Adam-Gibbs Relation Research Articles

Landscapes and fragilities.

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth, and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.

Glasses and local packings

A cell theory for glassforming liquids, amorphous solids and granular packings, is developed by combining geometrical properties of local packings with the ideas of inherent structures and free volume theory. We show that for hard-spheres the present theory reproduces well the equation of state, the approach to zero of the configurational entropy and the divergence of large relaxation times following both the Vogel–Tammann–Fulcher behavior and the Adam–Gibbs relation.

Recent results on the connection between thermodynamics and dynamics in supercooled water

We review recent results on the connection between thermodynamics and dynamics in a model for water. We verify the Adam–Gibbs relation between entropy and dynamic properties using computer simulations, which allow direct access to the relevant properties. We combine experimental measurements of entropy with the Adam–Gibbs hypothesis to predict dynamic properties in deeply supercooled states, which are difficult to access experimentally. We find evidence suggesting that the glass transition temperature of water may be significantly higher than previously reported, but is still consistent with recent measurements. Finally, we discuss the hypothesis that the dynamical behavior of deeply supercooled water undergoes a crossover from ‘fragile’ to ‘strong’ behavior.

Cell approach to glass transition

We present a novel theoretical approach to understanding the complex dynamicsof glass-forming liquids, granular packings and amorphous solids. This theory,which is an elaboration of the free volume and inherent structure approaches,allows one to retrieve the thermodynamical properties of these systems fromstudies of geometrical and topological properties of local, static configurationsalone. When applied to hard-sphere systems, the present theory reproduces with agood quantitative agreement the equation of state for the crystalline and thedisordered glassy phases. Moreover, we find that, as the density approaches acritical value close to the random close-packing density, the configurationalentropy approaches zero and the large relaxation time diverges according to theVogel–Fulcher behaviour, following also the Adam–Gibbs relation.

Exactly solvable model glass with facilitateddynamics

A model glass with fast and slow processes is studied. Thestatics is simple and the facilitated slow dynamics is exactlysolvable. The main features of a fragile glass appear: Kauzmanntransition, Vogel-Fulcher law, Adam-Gibbs relation and aging.The time evolution can be so slow that a quasi-equilibriumoccurs at a time-dependent effective temperature. The sameeffective temperature is derived from thefluctuation-dissipation ratio, which supports the applicabilityof out-of-equilibrium thermodynamics.

A glass transition scenario based on heterogeneities and entropy barriers

Abstract We propose a scenario for the glass transition based on the cooperative nature of nucleation processes and entropic effeets. The main point is the relation between the off-equilibrium energy dissipation and nucleation processes in off-equilibrium supercooled liquids which leads to a natural definition of the complexity. From the absence of coarsening growth we can derive an entropy-based fluctuation formula which relates the free-energy dissipation rate in the glass to the nucleation rate of the largest cooperative regions. As a by-product we obtain a new phenomenological relation between the longest relaxation time in the supercooled liquid phase and an effective temperature. This differs from the Adam-Gibbs relation in that it predicts no divergence of the primary relaxation time at the Kauzmann temperature and the existence of a crossover from fragile to strong behaviour.

Effective temperatures in an exactly solvable model for a fragile glass.

A model glass with facilitated dynamics is considered with one type of fast process (beta type) and one type of slow process (alpha type). On time scales where the fast processes are in equilibrium, the slow ones have a dynamics that resembles that of facilitated spin models. The main features are the occurrence of a Kauzmann transition, a Vogel-Fulcher-Tammann-Hesse behavior for the relaxation time, an Adam-Gibbs relation between relaxation time and configurational entropy, and an aging regime. The model is such that its statics is simple and its (Monte Carlo type) dynamics is exactly solvable. The dynamics has been studied both on the approach to the Kauzmann transition and below it. In certain parameter regimes it is so slow that a quasiequilibrium occurs at a time dependent effective temperature. Correlation and response functions are also computed, as well as the out of equilibrium fluctuation-dissipation relation, showing the uniqueness of the effective temperature, thus giving support to the rephrasing of the problem within the framework of out of equilibrium thermodynamics.

A glass transition scenario based on heterogeneities and entropy barriers

We propose a scenario for the glass transition based on the cooperative nature of nucleation processes and entropic effects. The main point is the relation between the off-equilibrium energy dissipation and nucleation processes in off-equilibrium supercooled liquids which leads to a natural definition of the complexity. From the absence of coarsening growth we can derive an entropy based fluctuation formula which relates the free energy dissipation rate in the glass with the nucleation rate of the largest cooperative regions. As by-product we obtain a new phenomenological relation between the largest relaxation time in the supercooled liquid phase and an effective temperature. This differs from the Adam-Gibbs relation in that predicts no divergence of the primary relaxation time at the Kauzmann temperature and the existence of a crossover from fragile to strong behavior.

A resolution for the enigma of a liquid’s configurational entropy-molecular kinetics relation

The literature data on the entropy and heat capacity of 33 glass-forming liquids have been used to examine the validity of the Adam–Gibbs relation between a liquid’s configurational entropy, Sconf, and its molecular kinetics. The critical entropy, sc*, of kB ln 2 (=0.956×10−23 J molecule−1 K−1) in the equation is less than even the residual entropy per molecule in a glass at 0 K, and this creates difficulties in determining the size of the cooperatively rearranging region, z*, in the liquid. It is argued that, z*=[1−(T0/T)]−1, and the temperature-invariant energy term, Δμ, is equal to RB, which has been determined from the knowledge of the Vogel–Fulcher–Tamman parameters B and T0, with R being the gas constant, and on the basis of the argument that the preexponential term of this equation is identical to that of the Adam–Gibbs relation. As the lattice modes in a glass are lower in frequency and more anharmonic than in its crystal, its vibrational entropy, Svib, would be higher than that of the crystal phase. Therefore, Sconf of a glass (and liquid) is significantly less than the difference between the entropy of the glass (and liquid) and the entropy of its completely ordered crystal phase. Both quantities, Svib and Sconf, have been estimated without reference to the vibrational spectra. The conclusions can be tested by determining z* and Δμ from measurements of the dielectric spectra of a liquid confined to nanometer-size pores. This is elaborated by a calculation for 3-bromopentane.

Cooperative relaxation in glass forming liquids

The Adam-Gibbs theory of cooperative relaxation in glass forming liquids is cast in differential form. The differential equations are examples of the differential equations of the renormalization group. It is shown that generalization of the Adam-Gibbs relation arise naturally from these differential equations. The size of the cooperative rearranging region is determined by the configuration restrictions associated with amorphous packings that can be described by the configurational entropy of the melt. The relation between the linear response of a system in thermal equilibrium to an external disturbance and fluctuations of relevant physical quantities in equilibrium are generalized to constrained systems.

Relaxation and flow mechanisms in ‘‘fragile’’ glass-forming liquids

Fragile glass-forming liquids are characterized by strongly non-Arrhenius temperature dependence of shear viscosity, and by unusually high heat capacity in the supercooled liquid above the glass transition. Using the inherent structure formalism, a theoretical model is developed to explain these characteristics. The vitrifying liquid is viewed as a dynamic patchwork of relatively strongly bonded (but amorphous) molecular domains that are separated by irregular walls of weakened bonds. Mean domain diameter ξ rises as temperature declines to minimize wall free energy, but the process is self-limiting due to intradomain frustration energy. Shear flow occurs by a ‘‘tear and repair’’ mechanism involving elemental wall areas of mean size ξ2. The relation of the present model to the tiling models for glass formation is explored, and helps to establish the presence of anomalous heat capacity in the supercooled liquid. The analysis suggests in strongly supercooled fragile liquids that the Stokes–Einstein formula may underestimate self-diffusion constants, and that the Adam–Gibbs relation for mean relaxation time in terms of calorimetric entropy may display systematic errors.