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