Transcript polarization-C3.ppt

~
The Α 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.
Introduction
•
•
~1Π – ~1Σ + system was first observed in comets by
The spectrum of the C3 A
X g
u
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 X~ state
~
Renner-Teller effect of the A state (=0.35)
─
─
─
─
•
1965, Gausset et al., vibrational and rotational analysis of the X~ 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.
~ ,000 state have been
2005, G. Zhang et al., perturbations of the A
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
A complexes are not well understood; the effect of the rare
gas atom on the Renner-Teller effet of C3 has not been found.
A'
P
Vb=2
A"
P
Vb=1
Vb=0
S
D unique level
P unique level
S
P unique level
à 1Pu
r
Q(2)
C3-Ar
b02-
B
A
C
Dispersed Fluorescence Intensity
25000
D
25050
D
Ar
C
C
C
A,B
222-
242262-
202-
0
Q(2)
28
500
2-
2102-
1000
Displacement From Excitation Frequency(cm-1)
C
  10  30
Y
Stop = atop (F⊥ + F⊥)
Z
Top PMT
F⊥
F⊥
Sside = aside (F // + F⊥)
F⊥
F//
X
The spectrum of C3 (excitation laser is horizontally polarized)
n2
n1
Upper
Renner-Teller
Component
n3
100-000
(n1’,n2’,n3’-n1”,n2”,n3”)
(perpendicular band)
01+1-000
Top PMT
(parallel band)
(F // + F⊥)
(F⊥ + F⊥)
25660
25680
25700
25720
25740
frequency / cm-1
Side PMT
25760
25780
25800
C3 and C3Ne
100-000
C3 and C3Kr
100-000
C3Ne
C3Kr
(F // + F⊥)
+
01 1-000
+
01 1-000
(F⊥ + F⊥)
25660
25680
25700
25720
25740
Frequency /cm
C3 and C3Ar
25760
25780
25800
25700
25720
25740
C3Ar
(F // + F⊥)
25760
25780
25800
25780
25800
-1
C3 and C3Xe
100-000
(parallel band)
+
25680
Frequency / cm
(perpendicular band)
01 1-000
25660
-1
100-000
C3Xe
+
01 1-000
(F⊥ + F⊥)
25660
25680
25700
25720
25740
Frequency / cm
-1
25760
25780
25800
25660
25680
25700
25720
25740
Frequency / cm
-1
25760
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)
=
I
 I

I
 I

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,
F  F
Polarization Ratio =
F  F 


Fluorescence Polarization
F =

M1
ˆ a  ˆ Z  J2, M2, Ω2 > 2

<J
,
M
,
Ω

3
3
1


 <J2, M2, Ω2
F =

M1
ˆ a  ˆ Z  J1, M1, Ω1 > 2
ˆ a  ˆ X  J2, M2, Ω2 > 2
<J
,
M
,
Ω

3
3
1


ˆ a  ˆ Z  J , M , Ω > 2
<J
,
M
,
Ω

1
1
1
 2 2 2

Parallel transition,
a= z
Perpendicular transition, a= 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).
Table I. Calculated Polarized LIF Intensities
F
P  S
S  S
 4 
F
4 J 13  15J 12  18J 1  8
15( J 1  1)( 2 J 1  1)
 4 
 z4  J 1  14 J 1  3
6 J 13  20 J 12  17 J 1  2
30( J 1  1)( 2 J 1  1)
 z4  J 1  13J 1  1
152 J 1  1
15 2 J 1  1
R lines of Perpendicular Transition
Relative population
1.0
0.8
J'=1
J'=3
J'=5
J'=7
J'=9
0.6
0.4
0.2
0.0
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
M'
1
2
3
4
5
6
7
8
9 10
• Polarization Ratio of the R(0) line of C3100-000 band,
(F// + F⊥)exp.
(F⊥ + F⊥)exp.
= 2.6 ± 0.2
calculated value from Table I:
(F// + F⊥)cal.
(F⊥ + F⊥)cal
= 4.5
Collisional Depolarization or Signal Saturation?
Laser Power Dependence
3.5
S = a × In
We did the experiments here!!
log S = log a + n log I
log(Signal of C3 R(0))
3.0
2.5
n=0.45  0.02
2.0
1.5
n=0.82 0.07
1.0
1.0
1.5
2.0
2.5
log(Laser Power)
3.0
3.5
Dye laser pulse energy 0.39mJ
01+1- 000
2
100- 000
2
P
R0
2
4
6
Q
0
8
2
4
6
8 10
R
(F⊥ + F⊥)
(F // + F⊥)
25692
25694
25696
25698
25700
25702
25760
25762
25764
25766
25768
25770
-1
Excitation Frequecy (cm )
2000 torr, 5% allene in He gas mixture expanded through a 500 nozzle
2
b12ρ
A23
b21ρ
A21
3
1
Effect of Saturation on the Fluorescence Polarization
 label the states connected by the laser excitation as 1> and 2>, and the
rest states not connected by the laser excitation as 3>
 during the laser pulse (Dt), the populations of each states were treated by
rate equations, ignoring the coherence effect.
dN 1 ( t )
  b12r N1(t) + (b12r+A21) N2(t),
dt
(1)
dN 2 ( t )

dt
(2)
b12r N1(t)   b12r+ -1) N2(t),
N3(t) = N0 t (t)
3)
where N0, N1(t), N2(t), and N3(t) refer to the total population, time-dependent
populations of level N1, N2, and N3. The directional Einstein coefficient b12 is
defined as,
2
2
2
b12=b21=82/h2 12 ( ˆ  ˆ ) =3B12 ( ˆ  ˆ ) .
r(n,,̂ ) denotes the laser energy density (energy per unit volume per unit
frequency interval) directed into the solid angle d with a given electric field
̂ .
Simultaneously solving Eqs. 1 and 2, the populations after the laser pulse (Dt)
are,
N1(t=Dt)=N0/2[(1+1/(21))  exp(12) Dt +
(11/(21))  exp((1+2)) Dt],
N2(t= Dt) = N0 b12r/21 [exp(12) Dt  exp((1+2)) Dt],
2 2
, where 1=(b12 r +1/42+b12rA21)
0.5
(4)
(5)
and 2= b12r+1/2.
f b12r>>A21, N2(Dt)N0/2, medium is transparent. If b12rA21, saturation may
occur.
The LIF intensity is,
I=K  N 2 ( Dt )(a21  a23 )d .
For the polarization measurements,
I

( t )dt  K  
N 0 B12 r
[exp( 1   2 )Dt  exp(( 1   2 ))Dt ]
2 1
F
   exp(( A21  A23 )t )dt .
Ftot
(6)
For the parallel polarization, Eq. (6) can be re-written by replacing the
polarization direction.
In this work, Doppler broadening and power broadening are expected.
Line broadening due to saturation can be written as,
s=(1+ S)0.5,
(7)
where s,  denote the saturated and unsaturated spectral width, and S is
defined as,
2 ( 1  2b12 r )  1
2 ( 1  2b12 r )  1
1

exp( 1   2 )Dt 
exp(( 1   2 )) Dt .
1 S
41
41
(8)
References:
1. R. Altkorn and R. N. Zare, Ann. Rev. Phys. Chem. 35, 265-89(1984).
2. W. DemtrÖder, Laser Spectroscopy, Basic Concept and
Instrumentations, Springer-Verlag (2003).
100-000 band
16
16
14
14
FWHM (GHz)
FWHM (GHz)
01+1-000 band
12
10
12
10
8
8
6
6
0.0
0.1
0.2
0.3
Laser Energy (mJ/pulse)
0.4
R(0), 2F
R(2), 2F
R(4), 2F
R(6), 2F
R(0), F+ F
R(2), F+F
R(4), F+F
R(6), F+F
0.0
0.1
0.2
0.3
Laser Energy (mJ/pulse)
0.4
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.
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.