Charge fluctuations and counterion condensation

We predict a condensation phenomenon in an overall neutral system, consisting of a single charged plate and its oppositely charged counterions. Based on the two-fluid model, in which the counterions are divided into a free and a condensed fraction, we argue that for high surface charge, fluctuations can lead to a phase transition in which a large fraction of counterions is condensed. Furthermore. we show that depending on the valence, the condensation is either a first-order or a smooth transition.