Force balances in systems of cylindrical polyelectrolytes

A detailed analysis is made of the model system of two parallel cylindrical polyelectrolytes which contain ionizable groups on their surfaces and are immersed in an ionic bathing medium. The interaction between the cylinders is examined by considering the interplay between repulsive electrostatic forces and attractive forces of electrodynamic origin. The repulsive force arises from the screened coulomb interaction between the surface charge distributions on the cylinders and has been treated by developing a solution to the linearized Poisson-Boltzmann equation. The boundary condition at the cylinder surfaces is determined as a self-consistent functional of the potential, with the input consisting of the density of ionizable groups and their dissociation constants. It is suggested that a reasonably accurate representation for the form of the attractive force can be obtained by performing a pairwise summation of the individual interatomic forces. A quantitative estimate is obtained using a Hamaker constant chosen on the basis of rigorous calculations on simpler systems. It is found that a balance exists between these repulsive and attractive forces at separations in good agreement with those observed in arrays of tobacco mosaic virus and in the A band myosin lattice in striated muscle. The behavior of the balance point as a function of the pH and ionic strength of the bathing medium closely parallels that seen experimentally.