Integral equation theory based on the Wertheim's two density formalism
is proposed to study interactions in highly asymmetric electrolyte (p
olyelectrolyte) solutions. The aqueous solution contains large and hig
hly charged polyions and small counterions having one elementary charg
e. The potential energy of interaction between counterions and polyion
s is divided into two parts, a strongly attractive part responsible fo
r association and a nonassociating part. Due to strong asymmetry in si
ze we can treat the counterions as singly bondable, while each polyion
may bond to several counterions. The two density theory yields very g
ood agreement with new and existing computer simulations for these sys
tems. This good agreement is extended into the region of parameters wh
ere ordinary HNC approximation does not give a convergent solution.