Projection from an atomistic chain contour to its primitive path

In this note, we propose a mapping from the spatial coordinates of an atomistic polymer chain to its ‘primitive path’ (PP), a concept being frequently used in the framework of reptation models. For the model to be presented, the projection preserves as much structure of the atomistic chain as appropriate to replace an atomistic chain on a prescribed (parameterized) coarse-grained level. We present an efficient numerical method to extract a PP as well as an analytic approach to study the conformational properties of the coarse-grained chain in an approximate fashion. The knowledge of the PP is a prerequisite to facilitate tests of mesoscopic descriptions of polymeric fluids, in particular in the framework of nonequilibrium thermodynamics, and allows for a thorough analysis of atomistic chain configurations on a ‘relevant’ coarse-grained level.