Evidence of growing spatial correlations at the glass transition from nonlinear response experiments

Abstract

The ac nonlinear dielectric response $\ddot{I}{‡}_3(\ddot{I}‰,T)$ of glycerol was measured close to its glass transition temperature $T_g$ to investigate the prediction that supercooled liquids respond in an increasingly non-linear way as the dynamics slows down (as spin-glasses do). We find that $\ddot{I}{‡}_3(\ddot{I}‰,T)$ indeed displays several non trivial features. It is peaked as a function of the frequency $\ddot{I}‰$ and obeys scaling as a function of $\ddot{I}‰\ddot{I}„(T)$, with $\ddot{I}„(T)$ the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules $N_{corr}(T)$, increases as the system becomes glassy, and $\ddot{I}{‡}_3$ decays as a power-law of $\ddot{I}‰$ over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the $T$ dependence of $N_{corr}$.

22 pages, 6 figures. With respect to v1, a few new sentences were added in the introduction and conclusion, references were updated, some typos corrected.