Asymptotic behavior of the entropy of chains placed on stripes

TL;DR

This study analyzes the asymptotic entropy behavior of flexible chains with varying monomer counts on stripes, revealing regular patterns at high densities and confirming mean-field predictions at low densities.

Contribution

It extends the analysis of chain entropy on stripes from dimers to chains with up to nine monomers and polymers, using transfer matrix methods.

Findings

Entropy exhibits regular asymptotic behavior for chains with 2 to 9 monomers.

Results align with analytical dimers case and mean-field predictions at low densities.

Identifies the influence of chain length and stripe width on entropy.

Abstract

By using the transfer matrix approach, we investigate the asymptotic behavior of the entropy of flexible chains with $M$ monomers each placed on stripes. In the limit of high density of monomers, we study the behavior of the entropy as a function of the density of monomers and the width of the stripe, inspired by recent analytical studies of this problem for the particular case of dimers (M=2). We obtain the entropy in the asymptotic regime of high densities for chains with $M=2,..,9$ monomers, as well as for the special case of polymers, where $M\to\infty$, and find that the results show a regular behavior similar to the one found analytically for dimers. We also verify that in the low-density limit the mean-field expression for the entropy is followed by the results from our transfer matrix calculations.