Self-organization with equilibration: a model for the intermediate phase in rigidity percolation

Experimental results for covalent glasses have highlighted the existence of a new self-organized phase due to the tendency of glass networks to minimize internal stress. Recently, we have shown that an equilibrated self-organized two-dimensional lattice-based model also possesses an intermediate phase in which a percolating rigid cluster exists with a probability between zero and one, depending on the average coordination of the network. In this paper, we study the properties...

There is growing evidence that electronic and molecular networks present some common universal properties, among which the existence of a self-organized intermediate phase. In glasses, the latter is revealed by the reversibility window obtained from complex calorimetric measurements at the glass transition. Here we focus on amorphous networks and we show how this intermediate phase can be understood from a rigidity percolation analysis on size increasing clusters. This provid...

Rigidity Percolation is studied analytically on randomly bonded networks with two types of nodes, respectively with coordination numbers $z_1$ and $z_2$, and with $g_1$ and $g_2$ degrees of freedom each. For certain cases that model chalcogenide glass networks, two transitions, both of first order, are found, with the first transition usually rather weak. The ensuing intermediate pase, although is not isostatic in its entirety, has very low self-stress. Our results suggest a ...

We review in this paper the signatures of a new elastic phase that is found in glasses with selected compositions. It is shown that in contrast with random networks, where rigidity percolates at a single threshold, networks that are able to self-organize to avoid stress will remain in an almost stress- free state during a compositional interval, an intermediate phase, that is bounded by a flexible phase and a stressed rigid phase. We report the experimental signatures and des...

I review computational studies of different models of elastic network self-organization leading to the existence of a globally isostatic (rigid but unstressed) or nearly isostatic intermediate phase. A common feature of all models considered here is that only the topology of the elastic network is taken into account; this allows the use of an extremely efficient constraint counting algorithm, the pebble game. In models with bond insertion without equilibration, the intermedia...

We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order to avoid stressed bonds may change the phase diagram. In contrast to what happens on random graphs and in some recent numerical studies at zero temperature, we do not find a true intermediate phase separating the usual rigid and floppy one...

Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments. Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions in...

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) glasse...

The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This ubiquitous heterogeneous nature of amorphous materials is intriguingly attributed to a complex role of entropy. Here, we show in disordered networks that the vibrational entropy increases by creating phase-separated structures when the int...

A Monte Carlo method is used in order to simulate the competition between the molecular relaxation and crystallization times in the formation of a glass. The results show that nucleation is avoided during supercooling and produce self-organization in the sense of the rigidity theory, where the number of geometrical constraints due to bonding and excluded volume are compared with the degress of freedom available to the system. Following this idea, glass transitions were obtain...