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~

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~

A'A"

unique level

unique level

unique level

Vb=2

Vb=1

Vb=0

à 1u

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-

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⊥

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⊥)

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⊥)

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

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).

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

• 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?

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

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⊥)

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)

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

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 ) .

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

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.