Direct Measurement of Lateral Correlations under Controlled Nanoconfinement

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 concentrations. The peak corresponds to a lateral surface correlation length $\xi \approx 12\mathrm{nm}$, 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 $D<\xi$. 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.

Figure 1

Schematic of the experiment set on the SIRIUS beam line [20] at the synchrotron radiation facility SOLEIL. The incident x rays fall at normal incidence on the confining mica surfaces of the SFAX, allowing the equatorial plane of the reciprocal space to be described. Back-silvered atomically smooth thin mica sheets ($\approx 5\mu \mathrm{m}$ thick) are glued down on hollow hemicylinders. Interferometry in white light allows the surface separation to be determined at $\pm 0.2\mathrm{nm}$. The upstream mica surface can be moved to approach or separate from the fixed exit mica surface. Taking advantage of the surface position stability (drift $<1\mathrm{nm}/\min$ [21]), the mirrors and objectives used to collect the light and the interferometric pattern are moved aside the optical axis. The SFAX is placed in an enclosure, from the beryllium window at the direct beam exit to the 2D detector at a $\sim 4.5\mathrm{m}$ distance from the SFAX, filled with helium to avoid spurious scattering by air and also oxidation of the 50 nm thick silver layer coating the back of the mica sheets and its degradation under high incident flux of x rays.

Figure 2

A slice at constant intensity of the scattering pattern observed in the geometry of Fig. 1 for mica surfaces immersed in an aqueous CTAB solution at $\approx 1/120$ cmc (24 h equilibration) and separated by $\sim 100\mathrm{nm}$. The beamstop, placed in the middle and mounted on a rod, houses a pin diode detector to monitor the sample transmission. After the background correction and normalization of the detector efficiency, an isotropic diffuse ring shows up at small angles in the equatorial plane when the slice is made at low intensity levels. Left: Radial averaging scattering pattern, with an enlargement of the peak.

Figure 3

Scattering curves (corrected for the scattering contribution of the mica sheets immersed in pure water using standard subtraction procedures) for different separations $D$ between the CTAB coated-mica surfaces. The scattering is independent of $D$ at high separations and nearly independent at low ones, with a stepwise (almost uniform) increase between $D=15$ and 13 nm. This is merely attributed to the redistribution of counterions (${\mathrm{Br}}^{-}$ from CTAB and $K^{+}$ dissociated from mica) when the structures on opposing surfaces start to interact. Antagonistic patches release their excess counterions, which leave as neutral salt, while agonistic patches take up some more counterions. The latter effect is weaker. With a period composed of three substripes, the inset illustrates three simple situations with the very same parallel structure but shifted by $1/3$ period either way. In the left case, the bare mica and monolayer both attract excess counterions; the two other cases facing monolayers attract more ${\mathrm{Br}}^{-}$, and antagonistic regions (hatchings) release the ${\mathrm{Br}}^{-}$ and half of the $K^{+}$. In all cases, the contrast is enhanced and the scattering of the period increased at the transition.

Figure 4

Left: Peak force mode AFM topographic image of a CTAB-coated mica surface immersed in an aqueous CTAB solution at $\approx 1/120$ cmc after 24 h equilibration.The bottom plot shows the height profile along the horizontal black line, revealing bare mica areas surrounded by adsorbed CTAB regions regular in thickness (1.7–1.9 nm). Right: FT of a $2\mu \mathrm{m}\times 2\mu \mathrm{m}$ AFM image compared with the x-ray scattering measured at large separations (Fig. 3). At large $Q$, the overall shapes can be superimposed, both revealing diffuse bumps located at similar positions.