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We study the distribution of multivalent counterions next to a dielectricslab, bearing a quenched, random distribution of charges on one of its solutioninterfaces, with a given mean and variance, both in the absence and in thepresence of a bathing monovalent salt solution. We use the previously derivedapproach based on the dressed multivalent-ion theory that combines aspects ofthe strong and weak coupling of multivalent and monovalent ions in a singleframework. The presence of quenched charge disorder on the charged surface ofthe dielectric slab is shown to substantially increase the density ofmultivalent counterions in its vicinity. In the counterion-only model (with nomonovalent salt ions), the surface disorder generates an additional logarithmicattraction potential and thus an algebraically singular counterion densityprofile at the surface. This behavior persists also in the presence of amonovalent salt bath and results in significant violation of the contact-valuetheorem, reflecting the anti-fragility effects of the disorder that drive thesystem towards a more ordered state. In the presence of an interfacialdielectric discontinuity, depleting the counterion layer at the surface, thecharge disorder still generates a much enhanced counterion density further awayfrom the surface. Likewise, the charge inversion and/or overcharging of thesurface occur more strongly and at smaller bulk concentrations of multivalentcounterions when the surface carries quenched charge disorder. Overall, thepresence of quenched surface charge disorder leads to sizable effects in thedistribution of multivalent counterions in a wide range of realistic parametersand typically within a distance of a few nanometers from the charged surface.

Asymmetric Coulomb fluids at randomly charged dielectric interfaces: Anti-fragility, overcharging and charge inversion