All That Matters

Symphonies are some of the most complex musical pieces. They involve different instruments, each with their own unique sound, and each instruments section playing their own tunes. Yet, what are symphonies in comparison to the complexity of life? Proteins for example, they are made of a limited number of building blocks, amino acids, but take highly complex shapes and assume a broad range of functions in the body.

Still, there is a commonality underlying such complex systems, in many cases they are hierarchical, which means they’re made of different objects on different scales – instruments playing tunes, amino acids forming proteins and so on. As David Spivak, Markus Buehler and others from MIT have described in a recent paper, a mathematical approach, known as category theory, can be used as a versatile tool that is capable of modelling complex systems by using the underlying rules governing a structure’s components. This is a very powerful approach and there is a lot to be gained by using this mechanism in materials science, to describe biomolecules or other hierarchical materials. Moreover, their approach makes it easy to connect different complex system. To put it crudely, understanding a Beethoven symphony may also provide insights into the properties of a protein, because category theory helps us links various complex systems.

Photo by Wayne Dixon via flickr.

To understand how this works, let’s take a look at an example provided by Buehler and colleagues – spider webs. These are made of individual fibres, consisting of smaller fibrils. The fibrils are made of a nanocomposite of crystal-like structures connected by flexible links. These structures are in turn made of various amino acids.

The complex structural hierarchy of spider silk (and other systems) is of course well-known. The problem researchers face is, however, that knowing the individual components of a material doesn’t necessarily mean that the properties of  the full system are known. For example, even though the molecular composition of a protein may be known, predicting its three-dimensional shape is notoriously difficult. It is the behaviour of structural elements in the context of their use that can be so difficult to understand. And this is where category theory is useful. […]

The past year has been a great year for science with major advances in several areas. Too many exciting results to mention here. Instead, to reflect about the past year I have chosen a representative paper for each month of the year that I hope can serve as an example of the great science going on in a number of research fields. Of course, this is a highly subjective and personal collection, and indeed there might be others worth mentioning. But the aim was also to provide a balanced overview of the year that covers a variety of topics.

Of course, if you have an exciting paper to add, please feel free to use the comments section below to let us know!

Anyway, enough said, here are some of my highlights from the past year:

Simulations of electronic excitations in an iron-based superconductor. Image by Oak Ridge National Laboratory via flickr.

JANUARY – iron-based superconductors

Since they were discovered in 2008, iron-based superconductors, the pnictides, have been one of the hottest topics in condensed matter physics. Part of their appeal stems from the fact that they are based on iron, which is a magnetic element. Normally, magnets and superconductivity exclude each other.

The iron-based compounds have a similar crystal structure as the so-called cuprates, which are the materials with the highest superconducting temperatures known. The mechanism for these high-temperature superconductors is unknown, and studying the iron-based superconductors may also be relevant to the understanding of the cuprates.

This paper published in Science shows for the first time that the electrons in the iron-based superconductors show a periodic arrangement that is different to the periodicity of the atoms in the crystal. Similar observations have been made in the cuprates, and their understanding is considered important to the mechanism of high-temperature superconductivity.

Chuang, T., Allan, M., Lee, J., Xie, Y., Ni, N., Bud’ko, S., Boebinger, G., Canfield, P., & Davis, J. (2010). Nematic Electronic Structure in the “Parent” State of the Iron-Based Superconductor Ca(Fe1-xCox)2As2 Science, 327 (5962), 181-184 DOI: 10.1126/science.1181083

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Stretchable electronic arrays. The LED sheets can be twisted by 720 degrees and considerably stretched. The wavy metal wires are visible in the image on the on the right. Reprinted by permission from Macmillan Publishers Ltd. Nature Materials (2010). doi:10.1038/nmat2879

Take a piece of silicon, try to bend it and it will break. Stretch a thin film of gold and it will rupture. Conventional metals and semiconductors are brittle and not elastic at all. But these are properties that you need when you want to use electronic devices in unusual places and for unusual applications. In biomedicine for example, if you want to put a diagnostic sensor on top of a muscle. In electronics, when you want to put a large-scale solar cell on the curved top surface of a car.

Sure, you can make a thin film and warp it around a cylinder, and if you do this with electronic circuits it is called flexible electronics. Organic electronics and very thin metal films on plastic can do this. But you cannot fit a two-dimensional sheet on a sphere without stretching it. For such applications you need what is called stretchable electronics, which is different to the flexible electronics that has been around for a while.

The latest milestone has been achieved by John Rogers and colleagues from the University of Illinois in Urbana-Champaign. They demonstrate (disclaimer: in my journal, Nature Materials) a fully biocompatible and implantable stretchable structure containing large arrays of light-emitting diodes and photodetectors. The sheets are stretchable and can be twisted by more than 720 degrees without damage, and can be brought into almost any desirable shape or configuration, says Rogers. “This advance suggests a technology that can complement features available with organic light emitting diodes, where peak brightness and lifetime are limited, and conventional inorganic LEDs, where relatively thick, brittle supports restrict the way that they can be integrated together and the substrates that can be used.”

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