Underscreening, overscreening and double-layer capacitance

•Increase of electrolyte concentration may cause massive ion clustering, diminishing 'free' ion concentration.•This increases the screening length, as screening is mainly provided by free ions.•Coulomb lattice gas model describes this behaviour under condition of massive ion clustering.•It leads, however, to pathologically small values of the linear response capacitance.•Overscreening at short distances may resolve this controversy.

There have recently been reports of extraordinarily long screening lengths in concentrated electrolytes and which vary non-monotonically with ion concentration. There were several attempts to explain these puzzling observations. In this communication we further explore possibilities to rationalise those results. Our analysis does not yet close the problem, but it highlights conflicting consequences of the models designed to reproduce those observations.