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Register a new userSelf-Organization and the Physics of Glassy Networks
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P. Boolchand
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Network glasses are the physical prototype for many self-organized systems, ranging from proteins to computer science. Conventional theories of gases, liquids, and crystals do not account for the strongly material-selective character of the glass-forming tendency, the phase diagrams of glasses, or their optimizable properties. A new topological theory, only 25 years old, has succeeded where conventional theories have failed. It shows that (probably all slowly quenched) glasses, including network glasses, are the result of the combined effects of a few simple mechanisms. These glass-forming mechanisms are topological in nature, and have already been identified for several important glasses, including chalcogenide alloys, silicates (window glass, computer chips), and proteins.
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In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.
The temperature dependence of the non-ergodicity factor of vitreous GeO$_2$, $f_{q}(T)$, as deduced from elastic and quasi-elastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the glassy phase, up to the glass transition temperature, and well above into the undercooled liquid state. Notwithstanding the investigated system is classified as prototype of strong glass, it is found that the temperature- and the $q$-behavior of $f_{q}(T)$ follow some of the predictions of Mode Coupling Theory. The experimental data support the hypothesis of the existence of an ergodic to non-ergodic transition occurring also in network forming glassy systems.
A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct networks for small clusters bound by the Morse potential for a selection of physically relevant parameters, in two and three dimensions. The properties of these unweighted and undirected networks are analysed to examine two features: whether they are small-world, where the shortest path between nodes involves only a small number or edges; and whether they are scale-free, having a degree distribution that follows a power law. Small-world character is present, but statistical tests show that a power law is not a good fit, so the networks are not scale-free. These results for clusters are compared with the corresponding properties for the molecular and atomic structural glass formers ortho-terphenyl and binary Lennard-Jones. These glassy systems do not show small-world properties, suggesting that such behaviour is linked to the structure-seeking landscapes of the Morse clusters.
We summarize current developments in the investigation of glassy matter using nonlinear dielectric spectroscopy. This work also provides a brief introduction into the phenomenology of the linear dielectric response of glass-forming materials and discusses the main mechanisms that can give rise to nonlinear dielectric response in this material class. Here we mainly concentrate on measurements of the conventional dielectric permittivity at high fields and the higher-order susceptibilities characterizing the 3-omega and 5-omega components of the dielectric response as performed in our group. Typical results on canonical glass-forming liquids and orientationally disordered plastic crystals are discussed, also treating the special case of supercooled monohydroxy alcohols.
In the present work, we employ broadband dielectric spectroscopy to study the molecular dynamics of the prototypical glass former glycerol confined in two microporous zeolitic imidazolate frameworks (ZIF-8 and ZIF-11) with well-defined pore diameters of 1.16 and 1.46 nm, respectively. The spectra reveal information on the modified alpha relaxation of the confined supercooled liquid, whose temperature dependence exhibits clear deviations from the typical super-Arrhenius temperature dependence of the bulk material, depending on temperature and pore size. This allows assigning well-defined cooperativity length scales of molecular motion to certain temperatures above the glass transition. We relate these and previous results on glycerol confined in other host systems to the temperature-dependent length scale deduced from nonlinear dielectric measurements. The combined experimental data can be consistently described by a critical divergence of this correlation length as expected within theoretical approaches assuming that the glass transition is due to an underlying phase transition.
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