A rigorous mathematical treatment for the excluded volume effect in monte carlo simulations of polymeric chains

In Monte Carlo simulations of polymeric chains, the chains are most often represented as spheres, or cylinders with flat ends. In this methodological paper, we adopt a representation of the chains as spherocylinders (continuous cylinders ending in semispheres). With such a representation the testing for chain overlap, which is the crucial step for the inclusion of the excluded volume effect in the simulations, can be defined in a rigorous geometrical framework. The treatment we then derive fulfills the following features: it allows a very simple, automatic, and exhaustive classification of all the possible configurations; and it provides a physical representation for steric hindrance effects more natural than the flat-ended cylinders. Notably, this representation avoids the introduction of artificial anisotropies in the treatments. This spherocylindrical representation is also well suited for several types of calculations that can be involved in elaborate Monte Carlo simulations.