Like-charge attraction in a one-dimensional setting: the importance of being odd

Abstract

From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract.

References in corpus (4)

• Differential Dynamic Microscopy to characterize Brownian motion and bacteria motility
• One-dimensional counterion gas between charged surfaces: Exact results compared with weak- and strong-coupling analysis
• Screening like-charges in one-dimensional Coulomb systems: Exact results
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Cited by in corpus (2)

• Like-charge attraction at short distances in a charge-asymmetric two-dimensional two-component plasma: Exact results
• Relaxation dynamics of two interacting electrical double-layers in a 1D Coulomb system