Free energy cost of localizing an end-monomer of a confined polymer

We develop and employ a simple Monte Carlo simulation method to calculate the free energy cost of localizing an end-monomer of a polymer to the inside surface of a confining cavity. The method is applied to a freely-jointed hard-sphere polymer chain confined to cavities of spherical, rectangular and cylindrical geometries. We consider cases where the other end of the polymer is free and where it is tethered to another point on the surface. We characterize the dependence of the free energy on the cavity size and geometry type, the localization position, the polymer length, and the effects of excluded volume interactions. The relevance of these results to the initial stages of polymer translocation through nanopores is discussed.