Probing the Birth and Ultrafast Dynamics of Hydrated Electrons at the Gold/Liquid Water Interface via an Optoelectronic Approach

The hydrated electron has fundamental and practical significance in radiation and radical chemistry, catalysis, and radiobiology. While its bulk properties have been extensively studied, its behavior at solid/liquid interfaces is still unclear due to the lack of effective tools to characterize this short-lived species in between two condensed matter layers. In this study, we develop a novel optoelectronic technique for the characterization of the birth and structural evolution of solvated electrons at the metal/liquid interface with a femtosecond time resolution. Using this tool, we record for the first time the transient spectra (in a photon energy range from 0.31 to 1.85 eV) in situ with a time resolution of 50 fs revealing several novel aspects of their properties at the interface. Especially the transient species show state-dependent optical transition behaviors from being isotropic in the hot state to perpendicular to the surface in the trapped and solvated states. The technique will enable a better understanding of hot electron driven reactions at electrochemical interfaces.


S-1 Experimental principles
This optoelectronic technique to probe the electrode-electrolyte interface combines optical perturbation of the system with coulostatic measurements. As described by Richardson 1,3,4 The introduction of the second pump creates a second photovoltage ∆V 2 only if both pulses match certain delay conditions that are photon energy-dependent. There is no measurable photovoltage change for completely detuned pulses.
Hence, the second pump will interact only with hydrated electrons and precursor states [see  A potentiostatic variant of the two-pulse technique was used to report on the picosecond dynamics of photoelectrons in hexane. 5 The detection scheme used by Scott was also different: A fast high voltage pulse (2 kV) moved the electrons out from the sample interface to the sensor electrode, 4 mm away.
The electrical double layer (EDL) acts as a capacitor with Q = C V , where Q is the charge, C is the capacitance of the EDL and V is the voltage. The presence of uncompensated charges in the EDL thus results in a photovoltage. At a concentration of 0.5 M Na 2 SO 4 in water, the Debye length λ D is ∼ 2.5 Å, meaning that we are only probing the charged species located closer than circa two bond lengths from the surface.
As noted above, a voltage can also be established by creating a temperature difference between electrodes. The temperature dependence of the voltage has been exploited previously in temperature jump measurements. 3,6,7 The total photovoltage due to heating of the metal-solution boundary is the sum of the internal drop of potential at the metal-solution boundary V i , of the thermodiffusion potential of the solution (Soret effect) V S , and of the thermal EMF of the metal heating resulting from an ultrafast pulse can yield, in gold, a transient electronic temperature T e as high as 1750 K, which results to an increase of the lattice temperature T l on the order of 15 K.

S-2.1 Spectroelectrochemical cell
The spectroelectrochemical cell (SEC) consists of a set of 3 gold electrodes ( through with two holes to allow the flow of the electrolyte, and separated by a 50 µm PTFE spacer cut in the shape shown in Fig. S2(b), using the assembly displayed in Fig. S2(c). Copper foil is used to electrically contact the electrodes externally.

S-5
The electrolyte consists of Na 2 SO 4 in deionized water (18.2 MΩ· cm, Millipore) at a concentration of 0.5 M. It is deaerated by bubbling dry N 2 in the reservoir for at least 30 min. before the measurement is started. The flow of the electrolyte is assured by a peristaltic pump at a rate of 6 µL / s. In order to avoid any spurious effect by species generated at the CE, the electrolyte inlet is located above the RE and the outlet above the CE.

S-2.2 Electrochemical measurements
A potentiostat (VSP, Bio-Logic Science Instruments) was employed to record the open circuit potential (OCP). It was found useful, before the coulostatic measurements, to "clean" the WE by performing a series of cyclic voltammetry (CV) sweeps until the CV data showed the appropriate profile for a polycrystalline gold electrode in a thin film configuration. The RE would be cleaned in a similar manner whenever the drift was becoming important.

S-2.3 Laser setup
The layout of the laser system that was employed in this study is shown in [Fig. S3]. In brief, the laser system is composed of a Ti:Sapphire oscillator (Vitara, Coherent) and regenerative amplifier photovoltage change due to the second pump pulse. The first pump delay stage is thus swept to find the maximal bleaching.

S-2.3.1 Generation of various wavelengths for the second pump's pulse
Various ultrashort pulses have been employed in this study as the second pump's pulses. They were generated as following: 670 and 720 nm The TOPAS' Signal outputs at 1340 and 1440 nm, respectively, were doubled in a BBO crystal and the fundamental beams were subsequently filtered out.

nm
The 800 nm residual from the TOPAS after the parametric process was separated from the Idler and Signal beams and attenuated to required energy.

S-2.4 Optoelectronic measurements
After the first pump beam shutter is opened, we let ∆V 1 reach an equilibrium value for approximately 10 min before the time delay series of the second pump beam is started. The shutter of the second pump beam is then sequentially opened and closed at 1 min intervals and the delay between the pulses of the first and second pumps is stepped at every repetition while photovoltage is continuously acquired in OCP mode. As can be seen in Fig

S-2.5 Data processing
The photovoltage change ∆V 2 due to the action of the second pump beam is first extracted in (postmeasurement) data processing from the as-measured photovoltage versus elapsed experimental time [shown in Fig. S1(b)]. It is defined as the difference of the photovoltage measured when the second beam has been impinging for 1 min to the photovoltage measured after the second pump beam has been shut off for 1 min. Each photovoltage spike thus corresponds to a different delay of the first and second pump pulses. The photovoltage change is then corrected for the measured pulse energy of the first (P 1 ) and second pump (P 2 ) beams and the absorptivity of water at the wavelength of the second pump for a given angle θ of the second pump beam, a water layer thickness d w and known water extinction coefficients α [8][9][10]    calculated from Snell's law and the second pump incidence angle in air (θ air = 0.95993 rad) with d CaF 2 = 3 mm and wavelength-dependent n CaF 2 and n w 11 . The different pulse energy values and water extinction coefficients are tabulated in Table S1. The correction to the raw photovoltage change ∆V raw 2 is expressed as: It is thus ∆V corr 2 that is presented in the main text as ∆V 2 for simplicity. Error on the data was estimated by propagation of the readout noise on ∆V raw 2 and the power fluctuation of the first and second pump laser beams P 1 and P 2 . S-9

S-2.6 Ultrafast pulse dispersion
The effect of CaF 2 optics (15 mm lens + 3 mm window) and water layer (50 µm) on the UV pulse duration (nominally 60 fs, 267 nm, at the amplifier's output) was calculated. [11][12][13] As seen in Fig. S4, the smallest pulse duration is ∼ 106 fs. Given that the output from the amplifier is ∼ 60 fs, that there should be no significant change of the pulse duration in the tripler, and that the curve shown in Fig. S4 is rather flat between 60 and 110 fs, a pulse FWHM of 110 fs for the UV light pulse duration is reasonable and will be used in data analysis and simulations.

S-3 Heating of the interface
Heating of the gold electrode has been simulated numerically using a two-temperature model

S-4 Models and fitting S-4.1 Three-state model
Aiming to model the dynamics at the interface, we used a system of five coupled ordinary differential equations that are solved numerically to find the populations N i at various states S 0 to S 4 in the system, of which 3 states are solution-side [ Fig. 3(a)]: S-10 where and I(t) is the intensity of the time-dependent UV pump pulse. In order to correctly capture the dynamics of the shoulder feature in Fig. 1(d Assuming that only electron populations on the solution side contribute to the signal, the photovoltage change ∆V 2 is related to populations N 2 , N 3 and N 4 through absorption coefficients a i : Only four parameters are thus adjusted for every excitation energy: three absorption coefficients and a delay offset.
Metals dynamics have been taken into account in the model, even though it was found to be mostly insensitive to them: We have therefore lumped the metal-side thermalization into an

S-11
Back capture by the electrode [orange arrow in Fig. 3(a)] has not been explicitly implemented but it is expected to contribute to the effective characteristic times. As the back capture rate is higher for electrons of higher energy, the contribution should be more important for τ 0 and τ 1 .

S-4.2 Two-state model
For the sake of comparison, we also implemented a simpler two-state model where the state S 3 is eliminated: and using: (S12) Using this set of equations, we were unable to obtain a common set of characteristic times that correctly described the traces at every wavelengths. For instance, τ 3 remained fairly unaffected with a value of 52.1 ps. However, τ 1 was very much dependent on the second pump wavelength.
Fitting the model at a second pump wavelength of 800 nm yielded a τ 1 with a value of 900 fs, while a fit at 4 µm gave a value of 110 fs. As can be attested in Fig. S6(a), a satisfying agreement at all second pump wavelengths cannot be reached with a model with only two states on the solution side.

S-5.2 Time delay traces
The full set of time delay traces for various second pump energies is presented in Fig. S6. A zoom near the origin is shown for all energies in Fig. S6(a), while longer traces are displayed in (b) for energies 1.24 to 1.85 eV. The fit results (red dashed lines, computed as described in section S-4) are overlaid on the data (gray circles). As described in the main text, the photovoltage response ∆V 2 to the UV excitation (first pump) is highly dependent on the second pump wavelength. At low energies, the signal rise and decay is fast, on the order of 100 fs. As the second pump energy is increased, the signal persists for much longer, with residual intensity at 100 ps at 1.55 eV and above. We also note the large changes in peak ∆V 2 . At 0.31 eV, the signal reaches approximately 0.18 mV, while the peak signal at 1.85 eV is more than 1000 times weaker. where τ 1 has been determined from a fit at a second pump wavelength of 800 nm (blue dasheddotted line) and 4 µm (green dotted line) as explained above. The discrepancy is most obvious at short delay times in Fig. S6(a).

S-5.4 Simulation of heating of the gold electrode surface by an ultrafast UV pulse
We have simulated the heating of the gold-water interface as described in § S-3 using the two-temperature model and calculated the temperature-related changes due to intraband and interband transitions. Results for both T e and T l are displayed in Fig. S8(a). The UV pulse interaction with the gold surface creates a transient hot electron population with T e rising up to 1750 K. The electron system's temperature T e nevertheless rapidly decreases as the hot electrons diffuse into the substrate and scatter with the lattice's phonons. Upon this action, the latter's temperature T l rises by about 15 K in 4 ps. It is noteworthy that neither temperature profile matches directly the delay-dependent ∆V 2 traces (Fig. S60. The reflectivity change ∆R/R 0 due to temperature-dependent Drude-like intraband transitions has been modeled according to Block et al. ( main text and supplementary materials). 20 The simulations results are presented in Fig. S9 with the evolution as function of delay in (a) and as a function of second pump energy in (b). We note from (a) that the general time-dependent ∆R/R 0 trace is similar to T e in Fig. S8(a). Also, ∆R/R 0 is much larger at lower energies, as can be expected from intraband transitions.
Similarly, we have computed the change in Fermi-Dirac (FD) electron distribution (∆ f / f 0 ) as a function of temperature (Fig. S10). In order to relate ∆ f / f 0 to the optical response due to S-16  interband transitions, a detailed knowledge of gold's complex permittivity in the k-space would be necessary. Nevertheless, the interband transition probability should be dependent on the FD electron distribution and we use here the readily available ∆ f / f 0 parameter to represent the temporal changes in the system. From Fig. S10(a), we can see that ∆ f / f 0 rapidly increases upon excitation, but decays almost as fast. In this case, the larger change can be seen at higher energies [ Fig S10(b)]. Fermi smearing is indeed maximal just above and below the interband threshold (∼ 2.38 eV), yielding the typical "first derivative" shape ( Fig. S11).

S-6 Discussion
S-6.1 Nature of the photovoltage ∆V 2 We discuss here four hypotheses for the origin of the photovoltage ∆V 2 and we expose arguments  Fig. 1(b), main text]. Secondly, perturbation of the normal interband transitions of gold results in a differential spectral shape reflecting the change of electron occupancy. 21 The electron occupancy change is itself described by the Fermi smearing induced by the first excitation pump  Fig. 2(b), main text]. Relatedly, the contribution of a surface plasmon resonance (SPR) can also be ruled out since gold's SPR is found around 600 nm and, due to momentum conservation, it cannot be excited in free space in the far field. The resonance maximum of a localized surface plasmon resonance (LSPR) may be pushed to the near-infrared, but they appear in cases where the electronic wavefunction is confined, such as in nanoparticles, patterned surfaces or roughened surfaces. Moreover, here also, a possible plasmon contribution does not hold against the all-ornothing experimental evidence provided by the switch from a 267 nm first pump to 400 nm. This behavior suggests the existence of an excitation threshold whose energy is higher than the SPR and interband transitions.
This leads to iv., the resonant excitation of species present at the interface, resulting in an increase in the amount of heat generated at the metal/solution boundary. In bulk water, the excess electron frequency-dependent dynamics are characterized by a high energy absorption band centered around 1.72 eV (720 nm) and by a low energy absorption band peaking in the terahertz region. As discussed in § S-1, a change in the metal-solution boundary temperature produces a potential difference between the electrodes. S-20

S-6.2 Effective spectra
The spectrum a 2 [top panel of Fig. 4(c), main text] corresponding to the hot electron population shows a profile that rises strongly at low energies. It can be best fitted by a Lorentzian peak shape centered at 0 with a full width at half maximum (FWHM) of (0.2 ± 0.1) eV. With the caveat emptor that the sparse data prevents us from reaching a definitive conclusion about the peak shape and position, we chose to use a Lorentzian function to model the a 3

S-6.3 Local concentration in the Helmholtz layers
According to the Gouy-Chapman-Stern model, in the absence of specific adsorption, the inner Helmholtz layer (IHL) of the interface will be covered by water molecules. If we assume the outer Helmholtz layer (OHL) of the interface is occupied by a monolayer containing an equal number of solvated cations and anions, the maximum local concentration of the cations (which have been shown to play more roles in interacting with solvated electron than anions) can be estimated as following: It is known that, in a 0.5 M Na 2 SO 4 solution, the molar ratio between Na + and H 2 O is 1:56. If we assume one ion is solvated by 4-6 water molecules, the ratio of the total number of cations and water molecules (including the IHL's water molecules and those solvating the SO 2− 4 ions) is roughly 1:10, which gives a concentration of about 6 M for Na + at the interface.
The excited electron gets bound to a CTTS state created by the potential well due to solvent S-21 polarization around the now neutral atom or molecule as the solvent molecules did not have the time to reorganize. Reorientation of the solvent molecules in the surroundings of the CTTS state destroys this state and separates the electron from the neutral particle. 27 The electron is thus found in a solvated state that is basically a modified ground state with s symmetry. Multiphoton absorption (more energetic pump) could also lead to ionization by promoting the electron directly to a continuum of states that can transfer to the water conduction band. The latter has more similarities with multiphoton ionization of neat water.
In our experiments, there is no strong incentive to believe that a true analog to a CTTS state is formed. The first UV pump has enough energy to provoke the emission from the hot excited states in the metal to the water conduction band. In fact, this process is more similar to the multiphoton ionization of water 28,29 because a transient hole is left behind in the metal which necessarily interacts with the electron through Coulombic forces. In analogy, the electron interacts with the H 2 O + ion in the water ionization process. In our experiment, in contrast to the multiphoton ionization of water, it is known from gold ultrafast dynamics that the transient hole is effectively screened on a time scale of a few femtoseconds 30 .
We must also distinguish between studies that follow the relaxation of electrons following generation (right after photodetachment or photoionization) and the relaxation of electrons excited from an equilibrated solvated state. 27 Our experiment is more similar to the former case.
Our experiment bears obvious similarities with the two-photon photoelectron spectroscopy (2PPE) technique on metal surfaces where photoemission is used to inject excess electrons in an amorphous ice layer, 31 whereas the detection method differs. In that regard, some level of coupling of the excess electrons to the substrate 32 can be expected, which is a plausible explanation for the transformation from state S 3 to state S 4 .
In summary, photoinjection from a metal electrode is an intermediate approach with its own particularities, which shares features with CTTS and multiphoton ionization of water, and which parallels the mechanism for excess electron generation from 2PPE. In this specific case, the UV photon has enough energy to excite an electron from gold's Fermi level to water's conduction Follows a rearrangement of the water molecules around the electron as described in the main text.