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

The ac nonlinear dielectric response ${\chi }_3(\omega ,T)$ 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 ${\chi }_3(\omega ,T)$ indeed displays several non trivial features. It is peaked as a function of the frequency $\omega$ and obeys scaling as a function of $\omega \tau (T)$, with $\tau (T)$ 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 ${\chi }_3$ decays as a power-law of $\omega$ 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 $N_{corr}$.