Unlike paper, atomically thin and smooth sheets like graphene are very 'sticky' thanks to van der Waals interactions. As a result, they easily fold onto themselves all the time – it is just harder to have them fold in a controllable way. Although interlayer coupling stabilizes these folds, it provides no control over the placement of the fold, let alone the final folded shape.

"We have no 'fingers' at the nanoscale that we can use to fold origami in the regular way that we do with macroscopic pieces of paper, so we need nano-paper that can fold itself," Vincent Crespi, Distinguished Professor of Physics, Materials Science and Engineering and Chemistry at Penn State, tells Nanowerk. "In our new work we show that you can encode origami instructions into the 2D sheets just by doping."

Reporting their findings in Nano Letters ("NanoVelcro: Theory of Guided Folding in Atomically Thin Sheets with Regions of Complementary Doping"), Crespi and first author Yuanxi Wang, a Research Associate in the 2-Dimensional Crystal Consortium at Penn State (and NSF-supported Materials Innovation Platform), describe how p-type and n-type doping of 2D sheets in selected areas could be exploited as two 'colors' to guide the sheets into preferred folded shapes where complementarily doped areas maximize their mutual overlap.

graphene origami folding

The two-colorable theorem in flat-foldable origami ensures that arbitrary folding patterns are in principle accessible to this complementary doping method. It can be combined with nanoscale crumpling (by, for example, passage of 2D sheets through holes) to obtain not only control over fold placements but also the ability to distinguish between degenerate folded states, thus attaining nontrivial shapes inaccessible to sequential folding. (Reprinted with permission by American Chemical Society)

Just like traditional paper origami that results in complicated 3D structures from 2D paper, graphene origami allows the design and fabrication of carbon nanostructures that are not naturally existing but of desirable properties, for instance programmable nanocages for hydrogen storage.

"While single folds, pleats and scrolls have been extensively studied for 2D materials in the context of nanoscale origami, our paper encourages researchers in the same field to realize/explore more ambitious and complex folds – going from toddler origami to kindergarten origami – such as the 'balloon base' folds in our paper enabled by doping," notes Wang.

Fold a sheet of paper multiple times into a flattened folded-up shape and then unfold it to look at the crease pattern that you just made. That crease pattern forms a set of polygons, like it was a map of a country with various states. That map can be colored with just two colors.

Wang and Crespi show that the two types of doping possible in a semiconductor – n-type (extra electrons) and p-type (removing some electrons) – can play the role of these two colors and guide the creased sheets into preferred folded shapes where complementarily doped areas maximize their mutual overlap.

Specifically, the n- and p-dopants separated by a van der Waals gap in 2D materials show a significant affinity due to cross-sheet charge transfer and Coulomb attraction.

This p/n affinity, and how to translate it into a preferred fold pattern, is a novel approach to fabricating 3D graphene structures.

"Subjecting a nanosheet to controlled crumpling, a device that is often studied in soft matter, is also new," Wang points out. "The motivation of our work was that the two available flavors of doping (p and n) coincides with the fundamental two-color theorem in origami."

"Another motivation was that the placement of any fold line in origami is not determined by the finger that pinches the fold, but the by preceding act of aligning/overlapping a face with a face (or an edge to an edge)," he adds. "This led us to encoding the fold information into the faces to be put in contact, instead of into the fold lines. The former is also easier to achieve experimentally by selective doping using patterned masks."

A given pattern of p-type and n-type doping on the sheet can fold up in more than one way and the two scientists wanted to investigate different ways of crumpling the sheet to get the folding started that can control which of these outcomes is most prevalent.

An analogy to that is when we unfolded a paper map and now want to fold it back up, the pattern (creases) is already there but there is more than one way to fold it.

"Fortunately" says Wang, "a 2D sheet will prefer a certain way while it is being crumpled; however, the detailed effects of various ways of crumpling is yet to be explored."