We use recently introduced three-point dynamic susceptibilities to obtain an experimental determination of the temperature evolution of the number of molecules N corr that are dynamically correlated during the structural relaxation of supercooled liquids. We first discuss in detail the physical content of three-point functions that relate the sensitivity of the averaged two-time dynamics to external control parameters such as temperature or density, as well as their connection to the more standard four-point dynamic susceptibility associated with dynamical heterogeneities. We then demonstrate that these functions can be experimentally determined with good precision. We gather available data to obtain the temperature dependence of N corr for a large number of supercooled liquids over a wide range of relaxation time scales from the glass transition up to the onset of slow dynamics. We find that N corr systematically grows when approaching the glass transition. It does so in a modest manner close to the glass transition, which is consistent with an activation-based picture of the dynamics in glassforming materials. For higher temperatures, there appears to be a regime where N corr behaves as a power-law of the relaxation time. Finally, we find that the dynamic response to density, while being smaller than the dynamic response to temperature, behaves similarly, in agreement with theoretical expectations.

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Spatial correlations in the dynamics of glassforming liquids: experimental determination of their temperature dependence.

Although broadly studied, molecular glass formers are not well investigated above their melting point. Correlation times down to 10−12 s are easily accessible when studying low-Tg systems by depolarized light scattering, employing a tandem-Fabry-Perot interferometer and a double monochromator. When combining these techniques with state-of-the-art photon correlation spectroscopy (PCS), broad band susceptibility spectra become accessible which can compete with those of dielectric spectroscopy (DS). Comparing the results with those from DS, optical Kerr effect, and NMR, we describe the evolution of the susceptibilities starting from the boiling point Tb down to Tg, i.e., from simple liquid to glassy dynamics. Special attention is given to the emergence of the excess wing contribution which is also probed by PCS and which signals a crossover of the spectral evolution. The process is attributed to a small-angle precursor process of the α-relaxation, and the apparent probe dependent stretching of the α-process ...

Evolution of the dynamic susceptibility in molecular glass formers: results from light scattering, dielectric spectroscopy, and NMR.

We analyze the temperature dependence of the segmental relaxation time τ of several low-Tg polymers with varying molar masses (M) as obtained from field-cycling 1H NMR relaxometry and dielectric spectroscopy. They are compared with those of molecular liquids (ML). Time constants in the range 3 × 10–12 s–1000 s, i.e., between Tg and 413 K, are covered. Describing τ(T) by the Vogel–Fulcher–Tammann (VFT) eq a systematic difference with respect to ML is found. While VFT fails for the latter it works well for polymers. The apparent activation energy at high temperatures shows a trend toward a temperature independent value E∞. For polymers, its M-dependence follows that of Tg(M), thus E∞(M) can be described by a Fox–Flory equation. Attempting to understand the difference among the two classes of liquids, we take recourse to our approach first applied to ML [J. Chem. Phys. 2013, 139, 084504]; i.e., we decompose the temperature-dependent activation energy E(T) controlling τ(T) in a constant high-temperature value...

Temperature Dependence of the Segmental Relaxation Time of Polymers Revisited

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.

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

Wide band dielectric spectroscopy has been used to study the bulk dynamics of the simple supercooled liquid m-toluidine. Following the temperature and frequency dependence of the dielectric response we find a stretched relaxation process, the stretching parameter of which is temperature dependent. The observed decoupling between rotational and translational diffusion parameters at low temperatures may be the result of heterogeneous dynamics.

The α-relaxation process in simple glass forming liquid m-toluidine. I. The temperature dependence of the dielectric response

An experimental study of the glass transition of meta-toluidine combining several light scattering techniques was performed. The structural relaxation time is measured in depolarized geometry from the glass transition temperature up to well above the melting point and found to vary over 13 time decades. An analysis by means of the idealized Mode Coupling Theory shows that, as found in other aromatic liquids, experimental results obtained in depolarized light scattering can be described by this theory above Tc in a two-decade frequency range. The polarized Brillouin doublet, measured in the backscattering geometry between 176 K and 300 K, is also analyzed. None of the sets of parameters we obtained in fitting those spectra could fulfil all the requirements of this Mode Coupling Theory.

http://bio4.fizyka.amu.edu.pl/pdf/JCP00Mtol.pdf

C. Alba-Simionesco

Papers

Light scattering study of the liquid–glass transition of meta-toluidine