Atomic hydrogen diffusion in metal lattices has been studied for a long time by QENS, e. g. [12]. The diffusion of atomic hydrogen on the surface of catalysts has
been studied scarcely [13, 14], this could be revisited since the neutron flux and the instrumentation has been tremendously improved since. Dihydrogen diffusion in porous media is a more recent topic. H2 diffusion is of interest for a number of industrial processes, including membranes for fuel cells or reactions with membrane reactors, where the zeolite acts as a porous membrane. Over the last years, a large number of studies have been conducted on MOFs, to explore the performance of these solids as energy carrier for H2. In general, for applications involving gas separation, a fast diffusion rate of the gas molecules into the porous system is as important as the adsorption uptake, the selectivity, or the regenerability.

There are few measurements on the diffusion of H2 in zeolites and MOFs, this is due to the difficulty in measuring fast sorption rates by macroscopic methods. There are also few theoretical studies, a classical approach being not sufficient at low temperatures since the de Broglie thermal wavelength is comparable to the diameter of the confining pores, requiring in this case a quantum mechanical treatment.

The self-diffusivity, Ds, of H2 in several zeolites was studied by pulsed-field gradient nuclear magnetic resonance (PFG-NMR) and QENS [15]. The self-diffu­sion coefficients were found to decrease with decreasing pore sizes of the zeolite structures, with one notable exception in silicalite. In this case, the diffusivities were found to be exceptionally small, the explanation being that H2 molecules are trapped within the pentasil chains forming the structure.

While the self-diffusivity can be determined from incoherent neutron-scattering, the transport diffusivity, Dt, can be derived from coherent neutron-scattering [16]. Normally, Dt is measured under the influence of concentration gradients, i. e. under non-equilibrium conditions. It may seem strange to derive a non-equilibrium quantity from experiments performed at equilibrium. This is because the scattering function corresponding to coherent scattering is related to the full correlation function, G(r, t), which is itself connected with the evolution of the particle density around equilibrium. This approach was already formulated by Onsager [17] in his regression hypothesis. It was later proven that the response of a system to an external perturbation can be evaluated from correlation functions of the sample at equilibrium.

For a comparison of the different results, the transport diffusivity is often rep­resented in terms of the so-called corrected diffusivity, D0, which is defined by the relation

(2.1)

where c denotes the adsorbate concentration in equilibrium with the pressurep. The term d lnp/dlnc is the thermodynamic factor. When the adsorption isotherms can be fitted with the Langmuir model, the thermodynamic factor is equal to or larger than 1 [18].