Photoelectron Angular Distributions from Liquid Water: Effects of Electron Scattering

Photoelectron angular distributions (PADs) from the liquid-water surface and from bulk liquid water are reported for water oxygen-$1s$ ionization. Although less so than for the gas phase, the measured PADs from the liquid are remarkably anisotropic, even at electron kinetic energies lower than 100 eV, when elastic scattering cross sections for the outgoing electrons with other water molecules are large. The PADs reveal that theoretical estimates of the inelastic mean free path are likely too long at low kinetic energies, and hence the electron probing depth in water, near threshold ionization, appears to be considerably smaller than so far assumed.

Figure 1

Right inset: Photon-flux normalized photoelectron spectra for $\mathrm{O}1s$ ionization ($h\nu =800\mathrm{eV}$) at three representative polarization angles ($\theta$). Solid lines are Gaussian fits to the data. Left inset: Sketch of the experimental geometry. The direction of electron detection by a hemispherical electron analyzer (EA, black arrow), liquid jet, and x-ray beam orthogonally intersect. The light-polarization vector $E$ (red arrow) is varied (change of $\theta$) with respect to the EA. Main figure: Peak areas at 800 eV as function of $\theta$, for ${\mathrm{H}}_2\mathrm{O}(\mathrm{l})$ (blue) and ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$ (red). Error bars largely result from experimental reproducibility. Solid lines are $f(\theta )$ fits (see text).

Figure 2

Experimental $\beta$ values for $\mathrm{O}1s$ ionization of ${\mathrm{H}}_2\mathrm{O}(\mathrm{l})$ and ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$. Error bars are from fitting. Dashed lines are calculated values for ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$ [26] (green) and for isoelectronic closed-shell ${\mathrm{O}}^{2-}$ ($\beta =2$) [2] (cyan) using time-dependent density functional theory (TD-DFT).

Figure 3

(a): Experimental (green) and modeled [cyan, violet, red; using IMFP/EMFP ratios from (c)] $\beta$ reduction for $\mathrm{O}1s$ ionization of ${\mathrm{H}}_2\mathrm{O}(\mathrm{l})$ relative to ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$ as a function of $e\mathrm{KE}$. (b): Computed IMFP and EMFP curves for liquid water from Tomita et al. [16] (blue, black) and Pimblott et al. [15] (violet, brown; cross sections were converted to MFP using a density of $\sim 3.35\times {10}^{22}\mathrm{molecules}/{\mathrm{cm}}^3$). The shading includes data from other calculations (for IMFP [17, 19] and EMFP [18, 19]). ${\mathrm{IMFP}}^{*}$ (red) is a flattened version for the range $<100\mathrm{eV}$ (see text). Green symbols are EALs obtained for an aqueous solution taken from Ref. 8, unaltered (circles) and corrected using $\beta$ values of Fig. 2 (diamonds). (c): IMFP/EMFP ratios calculated from the curves of Ref. 16 (blue) and from Ref. 15 (violet), and ${\mathrm{IMFP}}^{*}/\mathrm{EMFP}$ (red).