Polydisperse chains placed on a one-dimensional lattice

Using a transfer matrix technique, we calculate the entropy of polydisperse chains placed on an 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 equilibrium 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.