Direct Measurement of Lateral Correlations under Controlled Nanoconfinement P. K´ ekicheff, 1,2,* J. Iss, 1 P. Fontaine, 2 and A. Johner 1 1 Institut Charles Sadron, Universit´ e de Strasbourg, CNRS UPR22, 23 rue du Loess 67034 Strasbourg cedex 2, France 2 Synchrotron SOLEIL, Saint Aubin, 91192 Gif-sur-Yvette, France (Received 7 July 2017; published 15 March 2018) Lateral correlations along hydrophobic surfaces whose separation can be varied continuously are measured by x-ray scattering using a modified surface force apparatus coupled with synchrotron radiation, named SFAX. A weak isotropic diffuse scattering along the equatorial plane is revealed for mica surfaces rendered hydrophobic and charge neutral by immersion in cationic surfactant solutions at low concen- trations. The peak corresponds to a lateral surface correlation length ξ ≈ 12 nm, without long-range order. These findings are compatible with the atomic force microscopy imaging of a single surface, where adsorbed surfactant stripes appear surrounded by bare mica zones. Remarkably, the scattering patterns remain stable for gap widths D larger than the lateral period but change in intensity and shape (to a lesser extent) as soon as D< ξ. This evolution codes for a redistribution of counterions (counterion release from antagonistic patches) and the associated new x-ray labeling of the patterns. The redistribution of counterions is also the key mechanism to the long-range electrostatic attraction between similar, overall charge-neutral walls, reported earlier. DOI: 10.1103/PhysRevLett.120.118001 Controlled (e.g., patchy) or random inhomogeneously charged layers have recently attracted much attention again [1]. The disorder in the surface charge can be quenched [2] or annealed [3]. While the interaction between surfaces in the annealed case mainly involves polarization effects somewhat similar to van der Waals interactions, the quenched case is very sensitive to counterion release [4]. Some theoretical efforts were devoted to quenched systems involving multivalent counterions [5] for which strong and unexpected effects were described [6]. Even the interaction between homogeneously charged surfaces in water with monovalent counterions, for which the standard Poisson-Boltzmann mean-field theory [7] is naively expected to hold, turns out much more complicated due to the subtle interplay of the familiar electrostatics and counterion entropy with the structure of liquid water close to the surface [8–10]. (Although some insight into the chemistry-dependent, local dielectric response was gained recently from chemically realistic molecular dynamics simulations combined with the analytical theory [11].) Actually, even the sign of this interaction seems impossible to get from a generic continuous theory at short separations, and a microscopic description taking water explicitly into account is needed [9]. Luckily, at separations surpassing one (or a few) nanometer(s), the classical Poisson- Boltzmann theory turns out to work surprisingly well [9]. Accurate measurements sometimes reveal moderate corrections to the mean field [12]. A simple and standard way to control (modify) the charge of a surface is to incubate it in a solution of oppositely charged adsorbing species, typically adsorbing charged surfactants [13]. One of us studied mica surfaces with a bare area per (negative) elementary charge 1/σ 0 ¼ 48 Å 2 incubated in cationic surfactant (hexadecyltrimethy- lammonium bromide, CTAB) solutions of increasing concentration [14]. The surface force apparatus experiment measures repulsion at both very low and high CTAB concentrations [14]. In a narrow concentration range well below the critical micellar concentration of CTAB in water, the interaction is found attractive. The attraction was attributed to charge fluctuations which prevail over the weak average charge in the narrow regime of charge inversion [15,16]. This suggests some favorable correlation between the charge fluctuations on both surfaces. A direct measurement of surfactant-surfactant correlations by an in situ scattering technique is called for. The idea to set up such a technique came later [17,18], but the realization of an accurate apparatus faced major challenges. It is generally accepted that charged systems can adopt (more or less regular) microstructures rather than undergo macroscopic phase separation at no or low salt, the so-called compatibility enhancement by charge [19]. Typically, short-range repulsion between the incompatible species drives the separation, and the local electric neutral- ity breaking or the entropy of the counterions oppose charge separation. Microphase separation then appears as a compromise. The incomplete CTA þ monolayer on the oppositely charged mica is somewhat similar. Separation between a regular dense layer and the bare mica would separate the opposite charges or confine the counterions clouds of anions (cations) over the corresponding areas of PHYSICAL REVIEW LETTERS 120, 118001 (2018) 0031-9007=18=120(11)=118001(6) 118001-1 © 2018 American Physical Society