The effect of undulations on the electrostatic potential in a polyelectrolyte system

I consider the effect of macromolecular undulation on the electrostatic potential around a rod-like molecule. This effort is set to demonstrate the use of a particular perturbation technique through application to a geometrical system of general colloidal interest. The Poisson—Boltzmann equation together with a constant charge boundary condition on the well defined surface of an undulating cylinder is reformulated in integral equation form by use of Green’s theorem. A perturbation solution appropriate to the deformed boundary can be extracted when the Green function is approximated by that relevant to a reference, undeformed cylinder. Numerical results demonstrate that undulation causes significant deviations (increases) in electrochemical properties from expected behaviour, assuming rigid cylindrical symmetry. By considering the total free energy of the system it is found that electrostatics tend to diminish the extent of the undulations. The predicted deviations are briefly discussed in light of measured intermolecular electrostatic forces acting in a condensed phase of close-packed DNA. The perturbation technique has potential applications to mathematically similar problems occurring in hydrodynamics.