Modified diffusion equation for the wormlike-chain statistics in curvilinear coordinates

Abstract

One of the essential physical quantities used to study the conformation and structure of polymers is the so-called propagator in polymer theories. On the basis of the wormlike-chain statistical-physics model, we derive the partial diffusion equation that the propagator satisfies, for a curvilinear coordinate system. As it turns out, an additional term exists, that couples the rotating local coordinate frame with an orientation differential operator; this term has not been previously documented. In addition, for a wormlike chain moving on a curved surface, the external-field term needs to be supplemented by a surface curvature energy penalty.