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SPECTRAL DIFFUSION AND RELAXATION OF
PHOTOCHEMICAL HOLES ON LOGARITHMIC
TIME SCALES
J. Friedrich, D. Haarer
To cite this version:
Colloque C7, suppl6ment au nOIO, Tome 46, octobre 1985 page C7-357
SPECTRAL DIFFUSION AND RELAXATION OF PHOTOCHEMICAL HOLES ON
LOGARITHMIC T I M E SCALES
3 . F r i e d r i c h and D. Haarer
PkysikaZisches I n s t i t u t der Universitiit Bayreutk, 0-8580 Bayreutk, F.R.G.
Abstract: Photochemical holes b u r n t i n doped organic glasses evolve o n logarithmic time scales. T h e characteristic time dependet features can b e described u s i n g t h e concepts o f spectral d i f f u s i o n . Since t h e model has n o adjustable parameter t h e results p r o v i d e detailed i n s i g h t i n t h e long time relaxation behavior o f t h e glasses.
INTRODUCTION:
Glasses a r e well described as frozen l i q u i d s w i t h a temperature dependent vis- c o s i t y as g i v e n b y t h e Vogel-Fulcher-law
rl
= no
e x p A / k ( T - T o ) ( 1 )w i t h parameters 'lo, A, a n d T
.
T h e above equation can b e i n t e r p r e t e d w i t h i n t h e frame o f a n Arrhentus-law w i t f i a temperature dependent b a r r i e rwhich t h e system has t o overcome f o r thermally activated s t r u c t u r a l relaxation processes. A t T = To t h e b a r r i e r h e i g h t s d i v e r g e formally, i n d i c a t i n g t h a t o n t h e average t h e thermally activated relaxation processes become i n f i n e t e l y slow. T cannot be defined i n a s t r a i g h t f o r w a r d fashion. Within t h e f r e e volume model O? amorphous solids it can be i n t e r p r e t e d as t h e temperature a t which t h e free volume vanishes / I / . Since in an amorphous solid t h e b a r r i e r h e i g h t s can n o t be expected t o b e u n i f o r m b u t are characterized b y a d i s t r i b u t i o n , t h e r e are s t i l l relaxation processes even a t v e r y low temperatures. T h i s demonstrates t h a t a glass does n o t reach e q u i l i b r i u m o n experimental time scales. Hence, some of i t s physical parameters a r e n o t well defined as i n t h e case o f c r y s t a l s , b u t change as a f u n c t i o n o f time. T h i s was demonstrated f i v e years ago f o r t h e specific heat / 2 / , V e r y recently, we succeded in measuring t h e time dependence o f some optical properties, l i k e t h e area a n d t h e w i d t h o f "persistent" spectral holes. The hole b u r n i n g technique has p r o v e n t o b e a p o w e r f u l tool f o r t h e investigation of t h e amorphous state 1 3 1 . T h i s i s d u e t o t h e fact that, a t low temperatures, t h e w i d t h o f a spectral hole may b e several thousand times n a r r o w e r t h a n t h e inhomogeneous width, which reflects t h e average intermolecular interaction. Hence, a p e r s i s t e n t spectral hole i s a n extremely sensitive p r o b e f o r s t r u c t u r a l ( o r so called secon- d a r y ) relaxation processes which can occur o n v e r y long time scales. I n t h i s paper we demonstrate how one can g e t detailed q u a n t i t a t i v e information o n t h e
C7-35 8 JOURNAL
DE
PHYSIQUEs t r u c t u r a l r e l a x a t i o n dynamics o f a glass u s i n g s p e c t r a l holes as probes. We i n v e s t i g a t e d q u i n i z a r i n i n alcohol glass, whose p h o t o c h e m i s t r y has been d e s c r i b e d elsewhere 131. F o r comparison we i n v e s t i g a t e d also t h e p h o t o p h y s i c a l h o l e b u r n i n g system t e t r a c e n e i n ethanol 141.
EXPERIMENTAL RESULTS
Fig.1 shows a s u r v e y s p e c t r u m o f t h e syske,m q u i n i z a r i n i n a n EtOHIMeOH ( 3 : l ) alass a t 1.3 K. T h e small d i ~ a t 19440 cm i s t h e ~ h o t o c h e m i c a l hole. w h i c h i s ghown o n a n e x p a n d e d scale 'in t h e i n s e r t . I t s time ;?volution is shown. in Figs.2 a n d 3. We f o u n d t h a t
1 ) i t s area decreases l i n e a r l y o n a l o g a r i t h m i c scale 2) i t s w i d t h increases l i n e a r l y o n a l o g a r i t h m i c scale
3) b o t h r e l a x a t i o n processes o c c u r o r d e r s o f m a g n i t u d e slower i n d e u t e r a t e d glass
4) i t s degreee o f p o l a r i z a t i o n remains c o n s t a n t
Fig.4 shows t h e p h o t o p h y s i c a l hole b u r n i n g system, t e t r a c e n e in ethanol. Again, t h e h o l e area decays l i n e a r l y o n a l o g a r i t h m i c scale a n d i t s p o l a r i z a t i o n i s c o n s t a n t t h r o u g h o u t t h e e x p e r i m e n t a l p e r i o d o f r o u g h l y 1 week.
I . I
2KXX) 20m 19MX)
~ [ c m - ' ]
Fig. 1 : S u r v e y spectrum o f q u i n i z a r i n i n alcohol glass: T h e photochemical h o l e i s shown o n a n e x p a n d e d scale. B u r n i n g time: 2 min. Fig.2: A r e a a n d d e g r e e o f polariza- t i o n o f a photochemical h o l e as a f u n c t i o n o f time. System: q u i n i z a r i n in alcohol glass.
Fig.3: Hole w i d t h as a f u n c t i o n o f time. System: q u i n i z a r i n in alcohol glass.
TLS-model o f t h e amorphous state 151:
1) T h e relaxation o f t h e hole area: From low temperature specific heat e x p e r i - ments it is well k n o w n t h a t t h e energies o f t w o level t u n n e l i n g states ( T L S ) a r e u n i f o r m l y d i s t r i b u t e d . Consistent w i t h a u n i f o r m d i s t r i b u t i o n in e n e r g y i s a u n i f o r m d i s t r i b u t i o n in b o t h parameters, which characterize a TLS, namely t h e e n e r g y asymmetry A a n d t h e t u n n e l parameterX
.
A consequence o f a u n i f o r m d i s t r i b u t i o n o f A a n d X i s a v e r y asymmetric d i s t r i b u t i o n o f t u n n e l i n g relaxation r a t e s R, r o u g h l y g i v e n byEqu.3 is t h e s t a r t i n g p o i n t o f o u r theoretical model 161. Since t h e above d i s t r i - b u t i o n has t o b e normalized, t h e r e e x i s t t w o c u t - o f f values Rmin a n d Rmax, r e p r e s e n t i n g t h e slowest a n d t h e fastest t u n n e l i n g processes o f t h e system cons!- dered. Once Rm.,, a n d R a r e k n o w n t h e complete dynamics o f t h e TLS-system u n d e r considerafton is kn!%%. F o r t h e f i r s t time, we c o u l d estimate these parame- t e r s from hole b u r n i n g experiments. O u r arguments a r e t h e following: I n b o t h cases, q u i n i z a r i n a n d tetracene, t h e p h o t o p r o d u c t i s t r a p p e d i n some t u n n e l i n g state which is subject t o a d i s t r i b u t i o n o f relaxation rates a c c o r d i n g t o (3) r e - f l e c t i n g t h e local d i s o r d e r . A t time t one observes mainly those c e n t e r s r e l a x which a r e g o v e r n e d b y rates on t h e o r d e r R = l l t . Hence, t h e hole area is g i v e n b y i n t e g r a t i n g t h e above r a t e d i s t r i b u t i o n f r o m Rmin t o R = l l t . T h i s i n t e g r a l y i e l d s t h e number o f t u n n e l i n g c e n t e r s being, a t t ~ m e t, i n t h e p h o t o p r o d u c t state, and, t h u s , is p r o p o r t i o n a l t o t h e hole area. One d e r i v e s f o r t h e hole area A ( t ) a logarithmic decay law:
A 1 r e l a t i o n i s g i v e n b y t h e logarithm o f t h e t o rates R1 lR,i, normalizes t h e decay f u n c t i o n a t t h e time tl. T h e slope o f t h e above linear R l = l / t l i s an experimental parameter on t h e o r d e r o f l l m i n . Hence, R
.
, can b e d i r e c t l y determined f r o m t h e measured slope. T h e d i s p e r s i o n o f r a t e s m # I l ~ m i n is huge. We g e t f o r q u i n i z a r i n i n t h e protonated a n d i n t h e d e u t e r a t e d glass, respectively, t h e values8
[R1IRminIH = 1 0 , [R~IR,~,]~ =
For tetracene i n ethanol we found: Rl lRmin = 10".
2 ) T h e time e v o l u t i o n o f t h e 1inewidth:The time e v o l u t i o n o f t h e l i n e w i d t h occurs o n t h e same time scale as t h e decay o f t h e hole area. T o e x p l a i n t h e observed features we employ t h e concept o f s p e c t r a l d i f f u s i o n . We consider a molecule, l e f t i n t h e e d u c t state, which has, a t a time tl, a s h a r p t r a n s i t i o n f r e q u e n c y . As time evolves, t h e molecules r e l a x i n g f r o m t h e p r o d u c t t o t h e e d u c t s t a t e c r e a t e s t r a i n fields w h i c h lead t o a d i f f u s i o n o f e x c i t a t i o n energies o f t h e p r o b e molecules i n f r e q u e n c y space. As shown b y several a u t h o r s /7,8/, t h e lineshape o f t h e diffu- s i n g molecules is, u n d e r c e r t a i n conditions, Lorentzian. I t s w i d t h is p r o p o r t i o n a l t o t h e number n ( t - t l ) o f molecules h a v i n g 'flipped' w i t h i n t h e time i n t e r v a l t-tl:
C7-360 JOURNAL DE PHYSIQUE
The measured w i d t h y i s t h e sum o f a diffusional w i d t h a n d a time independent w i d t h y, which may b e t h e homogeneous width. If one suceeds in measuring separately t h e d i f f u s i o n a l w i d t h Y = Y;Yo, t h e n it i s easy t o show 191 t h a t a reduced p l o t yD(t)/yD(tl) y i e l d s a l o g a r ~ t h m i c law w i t h a slope factor determined solely b y Rmax, t h e maximum r a t e constant:
R can b e determined experimentally from t h e measured slope. I n o u r experi- mPd& 191 we estimated yo from t h e deuteration effect. A s seen in Fig.3, t h e extrapolated lines o f t h e protonated a n d deuterated sample show a cross o v e r a t a time ro o f 12 s. Clearly-r marks t h e onset o f spectral d i f f u s i o n a n d t h u s
y(
r
1
=yo.
Equ.7 allows @ot g i v e a'n estimate o f t h e maxiqum r a t e constant. For quiRizarrn i n t h e EtOHIMeOH glass we g e t Rm = 0.025 s.
We stress t h a t Rmax does n o t show a n y s i g n i f i c a n t dependence on deuteration.THE DEUTERATION EFFECT
I n case o f t h e q u i n i z a r i n system it i s well known t h a t t h e hole b u r n i n g photoche- m i s t r y i s d u e t o a p r o t o n t r a n s f e r reaction, hence, a change in t h e relaxation rates o f t h e deuterated system is t o b e expected. Deuteration changes t h e tunne- l i n g m a t r i x element A which depends i n an exponential fashion on t h e mass m o f t h e t u n n e l i n g particle0
i s determined b y t h e b a r r i e r h e i g h t Vo a n d t h e t u n n e l i n g distance d 2 112
At = ( V d 2 / % ) (91
It i s clear &at, if A' i s large, a n d hence t h e r a t e constant small, deuteration may b r i n g about a change o f many o r d e r s o f magnitude. On t h e o t h e r hand, if A ' is small, t h e deuteration e f f e c t w i l l b e small a n d will b e h a r d l y noticeable in t h e logarithmic slope factor. Since t h e slope factors f o r both, t h e decay o f t h e n o r - malized hole area (Equ.4) a n d t h e absolute w i d t h (Equ.6) a r e g o v e r n e d b y R t h e slowest r a t e o f t h e total system, a l a r g e deuteration e f f e c t is expected.
Y~I?;
i s indeed observed 161. R.
changes b y more t h a n 10 o r d e r s o f magnitude. A most i n t e r e s t i n g observatio%'?s t h e f a c t t h a t t h e isotope effect i n t h e linewidth data (Fig.3) vanish, if t h e y a r e scaled according t o Equ.7. Fig.5 shows t h a t all t h e data points o f Fig.3 l i e o n t h e same u n i f o r m plot:Or6nizarin m EtOH
/
MeOH 3 : 1 T = 4,BK T=1,35K o Ouinizarin in c~D,DD/ CD,OD 3 : 1T=4.21K* T=1,35Ko
.
..
e f f e c t as discussed above, w h i c h is o f negSgible i n f l u e n c e o n t h e logarithmic slope factor. From t h e measured isotope e f f e c t we can estimate t h e maximum b a r r i e r heights. Assuming t u n n e l i n g distances o n t h e o r d e r o f a few Angstroms, one calculates maximum b a r r i e r h e i g h t s on t h e o r d e r o f several thousand wave num- bers, i.e. much h i g h e r t h a n t h e thermal e n e r g y a t t h e glass t r a n s i t i o n tempera- t u r e k T g ' S u c h b a r r i e r h e i g h t s are, however, q u i t e c o n s t i s t e n t w i t h t h e Vogel- Fulcher-law (Equ.1). i n d i c a t i n g t h a t b a r r i e r formation is most l i k e l y a collective phenomenon.
POLARIZATION DIFFUSION
From t h e c o n s t a n t degree o f polarization we conclude t h a t o n t h e time scale o f t h e experiment, t h e r e is n o r e o r i e n t a t i o n o f d y e molecules l e f t in t h e g r o u n d state. T h i s r u l e s o u t t h e p o s s i b i l i t y t h a t t h e d y e molecules themselves a r e an a c t i v e p a r t o f t h e TLS-system o f t h e glass 141.
ACKNOWLEDGEMENT:
T h e a u t h o r s acknowledge a g r a n t f r o m t h e S t i f t u n g Volkswagenwerk. References :
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