Keywords: Density Functional Theory1, Classical Molecular Dynamics2, rippled graphene3, flexural phonons4, hydrogen storage5.Exploring new perspectives for green technologies is one of the challenges of the third millennium, in which the need for non--polluting and renewable powering has become primary. In this context, the use of hydrogen as a fuel is promising, since the energy released in its oxidation (~285 kJ/mole) is three times that released, on average, by hydrocarbons, and the combustion product is water (Ramage, 1983). Being hydrogen a vector of chemical energy, efficient conservation and non--dispersive transportation are the main goals. Three issues must be considered to this respect: (i) storage capacity (ii) storage stability (iii) kinetics of loading/release. Commercial technologies are currently based on cryo--compression or liquefaction of H2 in tanks. These ensure quite a high gravimetric density (GD, point (i)), namely 8--13% in weight of stored hydrogen, and a relatively low cost (Züttel 2003). However concerning points (ii) and (iii), these technologies pose problems of safety, mainly due to explosive flammability of hydrogen, and consequent unpractical conditions for transportation and use (Mori et al 2009). Therefore, research efforts are directed towards solid--state based storage systems (energy.gov, Bonaccorso et al 2015).Interactions of hydrogen with materials are classified as physisorption, occurring with H2 by means of van der Waals (vdW) forces, or chemisorption, i.e. chemical binding of H leading to the formation of hydrides (Mori et al 2009), requiring dissociative(associative) chemi(de)sorption of H2. Intermediate nature interactions, sometimes called "phenisorption", can also occur between hydrogen electrons and the electrons of external orbital of metals. Indeed, stable and robust (light) metal hydrides (Harder et al 2011, Sakintuna et al 2007 are currently considered an alternative to tanks. Their main drawback is the high chemi(de)sorption barrier, implying slow operational kinetics, which becomes acceptable only at very high temperature. Physisorption, conversely, generally results in barrierless and weak binding. It was considered as a storage mechanism in layered (Zhirko 2007) or porous (Sastre 2010) materials, and shown to be effective at low temperatures and/or high pressure. Therefore, it generally seems that if storage stability (ii) is improved then the loading/release kinetics (iii) is worsened.Graphene shows good potential to be an efficient hydrogen storage medium : carbon is among the lightest elements forming layered and porous structures, and graphene is probably the material with the largest surface to mass ratio. These two conditions are in principle optimal to produce high GD (point i). In addition, the chemical versatility of carbon allows it to interact with hydrogen both by physisorption (in sp2 hybridization) and chemisorption (Goler et al 2013) (in sp3 hybridization). ("Phenisorption" is also obtained by in graphene by functionalization with metals (Mash...
