Coil-Globule transition of a single short polymer chain - an exact enumeration study

TL;DR

This study uses exact enumeration to identify the minimal short polymer chain length that exhibits coil, globule, and theta phases, revealing unexpected scaling behavior even in very short walks.

Contribution

It demonstrates the existence of all three phases in very short self-avoiding walks through exact enumeration, highlighting the presence of scaling behavior.

Findings

Demonstrated coil and globule phases from free energy analysis

Identified theta phase using gyration radius distribution scaling

Found scaling behavior in very short walks, unexpectedly

Abstract

We present an exact enumeration study of short SAWs in two as well as three dimensions that addresses the question, `what is the shortest walk for which the existence of all the three phases - coil, globule and the {\it theta} - could be demonstrated'. Even though we could easily demonstrate the coil and the globule phases from Free Energy considerations, we could demonstrate the existence of a {\it theta} phase only by using a scaling form for the distribution of gyration radius. That even such short walks have a scaling behavior is an unexpected result of this work.