Phase Transition in a Bond Fluctuating Lattice Polymer

TL;DR

This study investigates phase transitions in a two-dimensional lattice polymer model, revealing two distinct first-order transitions from extended to collapsed and from collapsed to crystalline phases, influenced by boundary conditions.

Contribution

It provides a detailed analysis of phase transitions in a bond fluctuation lattice polymer model, including effects of walls and confinement, using Monte Carlo simulations.

Findings

Two first-order transitions identified: coil to globule and globule to crystalline.

Collapse transition occurs at lower temperature with walls present.

Transitions are discontinuous and characterized by heat capacity and free energy profiles.

Abstract

This report deals with phase transition in Bond Fluctuation Model (BFM) of a linear homo polymer on a two dimensional square lattice. Each monomer occupies a unit cell of four lattice sites. The condition that a lattice site can at best be a part of only one monomer ensures self avoidance and models excluded volume effect. We have simulated polymers with number of monomers ranging from 10 to 50 employing Boltzmann and non-Boltzmann Monte Carlo simulation techniques. To detect and characterize phase transition we have investigated heat capacity through energy fluctuations, Landau free energy profiles and Binder's fourth cumulant. We have investigated (1) free standing polymer (2) polymer in the presence of of an attracting wall and (3) polymer confined between two attracting walls. In general we find there are two transitions as we cool the system. The first occurs at relatively higher temperature. The polymer goes from an extended coil to a collapsed globule conformation. This we call collapse transition. We find that this transition is first order. The second occurs at a lower temperature in which the polymer goes from a collapsed phase to a very compact crystalline phase. This transition is also discontinuous. We find that in the presence of wall(s) the collapse transition occurs at lower temperature compared to a free standing polymer.