Theory of dynamics of entangled rod-like polymers by use of a mean-field Green function formulation. I. Transverse diffusion

A mean-field Green function theory is developed for investigating the dynamics of entangled rod-like polymers in solutions. We regard the hindrance of surrounding rods as a multiple (sequential) perturbation to the free transverse or lateral diffusion of a test rod (a rod in consideration) and incorporate the effects of the perturbation elements one by one into the mean-field Green function. Thus, an explicit expression for the transverse diffusion constant is obtained as a function of a rod length and a polymer concentration for solutions from dilute to semidilute.