The art of peeling tomatoes and the science of tearing

(Nanowerk Spotlight) Have you ever tried to peel a fresh tomato? Then you probably know that frustrating feeling when you end up with lots of little, mostly triangular pieces of skin. Of course you will also have remembered your grandma's trick to pour hot water over a tomato before skinning it; surprisingly, the skin then comes off easily in just a few large pieces. There are lots of other examples from our daily lives with similarly aggravating experiences: Frustrated by scotch tape that won't peel off the roll in a straight line? Angry at wallpaper that refuses to tear neatly off the wall? Cursing at the price sticker that doesn't come off in one piece? Or you dutifully follow the 'tear along the dotted line' instruction on a re-sealable bag only to be confronted with a tear that is anywhere but on the dotted line.
Physicists, mathematicians and materials engineers love these things because it gives them a chance to explain everyday phenomena with impressive looking formulas and diagrams. Wrinkling, folding and crumpling of thin films have been characterized by experiments, theory and numerical simulations. A new study now adds a new element: fracture. The results suggest that the coupling between elasticity, adhesion and fracture, imprinted in a tear shape, can be used to evaluate mechanical properties of thin films and could even be applied at the nanoscale.
tearing scotch tape
The problem: tway that adhesive tape tears in a triangular shape coming to a point. (Image: Donna Coveney)
"We explained why pulling a flap from an adhesive film always leads to pointy tears" Dr. Enrique Cerda explains to Nanowerk. "Our work is not limited to adhesive films such as scotch tape. Pointy tears are obtained when trying to pull down wallpaper, skin a fruit or open a package. We also  expect similar geometries at the nanoscale when tearing films made of a few layers of atoms. The mechanism that produces tears is very simple: pulling a flap focuses elastic energy in the line connecting the flap with the film and this energy can be released by narrowing the tear. To do that, the two sides of the flap act as fracture cracks that propagate into the film, making the flap longer, and converge to a point."
Cerda, a researcher in the Department of Physics at the University of Santiago de Chile, together with Michael LeBlanc from the University of Chicago and collaborators from the Centre National de la Recherche Scientifique (CNRS) in Paris and MIT in Cambridge, Massachusetts, has carried out a combined experimental and theoretical study to explore what is involved in determining the geometrical shapes observed when a film is ripped apart. In a paper published in the March 30, 2008 online edition of Nature Materials, they show how elasticity of thin sheets couples with adhesion and fracture to produce distinct shapes characterizing the tearing process ("Tearing as a test for mechanical characterization of thin adhesive films").
"The mechanism we describe explains the observed variation for the tear length and then its shape – this triangular shape of the tear encodes the mechanical parameters related to forms of energy involved in the process." says Cerda. "A longer tear will have a more pointy shape than a shorter one. Elastic energy is used to break the atomic bonds of the film material, so surface energy increases. When there is adhesion the narrowing process also implies that the atomic bonds between adhesive and  film are broken, and the adhesive is exposed to the air. Thus, a shorter tear will be obtained when the adhesive is very strong. It will be easier to break film-film bonds than adhesive-film bonds. A longer tear will be obtained in the opposite case."
The researchers provide a formula that predicts the tear shape based on three parameters that describe the three energies involved in the process – elasticity (stiffness), adhesive energy (how strongly the adhesive sticks to a surface) and fracture energy (how tough it is to rip). They propose a simple mechanism based on elasticity to understand the experimentally obtained, always triangular tear shapes:
A pulling force deforms the surface and focuses elastic energy in a ridge or fold that joins the flap with the film (the area where the tape is peeling from the surface). This energy can be released in two ways: by decreasing its curvature (unpeeling in the pulling direction) or by simply reducing the width of the ridge (becoming narrower). The actual direction is a combination of both effects, but always leads to a narrowing of the tear.
Tearing as a test for mechanical characterization of thin adhesive films tearing experiments with scotch tape
Left: Schematic representation of the experimental set-up. The film is attached to a solid plane using an adhesive. Then a flap is cut and joined to a metal rod that acts as a winch drum. The rotation of the rod pulls the flap and starts the tearing. Right: Experiments using a film very similar to scotch tape with a thickness of 70 µm. The film was adhered to a substrate and then a 4-cm-wide flap was pulled. The experiment was repeated seven times at the pulling speed shown in the legend. The seven resulting scanned tears are shown overlapped in the image. (Images: Dr. Cerda)
Armed with their new formula, the researchers can now measure the adhesion energy – which changes as a function of the substrate – very easily by studying the tear shape in each substrate (the adhesion energy of scotch tape, for instance, is different when applied to metal, plastic, or ceramics). This analysis can help to evaluate the mechanical properties of more complex systems that behave similarly to adhesive films.
Cerda points out that the formalism he and his collaborators have developed can be used to investigate the mechanical properties of thin adhesive films. "As thickness is reduced owing to new technologies, traditional methods used to measure mechanical properties of a material in bulk form are not applicable" he says. "For instance, materials engineers could use this method to calculate one of the three key properties, if the other two are known. This could be particularly useful in microtechnologies, such as stretchable electronics, where the characterization of thin material properties is very difficult. Or nanofilms deposited on a substrate can be peeled off and the observed tear shapes can provide information of the film material properties."
Cerda says that the researchers would like to know, for instance, the tear shapes in one layer of carbon atoms (graphene) to check how their analysis works at the atomic scale.
Another potential application is in packaging. Many industrial food and other products are packaged in materials that behave elastically. The key conclusion from the study is that fracture propagates with its own physical rules. If materials engineers learn to understand and control these rules we could ultimately all benefit from better designed packaging materials.
So, next time you scratch the edge of a scotch tape with your fingernail trying to tear off a piece, think of all the atomic bonds and surface energies you are about to mess with and try to appreciate the well-defined vertex angle of the resulting triangular, way too short piece. Or just start cursing.
By Michael is author of three books by the Royal Society of Chemistry:
Nano-Society: Pushing the Boundaries of Technology,
Nanotechnology: The Future is Tiny, and
Nanoengineering: The Skills and Tools Making Technology Invisible
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