ABSTRACT
In this chapter, applied mathematical modeling in conjunction with statistical mechanics is used to investigate the storage of hydrogen between graphene and inside graphene-oxide frameworks (GOFs), which comprise double-layered graphene sheets and are uniformly separated by the molecular ligands with certain densities. Hydrogen uptake is calculated for graphene and GOFs using the equations of state in both bulk gas and adsorption phases, where the molecular interactions between a hydrogen molecule and the host structure are determined by continuous approximation. First, we verify our numerical results by comparing the hydrogen storage between the graphene sheets using the present mathematical approach with that using computational simulations and experimental results. Then, we determine the optimal hydrogen storage structures for graphene oxide frameworks across wide ranges of temperatures and external pressures. Such variations in different optimal structures could be partially explained by the idea of the geometric effect and the extra energy induced by the ligands. Theoretical methodologies that address the gas storage inside nanostructures range from several fundamental equations such as Langmuir single-layer model and the Brunauer, Emmett, and Teller (BET) multilayer model to more sophisticated computational simulations such as molecular dynamics simulations, Monte Carlo simulations, and ab initio quantum mechanical-based principles. While the fundamental equations provide almost instantaneous estimations for the surface area and the heat of adsorption using the experimental adsorption isotherms, the computationally intensive simulations provide detailed predictions of almost all aspects of adsorption but require substantial prior experiences in the eld. The missing block between two extreme methodologies could be lled by the present hybrid mathematical and statistical approach, and other continuum-based
models proposed in the current literature (Shi, F., Bhalla, A., Chen, C., Gunaratne, G.H., Jiang, J., Meletis, E.I. 2011. Atomistically-informed continuum model for hydrogen storage on graphene. Interface 57-61). The present methodology provides more insights than that of fundamental equations but demands less specic knowledge than that of computational simulations. Most importantly it facilitates rapid numerical results and generates deductive results. The theoretical results obtained from this chapter are ready to be employed for other types of gases, for example, argon, methane, etc. and nanomaterials, for example, nanotubes, zeolites, etc. without conceptual difculties.
