FORMATION OF MOLECULAR HYDROGEN

ON A GRAPHITE SURFACE

FORMATION OF MOLECULAR HYDROGEN

ON A GRAPHITE SURFACE

S. Morisset[1], F. Aguillon [2], M. Sizun [2], V. Sidis [2]

[1] Laboratoire de Mécanique, Physique et Géosciences, Université du Havre, FRANCE

[2] Laboratoire des Collisions Atomiques et Moléculaires, Université Paris-Sud, FRANCE

- Composition: - gas (99%)

- dust grains(1%)

INTERSTELLAR MEDIUM

H

H2

He ~ 10%

~ 90%

Carbon

Silicate

- Physical conditions: - dense clouds: 103 - 107 H atoms / cm3 - low temperature ~10K

- Question:

How H2 is formed ?

INTRODUCTION - H2 : fundamental constituant in cold interstellar dust grains ~10 K

- Hypothesis of H2 formation:

Two mechanisms are known :

LANGMUIR-HINSHELWOOD ELEY-RIDEAL

2grain HHH

H adsorbed

Initially:

H coming from the gas phase

The graphite surface is modelled by a coronene: C24H12 ( V. Sidis, L. Jeloaica, A.G. Borisov and S.A. Deutscher in "Molecular hydrogen in space“, (Cambridge University Press2000) pp.89-97.)

DFT calculations show the existence of:

PHYSISORPTION WELLCHEMISORPTION WELL

H

H

ELEY RIDEAL

0.3 meV < E < 0.5eV 3,5 K < T < 5800 K

LANGMUIR-HINSHELWOOD

4meV < E < 50meV 46K < T < 580 K

WAVEPACKET METHOD

• DIRECT solution of the time dependent Schrödinger equation

• Evaluation of Hamiltonian action on the wave function :

Hdt

di

2

22

rm2T

Fourier method Gauss-Legendre method

tan1

r2T

2

2

2

2

z

HH

surface

R

r

θ

y

xφ

•Propagation performed by Lanćzos method

• Obtention of reaction probability by projection at each time step

of the wave function on rovibrational states of H2 formed

=> flux analysis method

WAVEPACKET METHOD

MAPPING - Mapping in reactive valley

Interaction zone

We have to handle short wavelengths a dense grid is necessary

A huge number of points is needed

We have to handle large wavelengths a large grid is necessary

Asymptotic zone

0 1 2 3 4 5 6 7 8 9 10-0,15

-0,14

-0,13

-0,12

-0,11

-0,10

-0,09

-0,08

-0,07

-0,06

-0,05

-0,04

-0,03

-0,02

-0,01

V(a

u)

H-H distance (au)

Collision energy

Potential minimum at each value of C-H distance

We introduce a new coordinate x’ , which is a function of x (the unmapped coordinate)

x grid : non equidistant x’ grid: equidistant !!!the step x in the interaction zone is smaller than in the asymptotic zone

MAPPING

- Mapping in reactive valley

- Advantages: - faster calculation (6x to 8x) - reduction of the number of gridpoints (500100)

m2P̂

T2

'x Fourier methodJ

1x'J

1i

P̂x'

où

(Borisov A.G. J.Chem.Phys. 114 7770 (2001))DB

1dx

'dxJ

avec

ELEY-RIDEAL MECHANISM

Sudden approximation the carbon atom is fixed

C H H’

x

y

z

Coronene plan

Coronene-H

C H H’

H-H’

=> 2 degrees of freedom

Carbon atom movement ~ surface « relaxation »

=> 3 degrees of freedom

0,0 0,1 0,2 0,3 0,4

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

3D 2D sudden

Pro

babi

lity

Ecoll

(eV)

REACTION PROBABILITY

0 20 40 60 80 100 120 140 160 180 200 220 240 2600,0

0,2

0,4

0,6

0,8

1,0

2D sudden 3D

Pro

babi

lity

T (K)

LANGMUIR-HINSHELWOODMECHANISM

R

x

r

R

φ

θ

Z2

Z1

z

y

plane and rigid surface

- H atoms are physisorbed- they can freely migrate on the surface

- the study :- full dimensionality

- ν (=jz) is a constant of motion- for each ν we perform a wavepacket calculation with 3 degrees of freedom (R, r, θ) 0 < ν < 16

PROBABILITY

0,01 0,02 0,03 0,04 0,050,0

0,2

0,4

0,6

0,8

1,0

Pro

ba

bili

ty

E(eV)

0,01 0,02 0,03 0,04 0,050,0

0,2

0,4

0,6

0,8

1,0

E(eV)

0,01 0,02 0,03 0,04 0,050,0

0,2

0,4

0,6

0,8

1,0

Pro

ba

bili

ty

E(eV)

0,01 0,02 0,03 0,04 0,050,0

0,2

0,4

0,6

0,8

1,0

E(eV)

0,01 0,02 0,03 0,04 0,050,0

0,2

0,4

0,6

0,8

1,0

Pro

ba

bili

ty

E(eV)

CROSS SECTION

0,01 0,02 0,03 0,04 0,050

1

2

3

4

5

tota

l cro

ss s

ectio

n (u

a)

Ecoll

(eV)

CONCLUSION

Methods

- Wavepacket calculation @ small collision energy- Mapping technique « small » grid

Eley-Rideal mechanism

- surface relaxation favours the reaction

Langmuir-Hinshelwood mechanism

- More efficient than ER

PERSPECTIVESEley-Rideal Mechanism

- The « relaxation » of the substrate favours the reaction Account of vibrational modes of ALL carbon atoms of the

surface- How H atom can chemisorb on the graphite surface? Potential wall 0.25eV

Rôle of deffects - Isotopic effects ?

HD, DH, D2, HT, TH, T2

- Chemisorption on other surfaces ? silica ? Ice ?

Langmuir-Hinshelwood Mechanism

- H lifetime on the grain is VERY low @ T>30K Alternative LH mechanism: physisorbed H collides chemisorbed H Rôle of the porosity of the surface other surfaces: silica ? Ice ?

- Isotopic effects ? HD, D2, TH, T2