Entropy of polydisperse chains: solution on the Bethe lattice

Polymer models with competing collapse interactions on Husimi and Bethe lattices

In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the interacting self-avoiding trail, and the vertex-interacting self-avoiding walk. These models are characterized by different microscopic interactions, giving rise, in the two-dimensional case, to collapse transitions of an apparently different nature. We expect that our results, even though of a mean-field type, could provide some useful information to elucidate the role of such different θ points in the polymer phase diagram. These issues are at the core of a long-standing unresolved debate.

Entropy of polydisperse chains: solution on the Husimi lattice

We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersity 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 polydispersity 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.

Comment on "Entropy of polydisperse chains: solution on the Bethe lattice" [J. Chem. Phys. 128, 184904 (2008)]

The results presented in the above-mentioned recent paper by Neto and Stilck [J. Chem. Phys.128, 184904 (2008)] represent special cases of a more general investigation by Gujrati on recursive lattices and have already appeared either in this journal or elsewhere. Even the methodology adopted by these authors is almost identical to that of Gujrati. We show that their Eq. (27) remains valid even when interactions are present.