Physics Reports 560 (2015) 1–75 Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep The role of local structure in dynamical arrest C. Patrick Royall a,b,c,∗, Stephen R. Williams d a HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK b School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, UK c Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, UK d Research School of Chemistry, The Australian National University, Canberra, ACT 0200, Australia article info a b s t r a c t Article history: Amorphous solids, or glasses, are distinguished from crystalline solids by their lack of long- Accepted 17 November 2014 range structural order. At the level of two-body structural correlations, glassformers show Available online 4 December 2014 no qualitative change upon vitrifying from a supercooled liquid. Nonetheless the dynamical editor: Randall Kamien properties of a glass are so much slower that it appears to take on the properties of a solid. While many theories of the glass transition focus on dynamical quantities, a solid's Keywords: resistance to flow is often viewed as a consequence of its structure. Here we address the Geometric frustration viewpoint that this remains the case for a glass. Recent developments using higher-order Locally favoured structures Model glassforming systems measures show a clear emergence of structure upon dynamical arrest in a variety of glass formers and offer the tantalising hope of a structural mechanism for arrest. However a rigorous fundamental identification of such a causal link between structure and arrest remains elusive. We undertake a critical survey of this work in experiments, computer simulation and theory and discuss what might strengthen the link between structure and dynamical arrest. We move on to highlight the relationship between crystallisation and glass-forming ability made possible by this deeper understanding of the structure of the liquid state, and emphasise the potential to design materials with optimal glassforming and crystallisation ability, for applications such as phase-change memory. We then consider aspects of the phenomenology of glassy systems where structural measures have yet to make a large impact, such as polyamorphism (the existence of multiple liquid states), ageing (the time-evolution of non-equilibrium materials below their glass transition) and the response of glassy materials to external fields such as shear. ' 2014 Elsevier B.V. All rights reserved. Contents 1. Introduction and motivation..................................................................................................................................................................3 2. Phenomenology.......................................................................................................................................................................................4 2.1. Critique of experimental and simulation techniques...............................................................................................................5 2.2. Common model systems............................................................................................................................................................6 2.3. Dynamics approaching the glass transition: the Angell plot...................................................................................................7 2.4. Dynamic heterogeneity and dynamic length scales.................................................................................................................8 2.5. Crystal nucleation and the limit of metastability .....................................................................................................................9 2.6. Dynamic arrest and soft matter.................................................................................................................................................9 2.7. Gelation ....................................................................................................................................................................................... 11 ∗ Corresponding author at: HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK. E-mail addresses: [email protected] (C.P. Royall), [email protected] (S.R. Williams). http://dx.doi.org/10.1016/j.physrep.2014.11.004 0370-1573/' 2014 Elsevier B.V. All rights reserved. 2 C.P. Royall, S.R. Williams / Physics Reports 560 (2015) 1–75 2.8. Jamming and the glass transition .............................................................................................................................................. 11 3. Theories of the liquid-to-glass transition.............................................................................................................................................. 12 3.1. Mode-coupling theory................................................................................................................................................................ 12 3.2. The energy landscape ................................................................................................................................................................. 12 3.3. Adam–Gibbs theory.................................................................................................................................................................... 13 3.4. Random first-order transition theory........................................................................................................................................ 13 3.5. Montanari–Semmerjian and the rationale for a static lengthscale ......................................................................................... 15 3.6. Frank and frustration.................................................................................................................................................................. 15 3.7. Geometric frustration................................................................................................................................................................. 16 3.8. Crystal-like and competing ordering......................................................................................................................................... 18 3.9. Quasispecies................................................................................................................................................................................ 19 3.10. Facilitation and dynamical phase transitions ........................................................................................................................... 19 4. Identifying structure in amorphous systems ........................................................................................................................................ 21 4.1. Two-point correlation functions................................................................................................................................................ 21 4.2. Voronoi polyhedra...................................................................................................................................................................... 23 4.3. Bond-orientational order parameters ....................................................................................................................................... 23 4.4. The common-neighbour analysis .............................................................................................................................................. 24 4.5. The topological cluster classification......................................................................................................................................... 24 4.6. Strategies for identifying a bond network ................................................................................................................................ 24 4.7. Order-agnostic approaches........................................................................................................................................................ 25 4.8. Details in two-point correlation functions: analysis of reciprocal space data........................................................................ 26 4.9. Higher-order structure from reciprocal space data.................................................................................................................. 27 4.10. Fluctuation electron microscopy ............................................................................................................................................... 27 4.11. Nanobeam electron diffraction.................................................................................................................................................. 28 4.12. Measuring lengths close to Tg in molecular glassformers........................................................................................................ 28 5. Structure in model glassformers............................................................................................................................................................ 30 5.1. Early measurements in amorphous systems ............................................................................................................................ 30 5.2. Towards a structural mechanism? ...........................................................................................................................................