05.01.2013

Computational materials science: Soft heaps and clumpy crystals

Journal name:

Nature

Volume:

493,

Pages:

30–31

Date published:

(03 January 2013)

DOI:

doi:10.1038/493030a

Published online

02 January 2013

A detailed simulation of the packing behaviour of deformable particles settles the debate about whether soft matter can adopt an unconventional crystal structure at high densities — it can. The hunt is now on for a real-world example.

Subject terms:

Materials science

Chemistry

At a glance

Figures

left

Figure 1: Two particles, one centre.

a–d, Soft particles formed from polymers can change shape and interpenetrate in such a way that their centres of mass coincide, as shown here for pairs of: polymer chains (a); polymer rings (b); three-armed polymer 'stars' (c); and dendrimers (connected stars; d). The centres of mass (red dots) of the green and purple particles coincide, even though not all of the monomers overlap. (Graphic courtesy of Lorenzo Rovigatti.)

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Figure 2: The formation of clumpy crystals in two dimensions.

a, At high density, soft particles (shown as transparent spheres; diameter corresponds to each particle's typical size) might adopt an arrangement in which they partially overlap with several neighbours. The total repulsion exerted on each particle by its neighbours is high. b, Alternatively, the same particles might form a regular lattice of 'clumps'; in this case, each clump contains an average of three overlapping particles. Particles belonging to distinct clumps do not interact, so that the overall repulsion exerted on each particle is less than that in a. Particles might also be able to hop between lattice sites (arrow). Lenz and colleagues' numerical simulations¹ reveal that dendrimeric soft particles form clumpy crystals. (Graphic courtesy of Lorenzo Rovigatti.)

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right

Imagine the Rome metro at rush hour: passengers are squeezed into close contact with one another. But there is a physical limit beyond which they cannot go, because their bodies cannot occupy the same space. This common experience has an equivalent at the molecular scale, in what physicists call excluded volume — strong repulsive forces, of quantum-mechanical origin, that prevent atoms from occupying the same space. Because of this phenomenon, dense arrangements of atoms and molecules result in solids that have lattice structures, in which each particle excludes neighbours from its site in the lattice. It is therefore surprising to read Lenz and colleagues' paper¹ in Physical Review Letters, which reports that the packing of soft particles may result in unusual crystals in which each lattice site is occupied not by a single particle, but by clumps of particles.

Soft particles are nanometre- or micrometre-sized macromolecules that have a deformable shape. Focusing on polymers, for example, one can envisage several different soft particles of increasing complexity (Fig. 1). These could be: linear chains; rings, in which the ends of a polymer chain are connected; stars, in which several polymer chains are joined at a common centre; and dendrimers, in which several stars are linked together. For a fairly small energy cost, the structures of soft particles can rearrange and interpenetrate to cope with excluded-volume constraints at the molecular scale. This allows the centres of mass of different soft particles to coincide, without any overlapping of the monomers (Fig. 1).