Jeppe C. Dyre

Towards a phenomenological definition of the term ‘gel’

Abstract The term ‘gel’ is used so indiscriminately that it has become ambiguous. Existing definitions are reviewed, examples of unfortunate uses of the term are discussed, and important phenomenological characteristics of gels are identified. We propose that the term ‘gel’ should be limited to systems which fulfil the following phenomenological characteristics: (a) they consist of two or more components one of which is a liquid, present in substantial quantity and (b) they are soft, solid, or solid-like materials. We further propose a definition of the solid-like characteristics of gels in terms of the dynamic mechanical properties, viz. a storage modulus, G′(ω), which exhibits a pronounced plateau extending to times at least of the order of seconds and a loss modulus, G″(ω), which is considerably smaller thatn the storage modulus in the plateau region.

Fundamental questions relating to ion conduction in disordered solids

A number of basic scientific questions relating to ion conduction in homogeneously disordered solids are discussed. The questions deal with how to define the mobile ion density, what can be learnt from electrode effects, what the ion transport mechanism is, the role of dimensionality and what the origins of the mixed-alkali effect, the time-temperature superposition, and the nearly constant loss are. Answers are suggested to some of these questions, but the main purpose of the paper is to draw attention to the fact that this field of research still presents several fundamental challenges.

Crossover to potential energy landscape dominated dynamics in a model glass-forming liquid

An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this “inherent dynamics” approach we find direct numerical evidence for the long held view that below a crossover temperature, Tx, the liquid’s dynamics can be separated into (i) vibrations around inherent structures and (ii) transitions between inherent structures [M. Goldstein, J. Chem. Phys. 51, 3728 (1969)], i.e., the dynamics become “dominated” by the potential energy landscape. In agreement with previous proposals, we find that Tx is within the vicinity of the mode-coupling critical temperature Tc. We further find that near Tx, transitions between inherent structures occur via cooperative, stringlike rearrangements of groups of particles moving distances substantially smaller than the average interparticle distance.

Some remarks on ac conduction in disordered solids

Alternating current conduction in disordered solids is discussed, from a general point of view. As regards experiment, it is argued that the observed power-law behavior of the frequency-depend ent conductivity, o-(w), is probably not fundamental, that the Ngai relation between dc and ac conductivity activation energies follows from independent experimental facts, that the shape of the modulus peak has no fundamental significance, and that there are interesting mechanical analogies to the observed ac electrical behavior. As regards hopping models for ac conduction, it is shown that three commonly used arguments against the existence of a distribution of activation energies are all incorrect. Also, it is shown that o-Qo) =~ o-(0) only if there are correlations in the directions of different charge carrier jumps; in particular this result implies o-Qo) = o-(0) for all frequencies in the continuous time random walk (CTRW) model. In the final section a number of open problems are listed, and suggestions are made for future work.

Pressure-energy correlations in liquids. I. Results from computer simulations

We show that a number of model liquids at fixed volume exhibit strong correlations between equilibrium fluctuations of the configurational parts of (instantaneous) pressure and energy. We present detailed results for 13 systems, showing in which systems these correlations are significant. These include Lennard-Jones liquids (both single- and two-component) and several other simple liquids, neither hydrogen-bonding liquids such as methanol and water, nor the Dzugutov liquid, which has significant contributions to pressure at the second nearest neighbor distance. The pressure-energy correlations, which for the Lennard-Jones case are shown to also be present in the crystal and glass phases, reflect an effective inverse power-law potential dominating fluctuations, even at zero and slightly negative pressure. An exception to the inverse power-law explanation is a liquid with hard-sphere repulsion and a square-well attractive part, where a strong correlation is observed, but only after time averaging. The companion paper [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)] gives a thorough analysis of the correlations, with a focus on the Lennard-Jones liquid, and a discussion of some experimental and theoretical consequences.

Pressure-energy correlations in liquids. II. Analysis and consequences

We present a detailed analysis and discuss consequences of the strong correlations of the configurational parts of pressure and energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the previous paper [N. P. Bailey et al., J. Chem. Phys. 129, 184507 (2008)]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the radial distribution function, as we demonstrate by an eigenvector analysis of the spatially resolved covariance matrix. The reason the effective power law works so well depends crucially on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential energy and virial, but little to their fluctuations, for density fluctuations which conserve volume. We also study in detail the zero temperature limit of the (classical) crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity, in more than one dimension; in one dimension the limiting value is exactly unity. In the second half of the paper we consider four consequences of strong pressure-energy correlations: (1) analyzing experimental data for supercritical argon we find 96% correlation; (2) we discuss the particular significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we reinterpret aging simulations of ortho-terphenyl carried out by Mossa et al. [Eur. Phys. J. B 30, 351 (2002)], showing their conclusions follow from the strongly correlating property; and (4) we briefly discuss the presence of the correlations (after appropriate time averaging) in model biomembranes, showing that significant correlations may be present even in quite complex systems.

Time-Temperature Superposition in Viscous Liquids

Dielectric relaxation measurements on supercooled triphenyl phosphite show that time-temperature superposition (TTS) is obeyed for the primary relaxation process at low temperatures. Measurements on other molecular liquids close to the calorimetric glass transition indicate that TTS is linked to an omega(-1/2) high-frequency decay of the loss, while the loss peak width is nonuniversal.

Strong Pressure-Energy Correlations in van der Waals Liquids

Strong correlations between equilibrium fluctuations of the configurational parts of pressure and energy are found in computer simulations of the Lennard-Jones liquid and other simple liquids, but not for hydrogen-bonding liquids such as methanol and water. The correlations that are present also in the crystal and glass phases reflect an effective inverse power-law repulsive potential dominating fluctuations, even at zero and slightly negative pressure. In experimental data for supercritical argon, the correlations are found to be approximately 96%. Consequences for viscous liquid dynamics are discussed.

Source of non-Arrhenius average relaxation time in glass-forming liquids

A major mystery of glass-forming liquids is the non-Arrhenius temperature-dependence of the average relaxation time. This paper briefly reviews the classical phenomenological models for this phenomenon - the free-volume model and the entropy model - and critiques against these models. We then discuss a recent model [Dyre, Olsen, and Christensen, Phys. Rev. B 53, 2171 (1996)] according to which the activation energy for the average relaxation time is determined by the work done in shoving aside the surrounding liquid to create space needed for a flow event. In this model the non-Arrhenius temperature-dependence is a consequence of the fact that the instantaneous (infinite-frequency) shear modulus increases upon cooling.Abstract A major mystery of glass-forming liquids is the non-Arrhenius temperature-dependence of the average relaxation time. This paper briefly reviews the classical phenomenological models for non-Arrhenius behavior – the free volume model and the entropy model – and critiques against these models. We then discuss a recently proposed model according to which the activation energy of the average relaxation time is determined by the work done in shoving aside the surrounding liquid to create space needed for a “flow event”. In this model, which is based on the fact that intermolecular interactions are anharmonic, the non-Arrhenius temperature-dependence of the average relaxation time is a consequence of the fact that the instantaneous shear modulus increases upon cooling.

Investigation of the shear-mechanical and dielectric relaxation processes in two monoalcohols close to the glass transition

Shear-mechanical and dielectric measurements on the two monohydroxy (monoalcohol) molecular glass formers 2-ethyl-1-hexanol and 2-butanol close to the glass-transition temperature are presented. The shear-mechanical data are obtained using the piezoelectric shear-modulus gauge method covering frequencies from 1 mHz to 10 kHz. The shear-mechanical relaxation spectra show two processes, which follow the typical scenario of a structural (alpha) relaxation and an additional (Johari-Goldstein) beta relaxation. The dielectric relaxation spectra are dominated by a Debye-type peak with an additional non-Debye peak visible. This Debye-type relaxation is a common feature peculiar to monoalcohols. The time scale of the non-Debye dielectric relaxation process is shown to correspond to the mechanical structural (alpha) relaxation. Glass-transition temperatures and fragilities are reported based on the mechanical alpha relaxation and the dielectric Debye-type process, showing that the two glass-transition temperatures differ by approximately 10 K and that the fragility based on the Debye-type process is a factor of 2 smaller than the structural fragility. If a mechanical signature of the Debye-type relaxation exists in these liquids, its relaxation strength is at most 1% and 3% of the full relaxation strength of 2-butanol and 2-ethyl-1-hexanol, respectively. These findings support the notion that it is the non-Debye dielectric relaxation process that corresponds to the structural alpha relaxation in the liquid.