Binding Force Between a Charged Wall and a Complex Formed by a Polyelectrolyte and an Electronically Responsive Cylinder

Recent experiments on DNA-assisted carbon nanotube (CNT) separation using ion exchange chromatography (IEC) suggest that the presence of an electronically responsive cylinder can affect the binding force between a polyelectrolyte (PE) and an oppositely charged wall embedded in a dilute solution. This is examined in this work by studying the force on a charged wall due to a complex consisting of two infinitely long cylinders with parallel axes (one representing the PE and the other being either metallic or dielectric). By considering the Debye-Huckel theory, the expressions for the binding force per unit length between the PE-cylinder complex and the oppositely charged wall are obtained for different electronic natures of the responsive cylinder. The results show that the binding force due to the PE near a grounded metallic cylinder is weaker than that due to the PE near a neutral dielectric cylinder, while a non-zero potential on the metallic cylinder can strongly affect the binding force.