THE EFFECT OF UNDULATIONS ON THE ELECTROSTATIC POTENTIAL IN A POLYELECTROLYTE SYSTEM

I consider the effect of macromolecular undulation on the electrostati c potential around a rod-like molecule. This effort is set to demonstr ate the use of a particular perturbation technique through application to a geometrical system of general colloidal interest. The Poisson-Bo ltzmann 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 solu tion appropriate to the deformed boundary can be extracted when the Gr een function is approximated by that relevant to a reference, undeform ed cylinder. Numerical results demonstrate that undulation causes sign ificant deviations (increases) in electrochemical properties from expe cted behaviour, assuming rigid cylindrical symmetry. By considering th e total free energy of the system it is found that electrostatics tend to diminish the extent of the undulations. The predicted deviations a re briefly discussed in light of measured intermolecular electrostatic forces acting in a condensed phase of close-packed DNA. The perturbat ion technique has potential applications to mathematically similar pro blems occurring in hydrodynamics.