Glassy Dynamics in Two Dimension (2d)

Abstract

This is the synopsis of the dissertation titled, Glassy Dynamics in Two Dimensions (2d), delivered by Santu Nath of the Physics Department, Indian Institute of Technology Roorkee, Uttarakhand- 247667. It is well-known that behaviour of phase transition in materials can be qualitatively different in different dimensions. For example, the Mermin-Wagner theorem argues that crystal phases will be unstable against thermal fluctuations in two dimensions, while crystals obviously exist in three dimensions. Similar qual itative comparisons for non-crystalline solids between two and three dimensions have recently attracted considerable interest in the literature. The aim of this thesis is to study model glass-forming liquids in two dimensions to address the question whether the physics of glass transition in two dimensions is same or different from three and higher dimensions. The study focuses on one specific effect that is present in two dimensions but not significant in three and higher dimension, namely the long wavelength fluctuations. Recent studies have shown that this affects the dynamics, but not the thermodynamics, in two dimensions. Incoherent Intermediate scattering function Fs(K, τ) is used to describe the dynamics, i.e. the characteristic timescales of structural relaxation time in two model glass-forming liquids denoted as 2DMKA and 2DR10. Instead of usual particle displacements, cage-relative displacements are computed and from which a two-point time correlation function, namely, cage-relative Intermediate scattering function (CR-Fs(K, τ)) is calculated. Recent studies suggest that the timescales obtained from this correlation function is almost independent of the effect of long wavelength fluctuations in two dimensions. Then the effect of spatial dimension on the physics of glass transition is studied by testing whether the Adam Gibbs relation between dynamics and thermodynamics is valid in two dimensions. A generalized Adam-Gibbs relation is considered and the exponents are computed for finite size systems. It is observed that the time scale computed by correcting for the long wavelength fluctuations depends on the nature of the interaction potential. However changing from standard to cage relative displacement does not change the qualitative behaviour of the system. In particular, the Adam Gibbs relation is not obeyed in two dimensions even after correcting for the long wavelength fluctuation.