Small angle neutron scattering and X-ray diffraction were used to study the effect of oxidation treatment on the structure and Li capacity of disordered carbons. The oxidation treatment increase the pore density and reduce the degree of parallel arrangement of graphene layers, all with no detectable change in pore size. Scattering from Li-doped samples indicates that the Lithium is most likely coating the pore surfaces rather than creating clusters inside the pores. The results are analyzed in terms of the newly proposed "potato-chips" (edge-connected graphene fragments, or "cards") model of amorphous carbons, from which we infer translation, or "surfing", of connected fragments during heat treatment.