Slow dynamics in supercooled liquids : matrix formalism, mode coupling and glass transition

Abstract

In this thesis, slow dynamics of supercooled liquids are investigated in the framework of the mode-coupling theory (MCT). Following the real-time generalized Langevin equation in Newtonian liquids, the dynamic Gaussian factorization scheme leads to mode-coupling (MC) closures. As an alternative approach to the projection operator technique, the matrix formalism based on the complete basis set is developed for studying dynamics in many-particle systems. In a dissipative system, the MC closures have to be obtained from irreducible memory kernels instead of standard memory kernels. The matrix formalism provides a new explanation of this preference by comparing linear and nonlinear relaxation time scales, and generalizes the irreducible memory kernel to higher orders. A simple kinetic spin model, the East model, is used to test the matrix formalism and the mode-coupling closures, where the dynamic Gaussian factorization scheme is replaced by a linear approximation due to the kinetic constraint. Next, slow dynamics in Brownian liquids is studied and generalization of MC closures is derived for both coherent and incoherent intermediate scattering functions. Predictions of nonergodic parameters for these two correlation functions in a hard-sphere colloidal suspension improve as the order of the MC closure increases. New glass-transition phenomena are revealed by applying the standard MC closure to a two-Yukawa colloidal suspension.