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 H2H2 He ~ 10% ~ 90% Carbon Silicate - Physical conditions: - dense clouds: H atoms / cm 3 - low temperature ~10K - Question: How H 2 is formed ?

INTRODUCTION - H 2 : fundamental constituant in cold interstellar dust grains ~10 K - Hypothesis of H 2 formation: Two mechanisms are known : LANGMUIR-HINSHELWOOD ELEY-RIDEAL H adsorbed Initially: H coming from the gas phase

The graphite surface is modelled by a coronene: C 24 H 12 ( V. Sidis, L. Jeloaica, A.G. Borisov and S.A. Deutscher in "Molecular hydrogen in space“, (Cambridge University Press2000) pp ) DFT calculations show the existence of: PHYSISORPTION WELL CHEMISORPTION 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 : Fourier methodGauss-Legendre method z H H surface R r θ y x φ

Propagation performed by Lanćzos method Obtention of reaction probability by projection at each time step of the wave function on rovibrational states of H 2 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 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 (500  100) Fourier method où (Borisov A.G. J.Chem.Phys (2001)) 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

REACTION PROBABILITY

LANGMUIR-HINSHELWOOD MECHANISM R x r R φ θ Z2Z2 Z1Z1 z y plane and rigid surface - H atoms are physisorbed - they can freely migrate on the surface - the study : - full dimensionality - ν (=j z ) 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

CROSS SECTION

CONCLUSION Methods - Wavepacket small collision energy - Mapping technique  « small » grid Eley-Rideal mechanism - surface relaxation favours the reaction Langmuir-Hinshelwood mechanism - More efficient than ER

PERSPECTIVES Eley-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, D 2, HT, TH, T 2 - Chemisorption on other surfaces ?  silica ? Ice ? Langmuir-Hinshelwood Mechanism - H lifetime on the grain is VERY T>30K  Alternative LH mechanism: physisorbed H collides chemisorbed H  Rôle of the porosity of the surface  other surfaces: silica ? Ice ? - Isotopic effects ?  HD, D 2, TH, T 2