Emission Resulting from Triplet-Triplet Annihilation - American

8 Metalloporphyrin Dimeric S Emission Resulting from Triplet-Triplet Annihilation 2

G. F. Stelmakh and M. P. Tsvirko

Downloaded by FUDAN UNIV on March 14, 2017 | http://pubs.acs.org Publication Date: October 15, 1986 | doi: 10.1021/bk-1986-0321.ch008

A. N. Sevchenko Research Institute of Applied Physical Problems, Minsk, 220106, USSR

S emission resulting from triplet-triplet annihilation is reported. It differs from prompt S emission in being red shifted by 80 to 500 cm . It also appears slightly narrower in halfwidth. The difference is ascribed to the fact that for triplet-triplet annihilation delayed fluorescence comes from a dimeric species before it has time to dissociate. 2

2

-1

T r i p l e t - t r i p l e t a n n i h i l a t i o n (TTA), i . e . , d e a c t i v a t i o n o f t r i p l e t m o l e c u l e s as a r e s u l t o f t h e i r i n t e r a c t i o n , i s one o f t h e main pathways o f t r i p l e t s t a t e decay i n s o l u t i o n s , c r y s t a l s and t h e g a s - p h a s e . TTA may become t h e d e t e r m i n i n g pathway o f t r i p l e t s t a t e d e a c t i v a t i o n under c o n d i t i o n s o f h i g h c o n c e n t r a t i o n s o f t r i p l e t s t a t e m o l e c u l e s r e s u l t i n g i n p a r t i c u l a r from powerful l a s e r photoexcitation. The e x i s t e n c e o f t h i s TTA b i m o l e c u l a r p r o c e s s makes i t p o s s i b l e to c a r r y o u t c o o p e r a t i v e e x c i t a t i o n o f energy r i c h m o l e c u l a r s t a t e s by l o w energy q u a n t a . I n p a r t i c u l a r , f o r m a t i o n o f upper e x c i t e d s i n g l e t s t a t e s as a r e s u l t o f TTA has been observed f o r s e v e r a l a r o m a t i c hydrocarbons ( 1 ) and m e t a l l o p o r p h y r i n s [2) by t h e d e m o n s t r a t i o n o f a n n i h i T a t i o n - i n d u c e d d e l a y e d f l u o r e s c e n c e (A0F) from upper s i n g l e t s t a t e s . S y s t e m a t i c r e s e a r c h o f two-quantum e x c i t a t i o n o f t e t r a p y r r o l i c pigments ( 2 , 3 ) has made i t e v i d e n t t h a t c o o p e r a t i v e t r i p l e t - t r i p l e t e x c i t a t i o n o f m e t a l l o p o r p h y r i n upper e l e c t r o n i c s t a t e s s u c c e s s f u l l y competes w i t h t h e p r o c e s s e s o f s t e p w i s e two-quantum e x c i t a t i o n . T h i s made us pay g r e a t e r a t t e n t i o n t o p o r p h y r i n TTA s i n c e h i g h quantum y i e l d s o f i n t e r s y s t e m c r o s s i n g t o t r i p l e t T^ s t a t e s i s c h a r a c t e r i s t i c o f t h e s e t y p e s o f compounds. ( I t should be mentioned t h a t i n t e r e s t i n p h o t o p r o c e s s e s i n e x c i t e d s t a t e s o f t e t r a p y r r o l i c pigments has been g r e a t l y i n c r e a s e d by development o f s o l a r energy c o n v e r t e r s based on m e t a l l o p o r p h y r i n s ( 4 , 5 ) ) .

0097-6156/ 86/ 0321 -0118$06.00/ 0 © 1986 A m e r i c a n C h e m i c a l Society

Gouterman et al.; Porphyrins ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

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S T E L M A K H A N D TSVIRKO

Triplet-Triplet Annihilation

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F o r s e v e r a l compounds p r o b a b i l i t i e s o f e x c i t e d s i n g l e t s t a t e f o r m a t i o n as a r e s u l t o f TTA processes have been determined i n o u r p r e v i o u s paper (16) w i t h t h e h e l p o f a method based on measurement of t h e r a t i o o f t h e i n t e g r a t e d i n t e n s i t i e s o f ADF and prompt f l u o r e s c e n c e (PF) under t h e c o n d i t i o n s o f powerful p h o t o e x c i t a t i o n (see T a b l e I ) . Table I P r o b a b i l i t i e s o f C o o p e r a t i v e S i S t a t e s ( P ) and S 2 S t a t e ( P 2 ) Formation as a R e s u l t o f TTA i n S o l u t i o n s a t Room Temperature (6J


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Notes: Π P and P 2 have been c a l c u l a t e d f o r one a n n i h i l a t i o n a c t o f two t r i p l e t m o l e c u l e s . 2) F o r t h e P 2 c a l c u l a t i o n i t was assumed t h a t p r o b a b i l i t i e s o f r a d i a t i v e S 2 > S t r a n s i t i o n a r e t h e same f o r one-photon o r c o o p e r a t i v e mechanism o f S 2 s t a t e e x c i t a t i o n . P r o b a b i l i t i e s of cooperative S i - e x c i t e d molecule formation ( P ) f o r m e t a l l o p o r p h y r i n s range from 0.1 t o 0.25 p e r one a c t o f TTA. A t the same time p r o b a b i l i t i e s o f S 2 s t a t e f o r m a t i o n from TTA (Po) which have been determined w i t h the assumption t h a t t h e ADF and the PF a r e e m i t t e d from i d e n t i c a l s t a t e s t u r n e d o u t t o be c o n s i d e r a b l y l e s s . T h i s d i f f e r e n c e between P and P 2 remained u n e x p l a i n e d s i n c e f o r two T i m o l e c u l e s t h e t o t a l e x c i t a t i o n energy i s s i m i l a r t o t h e S s t a t e energy as f a r as m e t a l l o p o r p h y r i n s a r e c o n c e r n e d . Thus one may e x p e c t t h a t some quasi r e s o n a n t upper s i n g l e t s t a t e i s being p r e d o m i n a n t l y g e n e r a t e d , i . e . , cooperative e x c i t a t i o n of s i n g l e t states takes place a c c o r d i n g t o t h e scheme 2 T i s > S i and c o r r e s p o n d i n g l y a = P2. In t h i s r e p o r t t h e TTA p r o c e s s has been s t u d i e d t a k i n g i n t o account new e x p e r i m e n t a l data i n d i c a t i n g t h a t t h e A0F e m i t t e d from m e t a l l o p o r p h y r i n upper e l e c t r o n i c s t a t e s i s o f d i m e r i c n a t u r e . Moreover low v a l u e s o f P 2 o b t a i n e d i n (6) can be e x p l a i n e d by the l e s s e r p r o b a b i l i t y o f dimer s i n g l e t s t a t e s e m i t t i n g i n comparison w i t h t h e monomer. But t r u e p r o b a b i l i t i e s o f S s t a t e f o r m a t i o n from TTA p r o c e s s e s may be q u i t e h i g h . We have been a b l e t o e s t a b l i s h s i m u l t a n e o u s r e l a t i o n s between d i f f u s i o n parameters and a n n i h i l a t i o n c h a r a c t e r i s t i c s o b t a i n e d from s p e c t r a l k i n e t i c measurements. We have c a r r i e d o u t a c o m p a r a t i v e study o f S^ s t a t e f l u o r e s c e n c e e m i t t e d from s e v e r a l m e t a l l o p o r p h y r i n s : Zn tetraphenylporphiη (Zn T P P ) , Zn - t e t r a b e n z p o r p h i n (Zn TBP) and Cd TBP f o r d i r e c t one-quantum e x c i t a t i o n and f o r a n n i h i l a t i n g twoquantum e x c i t a t i o n . Low c o n c e n t r a t i o n (C = 1 - 2 X 10-6|v|) a

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P O R P H Y R I N S : E X C I T E D STATES A N D D Y N A M I C S

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s o l u t i o n s have been s t u d i e d a t room t e m p e r a t u r e . S p e c t r a l luminescence measurements have been c a r r i e d out w i t h the Raman s p e c t r o m e t e r "Ramalog 4" and s p e c t r o f l u o r i m e t e r "Spex F l u o r o l o g " (more d e t a i l e d procedure o f measurements i s d e s c r i b e d i n (2)). The ADF has been measured i n deoxygenated s o l u t i o n s w i t h c o n t i n u o u s e x c i t a t i o n o f e i t h e r a r g o n , k r y p t o n o r helium-neon l a s e r s . The e x c i t i n g wavelengths corresponded t o t h e bands o f S > Si m e t a l l o p o r p h y r i n a b s o r p t i o n ( e x c i t a t i o n w a v e l e n g t h s : x = 5 1 4 . 5 ; 5 3 0 . 9 ; 568.2 nm f o r ZnTPP and x = 5 6 8 . 2 ; 632.8 nm f o r ZnTBP and CdTBP). A p p l i c a t i o n o f c o n t i n u o u s a n t i - S t o k e s e x c i t a t i o n makes i t p o s s i b l e to r e c o r d t h e e m i s s i o n from the S 2 s t a t e when the PF S2 > S i s absent ( 2 h Prompt S 2 > S f l u o r e s c e n c e has been measured a t d i r e c t S > S e x c i t a t i o n ( k r y p t o n l a s e r : λ χ = 4 0 6 . 7 ; 413.1 nm) o f oxygenated s o l u t i o n s ( i n t h i s case t h e ADF i s absent due t o s t r o n g quenching o f t r i p l e t s t a t e s by oxygen (2)). We have found t h a t e m i s s i o n s p e c t r a o f the c o o p e r a t i v e l y e x c i t e d ADF from upper e l e c t r o n i c s t a t e s and o f t h e one quantum e x c i t e d PF a r e d i f f e r e n t . ADF spectrum i s s h i f t e d i n the longwave d i r e c t i o n w i t h r e s p e c t t o PF spectrum (see T a b l e I I ) . The s h i f t e f f e c t depends on s o l v e n t t y p e . ADF s p e c t r a l s h i f t i s most c o n s i d e r a b l e and c o m p r i s e s 500 cm** (see F i g . 1) f o r the case o f ZnTPP i n decane. In p r i n c i p l e , f l u o r e s c e n c e s p e c t r a from s h o r t l i v e d upper m e t a l l o p o r p h y r i n s t a t e s i n s o l u t i o n can be s h i f t e d i n the longwave d i r e c t i o n w i t h v i b r a t i o n a l energy r e l a x a t i o n a t the c o s t o f short-wave e x c i t a t i o n ( 7 ) . However, i n our c a s e the energy d i f f e r e n c e o f a n n i h i l a t i n g and d i r e c t e x c i t a t i o n was s l i g h t U 1 0 cm-1) and c o u l d not l e a d t o such c o n s i d e r a b l e d i f f e r e n c e o f ADF and PF s p e c t r a . The observed d i f f e r e n c e can be e x p l a i n e d i n t h e f o l l o w i n g way: ADF t a k e s p l a c e i n b i o m o l e c u l a r complexes w h i l e t h e PF i s o r d i n a r y monomer f l u o r e s c e n c e . A t p r e s e n t i t i s u n i v e r s a l l y acknowledged t h a t TTA as t r i p l e t - t r i p l e t energy t r a n s f e r i s caused by exchange i n t e r a c t i o n o f e l e c t r o n s i n b i m o l e c u l a r complexes which t a k e s p l a c e d u r i n g m o l e c u l a r d i f f u s i o n e n c o u n t e r s i n s o l u t i o n ( i n gas phase m o l e c u l a r c o l l i s i o n s a r e examined; i n c r y s t a l s - t r i p l e t e x c i t o n d i f f u s i o n i s the r e s p o n s i b l e a n n i h i l a t i o n p r o c e s s ( 8 - 1 0 ) ) . No d o u b t , i n t e r a c t i o n o f m o l e c u l a r p a r t n e r s i n a d i f f u s i o n complex may l e a d t o the change o f p r o b a b i l i t i e s o f f l u o r e s c e n t s t a t e r a d i a t i v e and n o n r a d i a t i v e d e a c t i v a t i o n . N e v e r t h e l e s s , i t i s n o r m a l l y c o n s i d e r e d t h a t as a r e s u l t o f TTA the energy o f two t r i p l e t p a r t n e r s i s accumulated i n one m o l e c u l e which e m i t s the ADF ( 1 1 ) . I n t e r a c t i o n w i t h the second d e a c t i v a t e d p a r t n e r i s not taken i n t o a c c o u n t , i . e . i t i s assumed t h a t the ADF i s o f monomer n a t u r e and i t s spectrum c o i n c i d e s w i t h the PF s p e c t r u m . A p p a r e n t l y the l a t t e r may be t r u e when t h e ADF t a k e s p l a c e from S i s t a t e the l i f e t i m e o f which ( τ - 1 0 - 8 - 10-9 ) i s much l o n a e r than the l i f e t i m e o f d i f f u s i o n e n c o u n t e r complex (~ 10-10 . 1 0 - H s i n l i q u i d s o l u t i o n s ) . As a m a t t e r o f f a c t we have not observed c o n s i d e r a b l e ADF and PF s p e c t r a l d i f f e r e n c e when S^ métallo0

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Gouterman et al.; Porphyrins ACS Symposium Series; American Chemical Society: Washington, DC, 1986. e x

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Right Side: (2) S 2 > S Q f l u o r e s c e n c e spectrum ( x = 4 1 3 . 1 nm); (3) spectrum o f a n n i h i l a t i n g f l u o r e s c e n c e ( x = 5 3 0 . 9 nm).

Figure 1 Left Side: ( 1 ) S p l i t t i n g of e x c i t e d s i n g l e t s t a t e s in metalloporphyrin sandwich dimer o f symmetry ( a c c o r d i n g t o the data ( 1 6 ) .


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porphyrin fluorescence i s studied ( s i = 2 ns f o r Zn TPP and Zn TBP ( 7 , 1 2 ) ) . F o r Zn TPP i n t o l u e n e the s h i f t o f - 30 c m ' was w i t h i n the range of e x p e r i m e n t a l e r r o r . S2 s t a t e l i f e t i m e o f the observed m e t a l l o p o r p h y r i n s ( 2 = 2 - 5 ps ( 7 , 1 2 ) ) i s c o n s i d e r a b l y s h o r t e r than encounter complex l i f e t i m e ( T ) . Time of T which may be t r e a t e d as the time o f c o e x i s t a n c e of two m o l e c u l e s i n a s o l v e n t cage can be e s t i m a t e d p r o c e e d i n g from t h e t h e o r y of d i f f u s i o n i n s o l u t i o n s ( 1 3 ) : T

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(1)

where d = s o l v e n t m o l e c u l a r d i a m e t e r , D/^ = c o e f f i c i e n t o f the molecule-partner r e l a t i v e d i f f u s i o n . In our c a s e , D/^ = 2D, where D = c o e f f i c i e n t of m e t a l l o p o r p h y r i n m o l e c u l a r d i f f u s i o n which may be e s t i m a t e d by m o l e c u l a r r a d i u s r and s o l v e n t v i s c o s i t y η u s i n g the S t o k e s - E i n s t e i n f o r m u l a : D =

kT 6DTir

(2)

P r o c e e d i n g from the m o l e c u l a r volume Y = 400 cm /mole (12) and X - r a y d a t a (]A) and assuming t h a t r = 0.55 nm we g e t D = 4 X 10-6 c m / s e c , the c o e f f i c i e n t o f m e t a l l o p o r p h y r i n d i f f u s i o n a t room temperature i n s o l v e n t s w i t h t y p i c a l v i s c o s i t y η = 10-3 g cm-1 s e c - 1 . Assuming t h a t d = 0.5 nm ( t y p i c a l v a l u e f o r t y p i c a l s o l v e n t s ) we g e t from (1) x = 5.10-Hs » 2 Thus we may c o n s i d e r t h a t ADF from So s t a t e s t a k e s p l a c e i n a d i m e r i c complex which d i s s o c i a t e s a f t e r d e a c t i v a t i o n o f the c o o p e r a t i v e l y e x c i t e d S^ s t a t e . As i s known, the t r i p l e t and s i n g l e t t e t r a p y r r o l i c pigment s t a t e s a r e caused by e x c i t a t i o n of d e l o c a l i z e d it e l e c t r o n s o f the h e t e r o a r o m a t i c m a c r o c y c l e ( 1 5 J . The most f a v o u r a b l e s t r u c t u r e o f d i m e r i c complexes f o r m e t a l l o p o r p h y r i n TTA seems t o be a sandwich dimer as i n the case when m o l e c u l a r o r i e n t a t i o n o f p l a n e t o p l a n e ττ e l e c t r o n i c s h e l l s reaches the maximum o v e r l a p . Quantum c h e m i s t r y c a l c u l a t i o n s o f m e t a l l o p o r p h y r i n dimers i n d i c a t e s t h a t f o r the dimeric emission process the S s t a t e i s s p l i t i n t o s t a t e s of h i g h e r energy (S£) and lower energy ( S j ) . In the case o f a sandwich dimer o f D ^ symmetry, the f o l l o w i n g s t a t e s are seen: 3

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A t room temperature the s p l i t t i n g energy v a l u e ΔΕ (S$ S2) i s c o n s i d e r a b l y h i g h e r than t h a t o f thermal energy k t and f l u o r e s c e n c e from the lower S£ s t a t e w i l l t a k e p l a c e i n the d i m e r i c complex. In t h i s case f o r ADF the s p e c t r a l s h i f t w i t h r e s p e c t t o the PF spectrum i s determined by d i f f e r e n c e o f S s t a t e energy i n t h e monomer and S s t a t e energy i n the d i m e r . However, f o r d i m e r i c e m i s s i o n p r o c e s s e s the S^ s t a t e i s o n l y 2

2



124

s l i g h t l y s p l i t (ΔΕ ( S I + S j ) « kT except f o r v e r y s h o r t d i s t a n c e s between the p a r t n e r s ( 1 6 ) ) . T h i s may be a l s o a reason f o r the i n s i g n i f i c a n c e o f s p e c t r a l d i f f e r e n c e between the ADF and t h e PF from S i m e t a l l o p o r p h y r i n s t a t e s . The f o l l o w i n g c o n c l u s i o n o f the t h e o r y (16) i s e x t r e m e l y i m p o r t a n t . The r a d i a t i v e t r a n s i t i o n S > S i n a sandwich dimer i s f o r b i d d e n . In case o f a dimer o f D ^ symmetry, the t r a n s i t i o n S (4Eg) > S Q ( A i g ) i s f o r b i d d e n because o f p a r i t y . There i s no p r i n c i p l e d i f f e r e n c e i n the s p l i t t i n g nature o f S and S i s t a t e s f o r sandwich type dimers w i t h l e s s e r than D ^ symmetry and the S > S t r a n s i t i o n remains q u a s i f o r b i d d e n . T h i s makes i t p o s s i b l e t o e x p l a i n low P v a l u e s o b t a i n e d i n [16) by a decrease o f the S > S Q t r a n s i t i o n r a d i a t i v e p r o b a b i l i t y , i . e . , by d e c r e a s i n g o r S > S f l u o r e s c e n c e quantum y i e l d i n d i m e r i c TTA complexes. In t h e case of non-sandwich dimer s t r u c t u r e s w i t h l o c a t i o n o f s u b u n i t s i n one p l a n e , the S s t a t e a l s o i s s p l i t i n t o two s t a t e s ( h i g h 2 B and low 2 B 3 M ) . However, two r a d i a t i v e t r a n s i t i o n s S ( B ) > S and S 2 ( B 3 ) > S a r e a l l o w e d . In t h i s case t h e observed decrease i n ADF i n t e n s i t y cannot be e x p l a i n e d . Dependence o f ADF s p e c t r a l s h i f t on s o l v e n t type (see T a b l e I I ) a l s o c o n f i r m s the c o r r e c t n e s s o f a TTA complex sandwich s t r u c t u r e : the s h i f t d e c r e a s e s when s o l v e n t s which a r e a b l e t o c o o r d i n a t e w i t h metal c e n t r a l atoms a r e u s e d . H e r e , an e x t r a - l i g a n d i s b e i n g c r e a t e d perpendicular to the plane of porphyrin r i n g ( p y r i d i n e , d i m e t h y l f o r m a m i d e ) . E x t r a - l i g a n d presence c r e a t e s s t e r i c o b s t a c l e s f o r p o r p h y r i n m a c r o c y c l e s t o draw t o g e t h e r and as a r e s u l t o f t h i s i n t e r a c t i o n between t h e s u b u n i t s the c o r r e s p o n d i n g s p l i t t i n g energy A E ( S £ - S ) d e c r e a s e s . A l o n g w i t h t h e e x p e r i m e n t a l l y determined ADF s p e c t r a l s h i f t i t has been found t h a t f o r ZnTPP some ADF s p e c t r a l narrowing t a k e s p l a c e as compared t o the PF s p e c t r a (see T a b l e I I ) . I t seems t h a t the inhomogenous b r o a d e n i n g caused by d i f f e r e n t l o c a t i o n s o f the phenyl r i n g s w i t h r e s p e c t t o the p o r p h y r i n m a c r o c y c l e p l a n e (17) has i t s impact on the w i d t h o f t e t r a - m e s o - p h e n y l p o r p h y r i n s p e c t r a l bands. I t i s e v i d e n t t h a t when two ZnTPP m o l e c u l e s converge i n a sandwich dimer the freedom o f phenyl r i n g r o t a t i o n i s r e s t r i c t e d and t h i s decreases inhomogeneous b r o a d e n i n g . With e x t r a - l i g a n d presence which o b s t r u c t s c l o s e convergence o f m a c r o c y c l e p l a n e s the r o t a t i o n a l freedom does not decrease and t h a t i s why f o r ZnTPP i n p y r i d i n e s p e c t r a l n a r r o w i n g i s not o b s e r v e d . In g e n e r a l d e a c t i v a t i o n o f t r i p l e t e x c i t e d m o l e c u l e s i s determined by the k i n e t i c e q u a t i o n : 2

0

2

2

2

0

2

2


2

0

2

2

2

U

0

U

2 u

0

2

d [T ] I -at—

2

k [T ] m l

-

where k i s the t o t a l r a t e c o n s t a n t i m p u r i t y q u e n c h i n g , where k = k the n a t u r e o f e x c i t e d s i n g l e t s t a t e and i d e a s c o n c e r n i n g TTA mechanisms m

m

a

•

k

a

[T ] I

o f monomolecular decay and TTA. Data o b t a i n e d about c r e a t i o n d u r i n g TTA p r o c e s s e s which have been d e r i v e d on the


8.

125



b a s i s o f a n a l y s e s o f magnetic f i e l d e f f e c t s on t h e ADF (see ( 8 , 9 ) and r e f e r e n c e s t o them) make i t p o s s i b l e t o imagine a scheme ôT~ p o r p h y r i n TTA i n t h e f o l l o w i n g way:

k T

l

6

(S S ) 1

2

1

^(SiSoJ-^Z-ySi

0

+ s

0


k-d k

Ψ (S S ) 0

0

f2

k

fl

1

Ψ + h

2

(S S ) 0

0

+ h

λ

S

0

+ h

χ

Here ( Τ ^ ) * i s t h e e n c o u n t e r complex o f two t r i p l e t m o l e c u l e s o r , i n o t h e r words, a t r i p l e t p a i r w i t h energy 2E7. c a p a b l e o f d i s s o c i a t i n g back i n t o two t r i p l e t m o l e c u l e s o r wnich may undergo i n t r a c o m p l e x r e l a x a t i o n ( s p i n exchange, v i b r a t i o n a l relaxation, electron transfer) creating, for instance, either s i n g l e t , o r t r i p l e t , o r q u i n t e t dimers ( 8 , 9 ) , o r i o n - r a d i c a l p a i r s (18).

( 2 S o ) i n t h e scheme (4) denotes s i n g l e t e x c i t e d dimer and X i s any o t h e r e n e r g e t i c a l l y a l l o w e d s t a t e o f t h e r e l a x a t e d triplet pair. I n t e r m e d i a t e s t a g e s o f t r i p l e t p a i r r e l a x a t i o n may be c o m p l i c a t e d b u t t h e o n l y i m p o r t a n t t h i n g t o be mentioned i s t h a t one o f i t s f i n a l s t a g e s may be once a g a i n a m o l e c u l e i n t h e T^ s t a t e (both through S i s t a t e and b y p a s s i n g i t ( 8 ) ) . A n a l y s i s o f k i n e t i c e q u a t i o n s f o r t h e scheme (4) t a k i n g i n t o account s t e a d y - s t a t e concentrations leads to the f o l l o w i n g r e l a t i o n between t h e TTA r a t e c o n s t a n t k and c o n s t a n t k d , t h e d i f f u s i o n encounter r a t e : I k = k [ I - 2 (Q φ - R ) ] (5) a d t 1

s

a

where Q =

(k

T

ρ

+k I

k 4 3 k + k +k 4 5 6

i s t h e p r o b a b i l i t y o f S s t a t e c r e a t i o n from t h e t r i p l e t p a i r ( T i n ) * , i . e . , p r o b a b i l i t y of Si state c r e a t i o n per s i n g l e e n c o u n t e r o f two t r i p l e t m o l e c u l e s : x


(6)


126

k R =

ρ

(2k

-d

+k

3

6 k + k +k 4 5 6

(7)

i s p r o b a b i l i t y o f T i s t a t e c r e a t i o n from t h e t r i p l e t p a i r b y p a s s i n g the S i s t a t e :

τ

=

ρ

k

-d

+ k

I

+k 3

I

(8)


i s l i f e t i m e o f n o n - r e l a x a t e d t r i p l e t p a i r (Τι"Γι)*: #t = quantum y i e l d o f S i / v v * T"i i n t e r s y s t e m crossing E q u a t i o n (5) r e f l e c t s a well-known e x p e r i m e n t a l f a c t t h a t TTA r a t e c o n s t a n t i n l i q u i d s o l u t i o n s i s u s u a l l y l e s s than t h a t o f d i f f u s i o n r a t e ( f o r t e t r a p y r r o l i c pigments, f o r i n s t a n c e , k = ( 0 . 2 - 0.4) kd [ 1 9 ] . Q probability i s linked with P p r o b a b i l i t y of S i excited m o l e c u l e c r e a t i o n a t a n n i h i l a t i o n o f two t r i p l e t m o l e c u l e s {§) by the s i m p l e r e l a t i o n : a

a

P k a

a

= Q kd

(9)

Some q u a n t i t a t i v e c o n c l u s i o n s on TTA p r o c e s s e s can be made a f t e r e x a m i n a t i o n o f t h e c o n c r e t e case o f ZnTPP - a p o r p h y r i n which i s w i d e l y used i n photochemical r e s e a r c h . F o r ZnTPP i n t o l u e n e kg = 3 . 1 0 9 - 1 - s e c - m o l e - 1 ( 1 9 ) , P = 0.24 ( 6 ) , kd = 1.1 ' 1010 . ι . sec «mole-l ( c a l c u l a t e d a c c o r d i n g ί ο t h e s t a n d a r d e q u a t i o n kn = 8RT/3 η ( 1 0 , 1 3 ) ) . Then from (5) and (9) we g e t Q = 0.065 and R = 1.4. Combined a n a l y s i s o f t h e e q u a t i o n s (6) and (7) t a k i n g i n t o account c o n c r e t e p r o b a b i l i t y v a l u e s f o r Q and R and obvious i n e q u a l i t i e s : a

ki > 0

and 0 £ k4

+

k6 £ k4

+

k5

+

k6

l e a d s t o the f o l l o w i n g r e l a t i o n s between k i and and t h e r e v e r s e d i f f u s i o n r a t e c o n s t a n t k_d =

(10)

T

k

3 > 3.5 k i

0.43 k_ and a l s o

:

constants

(ID

< k i + k3 < 1.1 kd

d

- 1 c

(12)

k k

4 + k +k 4 5 6

Emission Resulting from Triplet-Triplet Annihilation - American

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