Everybody knows that cardboard paper can be a highly
anisotropic material. You can easily bend or roll it in one direction
and it is stiff in the other. If you take a close look you will find
that the paper is periodically buckled along one direction. We have now
exploited this phenomenon on the nanoscale to define the roll-up
direction of ultra-thin membranes on a substrate surface.

The intrinsic manipulation of thin inorganic or organic nanomembranes (including graphene)
on substrate surfaces has attracted great attention over recent years, since it allows to shape
two-dimensional layers into functional 3D objects of virtually any material, geometry and size.

However, there are fundamental limits in this shaping procedure, one of which is the
direction of shaping. We consider the simplest case, which is a 2D layer of rectangular shape.
If this layer is stressed, it will bend only from the "long" edges. However, for many purposes
bending from the "short" edge would be required. As we demonstrate in our work both theoretically
and experimentally, this problem can be solved by appropriately wrinkling the flat layer. We develop
a phase diagram for the direction of bending depending on wrinkle amplitude and strain gradient,
and experimentally verify our theoretical predictions.

Our findings provide fundamentally new way of control over formation of scrolled films and
nanomembranes with defined geometry and chirality. This can advance fields and applications
of self-folding nanostructures, rolled-up nanotubes and
carbon nanoscrolls (made of graphene).

P. Cendula, S. Kiravittaya, I. Mönch, J. Schumann, O. G. Schmidt
Directional roll-up of nanomembranes mediated by wrinkling
Nano Lett. 11, 236 (2011)

PDF from arxiv.org is attached.

A thin film subject to compressive strain can either bend (for large strain gradient) or wrinkle (for small strain gradient). The bending is traditionally used in thermostats (bimetal stripes), but couple of years ago, it was extended to the nanoscale thin films which can bend and roll-up to tubes with defined number of rotations. The wrinkles are also rather common in macro- and microscale thin films.
Here, we developed an equilibrium phase diagram for the shape of
compressively strained free-hanging films by total strain energy
minimization.

For small strain gradients Δε, the film wrinkles, while for sufficiently large Δε, a phase transition from wrinkling to bending occurs. We also consider competing relaxation mechanisms for free-hanging films, which have rolled up into tube structures, and we provide an upper limit for the maximum achievable number of tube rotations.

The published paper is found at http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRB...