Nonlinear dielectric response at the excess wing of glass-forming liquids

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Strong increase of correlations in liquid glycerol observed by nonlinear dielectric techniques

Nonlinear dielectric measurements are an important tool to access material properties and dynamics concealed in their linear counterparts, but the available data are often intermittent and, on occasion, even contradictory. Employing and refining a recently developed technique for high ac field dielectric measurements in the static limit, we ascertain nonlinear effects in glycerol over a wide temperature range from 230 to 320 K. We find that the temperature dependence of the Piekara factor a, which quantifies the saturation effect, changes drastically around 290 K, from ∂a/∂T = +1.4 to -130 in units of 10^-18 V² m^-2 K^-1. These high values of |a| quantify not only elevated dielectric saturation effects but also indicate a temperature driven increase in higher-order orientational correlations and considerable correction terms with respect to the central limit theorem. No signature of this feature can be found in the corresponding low field data.

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.

Shadow glass transition as a thermodynamic signature of β relaxation in hyper-quenched metallic glasses

One puzzling phenomenon in glass physics is the so-called 'shadow glass transition' which is an anomalous heat-absorbing process below the real glass transition and influences glass properties. However, it has yet to be entirely characterized, let alone fundamentally understood. Conventional calorimetry detects it in limited heating rates. Here, with the chip-based fast scanning calorimetry, we study the dynamics of the shadow glass transition over four orders of magnitude in heating rates for 24 different hyper-quenched metallic glasses. We present evidence that the shadow glass transition correlates with the secondary (β) relaxation: (i) The shadow glass transition and the β relaxation follow the same temperature-time dependence, and both merge with the primary relaxation at high temperature. (ii) The shadow glass transition is more obvious in glasses with pronounced β relaxation, and vice versa; their magnitudes are proportional to each other. Our findings suggest that the shadow glass transition signals the thermodynamics of β relaxation in hyper-quenched metallic glasses.

Mechanical and dielectric response within and beyond the linear regime

In this work a comparison of dielectric and mechanical data is presented based on experiments within the linear response limit and beyond that limit. The linear dynamic and shear-mechanical response is discussed in terms of the molecular supercooled liquid tetramethyl-tetraphenyl-trisiloxane. As the dynamics measured by the two methods depict the same temperature-dependence, the underlying cause for the observed responses is assumed to be identical for both methods, namely structural relaxation. The comparison of dielectric and mechanical measurements under high excitation amplitudes reveals that this cannot be assumed for the nonlinear response: Mechanical experiments on metallic glasses suggest that involved energies are clearly beyond k _B T, with observed nonlinear effects based on the activation of microstructural plastic rearrangements. In contrast, nonlinear dielectric measurements on another molecular glass-former involve energies clearly below k _B T, so that nonlinear dielectric effects occur due to energy uptake from the electric field or entropy-based changes in the dynamics, but are very unlikely connected to the triggering of plastic rearrangements by the applied electric field.

Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields

The generalized Langevin equation (GLE) can be derived from a particle-bath Hamiltonian, in both classical and quantum dynamics, and provides a route to the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT). All previous studies have focused either on particle-bath systems with time-independent external forces only, or on the simplified case where only the tagged particle is subject to the external time-dependent oscillatory field. Here we extend the GLE and the corresponding FDT for the more general case where both the tagged particle and the bath oscillators respond to an external oscillatory field. This is the example of a charged or polarizable particle immersed in a bath of other particles that are also charged or polarizable, under an external ac electric field. For this Hamiltonian, we find that the ensemble average of the stochastic force is not zero, but proportional to the ac field. The associated FDT reads as 〈F_{P}(t)F_{P}(t^{'})〉=mk_{B}Tν(t-t^{'})+(γe)^{2}E(t)E(t^{'}), where F_{p} is the random force, ν(t-t^{'}) is the friction memory function, and γ is a numerical prefactor.

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.

Complex Dynamics of Water in Protein Confinement

This paper studies single-molecule and collective dynamics of water confined in protein powders by means of molecular dynamics simulations. The single-particle dynamics show a modest retardation compared to the bulk but become highly stretched in the powder, with the stretching exponent of ≃0.2. The collective dynamics of the total water dipole are affected by intermolecular correlations inside water and by cross-correlations between the water and the protein. The dielectric spectrum of water in the powder has two nearly equal-amplitude peaks: a Debye peak with ≃16 ps relaxation time and a highly stretched peak with the relaxation time of ≃13 ns and a stretching exponent of ≃0.12. The slower relaxation component is not seen in the single-molecule correlation functions and can be assigned to elastic protein motions displacing water in the powder. The loss spectrum of the intermediate scattering function reported by neutron-scattering experiments is also highly stretched, with the high-frequency wing scaling according to a power law. Translational dynamics can become much slower in the powder than in the bulk but are overshadowed by the rotational loss in the overall loss spectrum of neutron scattering.

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.

Nonlinear permittivity spectra of supercooled ionic liquids: Observation of a "hump" in the third-order permittivity spectra and comparison to double-well potential models

We have measured the third-order permittivity spectra ε₃³ of a monocationic and of a dicationic liquid close to the glass transition temperature by applying ac electric fields with large amplitudes up to 180 kV/cm. A peak ("hump") in the modulus of ε₃³ is observed for a mono-cationic liquid after subtraction of the dc contribution from the imaginary part of ε₃³. We show that the origin of this experimental "hump" is a peak in the imaginary part of ε₃³, with the peak height strongly increasing with decreasing temperature. Overall, the spectral shape of the third-order permittivity of both ionic liquids is similar to the predictions of a symmetric double well potential model, although this model does not predict a "hump" in the modulus. In contrast, an asymmetric double well potential model predicts a "hump," but the spectral shape of both the real and imaginary part of ε₃³ deviates significantly from the experimental spectra. These results show that not only the modulus of ε₃³ but also its phase is an important quantity when comparing experimental results with theoretical predictions.

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.

Nonlinear dielectric effect in supercritical diethyl ether

Nonlinear dielectric effect (NDE) describes changes of dielectric permittivity induced by a strong electric field in a liquid dielectric. The most classical finding related to this magnitude is the negative sign of NDE in liquid diethyl ether (DEE), recalled by Peter Debye in his Nobel Prize lecture. This article shows that the positive sign of NDE in DEE is also possible, in the supercritical domain. Moreover, NDE on approaching the gas-liquid critical point exhibits a unique critical effect described by the critical exponent ψ ≈ 0.4 close to critical temperature (T(C)) and ψ ≈ 0.6 remote from T(C). This can be linked to the emergence of the mean-field behavior in the immediate vicinity of T(C), contrary to the typical pattern observed for critical phenomena. The multi-frequency mode of NDE measurements made it possible to estimate the evolution of lifetime of critical fluctuations. The new way of data analysis made it possible to describe the critical effect without a knowledge of the non-critical background contribution in prior.

Strain induced fragility transition in metallic glass

Relaxation dynamics are the central topic in glassy physics. Recently, there is an emerging view that mechanical strain plays a similar role as temperature in altering the relaxation dynamics. Here, we report that mechanical strain in a model metallic glass modulates the relaxation dynamics in unexpected ways. We find that a large strain amplitude makes a fragile liquid become stronger, reduces dynamical heterogeneity at the glass transition and broadens the loss spectra asymmetrically, in addition to speeding up the relaxation dynamics. These findings demonstrate the distinctive roles of strain compared with temperature on the relaxation dynamics and indicate that dynamical heterogeneity inherently relates to the fragility of glass-forming materials.

The equivalency of stress and temperature as driving force for the relaxation in metallic glasses is widely accepted. Here, Yu et al. examine this assumption in simulations and find that stress induces a fragile-to-strong transition in addition to accelerated relaxation dynamics as temperature does.

Cooperativity and heterogeneity in plastic crystals studied by nonlinear dielectric spectroscopy

The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane, where only the molecular reorientational degrees of freedom freeze without long-range order, is investigated by nonlinear dielectric spectroscopy. Marked differences to canonical glass formers show up: While molecular cooperativity governs the glassy freezing, it leads to a much weaker slowing down of molecular dynamics than in supercooled liquids. Moreover, the observed nonlinear effects cannot be explained with the same heterogeneity scenario recently applied to canonical glass formers. This supports ideas that molecular relaxation in plastic crystals may be intrinsically nonexponential. Finally, no nonlinear effects were detected for the secondary processes in cyclo-octanol.

Experimental study of dielectric property changes in DMSO–primary alcohol mixtures under low-intensity microwaves

By applying a low-intensity microwave to DMSO–primary alcohol mixtures, distinct dielectric property changes have been observed.

The β-relaxation in metallic glasses

Focusing on metallic glasses as model systems, we review the features and mechanisms of the β-relaxations, which are intrinsic and universal to supercooled liquids and glasses, and demonstrate their importance in understanding many crucial unresolved issues in glassy physics and materials science, including glass transition phenomena, mechanical properties, shear-banding dynamics and deformation mechanisms, diffusion and the breakdown of the Stokes–Einstein relation as well as crystallization and stability of glasses. We illustrate that it is an attractive prospect to incorporate these insights into the design of new glassy materials with extraordinary properties. We also outline important questions regarding the nature of β-relaxations and highlight some emerging research directions in this still-evolving field.

Frequency dependence of dielectric saturation

Dielectric saturation originates from the upper bound to dipole orientation, reached when all dipoles are aligned "perfectly" with respect to the electric field. For Debye-type dynamics, it is well established that the saturation effect is diminished at high frequencies relative to its steady-state value. Here, it is argued that a similar frequency dependence of this nonlinear dielectric effect is expected also for dispersive dynamics, provided that the system is dynamically homogeneous. By contrast, more realistic relaxation time dispersions based upon heterogeneous dynamics display a strongly reduced frequency dependence of dielectric saturation. Calculations demonstrate this effect in terms of both the fundamental and the third harmonic frequency susceptibilities. The relations of signatures of nonlinearity in different Fourier components of the response are briefly discussed.

Cooperativity and the freezing of molecular motion at the glass transition

The slowing down of molecular dynamics when approaching the glass transition generally proceeds much stronger than expected for thermally activated motions. This strange phenomenon can be formally ascribed to a temperature-dependent activation energy E(T). In the present work, via measurements of the third-order nonlinear dielectric susceptibility, we deduce the increase of the number of correlated molecules N(corr) when approaching the glass transition and find a surprisingly simple correlation of E(T) and N(corr)(T). This provides strong evidence that the noncanonical temperature development of glassy dynamics is caused by a temperature-dependent energy barrier arising from the cooperative motion of ever larger numbers of molecules at low temperatures.