Monovalent counterion distributions at highly charged water interfaces: Proton-transfer and Poisson-Boltzmann theory

Surface sensitive synchrotron–x-ray scattering studies reveal the distributions of monovalent ions next to highly charged interfaces. A lipid phosphate (dihexadecyl hydrogen phosphate) was spread as a monolayer at the air-water interface, containing CsI at various concentrations. Using anomalous reflectivity off and at the $L_3$ ${\mathrm{Cs}}^{+}$ resonance, we provide spatial counterion distributions $\left({\mathrm{Cs}}^{+}\right)$ next to the negatively charged interface over a wide range of ionic concentrations. We argue that at low salt concentrations and for pure water the enhanced concentration of hydroniums ${\mathrm{H}}_3{\mathrm{O}}^{+}$ at the interface leads to proton transfer back to the phosphate group by a high contact potential, whereas high salt concentrations lower the contact potential resulting in proton release and increased surface charge density. The experimental ionic distributions are in excellent agreement with a renormalized-surface-charge Poisson-Boltzmann theory without fitting parameters or additional assumptions.

Figure 1

(Color online) Surface pressure versus molecular area for DHDP for different CsI concentrations as indicated. Reflectivity and GIXD were performed at constant surface pressures $40\mathrm{mN}∕\mathrm{m}$ and $30\mathrm{mN}∕\mathrm{m}$. The dashed lines indicate the region in isotherms reported in this paper.

Figure 2

(Color online) Measured normalized XR curves and best fits (solid lines) for DHDP monolayers at various CsI concentrations at surface pressure $40\mathrm{mN}∕\mathrm{m}$ (curves are shifted, by a decade each, for clarity).

Figure 3

(Color online) (A) Normalized x-ray reflectivities measured at 16.2 and $5.012\mathrm{keV}$ of the DHDP monolayer spread on ${10}^{-3}\mathrm{M}$ CsI solution $(\pi =40\mathrm{mN}∕\mathrm{m})$. Solid lines are calculated reflectivities using the ED and AD profiles shown in (B). The two data sets were combined and refined to a model with common structural adjustable parameters. (C) The solid line, obtained from the difference of the two ED’s in (B), shows the experimental distribution of ${\mathrm{Cs}}^{+}$; the dashed and dashed-dotted lines are calculated by RPB and PB, respectively, convoluted and nonconvoluted as indicated (nonconvoluted calculations of PB and RPB are divided by 10).

Figure 4

(Color online) (A) Interfacial ${\mathrm{Cs}}^{+}$ distributions (solid lines and shaded areas) determined from anomalous reflectivities as outlined in Fig. 3 for various CsI bulk concentrations (shifted by $0.5\mathrm{M}$ for clarity). Calculated distributions based on RPB are shown with dashed lines. (B) Number of ${\mathrm{Cs}}^{+}$ ions per lipid $(\approx 41{\mathrm{\AA }}^2)$ (square symbols). The dashed line is the PB integrated over the first $15\mathrm{\AA }$, and the solid line is obtained from the RPB integrated over the same range.