Logarithmic Relaxation in a Kinetically Constrained Model

TL;DR

This paper uses Monte Carlo simulations on a modified kinetically constrained model to demonstrate logarithmic relaxation behavior in supercooled liquids, revealing different relaxation dynamics for fast and slow cells and drawing parallels with polymer blend simulations.

Contribution

Introduces a two-type cell kinetically constrained model showing logarithmic relaxation and distinct dynamics for fast and slow regions, extending understanding of supercooled liquid relaxation.

Findings

Fast cells show anomalous relaxation with concave-to-convex crossover.

Logarithmic relaxation observed over three decades in time.

Results resemble dynamic correlators in polymer blend simulations.

Abstract

We present Monte Carlo simulations in a modification of the north-or-east-or-front model recently investigated by Berthier and Garrahan [J. Phys. Chem. B 109, 3578 (2005)]. In this coarse-grained model for relaxation in supercooled liquids, the liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting respectively unexcited and excited local states in a mobility field. Change in local mobility (spin flip) for a given cell is permitted according to kinetic constraints determined by the mobilities of neighboring cells. In this work we keep the same kinetic constraints of the original model, but we introduce two types of cells (denoted as "fast'' and "slow'') with very different rates for spin flip. As a consequence, fast and slow cells exhibit very different relaxation times for spin correlators. While slow cells exhibit standard relaxation, fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in spin correlators by changing temperature or composition. At intermediate state points logarithmic relaxation is observed over three time decades. These results display striking analogies with dynamic correlators reported in recent simulations on a bead-spring model for polymer blends.