Simple model for attraction between like-charged polyions

We present a simple model for the possible mechanism of appearance of attra ction between like charged polyions inside a polyelectrolyte solution. The attraction is found to be short ranged, and exists only in the presence of multivalent counterions. It is produced by the correlations in layers of co ndensed counterions surrounding each polyion and is only weakly temperature dependent. We find the attraction to be maximum at zero temperature and di mish as the temperature is raised. The attraction is only possible if the n umber of condensed counterions exceeds the threshold, n > Z/2 alpha, where a is the valence of counterions and Z is the polyion charge.