Study of the heating effect contribution to the nonlinear dielectric response of a supercooled liquid

We present a detailed study of the heating effects in dielectric measurements carried out on a liquid. Such effects come from the dissipation of the electric power in the liquid and give a contribution to the nonlinear third harmonics susceptibility chi_3 which depends on the frequency and temperature. This study is used to evaluate a possible `spurious contribution to the recently measured nonlinear susceptibility of an archetypical glassforming liquid (Glycerol). Those measurements have been shown to give a direct evaluation of the number of dynamically correlated molecules temperature dependence close to the glass transition temperature T_g~190K (Crauste-Thibierge et al., Phys. Rev. Lett 104,165703(2010)). We show that the heating contribution is totally negligible (i) below 204K at any frequency; (ii) for any temperature at the frequency where the third harmonics response chi_3 is maximum. Besides, this heating contribution does not scale as a function of f/f_{alpha}, with f_{alpha}(T) the relaxation frequency of the liquid. In the high frequency range, when f/f_{alpha} >= 1, we find that the heating contribution is damped because the dipoles cannot follow instantaneously the temperature modulation due to the heating phenomenon. An estimate of the magnitude of this damping is given.

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 $N_{corr}$.