How to measure work functions from aqueous solutions

The recent application of concepts from condensed-matter physics to photoelectron spectroscopy (PES) of volatile, liquid-phase systems has enabled the measurement of electronic energetics of liquids on an absolute scale. Particularly, vertical ionization energies, VIEs, of liquid water and aqueous solutions, both in the bulk and at associated interfaces, can now be accurately, precisely, and routinely determined. These IEs are referenced to the local vacuum level, which is the appropriate quantity for condensed matter with associated surfaces, including liquids. In this work, we connect this newly accessible energy level to another important surface property, namely, the solution work function, eΦliq. We lay out the prerequisites for and unique challenges of determining eΦ of aqueous solutions and liquids in general. We demonstrate – for a model aqueous solution with a tetra-n-butylammonium iodide (TBAI) surfactant solute – that concentration-dependent work functions, associated with the surface dipoles generated by the segregated interfacial layer of TBA+ and I− ions, can be accurately measured under controlled conditions. We detail the nature of surface potentials, uniquely tied to the nature of the flowing-liquid sample, which must be eliminated or quantified to enable such measurements. This allows us to refer aqueous-phase spectra to the Fermi level and to quantitatively assign surfactant-concentration-dependent spectral shifts to competing work function and electronic-structure effects, where the latter are typically associated with solute–solvent interactions in the bulk of the solution which determine, e.g., chemical reactivity. The present work describes the extension of liquid-jet PES to quantitatively access concentration-dependent surface descriptors that have so far been restricted to solid-phase measurements. Correspondingly, these studies mark the beginning of a new era in the characterization of the interfacial electronic structure of aqueous solutions and liquids more generally.


Flow-Rate-Dependent Measurements of TBAI Aqueous Solutions
Figure S1: PE spectra of 12.5 mM (A) and 25 mM (B) TBAI(aq) showing the water 1b1 and I − 5p PE features as a function of flow rate from 0.5-2.0ml/min.Insets show the relative energy shift of the water 1b1 feature compared to 1 ml/min flow.The error bars are fit errors.The polynomial fit in the inset of B) is only a guide to the eye.PE spectra were recorded from aqueous solutions injected into the spectrometer at various flow rates and with representative concentrations of 12.5 and 25 mM TBAI, to assess their residual streaming potentials.Any energy shift in the spectra as a function of liquid flow rate can be extrapolated to zero flow, at which the streaming potential must vanish.Alternatively, should there be no shift, the absence of a streaming potential can be confirmed for any flow rate.Figure S1 shows the PE spectra for 12.5 mM (A) and 25 mM (B) solutions for flow rates from 0.5-2.0ml/min.All spectra were recorded at the P04 soft X-ray beamline 1 of the PETRA III synchrotron facility (Deutsches Elektronen-Synchrotron, DESY, Hamburg) at a photon energy of 401 eV and using the same spectrometer setup (EASI) and PtIr microplate assembly as in the laboratory experiments.The insets show the energy shift of the water 1b1 PE feature relative to the flow rate of 1 ml/min (dashed line), which Electronic Supplementary Material (ESI) for Chemical Science.This journal is © The Royal Society of Chemistry 2023 was utilized for all measurements presented in the main text.For 12.5 mM TBAI, no significant shift and thus no notable contribution of the streaming potential is observed.For 25 mM TBAI, while showing a clear trend towards higher energy shifts at higher flow rates, the difference between an (extrapolated) zero flow and 1 ml/min is below 15 meV.This gives us confidence that the contribution of the streaming potential is an insignificant fraction of the energy shifts discussed in the main text.

The Apparatus Fermi Level and Work Function
Measuring EF from metallic systems is straightforward.Since electronic states are occupied in conductors up to EF, the associated energy is revealed as a sharp, high-energy cutoff in PE spectra.In the absence of any disturbing potentials, the measured kinetic-energy value associated with EF corresponds to eKEEF = hν -eΦdet, with eΦdet being the work function of the detection system.This somewhat counterintuitive result originates from the fact that photoelectrons experience the contact potential difference between the sample and apparatus, ΔeΦ = eΦliq -eΦdet.The kinetic energy of the detected photoelectrons is thus modified by ΔeΦ, i.e., eKEEF = hν -eΦliq + ΔeΦ = hν -eΦdet.For semiconductors and insulators -i.e., condensed-phase systems exhibiting a band gap where the energy range around EF is devoid of available states for electrons -EF is not directly measurable.][4] Note that the measured Fermi-level-feature kinetic energy, eKEmeas, is somewhat arbitrary, as it may be subject to experimental offsets associated with the detection system, such as a poorly calibrated energy scale.It is not an issue for Fermi referencing if the measured energy scale is linear, since all spectra are measured with the same device and are thus subject to the same systematic measurement offsets, i.e., only relative kinetic energies are involved.This is the case for our hemispherical electron analyzer; care should be taken with nonlinear systems such as time-of-flight analyzers, though.Previously, we corrected eKEmeas with the offset factor for our system, determined as 0.224 ± 0.008 eV, which yielded eΦdet = 4.293 ± 0.009 eV. 5 In the present experiments, we measured the 3p peak of Argon gas after the LJ experiments and compared it with the reference value of 15.759735 ± 0.000001 eV 6 to confirm the energy-scale correction.This yielded a consistent eΦdet = 4.30 ± 0.04 eV; the somewhat larger error originates from observed fluctuations in the Ar 3p peak positions over multiple days.

Pitfalls and Considerations for Accurate Fermi Referencing
While Fermi-referenced measurements seem straightforward, if streaming potentials and any other extrinsic potentials have been considered or eliminated, grounded measurements are prone to interferences from suboptimal experimental conditions.Reliable measurements correspondingly necessitate the utmost care.We encountered several systematic experimental errors during our studies, which can negatively affect the measurement.Here, we give a brief overview of the associated potential pitfalls.
1) In the main text, it was noted that a consistent value was measured for the Fermi edge of our reference metal samples (eKEEF = 36.30eV), and that this value is stable, as it is an intrinsic property of our apparatus.We observed, however, that this value can be temporarily altered slightly -on the order of 50 meV or morewhen measuring certain samples, such as solutions containing organic compounds.This may stem from persistent surface-adsorption layers on the inner walls of the apparatus, which desorb over the course of days or even weeks.We correspondingly recommend the constant monitoring of the Fermi-edge position when attempting to measure Fermi-referenced spectra.
2) Another important aspect in LJ-PES is the continuous evaporation from the liquid surface, which forms some rather ill-defined adsorbate layer on all inner walls of the apparatus.This alters the surface potentials of the interaction chamber, which causes spectral shifts over time and with varying chamber pressure; for example, a shift of several hundred meV has been observed over a 2-4-hours period after starting experiments. 5 In the case of the glass-nozzle assembly, grounding was achieved via metallic inset tubes placed in between the HPLC pump and PEEK liquid delivery line prior to injection into the vacuum chamber.As flow characteristics of the solution in this metallic inset are altered, crystallization of solutes may occur, which deteriorates the grounding.We observed shifts on the order of ~100 meV of all PE spectra in such a case.Cleaning and reassembling the liquid delivery system recovered the original energetic positions of PE spectra.
4) Figure S3 compares PE spectra from the PtIr microplate, a new, passivated glass nozzle, and a glass nozzle after running solutions with a particularly high (or low) pH value.Large shifts (up to ~300 meV) of all PE spectra were observed in the latter case.The unshifted PE spectra could not be recovered, even after several days.It is very likely that the surface properties of the inner glass-nozzle walls were chemically altered, which could lead to a significant streaming potential, or alternative additional unwanted potentials.Furthermore, the metallic inset tube used to ground the solutions may have been corroded.Thus, we found that the glass-nozzle assembly is more prone to detrimental effects, and measurements from a PtIr microplate (or other nozzles which provide both proper grounding and chemical resistance) are preferred.and TBAI(aq) (light and dark green curves).However, the PE spectra shifted considerably after running solutions with a pH value well removed from 7; both a pH close to 0 and 14 was reached before the spectra shown here were measured.Specifically, shifts of ~250 meV and 310 meV were observed for reference water (red curve) and 25 mM TBAI(aq) (yellow curve), respectively.We noticed such shifts whenever solutions with particularly high or low pH values were measured prior to Fermi-referenced measurements with glass-capillary nozzles, suggesting a pH-induced deterioration of the glass and an associated change in liquid streaming potential.

Additional Figures
Figure S3:   and S3.Spectra have been normalized to unit height at the 1b1 band and shifted to maximum overlap at the highenergy shoulder to emphasize the change in shape.B) Values of the peak width as extracted from A) as a function of TBAI concentration.The widths were taken from the 1b1 band at 70% signal height (dashed line in panel A) and do not originate from the fits discussed in the main text.Fit results (FWHM values) from our previous study 7 have been added for comparison; this data has been arbitrarily scaled by a factor of 3 and aligned to the reference water value.
In the main text, it was explained that the liquid water 1b1 band was fitted by a single peak over a limited data range because of overlapping features from the gas phase, which made a full fit of the spectrum difficult.Thus, it was not possible to extract a peak width from the fit, due to the constrained nature of the procedure.Instead, in Fig. S4, we plot the total observed width of the PE band in the data directly at 70% band height, a value arbitrarily chosen to avoid interference from the signals of the nearby orbitals and the gas phase.The result in Fig. S4B serves as a confirmation of the overall trend of a broadening liquid-water 1b1 band, as observed in our previous study, 7 which is also replicated as a purple dashed line.This confirms that the shape of the liquid bands is the same, both in the grounded and biased measurements.Any presence of Vtot does not lead to additional broadening, since, similarly to the biased case, this potential leads to a rigid shift of all liquid features.This is furthermore consistent with the observed excellent match of biased and unbiased PE spectra; see, for example, Fig. 7A in the main text.

Figure S2 :
Figure S2:Exemplary valence PE spectra of reference water (with 50 mM NaCl added) and 25 mM TBAI(aq), measured from a grounded liquid jet with hν = 40.814eV.If properly prepared, PE spectra measured from a PtIr microplate are equivalent to the ones from a glass capillary for both reference water (light and dark blue curves) and TBAI(aq) (light and dark green curves).However, the PE spectra shifted considerably after running solutions with a pH value well removed from 7; both a pH close to 0 and 14 was reached before the spectra shown here were measured.Specifically, shifts of ~250 meV and 310 meV were observed for reference water (red curve) and 25 mM TBAI(aq) (yellow curve), respectively.We noticed such shifts whenever solutions with particularly Figure S3: Close-up on the A) gas and B) liquid 1b1: The data from Fig. 4 in the main text are shown without intensity normalization and vertical offsets, i.e., here, the PE intensities are shown as-measured.

Figure S4 :
Figure S4: A) Liquid 1b1 band shape as a function of TBAI concentration; the spectra are the same as in Figs.4and S3.Spectra have been normalized to unit height at the 1b1 band and shifted to maximum overlap at the highenergy shoulder to emphasize the change in shape.B) Values of the peak width as extracted from A) as a function of TBAI concentration.The widths were taken from the 1b1 band at 70% signal height (dashed line in panel A) and do not originate from the fits discussed in the main text.Fit results (FWHM values) from our previous study7

Figure S5 :
Figure S5:Peak width (FWHM) of the gas-phase 1b1 peaks as a function of TBAI concentration from peak fits to the PE spectra.Error bars represent the quadratic addition of fit errors (one sigma) and a general uncertainty in the measurement of 5 meV.Red dots indicate results from TBAI(aq) (5 mM NaCl have been added for concentrations at and below 1 mM TBAI to assure sufficient conductivity) and black triangles indicate reference water results (no TBAI but 50 mM NaCl).The minimal FWHM (indicating |Vtot| ≈ 0 V) is reached from about ~10 mM up to the highest concentration.The constant value of ~70 meV indicates that any changes are below our ability to measure peak widths in our experiment.