Nonlinear Susceptibility Experiments in a Supercooled Liquid: Evidence of Growing Spatial Correlations Close to T g

We give an overview of our recent works in which the a.c. nonlinear dielectric response of an archetypical glassformer (glycerol) was measured close to its glass transition temperature T g . The purpose was to investigate the prediction that the nonlinear susceptibility is directly related to the number of dynamically correlated molecules N { corr} (T). We explain that two nonlinear susceptibilities are available, namely χ3 (3) and χ3 (1), which correspond respectively to the nonlinear cubic response at the third harmonics and at the first harmonics. We describe how to measure these nonlinear responses, even if they yield signals much smaller than that of the linear response. We show that both \(\vert {\chi }_{3}^{(3)}(\omega,T)\vert\) and \(\vert {\chi }_{3}^{(1)}(\omega,T)\vert\) are peaked as a function of the angular frequency ω and mainly obeys critical scaling as a function of ωτα(T), where τα(T) is the relaxation time of the liquid. Both χ3 (3) and χ3 (1) decay with the same power-law of ω beyond the peak. The height of the peak increases as the temperature approaches T g : This yields an accurate determination of the temperature dependence of N { corr} (T), once the contribution of saturation of dipoles is disentangled from that of dynamical glassy correlations.