CiteULike: dchen's model

Two-order-parameter model of the liquid-glass transition. III. Universal patterns of relaxations in glass-forming liquids

Hajime Tanaka — 2008-05-13T17:22:55-00:00

Journal of Non-Crystalline Solids, Vol. 351, No. 43-45. (1 November 2005), pp. 3396-3413.

In the preceding companion papers (paper I and II), we propose a possible origin of the slow dynamics associated with the liquid-glass transition in the light of our two-order-parameter model of liquids. Our model suggests that there exist two levels of dynamic structural heterogeneity, namely, [`]locally favored structures and their clusters' and [`]metastable solid-like islands'. On the basis of this picture, we consider how all the dynamic modes associated with a glass transition, covering from the boson peak to the structural relaxation ([alpha]) mode, can be explained within the same model. We assign the boson peak to (quasi-) localized vibrational modes characteristic of locally favored structures and their clusters and the ultrafast mode to their overdamped states. We assign the fast [beta] mode to the restricted [`]translational' motion, while the slow [beta] mode to the restricted [`]rotational' (librational) motion characteristic of molecules in metastable islands, which exist only below . The [alpha] mode is associated with dynamics of creation and annihilation of metastable islands below . The appearance and disappearance of the modes as a function of the temperature are discussed, focusing on the behavior of locally favored structures and metastable solid-like islands.

Photoelastic verification of a mechanical model for the flow of a granular material

A Drescher — 2008-04-28T18:40:23-00:00

Journal of Mechanics Physics of Solids, Vol. 20 (October 1972), pp. 337-340.

Not Available

The Spot Model for random-packing dynamics

Martin Bazant — 2008-03-24T22:29:29-00:00

Mechanics of Materials, Vol. 38, No. 8-10. ( 2006), pp. 717-731.

The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions or crystal-like vacancy diffusion, but here we propose a cooperative mechanism for dense random-packing dynamics, based on diffusing "spots" of interstitial free volume. Simulations with the Spot Model can efficiently generate realistic flowing packings, and yet the model is simple enough for mathematical analysis. Starting from a non-local stochastic differential equation, we derive continuum equations for tracer diffusion, given the dynamics of free volume (spots). Throughout the paper, we apply the model to granular drainage in a silo, and we also briefly discuss glassy relaxation. We conclude by discussing the prospects of spot-based multiscale modeling and simulation of amorphous materials.

Two-order-parameter description of liquids. I. A general model of glass transition covering its strong to fragile limit

Hajime Tanaka — 2008-03-01T22:29:10-00:00

The Journal of Chemical Physics, Vol. 111, No. 7. (1999), pp. 3163-3174.

Two-order-parameter model of the liquid-glass transition. II. Structural relaxation and dynamic heterogeneity

Hajime Tanaka — 2008-03-01T21:35:15-00:00

Journal of Non-Crystalline Solids, Vol. 351, No. 43-45. (1 November 2005), pp. 3385-3395.

We propose that there exist two key temperatures relevant to glass transition: (i) a transition from the ordinary-liquid to the frustrated metastable-liquid (the Griffiths-phase-like) state at , which is characterized by the appearance of metastable high-density solid-like islands and the resulting appearance of the cooperative nature of [alpha] relaxation, and (ii) another transition into the spin-glass-like state and the resulting divergence of the [alpha] relaxation time at T0. is a density-ordering (melting) point of the corresponding hypothetical pure system that is free from disorder effects. Below , a system has a complex free-energy landscape characteristic of the frustrated metastable-liquid state; metastable solid-like islands with different densities coexist and fluctuate dynamically. In our model, the [alpha] mode is associated with dynamics of creation and annihilation of metastable islands below . The metastable solid-like islands are the origin of dynamic heterogeneity. We propose a modified Vogel-Fulcher law, which can phenomenologically describe the Arrhenius/Vogel-Fulcher crossover induced by a transition from the ordinary-liquid to the frustrated metastable-liquid state around . We also argue that the hidden crystalline ordering in metastable islands may cause the change in the structure factor of a supercooled liquid below , which is more enhanced upon cooling.

Ten questions on glassformers, and a real space `excitations' model with some answers on fragility and phase transitions

CA Angell — 2008-03-01T20:23:55-00:00

Journal of Physics: Condensed Matter, Vol. 12, No. 29. (2000), pp. 6463-6475.

We formulate ten questions, covering outstanding aspects of the phenomenology of glassforming liquids, which we believe must be properly answered by any successful theory of structural glassformers. The questions range across thermodynamic, mass transport and vibrational dynamics phenomena. While these questions will only be addressed properly by a collective variables approach (many aspects of which are reported in these proceedings) a number of them can be dealt with by use of simple physical models of appropriate form. Here we discuss one such model in which the existence of elementary configurational excitations of the amorphous quasilattice is proposed. These states, which may range from broken bonds to packing defects, can be excited independently in the majority of cases, or cooperatively in others. We summarize essential results of this model. These suggest that the source of the different fragilities in liquids (and the reason that structural glasses, alone among `glassy' systems, have marked heat capacity jumps at Tg) may lie largely in the way these configurational excitations couple to the vibrational modes of the system. The generation of low frequency modes in the density of vibrational states, as a direct consequence of the excitation of configurational states, explains why the quasi-elastic scattering from fragile liquids is so much stronger near and above Tg than in the case of strong liquids, and why the normal glass transition can be detected in picosecond time scale experiments. Interactions among the `excitations', or `defects', are taken into account using the one component system equivalent of the binary system `regular solution' model (which keeps only the first order term of the free energy of mixing expansion). We show that a liquid-liquid first order transition must occur at sufficiently strong defect-defect interactions. The highly overconstrained amorphous silicon quasilattice is a strong candidate for such a transition. We identify the `first order melting' of amorphous silicon, and the sudden, reproducible, termination of supercooling in experimental liquid silicon and germanium, with the phase transition predicted by the model. Many more cases of this phase transition may be anticipated, and a corresponding range of glasses with low residual entropies - approaching the `perfect' glass state - are predicted.