collision induced rotational energy transfer in fs coherent anti stokes raman ... · 2005-02-27 ·...

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


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 – FWMFs – FWM

slicing

Intra and inter molecular dynamics of combustion relevant species

SLS – synchrotron project


MotivationMotivation

• 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 RETdue to line mixing at higher pressure

→ improved parameter set for common RET models→ new RET scaling law: angular momentum gap scaling


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 N2)yields only the diagonal elements of Γ

Measurements of linewidths at low pressure (typically <1 amagat for N2)yields only the diagonal elements of Γ

N2-N2N2-N2

'JJJ'J

JJJ Γ−=Γ=≠Σγ


CARS(Coherent anti-Stokes Raman Scattering)

probe signal

Stokes (tunable)

pump

V=0

V=1

Stksigk

pkprk

• line-mixing effect (collision line narrowing) sensitive to non-diagonal elements of Γ

• but interference with non-resonant χ(3)

• line-mixing effect (collision line narrowing) sensitive to non-diagonal elements of Γ

• but interference with non-resonant χ(3)

M. L. Koszykowski, R.L. Farrow, R. E. Palmer, Opt. Lett. 10 (1985) 478.

fs - CARSfs - CARS

N2 (295K)N2 (295K)


• 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 experimentFs-CARS experiment

55 O

τ

Stokes

pump

signal

probe

Stksigk

pkprk

Stksigk

pkprk

-2 0 2 4 6

χNR


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

vibrations

Time-resolved CARSTime-resolved CARS


( ) ( ) ( ) [ ]

( ) [ ] ( )∑

∫ ∫

−−

∞

∞− ∞−

−

==

−−∝

ififif

2ifi

ii

2ti

sppr

)(t'Ct'iω(0)expρρα(0)),α(t't'χ

dtdt'ρα(0)),α(t'τt'*Eτt'EtE)S(τ

α

0 100 200 300 400 500 600 700 800 900

0.0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

/ -

Delay / ps

Signal simulationSignal simulation

~ exp(-t/τcol)

N2N2

(2cαe)-1

(2wexe)-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):...112 ++−+−= ⎟

⎠⎞⎜

⎝⎛⎟

⎠⎞⎜

⎝⎛ JJevexeeωif αωω

G. Knopp FRISNO-8 2005 Ein BokekP. 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 (N2-CARS)

Flame 1350 K

Simulation (no collisions)

( )2

∑− tJtJi

J~S eb γωτ


collisionscollisions

• Reorientation

• Velocity Change (Doppler)

• Interrupt phase of µ(t)no longer in step with Eno longer in step with

surrounding molecules

• Removes molecule from interaction

• Reorientation

• Velocity Change (Doppler)

• Interrupt phase of µ(t)no longer in step with Eno longer in step with

surrounding molecules

• Removes molecule from interaction

Additional signal modulationAdditional signal modulation

How does S(τ) look like ?How does S(τ) look like ?


χ(t) may factorize into two parts

χD(t)

inhomogenous Doppler broadening and velocity

changing collisions

χD(t)

inhomogenous Doppler broadening and velocity

changing collisions

χJ(t)

molecular dynamics including relaxation

processes

χJ(t)

molecular dynamics including relaxation

processes

∑=J

JD (t)(t)(t) χχχ

D.S. Kuznetsov et. al. ,Chemical Physics, 257, 117 (2000)

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−−=

TT

TTifD

ttc

tττ

στωexp1exp)( 2

222

χ

220 v-v2T2

TT == σ

ρστ D

Fs - CARS offers no single state resolution

↓Model for relaxation

Fs - CARS offers no single state resolution

↓Model for relaxation


Isolated linesIsolated lines

Σ Lorentzians (ω)Σ Exponential decays (t)

( )∑ −∝J

J2JJJ γttiωexpbρ(t)χ

N2-N2N2-N2

• Typically high J numbers survive longerγ γ (J)

(Cars transient reflects a higher temperature for long delays)

• Initial decay overemphasized


2320 2322 2324 2326 2328 2330

Inte

nsity

Ramanshift / cm-1

Interferences in time domain CARS are produced by different pathways i f, which cannot be resolved in the frequency domain.

0 20 40 60 80 1001E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Inte

nsity

probe delay / ps

Interference effect of low j numbers in the Q-branch

Frequency shift

mixing linesmixing lines

Increases the influence of low J numbers to early decay


Γ−= IG Jiω

Mixing lines:

( )2

JJJJJ τ~iexp)1-()()S(τ ∑ −∝ GPbAbA

( )∑ −∝J

J2JJJ ttiωexpbρ(t)χ ΓI

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).

Γ = ?Γ = ?

Γ

IGAAG ⎟⎠⎞⎜

⎝⎛ +== JJ γ~ω~i1-~

Def.:

Modeling line mixingModeling line mixing

Γ is described through the collision induced rates between specific rotational states. RETΓ is described through the collision induced rates between specific rotational states. RET


Collision is not sudden finite collision duration

Include adiabatic correction (Φ)

Collision is not sudden finite collision duration

Include adiabatic correction (Φ)

Energy Corrected Sudden (ECS)-ModelEnergy Corrected Sudden (ECS)-Model

( ) ( ) Lρρρ

LL

LJJ

LJJ Q

ΦΦ

LJ L

JJ

J JLJ0

0

'

'

2

0

'' 12 1'2

2

000' +

+ ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛++=Γ ∑ρρ

ρ

'' JJJJJJ Γ−=Γ

≠Σ

From a subset of rates Q(l 0) the complete collision matrix can be constructed

Important:

Full relaxation matrix for isotropic Raman N2 Q-branch bands Full relaxation matrix for isotropic Raman N2 Q-branch bands


A long standing thread through the literature is the search for simple heuristicswith which to predict probabilities for vibrational and rotational relaxation.

A long standing thread through the literature is the search for simple heuristicswith 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.

RET matrix must correctly describe the observed frequency dependence of the spectral lineshapes as function of pressure and temperature.

Requirements for the ModelRequirements for the Model


QL

EFCS

ECS-EECS-P

ParameterΦLModel

( ) 2n

2av2

∆JJ n12τωω1

−

− ⎟⎟⎠

⎞⎜⎜⎝

⎛−+

>>

( )[ ] ⎟⎠⎞

⎜⎝⎛ −+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −

kTωβexpα1LL

TT A L

N

00

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++−−

1)}L(Lχ{1ωωγγexp 2

0

2JJ'2

⎟⎠⎞

⎜⎝⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛+ kT

ω1)(βexpTT

12LA L

N

0

0

ECS – based modelsECS – based models

Parameters are strongly correlated!Parameters are strongly correlated!

Mark Horner, Thesis, University of Cape Town

A0 N β bc

A0 1 0.8574 0.9988 -0.8902N - 1 0.8421 -0.7067β - - 1 -0.9054bc - - - 1

A0, τav, α and/or β, N, [n=1,2]

A0, β, γ, ω0, N, χ

A0, τc, LcAECS ( )( )cL

1LL0 expA +−

( ) ⎟⎠

⎞⎜⎝

⎛−+1 ' τω2

expLL

cJJ


0 25 50 75 1001E-6

1E-5

1E-4

1E-3

0.01

0.1

1

(d)(c)

(b)(a)ECS-P

Bonamy et al. (1988) fit

norm

aliz

ed C

ARS

sign

al

probe delay (ps)0 20 40 60 80 100

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1ECS-E

Bonamy and Buldyreva (2000) fit

norm

aliz

ed C

ARS

sign

al

probe delay (ps)

0 20 40 60 80 1001E-6

1E-5

1E-4

1E-3

0.01

0.1

1EFCS

Kouzov (1999) fit

norm

aliz

ed C

ARS

sign

al

probe delay (ps)0 20 40 60 80 100

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1AECS

norm

aliz

ed C

ARS

sign

al

probe delay (ps)

Model fs –CARS experiment (N2-N2)Model fs –CARS experiment (N2-N2)


0 1 2 3 4 5 60

1

2

3

4

ECS-PECS_E

norm

aliz

ed s

um o

f squ

are

erro

rs

pressure [mb]


Model Source A0 (10-3 cm-1 /

amagat)

α or β bavχc (Å)

ε

ECS-P Buldyreva 53.34 1.069 1.045 3.19 This work 33.6 (1.3) 0.906 (13) 1.502 (81) 1.62

ECS-E Bonamy 2.937 1.206 1.215 2.73 This work 3.59 (11) 1.88(7) 0.85(3) 1.09

ECFS β γ ω0 (cm-1)

Kouzov 26.2 2 1.5 100 2.93 This work 26.1(3) 1.95 0.01 125(48) 1.12

A0

τc

(fs)

Lc / ћ ε

7.70 (44) 216.77(18.2) 3.92 (12) 1

7.45 (7) 225.57 (13.1) 4 1.002

AECS :

ResultsResults

• Fit results are better than using values from literature

• main differences appear inthe adiabatic correction

Accuracy of fs – CARS measurements encourages to find expressions with reduced number of parameters


The AECS modelThe AECS model

cτ∆E ≈

c20

2

21

τ2µr2χω lllE crot ===

Rotational energy of the collision intermediateRotational energy of the collision intermediate

Uncertainty in energy of the intermediateUncertainty in energy of the intermediate


The collision induced rotational energy transfer is limited by the possible energy fluctuations of the intermediate during τc .

1χ

21∆E∆E

rot≥⇒≥

cl0 lτc ~ const.0 lτc ~ const.

Within the experimental Accuracy : 2≡cl1≈χ


( )( )cL

1LL0L expAQ +−=

Base rates:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

+1 '

'τω2exp)ω(Φ

LLcJJ

JJL

Adiabatic correction:

Two fit parameters only: A0 and τcA0 and τc

2µsm

cL ≈

Transformation to the coordinates of the probed molecule


0 1 2 3 4 5 60

10

20

30

40

50

60

0 1 2 3 4 5 60

1

2

3

4

5

6

0 1 2 3 4 5 60

2

4

6

8

10

12

0 1 2 3 4 5 60

2

4

6

8

10

12

(a)

ECS_P

A0

(10-3

cm-1/a

mag

at)

pressure (bar)

(b)

ECS_E

A0

(10-3

cm

-1/a

mag

at)

p ressure (bar)

(c)

AECS (Lc f itted)

A0 (

10-3

cm

-1/a

mag

at)

pressure (bar)

(d)

AECS (Lc= 4 h)

A0

(10-3

cm

-1/a

mag

at)

p ressure (bar)

all transients between 0.2 and 5 bar fitted simultaneouslyall transients between 0.2 and 5 bar fitted simultaneously

Fitting constant A0Fitting constant A0

G. Knopp FRISNO-8 2005 Ein BokekExperimental data from G. O. Sitz and L. Farrow, J. Chem. Phys., 93, 7883,(1990).

2 4 6 8 10 12 14

1

10

(a)

Experiment AECS ECS_P ECS_E EFCS

Γ 0,J

(10-3

cm

-1/a

tm)

J

0 2 4 6 8 10 12

0.1

1

10 (b)

Experiment AECS ECS_P ECS_E EFCS

Γ 14, J

(10

-3 c

m-1/a

tm)

J0 10 20 30

0

20

40

60(b)

AECS ECS-P ECS-E

γ J (10

-3cm

-1/a

tm)

J

0 5 10 15 20 251E-3

0.01

0.1

1

10(a)

AECS ECS-P ECS-EΓ L

12,1

0 (1

0-3 c

m-1/a

tm)

L

Comparison to state to state ratesComparison to state to state rates


0 250 500 750 1000 1250 15000

50

100

150

200

250

τ c / fs

Temperatur / K

vb

2ln8vµτ av

2 ≈=l

c

∫

∫

∞

∞−

∞

∞−=dttV

dtttV

c)(

)(τ

0 50 100 150 2000

200

400

600

800

1000

300 K

1000 K

100 K

τ c [fs

]

l

V(t) ~ 12-6 Lennard-Jones potential (σ ~ 4Å ; εLJ ~ 80 cm-1)

V(t) ~ 12-6 Lennard-Jones potential (σ ~ 4Å ; εLJ ~ 80 cm-1)

Collision duration (?) τc~ 200fsCollision duration (?) τc~ 200fs

3k2T

)T(T

LJ0

10c

ετ

=

+∝ −


Temperature dependenceTemperature 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).

0 5 10 15 20 25 300

20

40

60

80

AECS ECS-E (Ref. [5])

295 K 500K 730 K 1000 K 1500 K

γ J (10

-3 c

m-1/ a

tm)

rotational Quantum number ! No additional ! fit parameter needed! No additional !

fit parameter needed

( )TTT

ECS

cc0

0

:

ττ =

( )TTTcc

00ττ =

AECS


Collisions with higher mass partnersCollisions with higher mass partners

0 25 50 75 100 125

N2-Kr

N2-Ar

N2-Ne

N2-He

CA

RS

sig

nal

probe delay (ps)

Still: AECS has onlytwo free fit parameters:

A0 and τc

Still: AECS has onlytwo free fit parameters:

A0 and τc

( )( )( )⎪⎩

⎪⎨⎧

>−≤−=

+

tcL

tLLL

L LLτωALL,AQ C

,expexpmin

00

10

Lt is defined by :Lt is defined by :

Modification needed: Partial pressure:N2≈ 500 mb, X ≈ 4.5 bar

( )ccL

tt LLL

τω 0

11 =+


What is the meaning of the AECS modification ?What is the meaning of the AECS modification ?

During τc the energy exchange has to be sufficient ∆E ωL0 τc < 1 to allow the angular momentum transfer.During τc the energy exchange has to be sufficient ∆E ωL0 τc < 1 to allow the angular momentum transfer.

)τωexp(AQ cL00L −=

0 5 10 15 20 250.0

0.2

0.4

0.6

0.8

1.0

(a) N2-N2

QL

AM

QL

E

QL

rotational quantum number0 5 10 15 20 25

0.0

0.2

0.4

0.6

0.8

1.0

(b) N2-Kr

QL

AM

QL

E

QL

rotational quantum number


Molecule with higher polarity (CO-CO)Molecule with higher polarity (CO-CO)

A0 (mK/amagat)

τc (fs)

Lc / ћ ε

4.06 (24) 152.7 (15.5) 4.07 (14) 1 4.17 (7) 151.4 (15.0)

4 1.003

30 40 50 60 70 80 90

1E-5

1E-4

1E-3

0.01

1.16 bar 2.78 bar5.13 bar no

rmal

ized

CAR

S si

gnal

probe delay (ps)

CO-CO


0001 01 0

0000 00 0

0101 01 0

0000 10 1

0100 10 1

0100 00 0

dark statesRaman-active transitions

1974 cm-1

1962 cm-1 1973 cm-1

0 20 40 60 80 100 120 140

710 mbar

1420 mbar

100 mbar

norm

aliz

ed C

AR

S s

igna

l

probe delay (ps)

0 5 10 15 20 25 30

FFT

wavenumber (cm-1)

Including VET

VET

vibγω −−= ΓIJiG

C2H2 – C2H2 collision system C2H2 – C2H2 collision system


0 10 20 30 40 500

20

40

60

80

100

120

140

γ J (10

-3 c

m-1

/ am

agat

J

A0 (10-3 cm-1/ amagat)

τc

(fs)

γvib

(109 Hz /amagat)

Lc / ћ ε

11.43(27) 615.1 9.54(58) 4.27(44) 1

13.28 (35) 654.1 10.0(3) 4 1.015

C2H2 – C2H2C2H2 – C2H2


Thanks for your attentionThanks 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 2ћ. Just a coincidence ?


END

collision induced rotational energy transfer in fs coherent anti stokes raman ... · 2005-02-27 ·...

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