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

Unifying different interpretations of the nonlinear response in glass-forming liquids

This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005)PRBMDO1098-012110.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.

Nonlinear dielectric effects in liquids: a guided tour

Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye's initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.

Anomalous Wien Effects in Supercooled Ionic Liquids

We have measured conductivity spectra of several supercooled monocationic and dicationic ionic liquids in the nonlinear regime by applying ac electric fields with large amplitudes up to about 180  kV/cm. Thereby, higher harmonic ac currents up to the 7th order were detected. Our results point to the existence of anomalous Wien effects in supercooled ionic liquids. Most ionic liquids studied here exhibit a conductivity-viscosity relation, which is close to the predictions of the Nernst-Einstein and Stokes-Einstein equations, as observed for classical strong electrolytes like KCl. These "strong" ionic liquids show a much stronger nonlinearity of the conductivity than classical strong electrolytes. On the other hand, the conductivity-viscosity relation of the ionic liquid [P_{6,6,6,14}][Cl] points to ion association effects. This "weak" ionic liquid shows a strength of the nonlinear effect, which is comparable to classical weak electrolytes. However, the nonlinearity increases quadratically with the field. We suggest that a theory for explaining these anomalies will have to go beyond the level of Coulomb lattice gas models.

Third harmonics nonlinear susceptibility in supercooled liquids: a comparison to the box model

The box model, originally introduced to account for the nonresonant hole burning (NHB) dielectric experiments in supercooled liquids, is compared to the measurements of the third harmonics P(3) of the polarisation, reported recently in glycerol, close to the glass transition temperature T(g) [C. Crauste-Thibierge, C. Brun, F. Ladieu, D. L'Hôte, G. Biroli, and J.-P. Bouchaud, Phys. Rev. Lett. 104, 165703 (2010)]. In this model, each box is a distinct dynamical relaxing entity (hereafter called dynamical heterogeneity (DH)) which follows a Debye dynamics with its own relaxation time τ(dh). When it is submitted to a strong electric field, the model posits that a temperature increase δT(dh), depending on τ(dh), arises due to the dissipation of the electrical power. Each DH has thus its own temperature increase, on top of the temperature increase of the phonon bath δT(ph). Contrary to the "fast" hole burning experiments where δT(ph) is usually neglected, the P(3) measurements are, from a thermal point of view, fully in a stationary regime, which means that δT(ph) can no longer be neglected a priori. This is why the version of the box model that we study here takes δT(ph) into account, which implies that the δT(dh) of the DHs are all coupled together. The value of P(3), including both the "intrinsic" contribution of each DH as well as the "spurious" one coming from δT(ph), is computed within this box model and compared to the P(3) measurements for glycerol, in the same range of frequencies and temperatures T. Qualitatively, we find that this version of the box model shares with experiments some nontrivial features, e.g., the existence of a peak at finite frequency in the modulus of P(3) as well as its order of magnitude. Quantitatively, however, some experimental features are not accounted for by this model. We show that these differences between the model and the experiments do not come from δT(ph) but from the "intrinsic" contribution of the DHs. Finally, we show that the interferences between the 3ω response of the various DHs are the most important issue leading to the discrepancies between the box model prediction and the experiments. We argue that this could explain why the box model is quite successful to account for some kinds of nonlinear experiments (such as NHB) performed close to T(g), even if it does not completely account for all of them (such as the P(3) measurements). This conclusion is supported by an analytical argument which helps understanding how a "space-free" model as the box model is able to account for some of the experimental nonlinear features.