the states of the c 3 -ar and c 3 -kr van der waals complexes: fluorescence polarization and...
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The states of the C3-Ar and C3-Kr van der Waals Complexes: Fluorescence Polarization
and Saturation
Jun-Mei Chao , Kan-Sen Chen, Shin-Shin Cheng,
Anthony J. Merer, and Yen-Chu Hsu
IAMS, Academia Sinica P. O. Box 23-166, Taipei, Taiwan, R.O.C.
Supported by Academia Sinica, Taiwan, and National Science Council, Taiwan, R. O. C.
Α~
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Introduction
• The spectrum of the C3 1Πu – 1Σg+ system was first observed in comets by
Huggins in 1882.• Its first laboratory study was reported in 1942 by Herzberg and his co-workers.
Since then many studies of the comet system of C3 have been carried out.
low bending frequency (63 cm-1) of the state Renner-Teller effect of the state (=0.35)
─ 1965, Gausset et al., vibrational and rotational analysis of the state.─ 1994, W. J. Balfour et al., more vibronic bands were reported.─ 2003, B. J. McCall et al., reassignment of the R(0) line of the (000-000) band.─ 2005, G. Zhang et al., perturbations of the ,000 state have been observed and analyzed.
• We have utilized the comet system to study the C3-Rg (Rg=Ne, Ar, Kr and Xe) van der Waals complexes (G. Zhang et al., J. Chem. Phys. 120, 3189(2004)). The states of these complexes are not well understood; the effect of the rare gas atom on the Renner-Teller effet of C3 has not been found.
X~
A~
A~
X~
A~
A~
X~
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A'A"
unique level
unique level
unique level
Vb=2
Vb=1
Vb=0
à 1u
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C
C
C
Ar
3010
Displacement From Excitation Frequency(cm-1)0 500 1000
25000 25050
A
B
A,B
Q(2)
Q(2)
C
C
Dis
per
sed
Flu
ore
scen
ce In
ten
sity
D
D
02-
C3-Ar
b
202-
222- 24
2-
262-
282-
2102-
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Top PMT
Side P
MT
Polarizer
Rhomb
Allene + Rare gas
ArF Laser
LIF Laser beam X
Y
Z
F⊥
Stop =top (F⊥ + F⊥)
F⊥
Sside = side (F // + F⊥)
Extinction ratio
Extinction ratio
= 1x10= 1x10 -3-3
Polarizer
Polarizer
F//
F⊥
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frequency / cm-1
25660 25680 25700 25720 25740 25760 25780 25800
Top PMT
Side PMT
100-000 (perpendicular band)
01+1-000 (parallel band)
1 2 3
(1’,2’,3’-1”,2”,3”)Upper
Renner-Teller Component
The spectrum of CThe spectrum of C3 3 ((excitation laser is horizontally polarized)
(F // + F⊥)
(F⊥ + F⊥)
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100-000
Frequency / cm-1
25660 25680 25700 25720 25740 25760 25780 25800
01+1-000
C3 and C3Ar
Frequency / cm-1
25660 25680 25700 25720 25740 25760 25780 25800
C3 and C3Xe
01+1-000
100-000
C3 and C3Kr
Frequency / cm-1
25660 25680 25700 25720 25740 25760 25780 25800
01+1-000
100-000
C3Ar
(perpendicular band)
(parallel band)
C3Kr
C3Xe
Frequency /cm-1
25660 25680 25700 25720 25740 25760 25780 25800
C3 and C3Ne100-000
01+1-000
C3Ne(F // + F⊥)
(F⊥ + F⊥)
(F // + F⊥)
(F⊥ + F⊥)
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Conventional polarization spectroscopy was obtained by modulating the fluorescence intensity by rotating the polarizer, which placed in front of the detector. And the Polarization Ratio (conventional) =
In this work, we simultaneously detect the fluorescence signals. The advantage is that shot-to-shot intensity fluctuation from the lasers can be minimized. The polarization ratio defined in this work is, Polarization Ratio =
IIII
FFFF
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Fluorescence Polarization
F = 1M
<J3, M3, Ω1 Zˆˆ J2, M2, Ω2 >
2
<J2, M2, Ω2 Zˆˆ J1, M1, Ω1 >
2
F = 1M
<J3, M3, Ω1 Xˆˆ J2, M2, Ω2 >
2
<J2, M2, Ω2 Zˆˆ J1, M1, Ω1 >
2
Parallel transition, = z
Perpendicular transition, = x or y
References, 1. R.N. Zare, Angular Momentum. Understanding Spatial Aspects in Chemistry and Physics. (Wiley, New York 1988). 2. J.T. Hougen, The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules. (NIST, Gaithersburg, 2001).
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F F
))(( 12115
818154
11
12
13
14
JJ
JJJ
))(( 12130
217206
11
12
13
14
JJ
JJJ
1215341
1
114
J
JJz
1215131
1
114
J
JJz
Table I. Calculated Polarized LIF Intensities
M'
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Rel
ativ
e p
opul
atio
n
0.0
0.2
0.4
0.6
0.8
1.0
J'=1 J'=3J'=5 J'=7J'=9
R lines of Perpendicular Transition
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• Polarization Ratio of the R(0) line of C3100-000 band,
calculated value from Table I:
(F(F//// + F + F⊥⊥))exp.exp.
(F(F⊥⊥ + F + F⊥⊥))exp.exp.
= 2.6 ± 0.22.6 ± 0.2
(F(F//// + F + F⊥⊥))cal.cal.
(F(F⊥⊥ + F + F⊥⊥))calcal
= 4.54.5
Collisional Depolarization or Signal Saturation?Collisional Depolarization or Signal Saturation?
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n=0.45 0.02
We did the experiments here!!
log(Laser Power)
1.0 1.5 2.0 2.5 3.0 3.5
log
(Sig
nal
of
C3 R
(0))
1.0
1.5
2.0
2.5
3.0
3.5
Laser Power Dependence
S = a × In
log S = log a + n log I
n=0.82 0.07
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25692 25694 25696 25698 25700 25702 25760 25762 25764 25766 25768 25770
Excitation Frequecy (cm-1)
2000 torr, 5% allene in He gas mixture expanded through a 500 nozzle
01+1- 000 100- 000
R
P
Dye laser pulse energy 0.39mJ
0 2 4
2
6 8R
0 2
2 Q4 6 8 10
(F // + F⊥)
(F⊥ + F⊥)
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b12ρ
b21ρ A21
A23
31
2
Effect of Saturation on the Fluorescence Polarization
label the states connected by the laser excitation as 1> and 2>, and therest states not connected by the laser excitation as 3> during the laser pulse (t), the populations of each states were treated byrate equations, ignoring the coherence effect.
dt
tdN)(1 b12 N1(t) + (b12+A21) N2(t), (1)
dt
tdN)(2 b12 N1(t) b12+ -1) N2(t), (2)
N3(t) = N0t(t) 3)
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where N0, N1(t), N2(t), and N3(t) refer to the total population, time-dependentpopulations of level N1, N2, and N3. The directional Einstein coefficient b12 isdefined as,
b12=b21=82/h2 122( ˆˆ )
2=3B12 ( )
2.
(,,̂) denotes the laser energy density (energy per unit volume per unitfrequency interval) directed into the solid angle d with a given electric field ̂.
Simultaneously solving Eqs. 1 and 2, the populations after the laser pulse (t)are,
N1(t=t)=N0/2[(1+1/(21)) exp(12) t + (11/(21)) exp((1+2)) t], (4)
N2(t= t) = N0 b12
/21 [exp(12) t exp((1+2)) t], (5)
, where 1=(b1222+1/42+b12
A21)0.5 and 2= b12
+1/2.
f b12>>A21, N2(t)N0/2, medium is transparent. If b12
A21, saturation mayoccur.
ˆˆ
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T h e L I F i n t e n s i t y i s ,
I = K daatN )()( 2 32 12 .
F o r t h e p o l a r i z a t i o n m e a s u r e m e n t s ,
.))(exp(
]))(exp()[exp()(
dttAAF
F
ttBN
KdttI
to t2 32 1
21211
1 20
2
( 6 )
F o r t h e p a r a l l e l p o l a r i z a t i o n , E q . ( 6 ) c a n b e r e - w r i t t e n b y r e p l a c i n g t h ep o l a r i z a t i o n d i r e c t i o n .
I n t h i s w o r k , D o p p l e r b r o a d e n i n g a n d p o w e r b r o a d e n i n g a r e e x p e c t e d .L i n e b r o a d e n i n g d u e t o s a t u r a t i o n c a n b e w r i t t e n a s ,
s = ( 1 + S ) 0 . 5 , ( 7 )
w h e r e s , d e n o t e t h e s a t u r a t e d a n d u n s a t u r a t e d s p e c t r a l w i d t h , a n d S i s
d e f i n e d a s ,
tb
tb
S
))(exp(
)()exp(
)(21
1
1 2121
1
1 21
4
122
4
122
1
1
.
( 8 )
R e f e r e n c e s :1 . R . A l t k o r n a n d R . N . Z a r e , A n n . R e v . P h y s . C h e m . 3 5 , 2 6 5 - 8 9 ( 1 9 8 4 ) .2 . W . D e m t r Ö d e r , L a s e r S p e c t r o s c o p y , B a s i c C o n c e p t a n d I n s t r u m e n t a t i o n s , S p r i n g e r - V e r l a g ( 2 0 0 3 ) .
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Laser Energy (mJ/pulse)
0.0 0.1 0.2 0.3 0.4
FW
HM
(G
Hz)
6
8
10
12
14
16
R(0), 2FR(2), 2FR(4), 2FR(6), 2FR(0), F + F R(2), F +F R(4), F +FR(6), F +F
100-000 band
Laser Energy (mJ/pulse)
0.0 0.1 0.2 0.3 0.4
FW
HM
(G
Hz)
6
8
10
12
14
16
01+1-000 band
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Results and Discussion
• Difficulty of this experiment: due to our way of generating C3
molecules by photolyzing allene, it is difficult to keep initial C3
concentration constant.
• The transition probability of 100-000 band is about 1.4 times of
01+1-000 band.
•Qualitative understanding is possible at lower laser power. Further simulation is necessary.
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Future Work
• Complete the polarization measurements of the C3 bands especially the high power regime.
• Apply fluorescence polarization study to characterize the C3-Rg bands.