Repulsion between oppositely charged rod-shaped macromolecules: Role of overcharging and ionic confinement

The interaction between two oppositely charged rod-shaped macro-ions in a micro-ion solution is investigated via Monte Carlo simulations of the primitive model. The focus is on the asymmetry in rod and/or ion charge, i.e., conditions where oppositely charged objects can repel one another. For equally and oppositely charged rods with asymmetric z:1 micro-ions, repulsion may be induced by overcharging one of the rods with the z valent ions. For asymmetrically charged rods in a symmetric z:z micro-ion solution, a repulsive interaction-at separation of the order of one ion diameter-can arise via an unbalanced osmotic pressure contribution from the ionic atmosphere in the inter-rod space, and an attractive interaction-at a smaller separation-may occur due to a "squeezing out" of the micro-ions from the space between the rods (with a consequent gain in entropy). The thermodynamics of each mechanism is investigated in terms of rod charge and size and micro-ion valence, size, and concentration. Our findings contribute to the understanding of the complex role of charge asymmetry on the interaction of, for example, oppositely charged polyelectrolytes, functionalized nanotubes, and rod-like biomolecules, e.g., viruses.