g , because so m a n y d a t a a r e l a c k i n g a b o u t t h e d e t a i l e d s t a t e of a p a r t l y i o n i z e d gas i n a d i s c h a r g e , t h e k i n d s of species p r e s e n t , a n d t h e k i n d s of c o l l i s i o n s t h e y c a n m a k e . F u r t h e r m o r e , one m a i n g r o u p of e x p e r i m e n t a l d a t a relates t o t h e r e l a t i v e l y w e l l c h a r a c t e r i z e d c o n d i t i o n s i n t h e p o s i t i v e c o l u m n of a l o w p r e s s u r e c o l d c a t h o d e g l o w d i s c h a r g e ; b u t t h e o t h e r relates t o o z o n i z e r discharges i n a m u c h h i g h e r range of p r e s s u r e , a d i s c h a r g e f o r m w h i c h , a l t h o u g h k n o w n f o r a c e n t u r y , h a s a t t r a c t e d few p h y s i c a l investigations. T h e f o r m a l t h e o r y of e x c i t a t i o n a n d c h e m i c a l r e a c t i o n i n t h e c o l d c a t h o d e g l o w d i s c h a r g e w a s g i v e n b y Emeléus a n d L u n t (22) i n 1936 i n a f o r m c o n v e n i e n t f o r d i s c u s s i n g t h e p h e n o m e n a i n t h e n e g a t i v e zones a n d t h e m o r e o r less i d e a l p l a s m a of a u n i f o r m p o s i t i v e c o l u m n , t h e d i s c h a r g e b e i n g e n v i s a g e d as t h a t a t t a i n a b l e i n a c y l i n d r i c a l tube between plane electrodes; there are, however, contemporary statements relating t o e x c i t a t i o n (59). F o r u n i f o r m p o s i t i v e c o l u m n c o n d i t i o n s L u n t (48) h a s g i v e n a revised a n d amplified account. I d e a l l y , t h e a n a l y s i s of E m e l é u s a n d L u n t enables c o m p u t a t i o n of t h e r e a c t i o n r a t e coefficients, P/p, β =

\p

where Zi a n d z correspond t o a n y t w o planes p e r -

(P/p)dz

2

Jzi p e n d i c u l a r t o t h e d i r e c t i o n of c h a r g e t r a n s p o r t , a n d η = P/X where V =

= (P/p)/(X/p)

=

β/V

Xdz, X b e i n g t h e field m a i n t a i n i n g t h e m e a s u r e d c h a r g e t r a n s p o r t .

F o r the conditions i n a u n i f o r m positive c o l u m n , w h i c h appears to be t h e i m p o r t a n t zone f o r ozone s y n t h e s i s , S, t h e r a t e coefficient of a n y specified k i n d of e l e c t r o n - r e a c t a n t collision occurring a t the rate S n n collisions per cc. per second e

r

w h e r e n a n d n d e n o t e t h e c o n c e n t r a t i o n s of electrons a n d r e a c t a n t s , r e s p e c t i v e l y , is given b y e

r

V°> Q(V)f(V)dV

JVe

(1)

I n t h i s r e l a t i o n Q(V) is t h e cross s e c t i o n f o r t h e r e a c t i o n as effected b y e l e c t r o n s of e n e r g y V a n d is zero f o r V < V , t h e c r i t i c a l e n e r g y ; f(V) i s t h e e l e c t r o n e n e r g y d i s t r i b u t i o n f u n c t i o n , a n d k is a n u m e r i c a l f a c t o r e q u a l t o 1.87 Χ 1 0 w h e n V i s expressed i n e l e c t r o n v o l t s a n d w h e n Q(V) i s i n u n i t s o f πα . e

8

2

0

I f W is t h e e l e c t r o n d r i f t v e l o c i t y i n t h e d i r e c t i o n of t h e e l e c t r i c field, t h e c u r r e n t d e n s i t y o r a m o u n t o f ( u n i t ) c h a r g e t r a n s p o r t p e r s q u a r e c e n t i m e t e r p e r s e c o n d i s n W. S i n c e Ρ is defined as t h e r e a c t i o n r a t e coefficient p e r u n i t c h a r g e t r a n s p o r t , i t f o l l o w s that e

Ρ =

φ

8

η

nW

^ = 8 n /W φ

r

(2)

e

w h e r e φ is a f a c t o r analogous t o t h e p h o t o c h e m i c a l q u a n t u m y i e l d a n d t a k e s i n t o a c c o u n t t h e s p e c i a l c i r c u m s t a n c e s d e t e r m i n i n g t h e y i e l d t h a t m a y arise i n discharges (22). S i n c e n = 3.54 Χ 1 0 p , w h e r e p is t h e p a r t i a l p r e s s u r e of t h e r e a c t a n t c o n c e r n e d i n m i l l i m e t e r s of m e r c u r y , i t f o l l o w s t h a t r

1 6

r

P/p

r

= 3.54 Χ 10 φ (S/W) !6


(3)

A D V A N C E S IN

298

CHEMISTRY SERIES

I f m o r e t h a n one k i n d of e l e c t r o n - r e a c t a n t r e a c t i o n is i n v o l v e d s i m u l t a n e o u s l y , as is p r o b a b l y t h e case f o r t h e o x y g e n - o z o n e r e a c t i o n , Ρ m u s t be r e p l a c e d b y t h e s u m of a l l t h e P ' s c o n c e r n e d , a n d i n d e r i v i n g these l a t t e r f r o m t h e o r y , c o r r e s p o n d i n g l y , S m u s t be r e p l a c e d b y t h e s u m of t h e >S's c o n c e r n e d . W h e n t h e c u r r e n t d e n s i t y is so l o w t h a t t h e gas consists a l m o s t e x c l u s i v e l y of m o l e c u l e s u n c h a n g e d b y t h e d i s c h a r g e , so t h a t p, t h e t o t a l p r e s s u r e , is s e n s i b l y t h e same as p , t h e p a r t i a l p r e s s u r e of t h e r e a c t a n t , a s p e c i a l case arises w h e n W, a n d V, t h e m e a n e l e c t r o n e n e r g y , are f u n c t i o n s of X/p as i n t h e e x p e r i m e n t a l c o n d i t i o n s a d o p t e d b y t h e T o w n s e n d s c h o o l f o r t h e i r m e a s u r e m e n t s (78). F o r t h e n S is a f u n c t i o n of X/p o n l y , a n d is c o m p u t a b l e w h e n f(V) a n d Q(V) a r e also k n o w n . R e l a t i o n 3 t h e n b e comes r

P/p

= 3.54 Χ ΙΟ φ/ι (X/p)

(4)

16


and correspondingly η

= Ρ/χ

= 3.54 χ ί ο " / φ

2

(x/ )

(5)

p

a n d i n t h i s case w h e n φ i s also i n d e p e n d e n t of t h e c u r r e n t d e n s i t y f o r a n y g i v e n v a l u e of X/p, i t f o l l o w s t h a t P/p

(6)

= a

T h e c i r c u m s t a n c e s a r e different w h e n t h e species e n g e n d e r i n g t h e o b s e r v e d r e a c t i o n c a n be s i m u l t a n e o u s l y g e n e r a t e d b y a n a d d i t i o n a l t w o - s t a g e e l e c t r o n i m p a c t process t h a t i n v o l v e s as t h e i n t e r m e d i a t e stage t h e g e n e r a t i o n of a m e t a s t a b l e species. F o r the s i m p l e s t c o n d i t i o n s t h e o r y t h e n l e a d s t o a r e l a t i o n of t h e f o r m , f o r X/p constant: P/p

(7)

= a + bj

w h e r e a a n d b are c o n s t a n t f a c t o r s a n d ; is t h e c u r r e n t d e n s i t y . W h a t a p p e a r s to be t h e first i d e n t i f i e d case of t h i s k i n d relates t o t h e e x c i t a t i o n of t h e 7 P state i n a d i s c h a r g e t h r o u g h m e r c u r y v a p o r (26, 55, p . 7 1 ) , 6 Λ ) , ι , 2 b e i n g t h e m e t a s t a b l e i n termediate state. 3

3

W h e n c o n t r a r i w i s e , t h e e x p e r i m e n t a l d a t a f o r c o n s t a n t X/p a r e l a t i o n of t h e f o r m P/p

= α -

cj -

df

-

c a n be r e p r e s e n t e d b y

···

(8)

t h e r e is a s t r o n g i n d i c a t i o n t h a t one o r m o r e u n s u s p e c t e d d e a c t i v a t i n g processes are o p e r a t i v e f o r t h e i m m e d i a t e p r o d u c t of a t w o - s t a g e process, o r f o r t h e final p r o d u c t . A n e x a m p l e of e a c h k i n d is a f f o r d e d b y t h e e x p e r i m e n t a l d a t a f o r t h e i n t e n s i t y of e m i s s i o n p e r u n i t c u r r e n t d e n s i t y of t h e V e g a r d - K a p l a n a n d s e c o n d p o s i t i v e b a n d s , r e s p e c t i v e l y , f r o m a u n i f o r m p o s i t i v e c o l u m n d i s c h a r g e t h r o u g h m o l e c u l a r n i t r o g e n (85). T h e r e a r e s o m e l i m i t a t i o n s t o t h e c o m p u t a t i o n of P/p a n d η f r o m R e l a t i o n s 3, 4, a n d 5. I n p r i n c i p l e , f(V) f o r o x y g e n c a n be d e t e r m i n e d as S m i t has d o n e f o r h e l i u m (67), b u t the necessary a u x i l i a r y d a t a are l a c k i n g , a n d no a p p r o x i m a t e solution appears to h a v e b e e n a t t e m p t e d . I n t h e absence of e x p e r i m e n t a l d a t a f o r p o s i t i v e c o l u m n d i s charges, i t is necessary t o assume a f o r m f o r f(V), t h e M a x w e l l i a n f o r m b e i n g u s u a l l y r e g a r d e d as a g o o d a p p r o x i m a t i o n . V a n d W a r e k n o w n f u n c t i o n s of X/p (33), b u t t h e i r v a l i d i t y f o r t h e m u c h h i g h e r c u r r e n t densities associated w i t h t h e d a t a of T a b l e s I V a n d V is u n c e r t a i n . F o r t h e f o r m a n d a m p l i t u d e of Q(V) f o r e a c h e l e c t r o n i m p a c t r e a c t i o n l i k e l y t o c o n t r i b u t e t o t h e o b s e r v e d s y n t h e s i s of ozone, i t is necessary t o r e l y m a i n l y o n t h e i n d i c a t i o n s f r o m t h e o r y . B u t t h e m a x i m u m v a l u e of φ, t h e n u m b e r of ozone m o l e c u l e s f o r m e d p e r o x y g e n m o l e c u l e e x c i t e d b y e l e c t r o n i m p a c t , m a y be t a k e n as 2 i n a c c o r d a n c e w i t h t h e p h o t o c h e m i c a l d a t a . D e s p i t e these l i m i t a t i o n s a n d u n c e r t a i n t i e s , some success has a t t e n d e d t h i s q u a n t i t a t i v e t h e o r e t i c a l a p p r o a c h t o t h e i n t e r p r e t a t i o n of e x p e r i m e n t a l d a t a i n u n i f o r m field c o n d i t i o n s w h e n t h e p h e n o m e n a a p p e a r t o be c o n c e r n e d w i t h a single i m m e d i a t e


LU NT—FORMATI O N IN ELECTRIC

299

DISCHARGE

p r o d u c t o f e l e c t r o n - r e a c t a n t c o l l i s i o n s , a l t h o u g h i n n o case h a v e t h e e x p e r i m e n t a l d a t a b e e n e x t e n s i v e e n o u g h t o p r o v i d e a s t r i n g e n t test o f t h e t h e o r y . I n a l l cases t h e M a x w e l l i a n f o r m h a s b e e n a s s u m e d t o b e a v a l i d a p p r o x i m a t i o n t o f(V), f o r w h i c h t h e r e i s s o m e j u s t i f i c a t i o n f o r u n i f o r m p o s i t i v e c o l u m n d i s c h a r g e s i n m o l e c u l a r gases. I n a d d i t i o n t o t h e r e s u l t s r e v i e w e d (22), t h i s a p p r o a c h gives r e a s o n a b l y g o o d a g r e e m e n t w i t h m o r e r e c e n t e x p e r i m e n t a l d a t a (28, 29, 32) f o r t h e T o w n s e n d coefficient of i o n i z a t i o n , a n d f o r t h e f o r m a t i o n of n e g a t i v e i o n s (47). T o m a k e s u c h c o m p a r i s o n s i n t e r m s of P/p o r η, i t i s p r e f e r a b l e t o select e x p e r i m e n t a l d a t a r e l a t i n g t o c o n d i t i o n s f o r w h i c h p /p does n o t differ s i g n i f i c a n t l y f r o m u n i t y , f o r 7 a n d W a r e k n o w n as f u n c t i o n s of X/p o n l y f o r t h e r e a c t a n t g a s . U s u a l l y i t is n o t d i f f i c u l t t o choose s u c h e x p e r i m e n t a l c o n d i t i o n s , a n d t h e y a r e o f t e n those i n w h i c h φ m a y be expected t o a t t a i n i t s m a x i m u m value. I d e a l l y this restriction o n p /p i s u n i m p o r t a n t , b u t t h e f a c t t h a t n o d a t a a r e a v a i l a b l e f o r V a n d W f o r e i t h e r ozone o r o z o n e - o x y g e n m i x t u r e s i s a d e t e r r e n t t o t h e m o r e c o m p l i c a t e d t a s k o f m a k i n g such comparisons for t h e stationary state, a n d i t is consequently d o u b t f u l whether D e v i n s ' s use of R e l a t i o n 1 i n t h a t c o n n e c t i o n (18) c a n l e a d t o u s e f u l c o n c l u s i o n s . r


r

I n oxygen the vertical transition that c a n account for the low-pressure photo c h e m i c a l s y n t h e s i s of ozone i s S ^ ~ 2 ~ ~ , a n d a t h i g h pressures i t appears t h a t t h e t r a n s i t i o n of l o w p r o b a b i l i t y 5 ^ ~ S also p l a y s a p a r t . A s these t r a n s i t i o n s c a n also be effected b y e l e c t r o n i m p a c t , t h e y a r e t h e first c h o i c e i n f o r m u l a t i n g a m e c h a n i s m l i k e l y t o a c c o u n t f o r t h e s y n t h e s i s o c c u r r i n g i n d i s c h a r g e s . T h e first i s a n a l l o w e d t r a n s i t i o n i n v o l v i n g a n e n e r g y a b s o r p t i o n of a b o u t 8 e.v., so t h a t t h e e x c i t e d m o l e c u l e i m m e d i a t e l y dissociates i n t o D a n d P a t o m s ; w h e n effected b y e l e c t r o n i m p a c t , t h e m a x i m u m v a l u e of Q(V) i s e s t i m a t e d t o b e a b o u t 1 πα a n d to occur for V = 40 ± 5 e.v. (41, 54). T h e v e r t i c a l excitation energy f o r t h e disallowed t r a n s i t i o n to t h e S state is a b o u t 6 e.v., so t h a t d i s s o c i a t i o n f o l l o w s a t once, i n t h i s case i n t o t w o P a t o m s . T h e m a x i m u m v a l u e of Q(V) i s e s t i m a t e d t o b e a b o u t 0.2 τ τ α * to occur for V = c a . 9 e.v. (28, 29, 32). F o r φ = 2 i t f o l l o w s t h a t t h e u p p e r l i m i t t o t h e v a l u e of η f o r ozone g e n e r a t e d i n e a c h of these w a y s is a b o u t 2 5 X 1 0 ~ a n d 33 X 1 0 ~ m o l e c u l e p e r e.v., r e s p e c t i v e l y . 3

3

3

3

1

3

w

M

+

2

0

3

M

+

3

0

2

a n c

2

2

T h u s i n a u n i f o r m p o s i t i v e c o l u m n d i s c h a r g e , t h e s i m u l t a n e o u s o c c u r r e n c e of these t w o e x c i t a t i o n processes b y e l e c t r o n i m p a c t t o a n e x t e n t t h a t w o u l d l e a v e a c o n s i d e r a b l e m a r g i n f o r e n e r g y a b s o r p t i o n i n o t h e r processes p r o v i d e s a m e c h a n i s m t h a t c o u l d account for the highest observed values given i n Tables I V a n d V . B u t the c r u c i a l q u e s t i o n is w h e t h e r t h i s m e c h a n i s m c a n a c c o u n t f o r t h e t r e n d of P/p a n d η w i t h X/p and w i t h the current density a n d c a n also a c c o u n t f o r t h e a b s o l u t e m a g n i t u d e s observed. T h e d a t a i n T a b l e s I V a n d V s h o w t h a t P/p a n d η increase r a p i d l y as X/p i s i n c r e a s e d , b u t these increases a r e also a s s o c i a t e d w i t h a p r o g r e s s i v e decrease i n The m e c h a n i s m e n v i s a g e d i n v o l v e s t w o s i m u l t a n e o u s processes, f o r e a c h of w h i c h P/p m a y be e x p e c t e d t o c o n f o r m w i t h R e l a t i o n 6 a n d t h u s t o be i n d e p e n d e n t of Consequently a n increase of V w i t h X/p, f o r w h i c h t h e r e is a m p l e i n d e p e n d e n t e v i d e n c e f o r o t h e r discharges, p r o v i d e s a q u a l i t a t i v e e x p l a n a t i o n of t h e t r e n d of t h e o b s e r v e d v a l u e s of P/p a n d η w i t h X/p. B u t as t h e r e a r e n o d a t a r e l a t i n g t o a r a n g e of ; w h e n X/p is c o n s t a n t , n o c o n c l u s i o n c a n b e d r a w n as t o w h e t h e r t h e e x p e r i m e n t a l d a t a c o n f o r m w i t h R e l a t i o n 6, o r w i t h R e l a t i o n s 7 o r 8 w h i c h a r e c h a r a c t e r i s t i c of a m e c h a n i s m different f r o m t h a t e n v i s a g e d . W h i l e t h e r e i s n o i m p o r t a n t u n c e r t a i n t y a b o u t t h e v a l u e f o r η, v a l u e s f o r P/p a n d X/p m a y be s m a l l e r t h a n those t a b u l a t e d b y a f a c t o r b e t w e e n 1 a n d 3, d e p e n d i n g o n t h e a c t u a l t e m p e r a t u r e of t h e gas i n t h e d i s c h a r g e ( T a b l e s I V a n d V ) . U n l e s s t h a t t e m p e r a t u r e , a n d hence t h e r e d u c e d v a l u e s of X/p, a r e d e t e r m i n e d o r e s t i m a t e d , t h e e x p e r i m e n t a l v a l u e s f o r P/p a n d η c a n n o t be c o m p a r e d w i t h t h e v a l u e s c a l c u l a t e d f r o m t h e o r y f o r t h e m e c h a n i s m e n v i s a g e d . I f t h e p r o v i s i o n a l r o u g h estimates of t h e gas t e m p e r a t u r e g i v e n i n t h e d i s c u s s i o n of T a b l e s I V a n d V a r e t o b e a c c e p t e d , i t c a n be s a i d t h a t t h e a g r e e m e n t b e t w e e n t h e c a l c u l a t e d a n d t h e e x p e r i m e n t a l v a l u e s is w i t h i n


300


a n o r d e r of m a g n i t u d e . B u t t h i s diffuse a g r e e m e n t c o u l d s c a r c e l y b e h e l d t o e s t a b l i s h t h e v a l i d i t y of t h e r e a c t i o n m e c h a n i s m p o s t u l a t e d . T h e e a r l i e r a n a l y s i s b y D e e g a n a n d Emeléus (17) is b a s e d o n s o m e w h a t different c o n s i d e r a t i o n s : i t s t a r t s b y e q u a t i n g R , a n a v e r a g e v o l u m e r a t e of ozone g e n e r a t i o n , w i t h φ n n 2 ( S ) (cf. R e l a t i o n s 1 a n d 2 ) w h e r e t h e s u m m a t i o n e x t e n d s t o a n u m b e r of e l e c t r o n i m p a c t r e a c t i o n s l i k e l y t o generate o x y g e n a t o m s , i n c l u d i n g v e r t i c a l t r a n s i t i o n s t o t h e S + a n d 2 - states, a n d t h e n seeks t h e r a n g e of V t h a t i s consistent w i t h p l a u s i b l e e x t r e m e v a l u e s f o r n n w i t h φ = 2. T h e y selected B r e w e r a n d W e s t h a v e r ' s d a t a f o r 7 = 2 0 m a . ( T a b l e V ) t o c o m p u t e R = 1.7 Χ 1 0 m o l e c u l e s p e r c c . p e r s e c o n d f o r t h e ( n o m i n a l ) pressure range 2.8 t o 14, o r p = 8.4, i g n o r i n g t h e f a c t t h a t b o t h R a n d X/p change g r e a t l y ; a n d i t w a s a s s u m e d t h a t t h e gas t e m p e r a t u r e was —180° C . T h i s p r o c e d u r e is e q u i v a l e n t t o c o n s i d e r i n g t h e r a t e , R, f o r t h e r e d u c e d p r e s s u r e ρ = 25.2 o r n = 8.7 Χ 1 0 , a n d t o a r e d u c e d v a l u e P/p = 0.052, p r a c t i c a l l y t h e same v a l u e as t h a t g i v e n i n T a b l e V f o r ρ = 9 w h e n t h e gas t e m p e r a t u r e i s t a k e n t o b e —180° C . T h e free v a r i a b l e s t h u s b e c o m e i n effect o n l y n a n d V. F o r t h e c o m p u t a t i o n of i t w a s a s s u m e d t h a t Q(V) i n R e l a t i o n 1 h a d t h e c o n s t a n t v a l u e 0.8 7Γ#Ο f ° r 6.0 < V < 6.2 e.v. a n d f o r V > 7 e.v. B y a s s u m i n g t h a t n lies b e t w e e n 1 0 a n d 1 0 c m . - , i t w a s f o u n d t h a t V m u s t l i e i n t h e r a n g e 0.75 t o 1.4 e.v. T h i s conclusion, a l t h o u g h valuable, provides n o more t h a n a n agreement i n order of m a g n i t u d e b e t w e e n t h e o b s e r v e d a n d c a l c u l a t e d r a t e s , w h e n i t is a p p r e c i a t e d t h a t t h i s a p p a r e n t l y n a r r o w r a n g e o f V c o r r e s p o n d s t o a n increase i n 5 (S) b y a f a c t o r a b o u t 2 5 0 . I f t h e m e a n gas t e m p e r a t u r e i s a s s u m e d t o b e s o m e w h a t h i g h e r , so t h a t n = 5x 1 0 c m . , a n d V i s a s s u m e d t o b e 1.0 e.v., n i s f o u n d t o b e 7.5 X 10°, c o r r e s p o n d i n g t o w h i c h W = 1.7 Χ 1 0 c m . p e r s e c o n d . T h e s e v a l u e s g i v e a j n u c h closer a g r e e m e n t w i t h t h e d a t a f o r l o w c u r r e n t densities (33) : t h e v a l u e s f o r V a n d W c o r r e s p o n d v e r y closely t o X/p = 1.5, w h i l e t h e c o r r e s p o n d i n g r e d u c e d v a l u e f r o m e x p e r i m e n t i s a b o u t 2. A n d a g a i n because of t h e l a c k of d a t a a t c o n s t a n t X/p, i t cannot be said t h a t t h e experimental d a t a are characteristic of t h e mechanism p o s t u lated. E m e l é u s a n d D e e g a n suggested t h a t a closer a g r e e m e n t b e t w e e n t h e e x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s m i g h t b e r e a c h e d i f , i n a d d i t i o n , i t were s u p p o s e d t h a t stepwise e x c i t a t i o n r e s u l t i n g i n d i s s o c i a t i o n o c c u r r e d v i a t h e h i g h l y m e t a s t a b l e Δ a n d ^ + states. I n t h i s case, unless d e a c t i v a t i o n t a k e s p l a c e t o a l a r g e e x t e n t , P/p w o u l d b e e x p e c t e d t o v a r y w i t h ; a c c o r d i n g t o R e l a t i o n 7 ; a n d i f these a d d i t i o n a l r e a c t i o n s were t o p l a y a p r e d o m i n a n t r o l e , i t m i g h t a c c o u n t f o r t h e f a c t t h a t t h e o b s e r v e d v a l u e s of η a r e so l a r g e w h e n t h e r e d u c e d v a l u e of X/p i s 1.5 o r less. H o w e v e r , other factors m a y need t o be t a k e n into consideration i n formulating a p l a u s i b l e r e a c t i o n m e c h a n i s m . A s t h e c u r r e n t d e n s i t y is i n c r e a s e d i n a c t u a l e x p e r i m e n t a l c o n d i t i o n s , t h e r e is u s u a l l y a c o r r e s p o n d i n g p r o g r e s s i v e increase i n t h e t e m p e r a t u r e of t h e gas, so t h a t t h e r e i s a c o r r e s p o n d i n g decrease i n p /p, t h e f r a c t i o n a l c o n c e n t r a t i o n of t h e r e a c t a n t species, w h i c h h a s b e e n i m p l i c i t l y a s s u m e d t o b e o x y g e n m o l e c u l e s i n t h e zero v i b r a t i o n a l l e v e l , $ - , v = 0. W h i l e t h e effect of t e m p e r a t u r e m a y b e s m a l l i n i n c r e a s i n g t h e f r a c t i o n a l c o n c e n t r a t i o n of t h e h i g h e r v i b r a t i o n a l l e v e l s , all of w h i c h are highly metastable, direct excitation b y electron impact m i g h t be r e s p o n s i b l e f o r a m u c h l a r g e r effect. T h e s e c o n s i d e r a t i o n s i l l u s t r a t e t h e n e e d f o r c a u t i o n i n selecting e x p e r i m e n t a l c o n d i t i o n s , a n d i n u s i n g t h e t h e o r e t i c a l R e l a t i o n s 1 t o 8 w h e n i t i s a s s u m e d t h a t p /p i s v e r y close t o u n i t y ; a n d t h e y a r e i m p o r t a n t i n a n y a n a l y s i s of t h e s t a t i o n a r y state i n discharges w h e n p /p i s less t h a n u n i t y f o r b o t h ozone a n d u n c h a n g e d o x y g e n m o l e c u l e s , a n d m a y n o t b e n e g l i g i b l e f o r o t h e r species present. T h e p o s s i b i l i t y t h a t a s i g n i f i c a n t f r a c t i o n of t h e r e a c t a n t gas m a y b e c o n v e r t e d i n t o v i b r a t i o n a l l y e x c i t e d m o l e c u l e s i n t h e g r o u n d e l e c t r o n i c state i s associated w i t h a f u r t h e r c o m p l i c a t i o n of t h e r e a c t i o n m e c h a n i s m w h i c h r e q u i r e s t o b e e x p l o r e d . F o r a n y v a l u e o f ν i n excess of some c r i t i c a l v a l u e , w h i c h a p p e a r s t o a b o u t 2, v e r t i c a l t r a n sitions f r o m t h e S ^ " " s t a t e generate m o l e c u l e s i n t h e 2 t * ~ state t h a t d o n o t dissociate &y

e

r

3

3

W

w

e

r

1 6

&y

a v

1 7


r

e

2

9

r

e

1 1

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1 7

- 3

e

6

1

< 7

1

r

s

g

r

r

3

3


< 7

LUNT—FORMATION IN

301

ELECTRIC DISCHARGE

but spontaneously radiate, emitting bands of the Schumann-Runge system; and there can be no corresponding generation of ozone. Nondissociating molecules in the S state may be generated in a similar way, but because these are metastable some m a y be dissociated by electron impact. T h e occurrence of such processes which involve as the initial step the generation of vibrationally excited reactant molecules in the ground electronic state m a y be regarded, i n terms of the mechanisms previously postulated, as equivalent to φ having a value less than 2, and possibly also to negative values of άφ/dj in which case P/p would vary according to Relation 8.


3

M

+

U n t i l the nature of ozonizer discharges is more clearly determined, it is doubtful whether the statistical theory of electron-reactant collisions for positive column condi tions remains applicable although Devins (18) has recently assumed that it does. T h e early data of G r a y (Table I) and the possibly less certain data of Warburg and R u m p (Table II) yield values of P/p that are not very sensitive to the current density for ozonizer discharges; this holds also for the recent data of Devins (Table I I I ) . T h i s is in marked contrast with the data of H e n r y (Table I V ) and of Brewer and Westhaver (Table V ) . There is also a large difference between the highest attained values for η: despite uncertainties i n the values for ozonizer discharges, they appear to be about twice those for the uniform positive column. Thus these two forms of the discharge appear to differ considerably i n their potency to effect the synthesis of ozone ; possibly also the reaction mechanisms involved are different. T h e kind of reaction mechanism that may occur in uniform positive column dis charges can be perceived in broad outline, but many auxiliary data are lacking to present a quantitative expression i n forms convenient and precise for comparison with experiment ; and the experimental data for ozone synthesis in discharges are inadequate to describe correspondingly precisely the electrical state of the gas in which synthesis has been observed. These gaps i n knowledge hinder the identification of the reaction mechanism i n discharges; and until they can be filled it is doubtful whether the present data for the synthesis b y discharges can be linked coherently with those for the photosynthesis and for other reactions in un-ionized gases. Acknowledgment It is a pleasure to record the assistance given in many discussions, especially b y Louis H e r m a n , Paris, T . C . Manley, Philadelphia, and H . S. W . Massey, L o n d o n . Literature

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Ibid., 1 7 , 1-29 (1905). W a r b u r g , E., Verh. deut. phys. Ges. 5, 382-91 (1903). W a r b u r g , Ε., Z. tech. Physik 4, 450-60 (1923); 5, 165-9 (1924); 6, 625-33 (1925). W a r b u r g , E., Leithäuser, G . , Ann. Physik 28, 1-16 (1909). Ibid., p p . 17-36. W a r b u r g , E., R u m p , W . , Z. Physik 32, 245-51 (1925).


RECEIVED for review May 17, 1957. A c c e p t e d J u n e 19, 1957.


303

The Mechanism of Ozone Formation in Electrical Discharges

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