We present a molecular dynamics study on the hydrogen storage capacity of recently synthesized polyphenylene dendrimers, a new type of carbon based materials. The study shows that the hydrogen storage is limited, in these materials, as in other carbon based materials, by the specific surface accessible to hydrogen molecules. The simulations indicate that storage does not occur at room temperature but it should be possible at low temperature and high pressures, followed by an efficient desorption at room temperature. The intrinsically weak surface-adsorbate physical interaction is responsible for the overall limited storage. For this reason we also investigate, with quantumchemical calculations on model systems, whether chemical substitution on carbon based materials, may be considered a valid strategy to increase the strength of the physisorption, to obtain more promising materials for hydrogen storage.