Polydisperse chains placed on a one-dimensional lattice

TL;DR

This paper uses transfer matrix techniques to analyze the entropy and size distribution of polydisperse chains on a one-dimensional lattice, revealing how polydispersivity affects entropy and chain size distribution.

Contribution

It provides a detailed calculation of entropy and chain size distribution for polydisperse chains considering different monomer activities, a novel analysis for this system.

Findings

Entropy has a maximum as a function of monomer density.

Polydispersivity increases entropy linearly with monomer density.

Chain size distribution follows an exponential relation.

Abstract

Using a transfer matrix technique, we calculate the entropy of polydisperse chains placed on a one-dimensional lattice, as a function of the density of internal and endpoint monomers. The polydispersivity is determined considering different activities for the two types of monomers, as is usual for equailibrium polymerization and living polymers. If the mean number of monomers in the chains is fixed, the entropy as a function of the density of monomers displays a maximum and is limited from below by the entropy of monodisperse chains. The increase of entropy due to the polydispersivity is a linear function of the density of monomers. We also calculate the distribution of chain sizes, obtaining an exponential relation.