A central result in the space geometry of closed twisted ribbons is Călugăreanu’s theorem (also known as White’s formula, or the Călugăreanu-White-Fuller theorem). This enables the integer linking number of the two edges of the ribbon to be written as the sum of the ribbon twist (the rate of rotation of the ribbon about its axis) and its writhe. We show that twice the twist is the average, over...

699 news & views etching of large sheets represents an attractive alternative because it is able to achieve uniform, organized arrays 7. Unfortunately, the complexity of the tools necessary for sub-10-nm patterning and an inability to control edge roughness represent significant limitations to this technique. Sprinkle, de Heer and colleagues report progress towards a very different approach, in...

Embedding non-hexagonal rings into sp2-hybridized carbon networks is considered a promising strategy to enrich the family of low-dimensional graphenic structures. However, non-hexagonal rings are energetically unstable compared to the hexagonal counterparts, making it challenging to embed non-hexagonal rings into carbon-based nanostructures in a controllable manner. Here, we report an on-surfac...

The magnetic properties of graphene-related materials, and in particular, the spin-polarized edge states predicted for pristine graphene nanoribbons (GNRs) with certain edge geometries have received much attention recently due to a range of possible technological applications. However, the magnetic properties of pristine GNRs are not predicted to be particularly robust in the presence of edge d...

We used scanning tunneling microscopy and spectroscopy (STM/S) techniques to analyze the relationships between the edge shapes and the electronic structures in as-grown chemical vapor deposition (CVD) graphene nanoribbons (GNRs). A rich variety of single-layered graphene nanoribbons exhibiting a width of several to 100 nm and up to 1 μm long were studied. High-resolution STM images highlight hi...

We describe a phenomenon of ribbon-to-fiber transformation observed in the process of spinning of single wall carbon nanotubes dispersed in polymer solutions. In the process of spinning, a gel-like ribbon comprised of nanotube bundles bound by polymer is withdrawn from a solvent bath. We show that upon crossing the liquid-air interface, the ribbon may either retain its flat shape or fold into a...

Graphene nanoribbons (GNRs) are promising candidates for next generation integrated circuit (IC) components; this fact motivates exploration of the relationship between crystallographic structure and transport of graphene patterned at IC-relevant length scales (<10 nm). We report on the controlled fabrication of pristine, freestanding GNRs with widths as small as 0.7 nm, paired with simultaneou...

A close to native structure of bulk biological specimens can be imaged by cryo-electron microscopy of vitreous sections (CEMOVIS). In some cases structural information can be combined with X-ray data leading to atomic resolution in situ. However, CEMOVIS is not routinely used. The two critical steps consist of producing a frozen section ribbon of a few millimeters in length and transferring the...

Abstract The presence of metal atoms at the edges graphene nanoribbons (GNRs) opens new possibilities toward tailoring their physical properties. We present here formation and high-resolution characterization indium (In) chains on graphene-supported GNRs. GNRs are formed when adsorbed hydrocarbon contamination crystallizes via laser heating into small ribbon-like patches a second graphitic laye...