Concentration fluctuation of stiff polymers. I: Static structure factor

The static structure factor g(k) of the concentrated solution of stiff polymers is calculated based on the generalized random phase approximation (RPA) which accounts for the nematic interaction (i.e., the interaction causing the nematic phase of stiff polymers) between the segments. The structure factor is obtained in the form of power series expansion with respect to k. The result is: (i) the correlation length ξ is independent of the nematic interaction, and is given by the conventional RPA; (ii) the sign of the coefficient of k4 changes from positive to negative as the nematic interaction is increased; and (iii) the structure factor of rigid rod, which can be calculated exactly, shows no anomaly below the critical concentration c*, but suddenly shows anomaly above c*.