Locally Favoured Structures and Dynamic Arrest

The mechanism by which a liquid may become arrested, forming a glass or gel, is a long standing problem of condensed matter physics. While possible dynamic mechanisms have received considerable attention, the prevailing view is that ``the arrangement of atoms and molecules in glass is indistinguishable from that of a liquid.'' On the contrary, here we present direct experimental evidence of a structural mechanism for dynamical arrest. In particular, long-lived (energetically) locally favoured structures (LFS), whose geometry may prevent the system relaxing to its equilibrium state, have long been thought to play a key role in dynamical arrest. Here we propose a general definition of LFS which we identify with a novel topological method and combine these with experiments on colloidal liquid-gel, and glass-liquid-glass transitions. In these systems, the equilibrium state is crystal-fluid coexistence, and a crystal respectively: in both colloidal gels and glasses, suppression of crystallisation forms a key part of dynamical arrest. The population of LFS is a strong function of (effective) temperature in the ergodic liquid phase, rising sharply approaching dynamical arrest. We show that the ``arms'' of the colloidal gel are entirely comprised of LFS, which we argue form on shorter timescales than crystallisation. Gelation and dynamical arrest are identified with the formation of a percolating network of LFS, which we show are intimately related to dynamical heterogeneities. We seek to demonstrate that LFS can provide a structural order parameter for dynamical arrest. In the case of the glass-liquid-glass transition exhibited by ``sticky spheres'' at high density, like the colloidal gel, the LFS provide a clear structural signature of dynamical arrest.