Electrostatic Persistence Length of Semiflexible and Flexible Polyelectrolytes

I have calculated the dependence of the electrostatic persistence length on the Debye screening length for semiflexible, strongly and weakly charged flexible polyelectrolytes. For semiflexible and strongly charged flexible polyelectrolytes the electrostatic part of the chain persistence length is proportional to the Debye screening length. This result is obtained by evaluating the bending angle fluctuations and in the framework of the Gaussian variational principle. A polyelectrolyte chain with linear dependence of the electrostatic persistence length on the Debye screening length has a lower free energy than that of a chain with the Odijk-Skolnick-Fixman electrostatic persistence length. In the case of weakly charged chains the electrostatic persistence length has a sublinear dependence on the Debye screening length which is due to inverse logarithmic dependence of the linear charge density of the chain of electrostatic blobs on the Debye screening length. This result was derived by applying a coarse-graining procedure to an initially flexible polyelectrolyte chain by representing it as a chain of electrostatic blobs. The blob size and chain persistence length are then found self-consistently by minimizing the chain’s variational free energy.