Onsager chains: Semi-flexible polymers revisited

Using a density functional approach we derive the equations describing the equilibrium orientational distribution of a system of chains composed of elongated segments that interact with segments located on other chains through excluded volume interactions and with neighbouring segments of the same chain through a potential that determines the chain flexibility. We analytically determine the limit of stability of the low density isotropic phase as a function of the number of segments and the chain stiffness. The approach turns out to be formally equivalent to a recently proposed mean-field theory by Petschek and Terentjev. Comparison with the Khoklov-Semenov theory shows that the latter is based on an additional assumption that is not valid in an orientationally ordered phase.