Evidence of Growing Spatial Correlations at the Glass Transition from Nonlinear Response Experiments

The ac nonlinear dielectric response χ₃(ω,T) of glycerol was measured close to its glass transition temperature Tg to investigate the prediction that supercooled liquids respond in an increasingly nonlinear way as the dynamics slows down (as spin glasses do). We find that χ₃(ω,T) indeed displays several nontrivial features. It is peaked as a function of the frequency ω and obeys scaling as a function of ωτ(T), with τ(T) the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules Ncorr(T), increases as the system becomes glassy, and χ₃ decays as a power law of ω 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 Ncorr.