The distribution of ions and charges at solid-water interfaces is of key importance in a number of phenomena and processes. In particular the development of micro- and nano-fluidics has strengthened the need for characterizing, understanding, modeling and controlling ion distributions in the electric double layer . Indeed, surface driven transport phenomena such as electro-osmosis or electrophoresis are sensitive to charge distribution, and phenomena occurring within the diffuse Gouy-Chapman layer become dominant in determining flow properties as channel size, Debye length and slip length become on the same order of magnitude, leading to unusual phenomena . With charged walls, channels can be filled with a unipolar solution of counter-ions, suggesting that the type and concentration of ions can be controlled by the surface charge density of the channel wall . Here, specific effects (size, polarisability, hydration of the ions) could allow for even finer control over the ion type .
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a-Experimental device mounted on DiffAbs (Soleil) beamline. b- Schematics of the x-ray standing wave technique.
The technique consists in creating a standing wave field at an interface by interference between the incident electromagnetic field and the substrate diffracted field (see figure). The standing wave phase depends on the deviation from the exact Bragg angle and can be varied in a controlled way. The standing wave field is used to excite the fluorescence of the ions and moves by half a diffraction plane spacing when scanning the Bragg peak. The resolution is a fraction of the crystal or multilayer period (we used 2.5nm Si-W multilayer substrates) and can be tuned to the specific needs of the experiment. A significant advantage of the standing wave technique over reflectivity is that it is element specific.
The samples consisted in a ultra-thin liquid layer (100nm) sandwiched between the multilayer substrate used to create the standing waves and an X-ray transparent flexible window. The substrates used in the experiment were Si-W multilayers (150 periods of 2.5nm). Their surface charge could be varied by varying the pH or coated by a silane monolayer to get a hydrophobic surface. The experiments are performed at Soleil (DiffAbs or SIRIUS beamline) at 7keV with a parallel beam (500μmx200μm) allowing to resolve the Bragg peak of the multilayers.
Fluorescence of a mixture of mM solutions of KCl and CsCl. b) Fluorescence intensity for each element as a function of the grazing angle of incidence across the Bragg peak. The Ca curve provides a reference as Ca is only an impurity in the membrane with no surface behavior.
The fluorescence curves were analyzed following the procedure of  using homemade software with a peak model  including a tail and a shelf. The background is built up by the shelf contributions, and the different peak parameters have a simple energy dependence. An example is given on figure for a mixture of 10-3M solutions of KCl and CsCl. One can recognize the Cl Ka line at 2622eV, the Ar line Cl Ka at 2957eV, the Ar Cl Kb at 3190eV (Ar is mainly present in the substrate; Ar is being used as a vector for multilayer deposition) with the K Ka line at 3313eV in the tail, the Ca Ka and Kb at 3690eV and 4014eV (from the membrane film) and the Cs Ka at 4288eV.The sensitivity to the element distribution can be appreciated from the differences in the two curves, 0.1 degree below the Bragg peak (2.02degree) and at the Bragg peak (2.09 degree).
We made a first analysis of the resulting standing waves curve (fluorescence intensity for each element as a function of the grazing angle of incidence across the Bragg peak, see figure) using a homemade software. The figure shows a shift in the chlorine distribution from the Cs+ and K+ distributions, consistent with the negatively charged surface. Small deviations due to alignment or detector efficiency were corrected using substrate fluorescence lines which do not depend on the solution.
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 Implementation of a spectrum fitting procedure using a robust peak model
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