Phosphorescence Decay and Dynamics in Polymer Solids

Chapter 8

Phosphorescence Decay and Dynamics in Polymer Solids Kazuyuki Horie

Downloaded by PURDUE UNIV on June 28, 2016 | http://pubs.acs.org Publication Date: November 30, 1987 | doi: 10.1021/bk-1987-0358.ch008

Institute of Interdisciplinary Research, Faculty of Engineering, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153, Japan

Non-exponential phosphorescence decay is frequently observed for various aromatic chromophores molecularly dispersed in polymer matrices. Various possible mechanisms for non-exponential decay are reviewed, and a dynamic quenching mechanism by polymer matrices including the effect of a time-dependent transient term in the rate coefficient is discussed in some detail. The biphotonic t r i p l e t - t r i p l e t annihilation mechanism is also introduced for the non-exponential decay under high-intensity and/or repeated laser irradiation. The i n f l u e n c e o f m o l e c u l a r s t r u c t u r e and motion o f polymer m a t r i c e s on t h e p h o t o p h y s i c a l and photochemical p r o c e s s e s o f m o l e c u l a r l y d i s p e r s e d chromophores i s a t o p i c o f i n c r e a s i n g i n t e r e s t . There a r e s e v e r a l reasons f o r t h i s a c t i v i t y . Polymer m a t r i c e s have been c o n s i d e r e d as c o n v e n i e n t media f o r s p e c t r o s c o p i c i n v e s t i g a t i o n s o f e x c i t e d t r i p l e t s t a t e s over wide temperature ranges, and c o n v e r s e l y , the use o f p h o t o p h y s i c a l l y d e t e c t a b l e probes a l l o w s t h e i n v e s t i g a t i o n o f t h e s t r u c t u r e o f polymer m a t r i c e s and o f p h o t o p h y s i c a l t r a n s i t i o n s connected w i t h changes i n the m o b i l i t y o f c e r t a i n s t r u c t u r a l u n i t s . Another reason f o r such s t u d i e s i s connected w i t h the p r a c t i c a l i n t e r e s t s c o n c e r n i n g t h e r e a c t i v i t y o f l o w - m o l e c u l a r w e i g h t compounds embedded i n polymer m a t r i c e s i n photomemory and p h o t o s e n s i t i v e polymer systems, and o f t h e r e a c t i v i t y o f a d d i t i v e s admixed t o polymers as s t a b i l i z e r s a g a i n s t p h o t o d e g r a d a t i o n and thermal d e g r a d a t i o n . The main d i f f e r e n c e between s o l i d - s t a t e r e a c t i o n s and those i n s o l u t i o n i s t h a t o f freedom o f m o l e c u l a r motion (1-3) due t o r e s t r i c t i o n o f m o b i l i t y o f r e a c t a n t s i n s o l i d s . Another i m p o r t a n t f e a t u r e i s the heterogeneous p r o g r e s s o f r e a c t i o n s (3,4) f r e q u e n t l y observed i n s o l i d s t a t e s due t o the m i c r o s c o p i c a l l y heterogeneous s t a t e s o f a g g r e g a t i o n o r f r e e volume d i s t r i b u t i o n o f t h e r e a c t i o n media. I n t h e case o f p o l y ( m e t h y l m e t h a c r y l a t e ) (PMMA), which i s an o r g a n i c g l a s s and i s u s u a l l y r e g a r d e d as an i n e r t m a t r i x f o r p h o t o p h y s i c a l and photochemical p r o c e s s e s , a marked d e v i a t i o n from

0097-6156/87/0358-0083$06.00/0 © 1987 American Chemical Society

Hoyle and Torkelson; Photophysics of Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

84

PHOTOPHYSICS OF POLYMERS

the e x p o n e n t i a l decay o f benzophenone phosphorescence has been o b s e r v e d ( 5 , 6 ) . A r r h e n i u s p l o t s o f phosphorescence i n t e n s i t y ( 7 ) , l i f e t i m e and d e p o l a r i z a t i o n (5,6,8,9) o f v a r i o u s chromophores i n polymer m a t r i c e s showed b r e a k s a t temperatures c o r r e s p o n d i n g t o t h e g l a s s t r a n s i t i o n (T ) and s u b g l a s s t r a n s i t i o n s (Τ , , T_ , Τ ) o f t h e m a t r i x polymers. I n the p r e s e n t paper, we d i s c u s s m a i n l y the n o n - e x p o n e n t i a l decay o f phosphorescence and i t s o r i g i n i n polymer m a t r i c e s . The e f f e c t o f m u l t i - p h o t o n p r o c e s s e s on the decay c u r v e s i s a l s o discussed.


D e v i a t i o n s o f Phosphorescence Decay from E x p o n e n t i a l i t y Solids

i n Polymer

The g e n e r a l p h o t o p h y s i c a l b e h a v i o r o f e x c i t e d t r i p l e t s t a t e s i s i n v a r i o u s t e x t b o o k s (10,11). The main p r o c e s s e s f o r a chromophore, A, a r e the f o l l o w i n g : 3 * A

*

A + h

V

phosphorescence (k .j.)

(D

p

nonradiative

deactivation

(2)

(kjj)

3 * A + Β

A +

3 * Β

triplet

energy t r a n s f e r

(3)

3 * A + A

A +

3 * A

triplet

energy m i g r a t i o n

(4)

3 * 3 * A + A

1* > A + A

triplet-triplet

(5)

annihilation

T r i p l e t - t r i p l e t energy t r a n s f e r was f i r s t c l e a r l y demonstrated by T e r e n i n and Ermolaev (12,13) who showed the phosphorescence o f naphthalene ( a c c e p t o r , B) r e s u l t a n t upon e x c i t a t i o n o f benzophenone (donor, A) f o l l o w e d by t r i p l e t energy t r a n s f e r from A t o Β i n r i g i d s o l u t i o n a t 77 K. T r i p l e t energy t r a n s f e r r e q u i r e s m o l e c u l a r o r b i t a l o v e r l a p between the donor and a c c e p t o r , and the t r a n s f e r e f f i c i e n c y depends on the energy gap between the energy l e v e l s o f the e x c i t e d t r i p l e t s t a t e s , E , o f the donor and a c c e p t o r . Such energy t r a n s f e r due t o the e l e c t r o n exchange i n t e r a c t i o n was t h e o r i z e d by Dexter (14), a f t e r whom the mechanism i s named. T

Stern-Volmer Model. When the chromophores a r e s u f f i c i e n t l y m o b i l e as i n f l u i d s o l u t i o n , the b i m o l e c u l a r quenching p r o c e s s o f A by a quenching m o l e c u l e , B, i n c l u d i n g the t r i p l e t energy t r a n s f e r and some c o l l i s i o n a l quenching, w i l l r e s u l t i n the s i n g l e e x p o n e n t i a l 3 * A + Β

>

A + Β

t r i p l e t quenching

(k^)

(6)

phosphorescence decay o f the donor chromophore, A. Thus, t h e phosphorescence decay p r o f i l e , l ( t ) , i s e x p r e s s e d by eq (7) I ( t ) = Cexp(-t/x) = C e x p [ - t ( l / x ^ + k ^ [ B ] ) ]

(7)


8.

HORIE

Phosphorescence Decay and Dynamics

85

where C i s a c o n s t a n t , and τ i s a s i n g l e l i f e t i m e , w h i c h i s r e l a t e d to t h e phosphorescence l i f e t i m e i n the absence o f quencher, = l / ( k p + k-rrj,), quenching r a t e c o n s t a n t , k , and the quencher c o n c e n t r a t i o n , [ B ] . The r e l a t i v e phosphorescence y i e l d , I / I , d e f i n e d as t h e r a t i o o f t h e y i e l d s i n t h e presence o f a c c e p t o r t o t h a t i n i t s absence, has a s o - c a l l e d Stern-Volmer c o n c e n t r a t i o n dependence ( 1 5 ) . τ

t

ο

I/I


n

e

T

ο

= 1/(1 + k τ [Β]) qο

(8)

P e r r i n Model. A t the o t h e r extreme, P e r r i n (16) c o n s i d e r e d t h e case where t h e donor and a c c e p t o r m o l e c u l e s a r e immobile, and energy t r a n s f e r o c c u r s i n s t a n t a n e o u s l y when t h e two m o l e c u l e s l i e w i t h i n a c r i t i c a l t r a n s f e r d i s t a n c e , R , and does n o t o c c u r a t a l l a t l a r g e intermolecular separations. The decay f u n c t i o n f o r donor phosphorescence i s g i v e n by I(t)

= 1

(t=0)

I(t)

= exp [-(t/τ ) - ( C / C ) ]

(9) n

O

D

(t>0)

O

where C i s t h e a c c e p t o r c o n c e n t r a t i o n , C i s a parameter c a l l e d t h e c r i t i c a l t r a n s f e r c o n c e n t r a t i o n (which i s d e f i n e d as t h e r e c i p r o c a l of t h e s p h e r i c a l volume o f t h e r a d i u s R ) . The r e l a t i v e y i e l d o f donor phosphorescence i s g i v e n by eq (10? f o r t h i s c a s e . I / I = exp(-C /C ) ο b o

(10)

D

I n o k u t i - H i r a y a m a Model. The P e r r i n model i s t o o s i m p l i f i e d , a l t h o u g h i t i s c o n v e n i e n t f o r p r a c t i c a l use. The s t a t i c t r i p l e t t r i p l e t energy t r a n s f e r between immobile chromophores d i s p e r s e d i n s o l i d s can be w e l l d e s c r i b e d by t h e I n o k u t i - H i r a y a m a t h e o r y (17). Based on t h e Dexter mechanism, w i t h a d i s t a n c e - d e p e n d e n t r a t e c o e f f i c i e n t f o r t r i p l e t energy t r a n s f e r , a n o n - e x p o n e n t i a l decay f u n c t i o n f o r donor phosphorescence i n a r i g i d s o l u t i o n was d e r i v e d as I(t)

= exp[-(t/x ) - r" (C /C )G(e t/x )] ο B o ο 3

T

n

where γ i s r e l a t e d t o D e x t e r ' s Ύ y

eh

q u a n t i t i e s by

= 2R IL ο

(12)

= 2ïïk /h'F (E)£ (E)dE Α ρ 2

ο

(11)

A

0

(13)

G(z) = Unz) +1.732(lnz) +5.934(lnz)+5.445 3

2

(14)

Mataga et al. ( 1 8 ) s t u d i e d energy t r a n s f e r from t h e e x c i t e d t r i p l e t of benzophenone t o naphthalene by l a s e r f l a s h p h o t o l y s i s a t 77K and showed t h a t t h e n o n - e x p o n e n t i a l decay c u r v e s o f t h e benzophenone t r i p l e t obey t h e I n o k u t i - H i r a y a m a e q u a t i o n ( e q ( 1 1 ) ) . I n o k u t i and Hirayama (17) themselves compared t h e d a t a on t r i p l e t - t r i p l e t t r a n s f e r between c e r t a i n a r o m a t i c m o l e c u l e s o b t a i n e d by T e r e n i n and Ermolaev w i t h eq (11) and r e p o r t e d t h a t a good f i t was found w i t h an a p p r o p r i a t e c h o i c e o f t h e parameters C^and γ.



86


Thus, i t i s thought t h a t the n o n - e x p o n e n t i a l phosphorescence decay o f donor i n the presence o f an a c c e p t o r i n an i m m o b i l i z e d system i s w e l l e x p l a i n e d by the I n o k u t i - H i r a y a m a model based on t h e s t a t i c t r i p l e t - t r i p l e t energy t r a n s f e r mechanism. T h i s model e x p e c t s a s i n g l e - e x p o n e n t i a l decay f o r the phosphorescence o f a chromophore i n t h e absence o f a c c e p t o r m o l e c u l e s . However, t h e phosphorescence decays o f o r g a n i c m o l e c u l e s m o l e c u l a r l y d i s p e r s e d i n polymer m a t r i c e s a r e known t o be n o n - e x p o n e n t i a l i n some cases even i n the absence o f o t h e r a d d i t i v e s . C o n s e q u e n t l y , o t h e r r e a s o n s s h o u l d be c o n s i d e r e d f o r such d e v i a t i o n s from e x p o n e n t i a l i t y . The d e v i a t i o n from a s i n g l e e x p o n e n t i a l c u r v e f o r the phosphor escence decay o f some chromophores d i s s o l v e d i n p l a s t i c s was f i r s t noted by O s t e r et al.(19) N o n e x p o n e n t i a l decay c u r v e s were o b t a i n e d f o r n a p h t h a l e n e and t r i p h e n y l e n e phosphorescence i n p o l y ( m e t h y l m e t h a c r y l a t e ) (PMMA) a t room temperature ( 2 0 ) , w h i l e e x p o n e n t i a l decays a t room temperature were o b s e r v e d i n PMMA f o r a n t h r a c e n e t r i p l e t ( 2 1 ) , pyrene ( 2 2 ) , and coronene phosphor escence ( 2 0 ) . Graves et al. (23) a n a l y z e d the temperature dependence o f phosphorescence parameters f o r a number o f a r o m a t i c hydrocarbons i n PMMA from 77 t o 400K and suggested the e x i s t e n c e o f i n t e r m o l e c u l a r t h e r m a l l y a s s i s t e d energy t r a n s f e r from t h e chromophore t o the h o s t p l a s t i c i n the h i g h e r temperature r e g i o n . E l - S a y e d et al. (20) i n t e r p r e t e d the n o n - e x p o n e n t i a l decay p r o f i l e s o f n a p h t h a l e n e and t r i p h e n y l e n e inPMMA a t room temperature i n terms o f a 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 mechanism. The d e c r e a s e of the e x t e n t o f n o n - e x p o n e n t i a l b e h a v i o r w i t h d e c r e a s i n g e x c i t a t i o n i n t e n s i t y and the o b s e r v a t i o n o f d e l a y e d f l u o r e s c e n c e were the bases of t h e i n t e r p r e t a t i o n . They suggested t h a t the n o n - e x p o n e n t i a l decays were o b s e r v e d f o r m o l e c u l e s h a v i n g f i r s t - o r d e r l i f e t i m e s o f the o r d e r o f s e v e r a l seconds. However, coronene w i t h a t r i p l e t l i f e t i m e o f 8.5s gave an e x p o n e n t i a l decay. They a l s o suggested r a t h e r h i g h c o n c e n t r a t i o n s o f the e x c i t e d t r i p l e t s t a t e o f t h e chromophore based on the d i f f u s i o n - c o n t r o l l e d 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 mechanism. L a t e r , J a s s i m et al. (24) proposed a n o t h e r type o f 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 mechanism f o r the none x p o n e n t i a l phosphorescence decay c o n s i s t i n g o f energy t r a n s f e r from the chromophore t o the m a t r i x polymer, t r i p l e t energy m i g r a t i o n through the m a t r i x polymer, and 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 between the chromophore t r i p l e t and the polymer t r i p l e t . H o r i e and M i t a (5) measured the phosphorescence decay o f benzo phenone i n PMMA o v e r a wide temperature range (80 t o 433K). N o n - e x p o n e n t i a l decays were o b s e r v e d f o r temperatures between T ( o n s e t o f e s t e r s i d e group r o t a t i o n o f the m a t r i x polymer) and Τ ( g l a s s t r a n s i t i o n t e m p e r a t u r e ) , and the decay p r o f i l e was ^ independent o f t h e i n t e n s i t y o f the e x c i t a t i o n l a s e r p u l s e over a 100 t i m e s change o f t h e i n t e n s i t y ( 2 5 ) . Thus, the n o n - e x p o n e n t i a l decay was a t t r i b u t e d t o a s i n g l e photon p r o c e s s comprised o f i n t e r m o l e c u l a r dynamic quenching o f the benzophenone t r i p l e t by e s t e r groups i n the s i d e c h a i n o f PMMA. D e t a i l e d d i s c u s s i o n o f t h e dynamic quenching mechanism w i l l be g i v e n i n the n e x t s e c t i o n . I t i s noteworthy t h a t the t r i p l e t decay c u r v e s a t room temperature o f v a r i o u s chromophores i n PMMA o b s e r v e d i n t h e l i t e r a t u r e can be d i v i d e d a p p r o x i m a t e l y i n t o two groups a c c o r d i n g t o the Ε o f the chromophores as i s shown i n T a b l e I . N o n - s i n g l e R


8. HORIE

87


e x p o n e n t i a l phosphorescence decay has been o b s e r v e d f o r chromophores w i t h an E^, s m a l l e r than t h a t o f PMMA (297 t o 301 k j ) ( 2 3 , 2 4 ) , w h i l e s i n g l e - e x p o n e n t i a l phosphorescence o r T-T a b s o r p t i o n decay i s o b t a i n e d f o r chromophores w i t h lower t r i p l e t energy l e v e l s . These r e s u l t s a l s o s u p p o r t t h e o c c u r r e n c e o f dynamic quenching f o r e x c i t e d - t r i p l e t - s t a t e chromophores by m a t r i x PMMA due t o an endot h e r m i c t r i p l e t energy t r a n s f e r mechanism. R e c e n t l y , R i c h e r t and B a e s s l e r ( 3 7 ) r e g a r d e d t h e n o n - e x p o n e n t i a l decay o f benzophenone as a d i s p e r s i v e t r i p l e t t r a n s p o r t phenomenon t o t r a p s i t e s , and approximated i t by a s t r e t c h e d e x p o n e n t i a l f i t ( I n I ( t ) + t/τ = - C ( t / t ) ) w i t h a time dependent d i s p e r s i o n ο ο parameter α. α


Phosphorescence Decay o f Benzophenone i n Polymer

Solids

T y p i c a l decay c u r v e s o f benzophenone (BP) phosphorescence ( a n a l y z e d a t 450 nm) a t v a r i o u s temperatures i n PMMA e x c i t e d by a 10-ns n i t r o g e n l a s e r p u l s e a t 337 nm a r e shown i n F i g . 1 ( 6 ) . The phosphorescence i n t e n s i t y , l ( t ) , d e c r e a s e s as a s i n g l e e x p o n e n t i a l below t h e temperature c o r r e s p o n d i n g t o the e s t e r s i d e - g r o u p r o t a t i o n (Τβ = - 3 0 ° C f o r PMMA). D e v i a t i o n s from a s i n g l e - e x p o n e n t i a l decay a r e o b s e r v e d f o r T>T^, w h i c h i n c r e a s e w i t h i n c r e a s i n g t e m p e r a t u r e , but t h e d e v i a t i o n becomes l e s s marked above t h e g l a s s t r a n s i t i o n temperature, Τ , o f t h e m a t r i x polymer and d i s a p p e a r s a t 1 5 0 ° C . A s i m i l a r t e m p l r a t u r e dependence o f t h e decay p r o f i l e was a l s o o b s e r v e d f o r benzophenone phosphorescence i n o t h e r a c r y l i c polymers (28) and i n p o l y s t y r e n e (PS) and p o l y c a r b o n a t e (PC) ( 2 9 ) . T r a n s i e n t s p e c t r a showed t h a t t h e whole c o u r s e o f t h e decay c u r v e i s due t o benzophenone t r i p l e t ( 6 ) , and t h e i r r a d i a t i o n i n t e n s i t y independence shown i n F i g . 2 e x c l u d e d t h e o c c u r r e n c e o f T-T a n n i h i l a t i o n under t h e p r e s e n t e x p e r i m e n t a l c o n d i t i o n s ( 2 5 ) . S i n c e t h e d e v i a t i o n i s n o t o b s e r v e d a t temperatures below T^ o f each a c r y l i c polymer o r Τγ o f p o l y s t y r e n e and p o l y c a r b o n a t e , t h i s quenching i s n o t suggested t o be o f a s t a t i c c h a r a c t e r l i k e t h e I n o k u t i - H i r a y a m a type mentioned i n t h e p r e v i o u s s e c t i o n . Instead, i t i s suggested t o be o f a dynamic c h a r a c t e r due t o c o l l i s i o n between the f u n c t i o n a l groups. The o c c u r r e n c e o f quenching was a s c e r t a i n e d by comparison w i t h t h e model quenching r a t e c o n s t a n t of benzophenone t r i p l e t by methyl a c e t a t e i n a c e t o n i t r i l e s o l u t i o n (3.9x10 M" S " a t 30°C) ( 2 8 ) . Quenching o f benzophenone t r i p l e t by p h e n y l o r phenylene g r o u j s j n p o l y s t y r e n e o r p o l y c a r b o n a t e has a l s o been s t u d i e d (1.2x10 M s~ f o r p o l y s t y r e n e i n benzene a t 30°C) ( 3 0 ) . These o r d e r s o f magnitude f o r t h e quenching r a t e c o n s t a n t s i n n o n v i s c o u s s o l u t i o n a r e r e a s o n a b l e f o r an u p h i l l - t y p e endothermic t r i p l e t energy t r a n s f e r mechanism. As t h e dynamic quenching f o r a phosphorophore g i v e s s i n g l e e x p o n e n t i a l decay i n n o n v i s c o u s s o l u t i o n ( S t e r n - V o l m e r model), i t i s n e c e s s a r y t o c o n s i d e r why t h e dynamic quenching i n polymer s o l i d s e s p e c i a l l y below T^ r e s u l t s i n a n o n - e x p o n e n t i a l decay p r o f i l e . K i n e t i c s f o r N o n - e x p o n e n t i a l Decay Due t o Dynamic Quenching The decay p r o c e s s o f t r i p l e t benzophenone, following:

(6,29)

3 BP, i s g i v e n by t h e


88

PHOTOPHYSICS OF POLYMERS Table I. Type of T r i p l e t Decay Curves and T r i p l e t Energies, E^, for Various Chromophores Dispersed i n PMMA at Room Temperature


( 2 7 )

chromophore

type of t r i p l e t decay

fluorene benzophenone triphenylene phenanthrene naphthalene

non-single-exponential non-single-exponential non-single-exponential s ingle-exponential non-single-exponential sing1e-exponentia1 single-exponential single-exponential single-exponential s ing1e-exponential

coronene benz i l pyrene anthracene

ν kj/mol 284 283 278 260 255 228 227 202 179

20

40

60

ms(é)

0

3

16

2ί

ms(ti

Ù

2 1

f

6

msfd

0 0

.

β

WO 16 rime

ref 20 5,6 20,24 24 20 24 20 26 22 21

60 VS(d) 2i

μ*(β)

F i g u r e 1. S e m i l o g a r i t h m i c decay curves o f benzophenone phospho rescence i n PMMA e x c i t e d by 10-ns n i t r o g e n l a s e r p u l s e a t 337 nm. Temperature and symbols f o r time s c a l e s a r e g i v e n b e s i d e t h e curves. (Reproduced from Reference 6. C o p y r i g h t 1984 American Chemical S o c i e t y .


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A

Ο

10

2 0 Time

3.0

( m sec )

F i g u r e 2. Phosphorescence decay p r o f i l e s o f BP i n PMMA a t 20°C. Excitation intensity: (1) 4.0 χ 1 0 , (2) 6.4 χ 1 0 , (3) 2.8 χ 10*2 p h o t o n / p u l s e . (Reproduced w i t h p e r m i s s i o n from Reference 25. C o p y r i g h t 1984, Pergammon.) 1 5

1 3


90


k 3

* BP

° >

3 * BP

+ [Q]

BP

(15)

k q

»

BP + [Q]

(16)

where k = kp^, + k^p i s the r a t e c o n s t a n t f o r spontaneous d e a c t i v a t i o n of benzophenone t r i p l e t , [Q] i s the c o n c e n t r a t i o n of e s t e r , p h e n y l , o r phenylene group i n the m a t r i x polymer. The b i m o l e c u l a r r a t e c o e f f i c i e n t , k , i s g i v e n by eq (17) i n c l u d i n g b o t h the d i f f u s i o n and c h e m i S a l s t e p s ( 3 0 ) : Q


,

4ÏÏRDN

q

=

L

1 + 4ïïRDN/k

,

1

1

+

R

-j

(17)

( l + 4ïïRDN/k)(πΟΤ)^

where D i s the sum of d i f f u s i o n c o e f f i c i e n t s f o r the c a r b o n y l groups i n benzophenone and f o r quenching groups i n the polymer, l i m i t e d by s i d e - c h a i n r o t a t i o n and l o c a l segmental m o t i o n o f the polymer c h a i n , R i s r e a c t i o n r a d i u s between the two groups, k i s the i n t r i n s i c ( c h e m i c a l ) r a t e c o n s t a n t t h a t would p e r t a i n i f the e q u i l i b r i u m c o n c e n t r a t i o n of the quenching groups were m a i n t a i n e d , and Ν i s Avogadro's number d i v i d e d by 10 . When k i s c o n t r o l l e d by the d i f f u s i o n p r o c e s s o f the two groups, eq (17? i s reduced t o eq ( 1 8 ) : k

q

= 4*RDN(1 + R/(ïïDt)^ = A + B / t *

(18)

with A = 4nRDN Β = 4R

2

^ (xD) N a

Thus, the r a t e c o e f f i c i e n t k i n c l u d e s a time-dependent term t h a t i s i m p o r t a n t a t the v e r y e a r l y Stage of r e a c t i o n where the s t e a d y - s t a t e d i f f u s i v e f l u x of the quenching group i s not y e t a t t a i n e d . As the decay r a t e of benzophenone t r i p l e t i s g i v e n by eq (19) 3

- d [ B P * ] / d t = (k

3

ο

+

k [Q])[ BP*] q %

3

= ( k + A[Q] + B [ Q ] t " ) ] B P * ] ο

(19)

A

we get 3

3

%

[ BP*] = [ B P * ] e x p [ - ( k + A [ Q ] ) t - 2B[Q]t ] o

(20)

o

3 * f o r t h e ^ c o n c e n t r a t i o n of benzophenone t r i p l e t , [ BP J , a t time t , where [ BP ] i s the i n i t i a l c o n c e n t r a t i o n o f benzophenone t ^ i p ^ e t . The phosphorescence i n t e n s i t y , l ( t ) , i s p r o p o r t i o n a l t o kp^L BP ]» so we get f i n a l l y r

In I ( t )

= -(k

+ A [ Q ] ) t - 2 B [ Q ] t * + In I

« -(t/τ) - C ( t / x )

%

+ In I ο

n

Q

(21)


8.

HORIE

91


where l/τ = k + A[Q] = k + 4 RDN[Q] ο ο Β

= CT-*/(2[Q])

= 4R (ÏÏD)^N 2

(22) ( 2 3 )

The c u r v e f i t t i n g f o r the phosphorescence decay c u r v e s w i t h eq ( 2 1 ) g i v e s the v a l u e s o f r e c i p r o c a l l i f e t i m e l/τ = k + A[Q] and a parameter B, w h i c h a r e shown i n F i g . 3 f o r the c a s e s o f PMMA and p o l y s t y r e n e . The breaks r e f l e c t the changes i n the m o l e c u l a r motions a t Τ , Τ (PMMA) o r Τ (PS, PC) c o r r e s p o n d i n g t o t h e l o c a l mode r l l a x a t i o n o f the main c h a i n , and Τ (PMMA) o r Τ (PS, PC) c o r r e s p o n d i n g t o the o n s e t o f r o t a t i o n ^ o f the s i d e - 2 h a i n e s t e r o r phenyl group o r the m a i n - c h a i n phenylene group. A r r h e n i u s p l o t o f 1 / f o r benzophenone i n p o l y ( m e t h y l a c r y l a t e ) (PMA) ( 6 ) showed another break a t 40°C (above Τ o f PMA) w h i c h c o r r e s p o n d s t o an a c t i v a t i o n - c o n t r o l l e d r e a c t i o n . Tfie d i f f u s i o n c o e f f i c i e n t , D, f o r r e a c t i n g c a r b o n y l groups c a l c u l a t e d from the v a l u e s o f 1/ τ and Β a t each temperature a l s o showed b r e a k s a t each t r a n s i t i o n temperature, as e x e m p l i f i e d i n F i g . 4 f o r the c a s e s o f PMMA, p o l y s t y r e n e and p o l y c a r b o n a t e . I t s h o u l d be noted t h a t D i n F i g . 4 i s d e f i n e d as t h e t r a n s l a t i o n a l d i f f u s i o n c o e f f i c i e n t f o r t h e r e a c t i n g f u n c t i o n a l groups but n o t f o r the m o l e c u l e . The d i f f u s i o n p r o c e s s a t temperatures below Τ would be caused by r o t a t i o n o f the benzophenone m o l e c u l e and segmental motion w i t h i n a few monomer u n i t s o f m a t r i x polymers. N e v e r t h e l e s s , the v a l u e s o f D i n ^ t h e s e polymers a t 100°C a r e compared t o the v a l u e o f D = 5.6x10" cm /s (32) f o r mass d i f f u s i o n o f e t h y l b e n z e n e i n p o l y s t y r e n e a t 30°C. The r e a c t i o n r a d i u s , R, amounts t o 3-5 À. The t r a n s i t i o n temperatures o f the m a t r i x polymers m o n i t o r e d by phosphorescence decay o f benzophenone i n c l u d i n g the case i n p o l y ( v i n y l a l c o h o l ) a r e summarized i n T a b l e I I . The α t r a n s i t i o n f o r PMMA and o t h e r a c r y l i c polymers and β t r a n s i t i o n f o r p o l y s t y r e n e , p o l y c a r b o n a t e , and p o l y ( v i n y l a l c o h o l ) a r e a t t r i b u t e d t o a l o c a l mode r e l a x a t i o n of the main c h a i n . The phosphorescence probe t e c h n i q u e i s e f f e c t i v e f o r the d e t e c t i o n o f t h i s s u b - g l a s s t r a n s i t i o n as w e l l as o t h e r r o t a t i o n mode t r a n s i t i o n s ( T o r Τ ) o f polymer m a t r i c e s . β γ Hydrogen A b s t r a c t i o n o f Benzophenone T r i p l e t i n P o l y ( v i n y l a l c o h o l )


t

τ

0

The phosphorescence o f BP (0.Π,) i n p o l y ( v i n y l a l c o h o l ) (PVA) f i l m (250 m i c r o n t h i c k n e s s ) e x c i t e d by a 10-ns n i t r o g e n l a s e r p u l s e a t 337 nm decays e x p o n e n t i a l l y f o r Τ < Τ (-100°C) o r Τ > Τ (85°C), but d e v i a t e s from s i n g l e e x p o n e n t i a l f o r ^ T < Τ < Τ . The S e v i a t i o n was a t t r i b u t e d t o the d i f f u s i o n - c o n t r o l l e d ^ h y d r o g e n ^ a b s t r a c t i o n r e a c t i o n between benzophenone t r i p l e t and the PVA m a t r i x ( 3 3 ) . The o c c u r r e n c e o f n o n - e x p o n e n t i a l decays i n p o l y ( v i n y l a l c o h o l ) where t h e r e i s no p o s s i b i l i t y o f t r i p l e t energy m i g r a t i o n i s an a d d i t i o n a l p r o o f o f the absence o f the T-T a n n i h i l a t i o n mechanism i n the phosphorescence decay o f benzophenone i n polymer m a t r i c e s . The d i f f u s i o n - c o n t r o l l e d r a t e c o e f f i c i e n t f o r hydrogen a b s t r a c t i o n , k , o f benzophenone t r i p l e t f o r PVA and t h e phosphorescence i n t e n s i t y , l ( t ) , were g i v e n by eqs (24) and ( 2 5 ) , i n a s i m i l a r manner t o the cases o f p h y s i c a l quenching o f t h e benzophenone phosphorescence by m a t r i x polymers.



92


5

6

7

1/T (ΐο- κ-') 3

Figure 3. Temperature dependence of reciprocal l i f e t i m e , l / τ , (Ο, Δ ) and contribution of non-exponential term, Β, (Φ,Α) f o r benzophenone phosphorescence i n PMMA ( 0 #) polystyrene a

200 100 π ι * ι ι ι

ι ι—ι—ι—ι—ι

4

1

Γ

n

d

-100 ι

5

i

n

»

6

Î/TCIO^K" ) 1

Figure 4. Arrhenius p l o t s of d i f f u s i o n c o e f f i c i e n t , D, of interacting groups f o r dynamic quenching of benzophenone t r i p l e t by phenyl, phenylene, and ester groups i n polystyrene ( #,•) , polycarbonate ( Ο , Δ ) , and PMMA ( • ) , respectively.


8.

Phosphorescence Decay and

HORIE

k

2

a

93

Dynamics

= 4ÏÏRDN(1 + R / ( D t ) ) = A + B / t

2

(24)

ïï

In I ( t ) = -(k

ο

+ A[PVA])t-2B[PVA]t^

+ In I

ο

(25)

The curve f i t t i n g for the experimental phosphorescence decay with eq (25) gives the values of l/τ = k + A[PVA] and B. The breaks at Τ = 85°C and Τ = 30°C and the appearance of Β at Τ = -100°C c f e a r l y r e f l e c t the change i n molecular motions of matrix poly(vinyl alcohol). In order to know the net quantum y i e l d for the benzophenone disappearance, δ(-ΒΡ), by hydrogen abstraction i n poly(vinyl alcohol), the change i n UV spectra of benzophenone at 256 nm i n the poly(vinyl alcohol) f i l m was followed during continuous i r r a d i a t i o n of 365 nm UV l i g h t . The Φ(-BP) given i n Table III i s very small for Τ < Τ , suggesting the predominant occurrence of backward reaction ^ °f benzophenone ketyl r a d i c a l i n the cage for the temperature range below Τ . The T-T absorption spectra and l i f e t i m e of the ketyl r a d i c a l were observed for Τ >120°C (34). The supposed reaction scheme for the photochemistry of benzophenone i n poly(vinyl alcohol) including the backward cage reaction i s summarized i n F i g . 5.


β

Phosphorescence Decay of Benzophenone under Multi-photon Conditions Salmassi and Schnabel (35) measured the decays of phosphorescence and t r i p l e t absorption of benzophenone i n PMMA and polystyrene under the high intensity i r r a d i a t i o n of 347 nm frequency-doubled ruby laser gingle pulse. The i n i t i a l t r i p l e t concentration amounted up to^6xl0 mol/1 i n comparison with the value of less than 6x10 mol/1 for the case (6,25) i n the preceding sections with the nitrogen laser pulse. In PMMA a single t r i p l e t decay mode following f i r s t - o r d e r kinetics was observed at Τ 410K. Two d i s t i n c t modes of t r i p l e t decay were observed i n the intermediate temperature range: a fast f i r s t - o r d e r process, the l i f e t i m e (ca. 4ys at 295K) being independent of the i n i t i a l t r i p l e t concentration, [ T ] , and a slow second-order process, the f i r s t h a l f l i f e t i m e being p r o p o r t i o n a l to [T] " . S i m i l a r l y , two d i s t i n c t modes of t r i p l e t decay were also o B t a i n e d with polystyrene m a t r i c e s for 180K

Phosphorescence Decay and Dynamics in Polymer Solids

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