Fig. 2 | Nature Communications

Fig. 2

From: Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations

Fig. 2

Structure and dynamics at deep supercooling. a Structural relaxation time in terms of Brownian time as a function of the reduced pressure Z and volume fraction ϕ for STED, confocal44 and simulations40. Key volume fractions are indicated on the top axis. Solid black line is a Vogel–Fulcher–Tammann fit to STED data (see text for details). Dashed green line is a power law fit from mode-coupling theory1. Crosses indicate state points equilibrated beyond the avoided mode-coupling transition. b Locally favoured structure populations from hard sphere experiments and simulations. Data and structures shown are 10-membered defective icosahedra (green) and 13-membered icosahedra (purple). Solid and dashed lines are a guide to the eye. Error bars correspond to standard deviation. c Static and dynamic lengthscales ξstatic and ξslow obtained for defective icosahedra and slow-moving particles respectively. Solid lines are fitted using Eq. (2). Error bars correspond to standard deviation. d Radial distribution function g(r) for sample state points at weak supercooling, close to the mode-coupling crossover and at deeper supercooling. Curves are offset for clarity. e gLFS(r), the spatial correlation of locally favoured structure and f gslow(r), the spatial correlation of immobility (Methods section) divided by g(r) for the same state points as d. Dotted lines are fits of the Ornstein–Zernike envelope function Eq. (5)