## Getting a grip on the compaction of wires

6 June 2017

An international team of physicists, involving Daniel Bonn and Mehdi Habibi of the UvA Institute of Physics, has shown how the complicated problem of close packing of wires can be better understood. Using a statistical model, the researchers were able to describe surprising experimental results, such as the fact that for thinner wires, the density of the final state is lower, not higher, than for thicker wires.

The maximum achievable compaction of objects of different shapes has fascinated scientists since Keplerâ€™s famous conjecture about the most efficient stacking of cannonballs on battleships. In a paper that was published in Nature Communications this week, Bonn, Habibi and collaborators present experimental and theoretical work on the optimum packing of quasi-1 dimensional objects: wires, a model system for e.g. the compaction of DNA polymers in our cells. In the experimental part, the researchers inserted plastic wires with different elasticity and friction into a spherical container - see figure 1a. The freedom of the wire to rotate while being inserted (its torsion) could also be varied. Figure 1b shows some of the different resulting crumpled states, ranging from very ordered to very disordered.

(a) The container in which the wires were inserted. (b) Different resulting states. Image: D. Bonn et al.

### Efficiency

To determine the efficiency of the crumpling, the researchers measured the packing density of the final crumpled states. Ordered states such as the leftmost image in figure 1b have a higher packing density than disordered states such as the rightmost image. One surprising result of the experiments was that thinner wires, contrary to what might be expected, have a less efficient crumpling process than thicker wires.

### Model

To better understand these experimental results, the physicists used a statistical model, a so-called 'self avoiding random walk model', to describe the crumpling process. The advantage of this model is that it is much less computationally expensive than other, previously used models. Their model was shown to indeed reproduce the crumpling efficiency results that were measured in the experiments.

The result is an important step forward in getting a better grip on the crumpling of one-dimensional objects. Not only does this have useful industrial applications, where one is often interested in the reverse process, the uncrumpling of wires; there are also many potential biological and medical applications, for example to the understanding of the way DNA molecules are compacted in cell nuclei and viral capsids.

### Reference

M. Reza Shaebani, Javad Najafi, Ali Farnudi, Daniel Bonn and Mehdi Habibi, Compaction of quasi-one-dimensional elastoplastic materials. Nature Communications 8, 15568 (2017),  DOI: 10.1038/ncomms15568.