We begin our discussion with the TEM results in Fig. 1. Lower magnification TEM imaging and electron diffraction confirms the successful preparation, i.e. a coverage of ca. 10% of the holes in the Quantifoil TEM grids with single- and few-layer graphene oxide membranes (Fig. 1a–c). Fig. 1d shows an atomically resolved exposure of single-layer GO. With the present setting of spherical aberration and defocus, dark contrast in this image can be directly interpreted in terms of atomic structure. This image (and many similar ones) show small patches of clean, defect free graphene (indicated by cir- cles), while most of the area is covered by adsorbates or func- tional groups with no obvious structure. The TEM images confirm that GO membranes consist of ordered (graphene- like) segments along with functionalized areas that alternate on a few-nm scale, in agreement with previous models [12,19] and experimental studies [21,22].