Interaction between parallel rodlike macroions

This paper gives a very simple method based on the characteristic property of the electric free energy to calculate the repulsive force between parallel rodlike macroions in a solution as a function of the charge density on rods. The total extensive force ( ∂f / ∂X ) of an assembly of m rods of length l and charge number n (charge density − ne o / l ) at small extension X in the absence of low molecular sals is given by magnified image where z is the valency of counterions and Q (= ne O 2 / εkTl ) is a dimensionless quantity representing the charge density. The repulsion between two parallel rods is given by putting m = 2. At large charge densities the repulsion is very much smaller than the direct coulomb force between charged rods, even at small distances. The addition of low molecular salts does not depress the repulsion appreciably, as long as the average concentration of salt ions is much smaller than the concentration of counterions accumulated in the space between rods. The effect of fluctuation of the coumerion distribution is also analyzed, and it is found that the attractive force due to the ion fluctuation may predominate over the above repulsive force in the case of polyvalent counterions and rods of high charge densities at small distances.