The gas-surface interaction of molecular hydrogen D2 with a thin film of porous amorphous solid water (ASW) grown at 10K by slow vapor deposition has been studied by temperature-programed-desorption (TPD) experiments. Molecular hydrogen diffuses rapidly into the porous network of the ice. The D2 desorption occurring between 10 and 30K is considered here as a good probe of the effective surface of ASW interacting with the gas. The desorption kinetics have been systematically measured at various coverages. A careful analysis based on the Arrhenius plot method has provided the D2 binding energies as a function of the coverage. Asymmetric and broad distributions of binding energies were found, with a maximum population peaking at low energy. We propose a model for the desorption kinetics that assumes a complete thermal equilibrium of the molecules with the ice film. The sample is characterized by a distribution of adsorption sites that are filled according to a Fermi-Dirac statistic law. The TPD curves can be simulated and fitted to provide the parameters describing the distribution of the molecules as a function of their binding energy. This approach contributes to a correct description of the interaction of molecular hydrogen with the surface of possibly porous grain mantles in the interstellar medium.

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