Nonlinear dielectric response in glass formers: Restoring forces and avoided spin-glass criticality.

Experimental measurements of nonlinear dielectric response in glass formers like supercooled glycerol or propylene carbonate have been interpreted as providing evidence for a growing thermodynamic length scale when lowering temperature. A heuristic picture based on coherently flipping "superdipoles" with disordered internal structure has been argued to capture the essence of the experimentally reported behavior, pointing to the key role of effectively disordered interactions in structural glasses. We test these ideas by devising an explicit one-dimensional model of interacting spins incorporating both the spin-glass spirit of the superdipole argument and the necessary long-time decorrelation of structural disorder, encoded here in a slow dynamics of the coupling constants. The frequency-dependent third-order response of the model qualitatively reproduces the typical humped shape reported in experiments. The temperature dependence of the maximum value is also qualitatively reproduced. In contrast, the humped shape of the third-order response is not reproduced by a simple kinetically constrained spin model with noninteracting spins. To rationalize these results, we propose a two-length-scale scenario by distinguishing between the characteristic length of dynamical heterogeneities and a rigidity length that accounts for the local tendency of spins to flip coherently as a block, in the presence of interactions. We show that both length scales are identical in the kinetically constrained spin model, while they have significantly different dynamics in the model of interacting spins.

Crossing the Frontier of Validity of the Material Time Approach in the Aging of a Molecular Glass.

We studied the physical aging of glycerol in response to upward temperature steps of amplitude ranging from 0.3 to 18 K. This was done using a specially designed experimental setup allowing quick heating of a liquid film while measuring the evolution of its dielectric properties. Despite the nonlinear evolution of these observables for large steps, a fictive temperature could be obtained. In the case of moderate step amplitudes, we checked that the material time approach in its simplest form, the single parameter aging (SPA), applies well. The memory kernel extracted from the quasi-linear regime was used to test its frontiers of validity for significant step amplitudes. We showed that the observations deviate from the prediction of the material time framework and of SPA simultaneously. As these approaches link aging to equilibrium dynamics, our results help set the bounds beyond which new theoretical arguments are needed.

Orientational dynamics in supercooled glycerol computed from MD simulations: self and cross contributions.

The orientational dynamics of supercooled glycerol is probed using molecular dynamics simulations for temperatures ranging from 323 K to 253 K, through correlation functions of first and second ranks of Legendre polynomials, pertaining respectively to dielectric spectroscopy (DS) and depolarized dynamic light scattering (DDLS). The self, cross, and total correlation functions are compared with relevant experimental data. The computations reveal the low sensitivity of DDLS to cross-correlations, in agreement with what is found in experimental work, and strengthen the idea of directly comparing DS and DDLS data to evaluate the effect of cross-correlations in polar liquids. The analysis of the net static cross-correlations and their spatial decomposition shows that, although cross-correlations extend over nanometric distances, their net magnitude originates, in the case of glycerol, from the first shell of neighbouring molecules. Accessing the angular dependence of the static correlation allows us to get a microscopic understanding of why the rank-1 correlation function is more sensitive to cross-correlation than its rank-2 counterpart.

Non-linear physical aging of supercooled glycerol induced by large upward ideal temperature steps monitored through cooling experiments.

The physical aging of supercooled glycerol induced by upward temperature steps of amplitude reaching 45 K was studied by a new method consisting in heating a micrometer-thick liquid film at a rate of up to 60 000 K/s, holding it at a constant high temperature for a controlled duration before letting it quickly cool down to the initial temperature. By monitoring the final slow relaxation of the dielectric loss, we were able to obtain quantitative information on the liquid response to the initial upward step. The so-called TNM (Tool-Narayanaswamy-Moynihan) formalism provided a good description of our observations despite the large distance from equilibrium, provided that different values of the nonlinearity parameter were used for the cooling phase and for the (much further from equilibrium) heating phase. In this form, it allowed to precisely quantify how to design an ideal temperature step, i.e., where no relaxation occurs during the heating phase. It helped bringing a clear physical understanding of how the (kilosecond long) final relaxation is related to the (millisecond long) liquid response to the upward step. Finally, it made possible the reconstruction of the fictive temperature evolution immediately following a step, evidencing the highly non-linear character of the liquid response to such large amplitude temperature steps. This work illustrates both the strengths and limitations of the TNM approach. This new experimental device offers a promising tool to study far-from-equilibrium supercooled liquids through their dielectric response.

Amorphous Order and Nonlinear Susceptibilities in Glassy Materials.

We review 15 years of theoretical and experimental work on the nonlinear response of glassy systems. We argue that an anomalous growth of the peak value of nonlinear susceptibilities is a signature of growing "amorphous order" in the system, with spin-glasses as a case in point. Experimental results on supercooled liquids are fully compatible with the random first-order transition (RFOT) prediction of compact "glassites" of increasing volume as temperature is decreased, or as the system ages. We clarify why such a behavior is hard to explain within purely kinetic theories of glass formation, despite recent claims to the contrary.

Searching for the Gardner Transition in Glassy Glycerol.

We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility χ_{3}^{(3)} from slightly below the usual glass transition temperature down to 10 K. According to the mean-field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then χ_{3}^{(3)}, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature T_{G}. We find instead that upon cooling |χ_{3}^{(3)}| decreases by several orders of magnitude and becomes roughly constant in the regime 100-10 K. We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol.