Topology of Disordered Networks and their Applications

The birth of Topological Constraint Theory (TCT) started with an innocent query—what optimizes the glass forming tendency of a melt—and led to the finding that such melts possess an ideal connectivity, i.e. a mean coordination number = 2.40 for 3D networks. Complex disordered molecular networks are viewed as composed of structural trusses, wherein nodes (atoms) are connected to each other by mechanical constraints (chemical bonds). And as the field evolved one recognized that the condition = 2.40, coincided with Maxwell’s stability criterion (n_c = 3) of macroscopic structures found in trusses or bridges. Vibrational analysis of 3D disordered networks led to their either being in a flexible phase or a stressed–rigid phase if the number of constraints per atom (nc) is less than 3 or greater than 3, with 3 being the number of degrees of freedom per atom. The approach worked well for sulfide and selenide glasses, but was next extended to include Tellurides and modified Oxides by inclusion of dangling ends and temperature-dependent constraints using Molecular Dynamics (MD) simulations. TCT thus evolved into a formidable tool for understanding “the disordered state of matter both in glasses and melts.” The discovery of Intermediate Phases (IPs) formed between the two elastic phase transitions—rigidity and stress, possessing n_c = 3—led to the notion of self-organization, with networks being rigid but unstressed, possessing a liquid-like entropy, and displaying spectacularly weak aging in these rather select phases. In the laboratory, these developments came to the fore once the recognition emerged that IP melts are super-strong in the fragile-strong classification, and lead to delayed homogenization of all melt compositions. The observation of rather abrupt rigidity- and stress-elastic phase transitions in dry and homogeneous glasses is consistent with their percolative nature.

The scope of this Research Topic includes understanding the flexible, intermediate, and stressed-rigid Topological phases of network glasses, and correlating these to respective melt dynamics using Rigidity Theory, MD simulations and statistical mechanics. Experiments designed around select material systems have not only served as test systems for validating theory, but have also opened a doorway to new materials with applications for emerging technologies. The experimental probes have included neutron scattering, anomalous x-ray scattering, NMR, Mossbauer spectroscopy, Raman scattering, Infrared reflectance, Diffuse light scattering, Modulated-DSC, Ovonic- threshold and -memory switching, and Ag-alloyed chalcogenides as bi-stable conducting bridges. Trends in fragility index, hardness, fracture-toughness, creep-compliance, non-reversing enthalpy of relaxation at T_g, ionic conductivity examined as a function of network connectivity , have proved insightful, as these observables are found to display a threshold behavior near the stress- and rigidity-transitions. Individual contributions of particular interest include (but are not limited to):

 -Identification of self-organized Si-C:H gate dielectrics as interconnects in integrated circuits
 -Understanding the role of resonant bonding in Telluride based Phase Change materials
 -Multi-component oxide glasses for flat panel displays, and as super-hard glasses
 -Topological analysis of Cements displaying a maximal fracture toughness and minimal creep compliance in the IP of Ca-Si-H₂O networks
 -Aspects of Topology common to Rigidity theory and Jamming

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