Two-Dimensional Melting of Hard Spheres Experimentally Unravelled After 60 Years

Researchers from the group of Professor Roel Dullens at Oxford’s Department of Chemistry have experimentally elucidated how melting of a two-dimensional solid of hard spheres occurs. With this work they resolve one of the most fundamentally important but still outstanding issues in condensed matter science. In addition, these results provide the cornerstone for the further understanding and development of two-dimensional materials.

The melting of a solid into a liquid is one of the most commonly experienced scientific phenomena. However, understanding this transformation is especially mysterious for solids in two-dimensions. Here, the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory proposes that an intermediate, partially disordered state, called the ‘hexatic’, exists between the solid and liquid. Substantial effort has been made towards the understanding of these ‘topological’ transitions, for which Kosterlitz and Thouless were awarded the 2016 Nobel Prize in Physics. Yet for the simplest interacting system of many particles, two-dimensional hard spheres, there has been an astonishing lack of consensus despite the first simulations being performed over 60 years ago.

Image: The interface between the liquid (top) and hexatic (bottom) states.

Two-dimensional hard spheres

Hard spheres are simply solid balls that cannot overlap. When these spheres are confined to monolayer, just like the balls on a snooker table, this corresponds to a system of two-dimensional hard spheres. A collection of hard spheres is the simplest possible system that exhibits melting from a solid into a liquid.

Colloidal particles

Colloidal particles have a typical size between a nanometre (a millionth of millimetre) and a micrometre (a thousandth of a millimetre). Spherical colloidal particles suspended in a liquid such as water are the best experimental realisation of micrometre-sized hard spheres (the scale bar in the image below corresponds to 1 micro-metre).

Recent research

Dr Alice Thorneywork and co-workers used optical microscopy to study monolayers of colloidal model hard spheres (see box 2) tilted by a small angle to introduce a gradient in the particle concentration. For hard spheres, the behaviour is governed only by this concentration, which allowed them to identify and characterize the liquid, hexatic, and solid states and the nature of the transitions between them in a single experiment. The results show that the melting occurs via a continuous solid-hexatic transition followed by a first order hexatic-liquid transition.