Charge Interactions in Cylindrical Polyelectrolytes

The Debye-Huckel equation is solved for the electrostatic interaction of point charges on the surface of a dielectric cylinder immersed in salt water. Numerical results are given for the potential as a function of axial separation for charges on the same side and on opposite sides of the cylinder, and for two values of the Debye screening length: infinity and unity, in units of the cylinder radius. Major deviations from the interaction in bulk solvent are found. The analytical results are also applied to the self-energy of a helical distribution of charge, and that part A\k of the self-energy which depends on salt concentration is isolated. The deviation of A‘k from its value for a uniformly charged cylinder is evaluated as a function of screening length. The deviation is small for DNA, and smaller for the CY helix. The deviation from a line of charge self-energy is much more significant, but all expressions for A\k agree if the salt concentration is low.