The THETA - temperature of Interacting Self Avoiding Walk on Face Centered Cubic Lattice

TL;DR

This paper introduces a new method to accurately estimate the theta temperature of Interacting Self Avoiding Walks on face-centered cubic lattices using shorter chains, aligning well with previous results.

Contribution

It presents a novel approach employing growth walk algorithms and pseudo order parameter method for reliable theta temperature estimation with shorter chains.

Findings

Estimated theta temperature is approximately 7.614.

Method agrees with previous high-chain-length simulation results.

Uses partition function zeroes for corroboration.

Abstract

Interacting Self Avoiding Walk (ISAW) on a lattice is a simple model to study the Coil to Globule transition of linear homopolymers. The temperature at which the transition takes place is called the theta temperature. The value of theta temperature depends on the chosen lattices. The value of theta temperature for ISAW on FCC lattice is reported as $6.46$ in a simulation study [J. Chem. Phys. {\bf 135}, 204903 (2011)]. Latter it has been reported as $7.614$ [J. Chem. Phys. {\bf 138}, 024902 (2013)]. Simulations in these two studies involved long chains with over 2000 monomers. In this paper, we present a method that gives a reliable estimate of the theta temperature of ISAW on FCC lattice using chains of shorter walk lengths (less than 100 monomers). We compute density states of ISAW on FCC lattice by employing growth walk algorithm and then we use the recently introduced pseudo order parameter method to estimate the theta temperature. The value obtained from our method agrees very well with latter reported result of $7.614$. In order to corroborate our result we also estimate the theta temperature using the celebrated partition function zeroes method.