Mechanisms of like-charge attraction in many-body systems

The physics of like-charge attraction in a collinear binary system of $N$ particles has been investigated via a polarizable-ion model. It was found that like-charge attraction between an array of $(N-1)$ type-A particles on the left and a single type-B particle on the right is conditional upon a sufficient degree of dissimilarities between the two types of particles. By assuming that (1) the particles of one type are strongly polarizing (but weakly polarizable) such that the Coulomb fields they produce are dominant all over other electric fields, and that (2) the particles of the other type are strongly polarizable (but weakly polarizing) such that their Coulomb-field-induced dipoles are the only polarization effects worth considering, a good agreement between our approximate analytic theory and exact numerical solutions has been obtained. Our analytic results show that the attractive components of the electrostatic force between the two types of particles could be thought of as arising from imaginary charges induced in the polarized particle(s) by the polarizing ones, resulting in a screening of the real charge(s) in the polarized particle(s). Like-charge attraction occurs if the field contributions from the imaginary charges collectively outweigh the field contribution(s) from the real charge(s).