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

TL;DR

This study investigates heating effects in dielectric measurements of supercooled liquids, demonstrating that such effects are negligible below 204K and at the peak of nonlinear response, ensuring the validity of previous nonlinear susceptibility measurements.

Contribution

The paper provides a detailed analysis showing heating effects do not significantly influence nonlinear dielectric measurements near the glass transition, validating prior experimental results.

Findings

Heating effects are negligible below 204K at all frequencies.

Heating contribution is insignificant at the maximum of chi_3 response.

Damping of heating effects occurs at high frequencies where f/f_α >= 1.

Abstract

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.