How do the properties of a glass depend on the cooling rate? A computer simulation study of a Lennard-Jones system

Using molecular dynamics computer simulations we investigate how the glass transition and the properties of the resulting glass depend on the cooling rate with which the sample has been quenched. This is done by studying a two component Lennard-Jones system which is coupled to a heat bath whose temperature is decreased from a high temperature, where the system is a liquid, to zero temperature, where the system is a glass. The temperature $T_b$ of the heat bath is decreased linearly in time, i.e. $T_b=T_0-\gamma t$, where $\gamma$ is the cooling rate. In accordance with simple theoretical arguments and with experimental observations we find that the glass transition, as observed in the specific heat and the thermal expansion coefficient, becomes sharper when $\gamma$ is decreased. A decrease of the cooling rate also leads to a decrease of the glass transition temperature $T_g$ and we show that the dependence of $T_g$ on $\gamma$ can be rationalized by assuming that the temperature dependence of the relaxation times of the system is given by either a Vogel-Fulcher law or a power-law. By investigating the structural properties of the glass, such as the radial distribution functions, the coordination numbers and the angles between three neighbor-sharing particles, we show how the local order of the glass increases with decreasing cooling rate. The enthalpy and the density of the glass decrease and increase, respectively, with decreasing $\gamma$. By investigating the $\gamma$ dependence of clusters of nearest neighbors, we show how these observations can be understood from a microscopic point of view. We also show that the spectrum of the glass, as computed from the dynamical matrix, shows a shift towards higher frequencies when $\gamma$ is decreased. All these effects show that there is a significantComment: 20 pages of RevTex, Figures available upon request from W. Ko

Kovacs effects in an aging molecular liquid

We study by means of molecular dynamics simulations the aging behavior of a molecular model of ortho-terphenyl. We find evidence of a a non-monotonic evolution of the volume during an isothermal-isobaric equilibration process, a phenomenon known in polymeric systems as Kovacs effect. We characterize this phenomenology in terms of landscape properties, providing evidence that, far from equilibrium, the system explores region of the potential energy landscape distinct from the one explored in thermal equilibrium. We discuss the relevance of our findings for the present understanding of the thermodynamics of the glass state.Comment: RevTeX 4, 4 pages, 5 eps figure

Temperature in nonequilibrium systems with conserved energy

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.Comment: 4 pages, 1 figure, final versio

Thermodynamics of black holes: an analogy with glasses

The present equilibrium formulation of thermodynamics for black holes has several drawbacks, such as assuming the same temperature for black hole and heat bath. Recently the author formulated non-equilibrium thermodynamics for glassy systems. This approach is applied to black holes, with the cosmic background temperature being the bath temperature, and the Hawking temperature the internal temperature. Both Hawking evaporation and absorption of background radiation are taken into account. It is argued that black holes did not form in the very early universe.Comment: 4 pages revtex; submitted to Phys. Rev. Let

Thermodynamics of the glassy state: effective temperature as an additional system parameter

A system is glassy when the observation time is much smaller than the equilibration time. A unifying thermodynamic picture of the glassy state is presented. Slow configurational modes are in quasi-equilibrium at an effective temperature. It enters thermodynamic relations with the configurational entropy as conjugate variable. Slow fluctuations contribute to susceptibilities via quasi-equilibrium relations, while there is also a configurational term. Fluctuation-dissipation relations also involve the effective temperature. Fluctuations in the energy are non-universal, however. The picture is supported by analytically solving the dynamics of a toy model.Comment: 5 pages, REVTEX. Phys. Rev. Lett, to appea

The Glass Transition Temperature of Water: A Simulation Study

We report a computer simulation study of the glass transition for water. To mimic the difference between standard and hyperquenched glass, we generate glassy configurations with different cooling rates and calculate the $T$ dependence of the specific heat on heating. The absence of crystallization phenomena allows us, for properly annealed samples, to detect in the specific heat the simultaneous presence of a weak pre-peak (``shadow transition''), and an intense glass transition peak at higher temperature. We discuss the implications for the currently debated value of the glass transition temperature of water. We also compare our simulation results with the Tool-Narayanaswamy-Moynihan phenomenological model.Comment: submitted to Phys. Re

Thermodynamic picture of the glassy state

A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations and the Prigogine-Defay ratio. As a second part, the approach connects the response of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized non-equilibrium way.Comment: Proceedings of the Conference "Unifying Concepts in Glass Physics", ICTP, Trieste, 15 - 18 September 199

Minimal model for beta relaxation in viscous liquids

Contrasts between beta relaxation in equilibrium viscous liquids and glasses are rationalized in terms of a double-well potential model with structure-dependent asymmetry, assuming structure is described by a single order parameter. The model is tested for tripropylene glycol where it accounts for the hysteresis of the dielectric beta loss peak frequency and magnitude during cooling and reheating through the glass transition.Comment: Phys. Rev. Lett. (in press

Observation of Fluctuation-Dissipation-Theorem Violations in a Structural Glass

The fluctuation-dissipation theorem (FDT), connecting dielectric susceptibility and polarization noise was studied in glycerol below its glass transition temperature Tg. Weak FDT violations were observed after a quench from just above to just below Tg, for frequencies above the alpha peak. Violations persisted up to 10^5 times the thermal equilibration time of the configurational degrees of freedom under study, but comparable to the average relaxation time of the material. These results suggest that excess energy flows from slower to faster relaxing modes.Comment: Improved discussion; final version to appear in Phys. Rev. Lett. 4 pages, 5 PS figures, RevTe

Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence

This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies. It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: 1) An introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), 2) A description of the basic analytical tools and results derived in the framework of some exactly solvable models, 3) A detailed report of the current evidence in favour of the QFDT and 4) A brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.Comment: 120 pages, 37 figures. Topical review paper . Several typos and misprints corrected, new references included and others updated. to be published in J. Phys. A (Math. Gen.