Ion Depletion Near a Solution Surface: Is Image-Charge Repulsion Sufficient?

Grazing-incidence Rutherford backscattering and angle-resolved x-ray photoelectron spectrometry are used to determine the ion-concentration profiles near the surface of a solution consisting of a salt (TEABr) in a weakly polar organic liquid (polyethylene glycol) with atomic-layer depth resolution. The predictions of a model, in which ions in solution are repelled from the surface due to a screened Coulomb interaction with their image charge, are in good agreement with measured ion profiles. This contrasts with the behavior of salts in aqueous and highly polar organic solutions.

Figure 1

(a) RBS spectra taken with a conventional Si detector (energy resolution $\sim 14\mathrm{keV}$) at a high incident angle, of a 5 wt % solution of TEABr in PEG 400 at 288 K. The kinematic energies for scattering of different elements at the surface are marked. (b) High-resolution RBS spectra in the energy range of the Br surface edge measured with a magnetic spectrometer (black lines). Incident angles as indicated. Red solid lines are simulated spectra [12] for the respective angles using the Br depth profile given in panel (c). Dashed red lines indicate simulations for a target without surface depletion; the two steps are due to the two Br isotopes (masses 81 and 79 amu), respectively [12]). The vertical dash-dotted line marks the ${}^{81}\mathrm{Br}$ surface edge. (c) Retrieved Br depth profile; the gray-shaded area depicts the region in which alternative profiles would fit the data equally well. Integrating the profile yields a mean depletion depth of $0.53\pm 0.11\mathrm{nm}$.

Figure 2

(a) Average depletion layer thickness (orange line) for both $\mathrm{Br}{}^{-}$ and $\mathrm{TEA}{}^{+}$ ions, as inferred from angle-resolved XPS measurements (yellow shaded region: uncertainty range taking only random error into account). (b) Orange line and yellow shaded area: Br profile from high-resolution RBS measurements as in Fig. 1.Dashed gray curve: Onsager-Samaras prediction for bulk screening. Dotted gray line: assuming no screening. Solid curve: solution for a constant, screening length chosen to minimize the free energy in the perturbation approach of Yeh and Chen [20]. Note that none of the curves contain any free parameters.