Statistical Mechanics of Finite Length Semiflexible Wormlike Polymers

Abstract

The wormlike chain is a fundamental model in polymer physics used for describing the statistics of semiflexible polymers. It is a general model applicable to many polymers, with double-stranded DNA being a notable example. Previous theoretical work has focused on long polymers, where subtle differences in the choice of statistical ensemble are not relevant. This worked well in explaining early data on polymer stretching, but as more modern techniques have allowed for the stretching of shorter, more rodlike polymers, finite length ensemble effects have become visible in experimental measurements and computer simulations. Here, these effects are computed, and a full picture of wormlike chain statistical mechanics is presented. The new results are compared against several decades of polymer stretching literature, and are found to describe previously unexplained behaviour. Finally, the broad use of the model is demonstrated by applying it to DNA wrapped carbon nanotubes, a system that requires considering polymer flexibility, and predicting the pitch of the helical structure formed by these complexes.