Theoretical Study of Glass Transition and Slow Dynamics

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The main theme of the present research project is to understand the dynamical properties of vitrification process in a unified manner and to elucidate the physics of the glass forming process. We studied the trapping diffusion model (TDM) more throughly and gave the theoretical foundation of the model. We also performed a molecular dynamics simulation to find out the changes in dynamical properties of supercooled liquids.We extended the TDM to include the trapped motion as well as the non-trapped jump motion and obtained the dynamical structure factor. We showed that the main relaxation time obeys the Vogel-Fulcher law and obtained the non-Gaussianity which agees qualitatively with experiments.We also devised a new technique (log-Cole-Cole analysis) with which we can find easily the nature of the relaxation.The extensive MD simulation was carried out for a binary soft shpere system covering the liquid state, supercooled liquid state and glassy state. We found the Vogel-Fulcher law for the main relaxation time, Boson-peak and the fast process.We proposed an ideal three model mode consisting of an oscillation and two kinds of stochastic motions and showed that this model can reproduce the dynamical charasteristics of supercooled liquids.The foundation of the TDM was discussed extensively and it was shown that similar dynamics would be commonly observed in systems with activation processes with randam activation energies. We also showed that the divergence of various moments signifies the dynamical transitions and that the difference of temerature multiplied by the excess entropy from its value the glass transition point can serve as the scaling parameter for the transition.