Slow Relaxation Near the Glass Transition: from the Tanaka model to glycerol Itamar Procaccia The Institute of Theoretical Physics The Chinese University of Hong Kong Work with: E. Lerner, T.S. Lo, V. Ilyin, H.G.E. Hentschel, I. Regev CUHK Sept 2008 Itamar Procaccia The Institute of Theoretical Physics The Chinese University of Hong Kong Work with: E. Lerner, T.S. Lo, V. Ilyin, H.G.E. Hentschel, I. Regev CUHK Sept 2008

The Shintani-Tanaka model: One component liquid with anisotropic potential

For the system crystallizes into hexagonal lattice with disordered ‘spins’. (The ground state has anti-ferromagnetic order). For the system fails to crystallize. Relaxation times were measured via the ‘spin’ autocorrelation function The results were fitted (as is customary in the field) to a stretched exponential form and the relaxation time was fitted to the Folger-Fulcher form Locally favoured structure

In the interesting range of temperatures 0<T<0.5 one observes 36 different stars with In more than 98% of the n-stars the central particle has the ‘good’ angle with respect to two of its neigbors.

Combinatorics The first factorial is the number of ways to choose the ‘good’ edges of the central particle This leaves I+j+k-2 edges to choose the red edges from There are 2-k green edges, and i red edges, and thus i-k+2 spins in ‘bad’ orientations. Therefore i+j+k-(I-k+2) ‘good’ ones.

The constraint Total number of ‘green’ and ‘blue’ interactions in the system:

The partition function AFM crystal

The decrease of a concentration to zero introduces a natural length-scale

Modeling the relaxation functions

The physics of the slowing down

Broad-band dielectric spectroscopy

Imagine clusters of correlated molecules in a bath of ‘liquid’.

The relaxation time The distribution of cluster sizes

The Gibbs free energy The chemical potential of the smallest cluster Constraint (very important !!)

Changing surface energy

Experiments in pores

The riddle of the data collapse