The optimum average nanopore size for hydrogen storage in carbon nanoporous materials

Abstract

A thermodynamical model of hydrogen storage in slitpores is presented and applied to carbon and BN nanoporous materials. The model accounts for the quantum effects of the molecules in the confining potential of the slitpores. A feature of the model is a new equation of state (EOS) of hydrogen, valid over a range of pressures wider than any other known EOS, obtained using experimental data in the range 77–300 K and 0–1000 MPa, including data in the region of solid hydrogen. The model reproduces the experimental hydrogen storage properties of different samples of activated carbons and carbide-derived carbons at 77 and 298 K and at pressures between 0 and 20 MPa, for an average nanopore width of about 5 Å. The model predicts that in order to reach the US Department of Energy hydrogen storage targets for 2010, the nanopore widths should be equal to or larger than 5.6 Å for applications at low temperatures, 77 K, and any pressure, and about 6 Å for applications at 300 K and at least 10 MPa.

Introduction

Much effort has been dedicated to investigate the possibilities of an efficient hydrogen storage for on-board automotive applications. There are well defined storage targets in order to have a hydrogen-based vehicle whose performance equals that of the present fossil fuel based vehicles. The goals established by the US Department of Energy (DOE) for the year 2010 are¹ at least 6 wt% of hydrogen and a hydrogen molar volume lower than 44.76 cm³/mole. Molecular hydrogen can be stored as physisorbed on low weight materials with a large specific surface area (SSA): carbon nanotubes [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], activated carbons (ACs), carbide-derived carbons (CDCs) and other carbon nanostructures [10], [13], [14], [15], [16], [17], alkali-doped carbon nanotubes and nanostructures [18], [19], [20], [21], [22], [23], and metal-organic frameworks (MOFs) [24], [25], [26], [27], [28], [29].

One operational requisite is the reversible adsorption at room temperature and low and medium pressures. Thermodynamic estimations [6] showed that, for this to occur, the binding energy of molecular hydrogen to those surfaces should be about 300–400 meV/molecule. The binding energy of a hydrogen molecule to a typical graphitic surface is only about 100 meV/molecule. Hence, it is necessary to increase the binding energy by a factor of three or four. A possible way is to allow the interaction of the molecule with two or more surfaces at the same time. This can be achieved inside nanopores. A graphene slitpore gives a simple model for the pores existing in nanoporous carbon materials such as ACs and CDCs. That slitpore consists of two parallel graphene layers separated a certain interlayer distance d.

The purpose of this work is the understanding and prediction of the hydrogen storage properties of carbon and BN nanoporous materials. Comparison is made with experiments for ACs and CDCs. Patchkovskii et al. [11] proposed a thermodynamical model to study the hydrogen storage in graphene slitpores. We have introduced some important corrections and the improved models are described in Sections 2 Model for hydrogen storage in slitpores, 3 The Mills–Younglove model. One of the improvements consists in using a new equation of state for hydrogen valid in the region 0–1000 MPa and 77–300 K, by fitting experimental data [30], [31]. Tests of the results given by the different models when applied to graphene slitpores are presented in Section 4. The new models correct unphysical results of the original model at low temperatures. In Section 5 we show that our model reproduces well the experimental trends of a wide set of samples of ACs and CDCs, like the saturation of gravimetric capacities for increasing pressure at 77 K, and the linear behaviour with pressure at 300 K. The theoretical results also agree quantitatively with the experimental results on different samples of ACs and CDCs at 77 and 298 K and at different pressures [10], [14], [15], [17], [21] for graphene slitpores of about 5.0–5.1 Å. Finally, our model predicts that carbon and BN nanoporous materials with nanopores of 5.6 and 6.0 Å of width may reach the DOE targets at 77 and 300 K, respectively.