Thesis Presentation

Absolute Level-to-Level Rate Constant

Distributions in 7Li + 7Li2*

Inelastic Collisions and Exchange

Reactions

Steve Coppage

Wesleyan University

Physics Department

Middletown, CT

Spring 2009

•Foundations

•The Experiment

•The Data

•Modeling

Li + 7Li2* Collisions – Foundations

Rate constants are a measure of the level-to-level molecular dynamics of collisions and reactions. They provide the experimental underpinning for modeling molecular energy transfer and testing potentials of physical systems.

Laser-induced fluorescence is a technique to measure the relative populations of excited –state levels populated by collisions with a single excited state level.

7Li nuclei have spin 3/2. They behave as fermions. In the vapor phase, this results in an ortho-para mixture of odd and even rotational levels.

Assuming the nuclear state does not change in a collision, the molecular rotational level can only change by an even j.

Odd-j change is permitted in an exchange reaction. Observation of odd-j rotational change is observation of a change in the nuclear spin state or an exchange reaction.

Ground State

A State

14,903 cm-1

Ratcliff, Fish, and Konowalow,

J. Mol. Spec.,122, 293 (1987)

7Li2 Molecular

Potentials

Parent Lines are the result of Elastic Collisions or no Collision

and appear across many vibrational bands.

Red laser light

at

14477.26 cm-1

excites

v=0, j=18

in the

ground state

to v=2, j=19

in the

excited state.

Satellite Lines are the results of Inelastic Collisions or

Exchange Reactions and also appear across vibrational bands.

What is a Rate Constant?

Second, solve for the ratios of the densities of the final and initial levels, which is

directly proportional to the ratio of the satellite to parent line intensities.

First, write a rate equation and set it to 0 to represent a steady state.

The lifetimes and densities of Li and Li2 are known and tabulated. For v=2, j=11, the

inverse lifetime is ~5.6*107 Hz. The number density, nLi , of lithium at 660ºC ~

2·1015 cm-3. The first term in parenthesis is ~ 3·10-8 cm3/s

The ratio of the densities of the final and initial levels is calculated from our

measurements.

The rate constant has units of cm3/s. When divided by an average velocity, one can

get a thermally averaged cross section, cm2. <v> at 660ºC ~ 1900 m/s. A rate

constant of 10-12 cm3/s gives a thermally averaged cross section ~ .05 2.

n f

n i

k if n Li

f k Q n Li

tn f

d

dk if n i n Li k Q n f n Li f n f 0

k if

n f

n i

f

n Li

k Q

Experimental Setup

Schematic of the Apparatus. LPC Laser Power Controller, A 10nm FWHM Band pass

Filter, B-Polarization Rotator (~54.7º off-horizontal), C-Polarization Analyzer (set to

horizontal polarization), D-Beam Stop

The Cell

Photo Courtesy of

B. Stewart

12440-12550 11/14/06 660ºC .200 Torr

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

12440 12450 12460 12470 12480 12490 12500 12510 12520 12530 12540 12550 12560

WaveNo(cm-1

)

Co

un

t

v=2 j=19

A Typical Measurement

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

kif

[cm

3/s

]

jf

ji = 3

ji = 19ji = 11

ECS Paameters

a=5.673e-9lc=6.399e-8

γ=1.279j*=57.835

ji = 3

Ne ji = 30

ji = 11

0.0E+00

2.0E-12

4.0E-12

6.0E-12

8.0E-12

1.0E-11

1.2E-11

1.4E-11

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Vibrationally Inelastic Collisions (VI) vi = 2, vf = 1

ji = 3

ji = 11

ji = 19

Ne ji = 30

0.0E+00

2.0E-12

4.0E-12

6.0E-12

8.0E-12

1.0E-11

1.2E-11

1.4E-11

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Vibrationally Inelastic Collisions (VI) vi = 2, vf = 0

ji = 3

ji = 11

ji = 19

Ne ji = 30

0.0E+00

1.0E-12

2.0E-12

3.0E-12

4.0E-12

5.0E-12

6.0E-12

7.0E-12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Vibrationally Inelastic Collisions (VI) vi = 2, vf = 3

ji = 3

ji = 11

ji = 19

Ne ji = 30

Exchange Reactions

0.E+00

1.E-12

2.E-12

3.E-12

4.E-12

5.E-12

6.E-12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Exchanges (E) vf = 2

ji = 3

ji = 11

ji = 19

0.0E+00

5.0E-13

1.0E-12

1.5E-12

2.0E-12

2.5E-12

3.0E-12

3.5E-12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Exchanges (E) vf = 1

ji = 3

ji = 11

ji = 19

0.0E+00

5.0E-13

1.0E-12

1.5E-12

2.0E-12

2.5E-12

3.0E-12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Exchanges (E) vf = 0

ji = 3

ji = 11

ji = 19

Exchange Reactions with Prior/Statistical Distributions

0.0

0.5

1.0

1.5

2.0

2.5

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80

kif

[1

0-1

2cm

3/s

]

jf

v'=2,j'=11

vf =2

0.0

0.5

1.0

1.5

2.0

2.5

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80

kif

[1

0-1

2cm

3/s

]

jf

vf =1

v'=2, j'=11

0.0

0.5

1.0

1.5

2.0

2.5

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80

kif

[1

0-1

2cm

3/s

]

jf

vf=0

v'=2, j'=11

Modeling with QCT

QCT stands for quasi-classical trajectories, a Monte Carlo simulation of

many collisions over a random sampling of initial conditions.

LEPS Potential

LEPS stands for London, Eyring, Polanyi, and

Sato

First used with H3, it is a mixture of an

attractive singlet state with a repulsive triplet

state. Whitehead used one to model the

ground state Li exchange reaction.

We use a fit to the A-state singlet to assure

correct asymptotic behavior and vary the

triplet parameters to find the best QCT fit.

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

200.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0

Cro

ss S

ectio

n (Å

2)

Energy (kcal/mole)

Whitehead Trajectory Study 1976/Wesleyan 2008 Total Reaction Cross Sections, v=0 j=10

1976 2008

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Rotationally Inelastic Collisions (RI) with QCT

vi = vf = 2ji = 3

ji = 11

ji = 19

0.0E+00

2.0E-12

4.0E-12

6.0E-12

8.0E-12

1.0E-11

1.2E-11

1.4E-11

1.6E-11

1.8E-11

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Vibrationally Inelastic Collisions (VI) with QCT

vi = 2, vf = 1

0.0E+00

2.0E-12

4.0E-12

6.0E-12

8.0E-12

1.0E-11

1.2E-11

1.4E-11

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

kif

[cm

3/s

]

jf

Vibrationally Inelastic Collisions (VI) vi = 2, vf = 0

-200

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

01

23

45

67

89

10

1,800-2,000

1,600-1,800

1,400-1,600

1,200-1,400

1,000-1,200

800-1,000

600-800

400-600

200-400

0-200

-200-0

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

0 1000 2000 3000 4000 5000v (m/s)

Laser-prepared relative velocity distribution (929K)

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

1800-2000

1600-1800

1400-1600

1200-1400

1000-1200

800-1000

600-800

400-600

200-400

0-200

-200-0

0.0E+00

5.0E-13

1.0E-12

1.5E-12

2.0E-12

2.5E-12

3.0E-12

3.5E-12

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68

kif

[cm

3/s

]

jf

Exchanges – vf = 2

Exchanges – vf = 1

Acknowledgements

Brian Stewart, Thesis Advisor

Paula Matei, Ramesh Marhatta

Lutz Hüwel and Reinhold Blümel, Committee Members

The Wesleyan Chemical-Physics Community

References

S. Coppage, P. Matei, B. Stewart, J. Chem. Phys., 128, 241103 (2008)

Levine Raphael D. , Molecular Reaction Dynamics, Clarendon Press,

N.Y. (2005)

Whitehead, J. C. , Molecular Physics, 1, 177 (1975)