Equivalence of statistical ensembles in stretching single flexible polymers

Abstract

The entropies and free energies are determined of single flexible polymers, which are stretched under various conditions, utilizing the maximum entropy principle. Ensembles are considered, where either the end-to-end vector is fixed or a force is applied at a chain end, which corresponds to an isometric or an isotensional ensemble, respectively. In addition, an ensemble is studied, where the mean square end-to-end distance is fixed. Results are presented for Gaussian chains as well as chains of rigid segments with and without excluded volume interactions. By comparing free energies, it is demonstrated that the various ensembles are equivalent for single, flexible polymer stretching. In general, it is shown that the maximum entropy principle provides a relation between the partition functions of different ensembles in form of a Laplace transformation and simultaneously a relation between the generalized thermodynamic potentials in form of a Legendre transformation, which establishes equivalence of the corresponding ensembles.