Dielectric hole burning in the high frequency wing of supercooled glycerol

Mechanical spectral hole burning in glassy polymers-Investigation of polycarbonate, a material with weak β-relaxation

Mechanical spectral hole burning (MSHB) has been used to investigate the nonlinear dynamics in polymers, ranging from melts, solutions, block co-polymers, and glasses. MSHB was developed as an analog to the dielectric spectral hole burning method, which is not readily applicable in polymers due to weak dielectric response. While similar holes were observed in both mechanical and dielectric hole burning, the interpretations were different. In the latter case, it has been argued that the holes are related to dynamic heterogeneity as related to an increase in the local temperature of molecular sub-ensembles (spatial heterogeneity), while in the former case, the holes have been related to the type of dynamics (rubbery, Rouse, etc.). Recent work from our laboratories used MSHB to investigate glassy poly(methyl methacrylate) and showed evidence of hole burning and supported the hypothesis that the origin of holes was related to dynamic heterogeneity as evidenced by the holes being developed near the strong β-relaxation in PMMA. In this work, MSHB is used to study polycarbonate, which has a weak β-relaxation, and the results are compared with those observed in PMMA. We observe that the polycarbonate exhibits weak holes and the nature of the holes with a change in pump amplitude and frequency is different than observed in PMMA. These results support the hypothesis that the hole burning observed in amorphous polymers below the glass transition temperature is related to the strength of the β-transition, which, in turn, is related to molecular level heterogeneity in the material dynamics.

Mechanical spectral hole burning of an entangled polymer solution in the stress-controlled domain

Nonresonant spectral hole burning has proven to be a versatile method to characterize the dynamics of complex fluids, including polymers. Early work focused on dielectric susceptibility measurements in glass forming liquids, while recent work from our lab used mechanical viscoelastic measurements to investigate polymer melts and solutions. While the observed results were similar, the interpretations were different, with the former being interpreted by attributing the "holes" in the response as being due to dynamic heterogeneity in the system that is related to the glass or other transition, while the latter was interpreted in a way that suggested that the observed holes depend on the type of dynamics (Rouse, terminal, etc.) rather than an identifiable spatial heterogeneity. In this work, we have expanded mechanical spectral hole burning (MSHB) into the stress-controlled domain and carried out experiments in the rubbery regime of a polystyrene solution, similar to one which was tested previously with strain-controlled MSHB. The effects of pump stress amplitude, pump frequency, and waiting time were investigated. The mechanical holes in both directions (vertical and horizontal) were successfully burned, unlike the strain-controlled MSHB experiments on the same polystyrene solution, in which vertical holes were at best incomplete. The hole intensity exhibits a linear relationship with the amount of energy dissipated in the system during the large mechanical pump modification. The results suggest that the stress-controlled MSHB can be combined with strain-controlled MSHB to build a more complete framework to investigate the dynamics of polymeric materials and is consistent with the dynamic heterogeneity being related to the type of dynamics rather than to localized heating effects.

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 dielectric response at the excess wing of glass-forming liquids

We present nonlinear dielectric measurements of glass-forming glycerol and propylene carbonate applying electrical fields up to 671 kV/cm. The measurements extend to sufficiently high frequencies to allow for the investigation of the nonlinear behavior in the regime of the so-far mysterious excess wing, showing up in the loss spectra of many glass formers as a second power law at high frequencies. Surprisingly, we find a complete lack of nonlinear behavior in the excess wing, in marked contrast to the α relaxation where, in agreement with previous reports, a strong increase of dielectric constant and loss is found.

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.

Why retardation takes more time than relaxation in a linear medium

For a linear medium, it is shown that the ratio of average relaxation to retardation time is given by the ratio of the high- to the low-frequency limit of the dielectric constants, tau(M)/tau(epsilon)=epsilon_{infinity}/epsilon(s) . This statement holds for dispersive dynamics, i.e., it is not limited to the special case of exponential responses. A second general relation is found for the relative relaxation-time dispersions, which implies that the relaxation is always more stretched than its retardation counterpart. A difference equation for the charge buildup is established which provides a rationale for why retardation requires more time than its relaxation counterpart. According to the equation, the slowness of the charge buildup is due to a renewal process of continuous re-investment of potential made redundant by relaxation. The relevance of the results to experimental situations is also discussed.

Nonlinear dielectric response and thermodynamic heterogeneity in liquids

If large amplitude time-dependent fields (e.g., dielectric, magnetic, mechanical) are applied to a sample that displays relaxational modes, some energy of the external field is absorbed by the slow degrees of freedom. The weak coupling of these modes to the phonon bath leads to long persistence times of the resulting higher fictive temperature. Assuming heterogeneities regarding dielectric and thermal relaxation times, extremely strong nonlinear dielectric effects are predicted and experimentally verified. For glycerol at T = 213 K, the dielectric loss measured at 280 kV/cm increases by more than 6% over its low-field value. This nonlinearity shows a characteristic frequency dependence and implies that dielectric and thermal time constants are locally correlated in viscous liquids.

Kerr effect as a tool for the investigation of dynamic heterogeneities

We propose a dynamic Kerr effect experiment for the distinction between dynamic heterogeneous and homogeneous relaxations in glassy systems. The possibility of this distinction is due to the inherent nonlinearity of the Kerr effect signal. We model the slow reorientational molecular motion in supercooled liquids in terms of noninertial rotational diffusion. The Kerr effect response, consisting of two terms, is calculated for heterogeneous and for homogeneous variants of the stochastic model. It turns out that the experiment is able to distinguish between the two scenarios. We furthermore show that exchange between relatively "slow" and "fast" environments does not affect the possibility of frequency-selective modifications. It is demonstrated how information about changes in the width of the relaxation-time distribution can be obtained from experimental results.

Heterogeneous thermal excitation and relaxation in supercooled liquids

We investigate a phenomenological model which rationalizes the effects of dielectric hole burning on the basis of heterogeneous dielectric and specific heat relaxation in supercooled liquids. The quantitative agreement between model predictions and dielectric hole-burning observations is lost if the assumption of correlated dielectric and thermal relaxation times is removed from the model. This suggests that dynamically distinct domains in real liquids are associated with a time constant which characterizes both the structural and thermal relaxation behaviors. The calculations demonstrate that the observed burn-induced modifications reflect the spectral selectivity and persistence time of the fictive temperatures within these domains, and that 100 or more cycles of the sinusoidal burn field can be required to saturate the heat accumulated in the slow degrees of freedom. It is also shown that the recovery of dielectric holes is entirely accounted for by the model, and that the persistence times do not provide direct insight into rate exchange processes. Additionally, the model predicts that the heating effects considered here are a significant source of nonlinear dielectric behavior, even in the absence of deliberate frequency selective hole burning.

Emergence of the genuine Johari–Goldstein secondary relaxation in m-fluoroaniline after suppression of hydrogen-bond-induced clusters by elevating temperature and pressure

The dielectric spectra of the glass former, m-fluoroaniline (m-FA), at ambient pressure show the presence of a secondary relaxation, which was identified in the literature as the universal Johari-Goldstein (JG) beta relaxation. However, published elastic neutron scattering and simulation data [D. Morineau, C. Alba-Simionesco, M. C. Bellisent-Funel, and M. F. Lauthie, Europhys. Lett. 43, 195 (1998); D. Morineau and C. Alba-Simionesco, J. Chem. Phys. 109, 8494 (1998)] showed the presence of hydrogen-bond-induced clusters of limited size in m-FA at ambient pressure and temperature of the dielectric measurements. The observed secondary relaxation may originate from the hydrogen-bond-induced clusters. If so, it should not be identified with the JG beta relaxation that involves essentially all parts of the molecule and has certain characteristics [K. L. Ngai and M. Paluch, J. Chem. Phys. 120, 857 (2004)], but then arises the question of where is the supposedly universal JG beta relaxation in m-FA. To gain a better understanding and resolving the problem, we perform dielectric measurements at elevated pressures and temperatures to suppress the hydrogen-bond-induced clusters and find significant changes in the dielectric spectra. The secondary relaxation observed at ambient pressure in m-FA is suppressed, indicating that indeed it originates from the hydrogen-bond-induced clusters. The spectra of m-FA are transformed at high temperature and pressure to become similar to that of toluene. The new secondary relaxation that emerges in the spectra has properties of a genuine JG relaxation like in toluene.

Nonresonant dielectric hole burning in neat and binary organic glass formers

Binary mixtures of the molecular glass former 2-picoline in oligostyrene, in which the dielectric response of 2-picoline exhibits a particularly broad distribution of correlation times, are investigated by nonresonant dielectric hole-burning (NDHB) spectroscopy and the results are compared with NDHB in neat systems, in particular, glycerol. It turns out that in both substance classes spectral selectivity is achieved, which indicates that dynamics is heterogeneous, i.e., slow and fast responses coexist in the material. However, in binary systems the position of the spectral modifications is completely determined by the spectral density of the pump field, and thus shifts linearly with burn frequency as expected, also at pump frequencies around the alpha-relaxation maximum. It is shown that in binary systems the lifetime tau(rec) of the spectral modifications is determined by the burn frequency omega(p) and exceeds its inverse by about one order of magnitude, indicating long-lived dynamic heterogeneity. The data are described in terms of a previously suggested model of dynamically selective heating, which was extended to include intrinsic nonexponential relaxation. It turns out that the spectral broadening in binary mixtures is not only due to pronounced dynamic heterogeneity, but partially also due to intrinsic broadening of the relaxation function.

Mechanical hole burning spectroscopy: evidence for heterogeneous dynamics in polymer systems

We have developed a mechanical spectral hole burning (MSHB) scheme that is analogous to nonresonant dielectric spectral hole burning (DSHB). DSHB experiments have been performed close to the glass temperature and interpreted in terms of dynamic heterogeneity. Here we find that holes are burned far above the glass temperature and in the terminal regimes for a branched polymer melt and a polymer solution. The results suggest that MSHB is a potentially powerful tool with which to examine dynamics of complex fluids.

Relation between the α-Relaxation and Johari−Goldstein β-Relaxation of a Component in Binary Miscible Mixtures of Glass-Formers

The coupling model was applied to describe the alpha-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the alpha-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x --> 0 and x --> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau(alpha)/tau(JG), the ratio of the alpha-relaxation time, tau(alpha), to the Johari-Goldstein (JG) secondary relaxation time, tau(JG), of the same component A. This prediction enables us to obtain the coupling parameter, n(A), of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n(A) of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n(A) obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n(A) with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau(alpha)/tau(JG) of component A changes with composition, x. The data of tau(alpha) and tau(JG) of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.

Comment on "Origin of the excess wing and slow beta relaxation of glass formers: a unified picture of local orientational fluctuations"

In a recent paper [Phys. Rev. E 69, 021502 (2004)]], Tanaka commented on an old coupling model interpretation of the Johari-Goldstein (JG) secondary relaxation [J. Chem. Phys. 115, 1405 (2001)]]; namely, that it implies not all molecules contribute to the JG relaxation. In this Comment, I point out to the readers that this old interpretation has been revised in recent publications [J. Phys.: Condens. Matter 15, S1107 (2003)]; J. Phys. Chem. B 107, 6865 (2003)]; J. Chem. Phys. 120, 857 (2004)]; Macromolecules 37, 8123 (2004)]]. In the new interpretation, essentially all molecules contribute to the JG relaxation. Another comment of Tanaka that applies to both the old and the new interpretation is discussed and shown to be of no practical significance.

Nonresonant holeburning in the Terahertz range: Brownian oscillator model

The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the response should be feasable. This means that it is possible to specifically address various parts of the spectrum. An experimental realization of nonresonant holeburning in the Terahertz regime therefore is expected to shed further light on the nature of the vibrations around the so-called boson peak.

Classification of secondary relaxation in glass-formers based on dynamic properties

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time taubeta and the primary relaxation time taualpha at any chosen taualpha; (3) whether taubeta is approximately equal to the independent (primitive) relaxation time tau0 of the coupling model; (4) whether both taubeta and tau0 have the same pressure and temperature dependences; (5) whether it is responsible for the "excess wing" of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Deltaepsilonbeta and taubeta across the glass transition temperature Tg; (8) the changes of Deltaepsilonbeta and taubeta with aging below Tg; (9) whether it arises in a glass-former composed of totally rigid molecules without any internal degree of freedom; (10) whether only a part of the molecule is involved; and (11) whether it tends to merge with the alpha-relaxation at temperatures above Tg. After the secondary relaxations in many glass-formers have been characterized and classified, we identify the class of secondary relaxations that bears a strong connection or correlation to the primary relaxation in all the dynamic properties. Secondary relaxations found in rigid molecular glass-formers belong to this class. The secondary relaxations in this class play the important role as a precursor or local step of the primary relaxation, and we propose that only they should be called the Johari-Goldstein beta-relaxation.