The above observations of continued increases in conductivity in the two directions are worth comparison with the conducting behaviors of the polyurethane nanocomposites containing horizontally-aligned graphene sheets. The composites containing self-aligned, reduced graphene oxide (rGO) presented two largely different variations in electrical conductivity depending on the measurement direction with respect to the alignment [46]: the conductivity measured along the alignment increased similarly to that for the parallel to alignment in Fig. 6a, whereas that measured through the thickness direction tended to abruptly drop at rGO content above the percolation threshold after the initial increase. There are two possible reasons that may be responsible for the totally different conducting behavior in the thickness direction of the aligned rGO composites, namely (i) there were increasingly fewer conducting networks established along the perpendicular direction; and (ii) the presence of insulating oxygenated groups on the rGO basal plane and edges effectively prevented the electron hopping from taking place between the adjacent conductive fillers [47]. It appears, however, that the electron hopping easily took place even through the perpendicular direction in the composites containing aligned, mildly-functionalized CNTs used in this study (Fig. 6b).