The physisorptive capacity of graphite-based nanomaterials for hydrogen is strongly dependent on their internal surface areas and pore dimensions. We have made electrospun graphitic nanofibres (GNF): promising nanostructures that we have doped with potassium to improve H2 storage capacity, opening the intergraphene spaces to H2 and increasing the binding through charge transfer. By analogy with our recent work on the graphite intercalate KC24(H2)x, we aim to study the para-H2 binding and diffusion in a K-doped GNF sample as a function of H2 loading. Access to a wide energy range is essential to probe H2 sites strongly bound close to K ions. Using TOSCA will allow us to study H2 librations in the 50 meV region while a complementary low-energy INS experiment to study tunnelling and diffusion is proposed on IRIS, assessing the tuneability of these materials for hydrogen storage.