Two-Level Solutions to Exponentially Complex Problems in Glass Science: Invited Talk

Glass poses an especially challenging problem for physicists. The key to making progress in theoretical glass science is to extract the key physics governing properties of practical interest. In this spirit, we discuss several two-level solutions to exponentially complex problems in glass science. Topological constraint theory, originally developed by J.C. Phillips, is based on a two-level description of rigid and floppy modes in a glass network and can be used to derive quantitatively accurate and analytically solvable models for a variety of macroscopic properties. The temperature dependence of the floppy mode density is used to derive the new MYEGA model of supercooled liquid viscosity, which offers improved descriptions for the temperature and composition dependence of relaxation time. The relaxation behavior of the glassy state can be further elucidated using a two-level energy landscape that captures both primary and secondary relaxation modes. Such a model also offers the ability to calculate the distinguishability of particles during glass transition and relaxation processes. Two-level models can also be used to capture the distribution of various network-forming species in mixed-network glasses of industrial interest, such as borosilicates. The two-level model also gives the thermal history dependence of network former speciation without any additional parameters.