  We study the spatial and orientational distribution of rodlike counterions
(such as mobile nanorods) as well as the effective interaction mediated by them
between two plane-parallel surfaces that carry fixed (quenched) heterogeneous
charge distributions. The rodlike counterions are assumed to have an internal
charge distribution, specified by a multivalent monopolar moment and a finite
quadrupolar moment, and the quenched surface charge is assumed to be randomly
distributed with equal mean and variance on the two surfaces. While equally
charged surfaces are known to repel within the traditional mean-field theories,
the presence of multivalent counterions has been shown to cause attractive
interactions between uniformly charged surfaces due to the prevalence of strong
electrostatic couplings that grow rapidly with the counterion valency. We show
that the combined effects due to electrostatic correlations (caused by the
coupling between the mean surface field and the multivalent, monopolar, charge
valency of counterions) as well as the disorder-induced interactions (caused by
the coupling between the surface disorder field and the quadrupolar moment of
counterions) lead to much stronger attractive interactions between two randomly
charged surfaces. The interaction profile turns out to be a nonmonotonic
function of the intersurface separation, displaying an attractive minimum at
relatively small separations, where the ensuing attraction can exceed the
maximum strong-coupling attraction (produced by multivalent monopolar
counterions between uniformly charged surfaces) by more than an order of
magnitude.
