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. 61.20.Qg, 61.25.Hq, 87.15.Da

Using both small-amplitude and singular-perturbation theories we predict theoretically that the presence of surface charge modulations gives rise to an enhancement of the counterion density near the surface above and beyond that of a uniform, charged surface. We confirm these predictions with Monte Carlo simulations. Our study focuses on the weak- to moderate-coupling regime which is complementary to a similar investigation performed by Moreira and Netz (Europhys. Lett., 57 (2002) 911) in the strong-coupling case.

PACS. 82.70.-y -Disperse systems; complex fluids. PACS. 61.20.Qg -Structure of associated liquids: electrolytes, molten salts, etc..Abstract. -We predict theoretically that long-wavelength surface charge modulations universally reduce the pressure between the charged surfaces with counterions compared with the case of uniformly charged surfaces with the same average surface charge density. The physical origin of this effect is the fact that surface charge modulations always lead to enhanced counterion localization near the surfaces, and hence, fewer charges at the midplane. We confirm the last prediction with Monte Carlo simulations.

We predict the fluctuation contribution to the interaction between two surfaces with both mobile layer charges and delocalized counterions. The correlation (coupling) between the layer-charge fluctuations and the counterion fluctuations (around a piecewise homogeneous mean-field density profile) is taken into account in the Gaussian approximation. We find that this correlation significantly increases the magnitude of the interlayer fluctuation attraction. The counterion fluctuation pressure is calculated as a function of the intersurface distance and we show how the large and small distance limits correspond to three-dimensional (3D) and 2D fluctuations, respectively. In addition, we predict the charge density-density correlation functions. Experimental implications of the model are discussed.

We calculate the static properties of macroion density fluctuations in both bulk and in confined, strongly interacting, macroion suspensions (macroions interact via the Derjaguin-Landau-Verwey-Overbeek potential) in terms of a simple density-functional ansatz. We show how to map a strongly interacting suspension to a weakly interacting one and obtain the renormalized charge, diameter and scattering structure factors analytically. The model is extrapolated to predict crystalline order in terms of a Hansen-Verlet-type of criterion as well as an effective hard-sphere crystallization condition, and good agreement with simulations is found. The increase in correlations observed in recent experiments in two, confined layers is demonstrated.