Transcript WG11.pptx

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MEASUREMENT OF ROTATIONAL STATETO-STATE RELAXATION COEFFICIENTS BY
RAMAN-RAMAN DOUBLE RESONANCE.
APPLICATION TO SELF-COLLISIONS IN
ACETYLENE.
J. L. DOMENECH, R. Z. MARTINEZ AND D. BERMEJO
Molecular Physics Department
Instituto de Estructura de la Materia (CSIC)
Serrano 123, 28006 Madrid, Spain
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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MOTIVATION
X (v, J i)M  X (v, J  f )M ;
with rate constant k f i
• Rotational energy transfer rates are relevant in a number of important
problems: energy balance in astrophysical environments, non LTE
problems, plasma diagnostics, pressure broadening of spectral lines, etc.
• Intermolecular PES are often validated by checking their ability to
reproduce the state to state collision cross sections derived from the PES
and some calculation (CC, CS, classical trajectories…).
• Experimentally, the state-to-state rates have been derived from: sound
propagation measurements, crossed molecular beam scattering
experiments, time evolution of non-equilibrium populations (double
resonance experiments, free jet mapping), line-mixing and broadening
measurements... Raman spectroscopy has provided a wealth of
information.
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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MOTIVATION
• Pressure broadening and line-mixing of Raman spectra of polarized Qbranches are largely dominated by rotationally inelastic collisions (the
polarizability tensor is not affected by elastic reorientations)
• The relationship between pressure broadening coefficients and stateto-state rate coefficients can be very simple in isotropic Raman Qbranches (within some assumptions):




(v, J iv', J i ') P 1  klower
kupper
ji 
ji 
2 c 2 

ji '
 ji



• In principle, by an inversion procedure, the k’s can be obtained from
the widths as a function of J. However, the number of unknowns is
generally higher than the experimental data available, and it is
necessary to resort to fitting and scaling laws that relate the rate
coefficients to a smaller number of parameters (EGL, IOS, ECS,…)
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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MOTIVATION
• A more direct approach to obtain the state-to-state rates is to monitor
the time evolution of non-equilibrium populations with rotational state
resolution. Time-resolved pump-probe techniques have been widely
used to address this type of problems:
– Pump: IR absorption, Stimulated Raman effect
– Probe: LIF, REMPI, IR absorption
• Our group has long experience in the measurement of collisional
effects on high resolution Raman and IR spectra.
• We have also developed a Raman-Raman double resonance technique
to record high resolution spectra from vibrationally excited states
• Could we use our Stimulated Raman techniques to obtain rotational
energy transfer rates?
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
“Inverse Raman Spectroscopy”, aka Stimulated
Raman Spectroscopy
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It is a particular case of Coherent Raman Spectroscopy (CARS, SRS,
RIKES, SRGS, ASTERISK, …)
Four EM fields couple through (3), that becomes resonant when the
frequency difference between any two of them matches a Raman allowed
transition.
1 2 3 4
1 2
R
José Luis Doménech
Instituto de Estructura de la Materia
Inverse
Raman
R
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Double resonance Raman-Raman spectroscopy of
vibrationally excited states
529 nm
532 nm
591 nm
594 nm
V=2
3
2
1
0
J
V=1
3
2
1
0
J
3
2 J
1
0
Ground
state
Pump
José Luis Doménech
Instituto de Estructura de la Materia
Spectroscopy
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Raman-Raman double resonance with time resolution
Virtual
state
Virtual
state
tens of ns
591 nm
532 nm
V=2
3
2
1
0
J
V=1
3
2
1
0
J
3
2 J
1
0
Ground
state
Bombeo
Pump
José Luis Doménech
Instituto de Estructura de la Materia
If we pump a single level of
v=1, and record spectra of
v=2←v=1 at controlled time
delays, (i.e. number of
collisions) we can monitor
the time evolution of the
rotational populations, and
obtain the state-to-state
coefficients.
Espectroscopía
Spectroscopy
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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•
If there are no other gain (pumping is over), or loss mechanisms (vibrational
relaxation, fluorescence, diffusion out of the probe volume), the change of
population of a given level is due to rotationally inelastic collisions, and can be
expressed:
dN f   k f i Ni Pdt   ki f N f Pdt
i f
•
i f
In matrix form, for all levels, applying the sum rule
k f  f   ki f
i f
•
The number of unknowns can be reduced by the the detailed balance condition:
 Ei  E f 
(2 Ji 1)
k f i ki f
exp  
(2 J f 1)
kT 

José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental approach
•
•
•
For acetylene at 150 K, we can observe up to J=21. Considering
only the odd levels, there are 55 unknowns.
Our approach is to record the populations of all accessible levels as
a function of the time delay between pump and probe stages, and
pump as many J levels in v=1 as possible.
The integrated master equation (our fitting function) is:
Eigenvectors of K
José Luis Doménech
Instituto de Estructura de la Materia
Eigenvalues of K
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental Setup
Stimulated
Brillouin Scattering
Pulse compressor
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results
SRS signal
Pump SBS
Pump PDA
José Luis Doménech
Instituto de Estructura de la Materia
Probe PDA
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results
C2H2, Pump J=7, 150 K, 1 mbar
0.45
probe J=7
probe J=3
0.4
0.35
0.3
signal / mV
0.25
0.2
0.15
0.1
0.05
400 ns
0
-0.05
-5
0
José Luis Doménech
Instituto de Estructura de la Materia
5
10
15
time / ns
20
25
30
400
35
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results: normalization
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Pump J=1, 150 K, 1 mbar
0.9
0.8
relative populations
0.7
1
3
0.6
5
0.5
7
9
11
0.4
13
15
0.3
17
19
21
0.2
0.1
0
-0.1
5
10
20
15
25
30
time / ns
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results: the matrix
Ji
Jf
1
3
5
7
9
11
13
15
17
19
21
1
3
5
7
9
11
13
15
17
19
21
-55.26
22.58
13.32
8.74
6.32
2.93
1.00
0.32
0.04
0.02
0.01
10.83
-48.19
17.27
9.03
5.45
3.04
1.80
0.70
0.07
0.01
0.00
4.97
13.45
-47.94
15.17
6.59
4.05
2.10
1.02
0.51
0.07
0.00
3.20
6.91
14.90
-48.90
12.68
6.22
3.11
1.53
0.28
0.07
0.00
2.68
4.82
7.49
14.67
-46.38
9.69
4.05
2.04
0.71
0.24
0.00
1.64
3.56
6.08
9.51
12.82
-45.47
7.21
3.22
1.25
0.17
0.01
0.83
3.14
4.71
7.10
8.00
10.76
-43.57
6.71
2.29
0.02
0.01
0.45
2.06
3.83
5.83
6.74
8.02
11.21
-45.33
7.17
0.03
0.01
0.10
0.36
3.58
1.99
4.37
5.79
7.10
13.31
-52.74
11.80
4.33
0.10
0.10
0.99
1.08
3.06
1.62
0.10
0.10
24.30
-31.49
0.04
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
20.27
0.10
-21.17
Units: s-1Torr-1;
s.d. ~10 %
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Experimental results: some caveats
• The work is in progress. There are still more measurements to do,
specially to improve the observations when pumping on J=19, J=21.
• The fit has 9 x 25 x 11 = 2475 experimental data points, to determine
55 k’s.
• However, no restriction or scaling/fitting law has been imposed on the
elements of the K matrix, other than detailed balance, sum rule and
forcing the constants in columns J=19, J=21 to be positive
• The procedure implicitly assumes a structureless collision partner.
Therefore the k’s are averages over the rotational levels of the collider
(mostly ground state molecules)
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009
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Summary and future work
• We have developed an experimental technique based on SRS pump
and SRS probe, able to monitor the evolution of rotational populations
in vibrationally excited levels.
• The work is in progress but these preliminary results show the
possibility of extracting state-to-state rate constants without resorting
to scaling or fitting laws for acetylene at 150 K.
• Future work:
– Improve the S/N in J=19, 21. Higher pressures, improve pulse
compression.
– Explore the possibility of obtaining the complete evolution within a
single shot of the spectroscopy PDA.
– Extensive comparisons with calculations and new self-broadening
measurements.
– H2, both in self collisions and as collision partner.
José Luis Doménech
Instituto de Estructura de la Materia
64th OSU International Symposium on Molecular Spectroscopy
June 22-26, 2009