COLLISION INDUCED ROTATIONAL ENERGY TRANSFER IN

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COLLISION INDUCED ROTATIONAL ENERGY TRANSFER IN
FS COHERENT ANTI STOKES RAMAN SCATTERING OF
SMALL MOLECULES
Gregor Knopp Paul Scherrer Institute CH-5232
Villigen PSI , Switzerland
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Paul Scherrer Institute ? General Energy
Department? Combustion Research ? Reaction
Analysis T. Gerber, P. Radi, P. Beaud, M. Tulej,
T. Dreier, M. Johnson, A. Walser, M. Meisinger,
D. Cannavo.
Frequency-resolved spectroscopyFemtosecond
spectroscopy Femtosceond X-rays
TC FWM Fs FWM slicing
Intra and inter molecular dynamics of combustion
relevant species SLS synchrotron project
? ? ?
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Motivation

• For many years the IOS/ECS approximation has
  been used together with energy gap scaling
  laws to predict probabilities for vibrational
  and rotational relaxation
• Experimental techniques to determine RET
  parameters
• - experimental collision-induced state-to-state
  rates (difficult large error bars)
• linewidth measurements (limited to low
  pressures) ? only diagonal elements of G
• Time-resolved CARS shows high sensitivity to
  RET due to line mixing at higher pressure
• ? improved parameter set for common RET
  models
• ? new RET scaling law angular momentum
  gap scaling

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Collision-induced line broadening (inverse Raman
spectroscopy)
N2-N2
Measurements of linewidths at low pressure
(typically lt1 amagat for N2)yields only the
diagonal elements of G
L.A. Rahn, R.E. Palmer, J. Opt. Soc. Am. B 3
(1986) 1164.
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CARS(Coherent anti-Stokes Raman Scattering)
N2 (295K)
M. L. Koszykowski, R.L. Farrow, R. E. Palmer,
Opt. Lett. 10 (1985) 478.

• line-mixing effect (collision line narrowing)
  sensitive to non-diagonal elements of G
• but interference with non-resonant c(3)

fs - CARS
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Fs-CARS experiment

• 1 mJ, 1kHz TiS laser OPA
• temporal resolution 100 fs
• forward BOXCAR configuration
• cell pressure up to 5 bar
• room temperature
• only isotropic signal (magic angle)

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Time-resolved CARS
rotations ?   
 
vibrations ?
rotations vibrations ?
Incoherent processes are Radiative decay
Collisions
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Signal simulation
N2
To observe coherent effects the observation time
for a cw field or the pulse duration for a
pulsed field must be shorter than the time
constant of any decay mechanism
exp(-t/tcol)
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Temperature dependence (N2-CARS)
Flame 1350 K
Simulation (no collisions)
P. Beaud, H.-M.Frey, T. Lang, M. Motzkus, Chem.
Phys. Lett. 344 (2001) 407.T. Lang, M. Motzkus,
H.-M. Frey, P. Beaud, J. Chem. Phys. 115 (2001)
5418.
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collisions

• Reorientation
• Velocity Change (Doppler)
• Interrupt phase of m(t)
• ? no longer in step with E
• no longer in step with surrounding molecules
• Removes molecule from interaction

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c(t) may factorize into two parts
cJ(t) molecular dynamics including relaxation
processes
cD(t) inhomogenous Doppler broadening and
velocity changing collisions
Fs - CARS offers no single state resolution ?
Model for relaxation
D.S. Kuznetsov et. al. ,Chemical Physics, 257,
117 (2000)
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Isolated lines

• Typically high J numbers survive longer
• g ? g (J)
• (Cars transient reflects a higher temperature
  for long delays)

S Lorentzians (w) S Exponential decays (t)

• Initial decay overemphasized

N2-N2
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mixing lines
Interferences in time domain CARS are produced by
different pathways i ? f, which cannot be
resolved in the frequency domain.
Interference effect of low j numbers in the
Q-branch

• Increases the influence
• of low J numbers to
• early decay

• Frequency shift

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Modeling line mixing
G
Mixing lines
Def.
Diag.
M.L. Koszykowski, R.L. Farrow, and R.E. Palmer,
Opt. Lett. 10, 478 (1985).
Parameter from J.V. Buldyreva, L Bonamy, Phys.
Rev. A 60, 370, (1999)
G ?
G is described through the collision induced
rates between specific rotational states. ?
RET
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Energy Corrected Sudden (ECS)-Model
Full relaxation matrix for isotropic Raman N2
Q-branch bands
Important
From a subset of rates Q(l?0) the complete
collision matrix can be constructed
Collision is not sudden ? finite collision
duration ? Include adiabatic correction (F)
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Requirements for the Model
RET matrix must correctly describe the observed
frequency dependence of the spectral lineshapes
as function of pressure and temperature.
A long standing thread through the literature is
the search for simple heuristics with which to
predict probabilities for vibrational and
rotational relaxation.
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ECS based models
A0, tav, a and/or b, N, n1,2
A0, b, g, w0, N, c
A0, tc, Lc
AECS
Parameters are strongly correlated!
Mark Horner, Thesis, University of Cape Town
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Model ?? fs CARS experiment (N2-N2)
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Results

• Fit results are better than
• using values from literature
• main differences appear in
• the adiabatic correction

AECS
Accuracy of fs CARS measurements encourages
to find expressions with reduced number of
parameters
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The AECS model
Rotational energy of the collision intermediate
Uncertainty in energy of the intermediate
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The collision induced rotational energy transfer
is limited by the possible energy fluctuations of
the intermediate during tc .
0 ? l tc const.
Within the experimental Accuracy
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Transformation to the coordinates of the probed
molecule
Adiabatic correction
Base rates
A0 and tc
Two fit parameters only
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Fitting constant A0
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Comparison to state to state rates
Experimental data from G. O. Sitz and L. Farrow,
J. Chem. Phys., 93, 7883,(1990).
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Collision duration (?) tc 200fs
V(t) 12-6 Lennard-Jones potential (s 4Å
eLJ 80 cm-1)
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Temperature dependence
! No additional ! fit parameter needed
Experimental data from Rahn and Palmer, J. Opti.
Soc. Am. B 3,1164 (1986). ECS-E Values Bonamy
and Buldyreva, Phys. Rev. A 63, 12715, (2000).
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Collisions with higher mass partners
Modification needed
Partial pressure N2 500 mb, X 4.5 bar
Lt is defined by
Still AECS has only two free fit parameters A0
and tc
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What is the meaning of the AECS modification ?
During tc the energy exchange has to be
sufficient DE ? wL0 tc lt 1 to allow the angular
momentum transfer.
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Molecule with higher polarity (CO-CO)
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C2H2 C2H2 collision system
VET
Including VET
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C2H2 C2H2
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Thanks for your attention

• Fs- CARS excellent method for RET investigations
• The new AECS scaling law was introduced and
  proved on
• - N2-N2
• - CO-CO
• - N2-Rare gas
• - C2H2-C2H2 collisions systems
• Two free fit parameters only for all investigated
  pressures
• and temperatures.
• Without significant loss of accuracy the angular
  momentum scaling parameter lc can be set to 2?.
  Just a coincidence ?

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