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Register a new userDoes the potential energy landscape of a supercooled liquid resemble a collection of traps?
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Added by
Aimorn Saksaengwijit
Publication date
2005
fields
Physics
and research's language is
English
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It is analyzed whether the potential energy landscape of a glass-forming system can be effectively mapped on a random model which is described in statistical terms. For this purpose we generalize the simple trap model of Bouchaud and coworkers by dividing the total system into M weakly interacting identical subsystems, each being described in terms of a trap model. The distribution of traps in this extended trap model (ETM) is fully determined by the thermodynamics of the glass-former. The dynamics is described by two adjustable parameters, one characterizing the common energy level of the barriers, the other the strength of the interaction. The comparison is performed for the standard binary mixture Lennard-Jones system with 65 particles. The metabasins, identified in our previous work, are chosen as traps. Comparing molecular dynamics simulations of the Lennard-Jones system with Monte Carlo calculations of the ETM allows one to determine the adjustable parameters. Analysis of the first moment of the waiting distribution yields an optimum agreement when choosing M=3 subsystems. Comparison with the second moment of the waiting time distribution, reflecting dynamic heterogeneities, indicates that the sizes of the subsystems may fluctuate.
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Below the melting temperature $T_m$ crystals are the stable phase of typical elemental or molecular systems. However, cooling down a liquid below $T_m$, crystallization is anything but inevitable. The liquid can be supercooled, eventually forming a glass below the glass transition temperature $T_g$. Despite their long lifetimes and the presence of strong barriers that produces an apparent stability, supercooled liquids and glasses remain intrinsically metastable state and thermodynamically unstable towards the crystal. Here we investigated the isothermal crystallization kinetics of the prototypical strong glassformer GeO$_2$ in the deep supercooled liquid at 1100 K, about half-way between $T_m$ and $T_g$. The crystallization process has been observed through time-resolved neutron diffraction for about three days. Data show a continuous reorganization of the amorphous structure towards the alpha-quartz phase with the final material composed by crystalline domains plunged into a low-density, residual amorphous matrix. A quantitative analysis of the diffraction patterns allows determining the time evolution of the relative fractions of crystal and amorphous, that was interpreted through an empirical model for the crystallization kinetics. This approach provides a very good description of the experimental data and identifies a predator-prey-like mechanism between crystal and amorphous, where the density variation acts as blocking barrier.
Using the potential energy landscape formalism we show that, in the temperature range in which the dynamics of a glass forming system is thermally activated, there exists a unique set of basis glass states each of which is confined to a single metabasin of the energy landscape of a glass forming system. These basis glass states tile the entire configuration space of the system, exhibit only secondary relaxation and are solid-like. Any macroscopic state of the system (whether liquid or glass) can be represented as a superposition of basis glass states and can be described by a probability distribution over these states. During cooling of a liquid from a high temperature, the probability distribution freezes at sufficiently low temperatures describing the process of liquid to glass transition. The time evolution of the probability distribution towards the equilibrium distribution during subsequent aging describes the primary relaxation of a glass.
Landaus theory of phase transitions is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the minima in a potential-energy landscape have negligible influence on the dynamics. Instead the dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the internal-energy maximum. The temperature dependence of the fluctuations yields VTF-like relaxation rates and approximate time-temperature superposition, consistent with the WLF procedure for analyzing the dynamics of complex fluids; while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.
It is difficult to relate the properties of liquids and glasses directly to their structure because of complexity in the structure which defies precise definition. The potential energy landscape (PEL) approach is a very insightful way to conceptualize the structure-property relationship in liquids and glasses, particularly on the effect of temperature and history. However, because of the highly multi-dimensional nature of the PEL it is hard to determine, or even visualize, the actual details of the energy landscape. In this article we introduce a modified concept of the local energy landscape (LEL) which is limited in phase space, and demonstrate its usefulness using molecular dynamics simulation on a simple liquid at high temperatures. The local energy landscape is given as a function of the local coordination number, the number of the nearest neighbor atoms. The excitations in the LEL corresponds to the so-called beta-relaxation process. The LEL offers a simple but useful starting point to discuss complex phenomena in liquids and glasses.
We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.
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