Ergodicity failure near structural glass transformations

Relaxation timescale for glass-forming materials is analyzed within a self-consistent description introduced within percolation theory treatment of the Adam–Gibbs model. The ergodic–non-ergodic phase diagram is proposed for the case of molecular supercooled liquids in terms of the ergodic-phase instability temperature TE vs fragility. TE, being below and close to the glass-transformation temperature Tg, is established through violation of the ergodic hypothesis, i.e. by a crossover from the Gaussian (‘ergodic’) to a non-Gaussian dynamics of evolution of clusters. The finite-size fractal cluster distribution is deduced from the known Stauffer scaling form. Crossover of the compact-structure (‘ergodic’) clusters to the hole-like glassy clusters is attributed to their critical-size thermal fluctuations.