Entropy of polydisperse chains: solution on the Husimi lattice

Abstract

We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain. We solve the problem exactly on a Husimi lattice built with squares and with arbitrary coordination number, obtaining an expression for the entropy as a function of the density of monomers and mean molecular weight of the chains. We compare this entropy with the one for the monodisperse case, and find that the excess of entropy due to polydispersivity is identical to the one obtained for the one-dimensional case. Finally, we obtain a distribution of molecular weights with a rather complex behavior, but which becomes exponential for very large mean molecular weight of the chains, as required by scaling properties which should apply in this limit.

arXiv comment9 pages, 10 figures, revised version accepted for publication in J. Chem. Phys

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Cited by in corpus (5)

• Hierarchical Lattice Models of Hydrogen Bond Networks in Water
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Thermodynamic properties of rod-like chains: entropic sampling simulations
• Non-equilibrium effects in chaperone-assisted translocation of a stiff polymer
• Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit