Equilibrium and transport properties of constrained systems

TL;DR

This thesis investigates the behavior of constrained systems, including polymer end-to-end distributions, phase transitions in confined particles, and heat transport in strained 2D solids, using simulations and theoretical models.

Contribution

It introduces a comprehensive analysis of constrained systems with new insights into polymer behavior, phase diagrams, and heat transport mechanisms under confinement.

Findings

Multimodality in WLC polymer distributions identified

Phase diagrams for various potentials match previous simulations

Reversible plastic failure and layering transitions observed in 2D solids

Abstract

Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm Like Chain (WLC) polymer whose ends are positionally (and orientationally) constrained. We use Monte-Carlo simulations (MC) and a theoretical mapping of the WLC to a quantum particle moving on the surface of an unit sphere to find multimodality in Helmholtz ensemble as a generic signature of semi-flexibility. Secondly, we study Laser Induced Freezing using a Kosterlitz-Thouless type renormalization group calculation and a restricted MC simulation to obtain phase diagrams for Hard Disk, Soft Disk and DLVO potentials. They show very good agreement with phase diagrams simulated by other groups. Lastly, we study the strain response and failure mechanism of a two-dimensional solid confined within a hard wall channel using MC and molecular dynamics simulations. We find a reversible plastic failure through solid-smectic coexistence and observe layering transitions. Mean field calculations can capture some of these features. We study the heat transport in this system thorugh nonequilibrium molecular dynamics simulations and find strong signatures of the transitions. We propose a simple free volume calculation that reproduces some qualitative features of the strain response of heat current for small strains.