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G. Knopp FRISNO-8 2005 Ein Bokek 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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G. Knopp FRISNO-8 2005 Ein Bokek 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 spectroscopy Femtosecond 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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G. Knopp FRISNO-8 2005 Ein Bokek 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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G. Knopp FRISNO-8 2005 Ein Bokek Collision-induced line broadening (inverse Raman spectroscopy) L.A. Rahn, R.E. Palmer, J. Opt. Soc. Am. B 3 (1986) 1164. Measurements of linewidths at low pressure (typically <1 amagat for N 2 ) yields only the diagonal elements of N 2 -N 2

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G. Knopp FRISNO-8 2005 Ein Bokek CARS (Coherent anti-Stokes Raman Scattering) V=0 V=1 line-mixing effect (collision line narrowing) sensitive to non-diagonal elements of but interference with non-resonant (3) line-mixing effect (collision line narrowing) sensitive to non-diagonal elements of but interference with non-resonant (3) M. L. Koszykowski, R.L. Farrow, R. E. Palmer, Opt. Lett. 10 (1985) 478. fs - CARS N 2 (295K)

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G. Knopp FRISNO-8 2005 Ein Bokek 1 mJ, 1kHz Ti:S laser & OPA temporal resolution ~100 fs forward BOXCAR configuration cell pressure up to 5 bar room temperature only isotropic signal (magic angle) Fs-CARS experiment NR

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G. Knopp FRISNO-8 2005 Ein Bokek rotations Incoherent processes are: Radiative decay + Collisions Incoherent processes are: Radiative decay + Collisions T. Lang, M. Motzkus, H.-M. Frey and P. Beaud, J. Chem. Phys., 115 (2001). rotations & vibrations Time-resolved CARS

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G. Knopp FRISNO-8 2005 Ein Bokek Signal simulation ~ exp(-t/ col ) N2N2 N2N2 (2c e ) -1 (2w e x e ) -1 typical periods 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 Q-branch transitions ( v = 0 → v =1 ):

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G. Knopp FRISNO-8 2005 Ein Bokek 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. Temperature dependence (N 2 -CARS) Flame 1350 K Simulation (no collisions)

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G. Knopp FRISNO-8 2005 Ein Bokek collisions Reorientation Velocity Change (Doppler) Interrupt phase of t no longer in step with E no longer in step with surrounding molecules Removes molecule from interaction Reorientation Velocity Change (Doppler) Interrupt phase of t no longer in step with E no longer in step with surrounding molecules Removes molecule from interaction Additional signal modulation How does S( ) look like ?

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G. Knopp FRISNO-8 2005 Ein Bokek (t) may factorize into two parts D (t) inhomogenous Doppler broadening and velocity changing collisions D (t) inhomogenous Doppler broadening and velocity changing collisions J (t) molecular dynamics including relaxation processes J (t) molecular dynamics including relaxation processes D.S. Kuznetsov et. al.,Chemical Physics, 257, 117 (2000) Fs - CARS offers no single state resolution ↓ Model for relaxation Fs - CARS offers no single state resolution ↓ Model for relaxation

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G. Knopp FRISNO-8 2005 Ein Bokek Isolated lines Lorentzians ( ) Exponential decays (t) N 2 -N 2 Typically high J numbers survive longer (J) (Cars transient reflects a higher temperature for long delays) Initial decay overemphasized

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G. Knopp FRISNO-8 2005 Ein Bokek 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 Frequency shift mixing lines Increases the influence of low J numbers to early decay

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G. Knopp FRISNO-8 2005 Ein Bokek Mixing lines: Diag.: Parameter from J.V. Buldyreva, L Bonamy, Phys. Rev. A 60, 370, (1999) M.L. Koszykowski, R.L. Farrow, and R.E. Palmer, Opt. Lett. 10, 478 (1985). ? Def.: Modeling line mixing is described through the collision induced rates between specific rotational states. RET is described through the collision induced rates between specific rotational states. RET

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G. Knopp FRISNO-8 2005 Ein Bokek Collision is not sudden finite collision duration Include adiabatic correction ( ) Collision is not sudden finite collision duration Include adiabatic correction ( ) Energy Corrected Sudden (ECS)-Model From a subset of rates Q (l 0) the complete collision matrix can be constructed Important: Full relaxation matrix for isotropic Raman N 2 Q-branch bands

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G. Knopp FRISNO-8 2005 Ein Bokek A long standing thread through the literature is the search for simple heuristics with which to predict probabilities for vibrational and rotational relaxation. A long standing thread through the literature is the search for simple heuristics with which to predict probabilities for vibrational and rotational relaxation. RET matrix must correctly describe the observed frequency dependence of the spectral lineshapes as function of pressure and temperature. Requirements for the Model

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G. Knopp FRISNO-8 2005 Ein Bokek Model LL QLQL Parameter ECS-E ECS-P EFCS ECS – based models Parameters are strongly correlated! Parameters are strongly correlated! Mark Horner, Thesis, University of Cape Town A 0, av, and/or , N, [n=1,2] A 0, , , 0, N, A 0, c, L c AECS

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G. Knopp FRISNO-8 2005 Ein Bokek Model fs –CARS experiment (N 2 -N 2 )

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G. Knopp FRISNO-8 2005 Ein Bokek

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AECS : Results Fit results are better than using values from literature main differences appear in the adiabatic correction Accuracy of fs – CARS measurements encourages to find expressions with reduced number of parameters

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G. Knopp FRISNO-8 2005 Ein Bokek The AECS model Rotational energy of the collision intermediate Uncertainty in energy of the intermediate

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G. Knopp FRISNO-8 2005 Ein Bokek The collision induced rotational energy transfer is limited by the possible energy fluctuations of the intermediate during c. 0 l c ~ const. 0 l c ~ const. Within the experimental Accuracy :

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G. Knopp FRISNO-8 2005 Ein Bokek Base rates: Adiabatic correction: Two fit parameters only: A 0 and c Transformation to the coordinates of the probed molecule

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G. Knopp FRISNO-8 2005 Ein Bokek all transients between 0.2 and 5 bar fitted simultaneously Fitting constant A 0

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G. Knopp FRISNO-8 2005 Ein Bokek Experimental data from G. O. Sitz and L. Farrow, J. Chem. Phys., 93, 7883,(1990). Comparison to state to state rates

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G. Knopp FRISNO-8 2005 Ein Bokek V(t) ~ 12-6 Lennard-Jones potential ( ~ 4Å ; LJ ~ 80 cm -1 ) V(t) ~ 12-6 Lennard-Jones potential ( ~ 4Å ; LJ ~ 80 cm -1 ) Collision duration (?) c ~ 200fs

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G. Knopp FRISNO-8 2005 Ein Bokek Temperature dependence 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). ! No additional ! fit parameter needed ! No additional ! fit parameter needed AECS

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G. Knopp FRISNO-8 2005 Ein Bokek Collisions with higher mass partners Still: AECS has only two free fit parameters: A 0 and c Still: AECS has only two free fit parameters: A 0 and c L t is defined by : Modification needed: Partial pressure: N 2 ≈ 500 mb, X ≈ 4.5 bar

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G. Knopp FRISNO-8 2005 Ein Bokek What is the meaning of the AECS modification ? During c the energy exchange has to be sufficient E L0 c < 1 to allow the angular momentum transfer.

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G. Knopp FRISNO-8 2005 Ein Bokek Molecule with higher polarity (CO-CO) CO-CO

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G. Knopp FRISNO-8 2005 Ein Bokek Including VET VET C 2 H 2 – C 2 H 2 collision system

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G. Knopp FRISNO-8 2005 Ein Bokek C 2 H 2 – C 2 H 2

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G. Knopp FRISNO-8 2005 Ein Bokek Thanks for your attention Fs- CARS excellent method for RET investigations The new AECS scaling law was introduced and proved on - N 2 -N 2 - CO-CO - N 2 -Rare gas - C 2 H 2 -C 2 H 2 collisions systems Two free fit parameters only for all investigated pressures and temperatures. Without significant loss of accuracy the angular momentum scaling parameter ℓ c can be set to 2ћ. Just a coincidence ?

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G. Knopp FRISNO-8 2005 Ein Bokek END

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