Observation of 4^th-order water oxidation kinetics by time-resolved photovoltage spectroscopy

Summary

Artificial photo-driven water oxidation has been proposed over half a century through a four-charge involved multiple-step oxygen evolution process. However, the knowledge of the intrinsic activity, such as the rate-law of the water oxidation reactions, has been inadequately studied. Up to date, the highest order reported is the third one under photoelectrochemical condition. In this work, we identified the fourth-order charge decay reactions on hematite by using a time-resolved surface photovoltage probe technique. A theoretical turnover frequency (TOF) > 100 nm⁻²·s⁻¹ can be expected for O₂ molecules when the hole density >0.1 nm⁻². This work demonstrates a facile and robust method to investigate the high-order reaction kinetics. More excitingly, this research built the bridge between the rate-law, rate-determining step, and energy barrier of intermediates.

Graphical abstract

Highlights

• •The serial-parallel reaction model is proposed for charge reaction kinetic study
• •Charge reaction analyzed by the time-resolved surface photovoltage technique
• •Fourth-order water oxidation is observed on hematite surface
• •The reaction order depends on the rate-limiting step and the initial intermediates

Chemistry; Chemical reaction; Catalysis; Surface chemistry; Materials characterization techniques

Introduction

As the first step in natural photosynthesis, water oxidation is arguably one of the most important chemical reactions in the nature (Vinyard et al., 2013). It produces two species, electrons and protons, that are critical to downstream chemical transformations (Tachibana et al., 2012). When the terminal product is diatomic oxygen, the reaction involves up to 4 electrons and 4 protons and, thereby, can be highly complex (Vinyard et al., 2013; Yang and Wang, 2018). Despite intense research for over half a century, understanding the detailed reaction mechanisms remains limited, especially when the reaction is carried out on heterogeneous catalyst surfaces (Helfferich, 2004; Muñoz-Batista et al., 2019; Naito et al., 2021; Suen et al., 2017; Wang et al., 2021; Yang et al., 2018; Zhou et al., 2019), which has been a key reason for the slow progress in developing this reaction into a scale-up industrially relevant process (Lewis, 2016; Mei et al., 2020; Moniz et al., 2015; Xie et al., 2017; Yuan et al., 2020). Nowadays, a catalyst that can simultaneously meet the desired targets in terms of expense, efficiency, and durability for water oxidation has yet to be exploited for overcoming such important challenges in modern chemistry (Ager et al., 2015; Hisatomi and Domen, 2019; Kment et al., 2017; Roger et al., 2017). Because the surface chemical reaction kinetics on photocatalysts are generally several orders of magnitudes slower than the charge generation and separation processes in solid (Kment et al., 2017; Shen et al., 2016), the study on reaction kinetics relative to photogenerated charge density becomes important for photocatalysis (Mesa et al., 2020; Wadsworth et al., 2019). To apprehend the limitations in the photogenerated charge-driven water oxidation, we must quantitatively consider the rate law of the charge reaction (Yang et al., 2021).

In principle, for a multiple-step reaction that involves up to 4 electrons in a catalytic process, numerical calculation prediction (Cao et al., 2021) suggested the rate order of charge reaction could be up to 4, when all 4 charges are accumulated prior to the final, single-transfer step. When the RDS is at an earlier elemental step, lower reaction orders, such as third-, second-, or first-order, are possible. Experimentally, the most commonly reported reaction order for water oxidation is first-order for heterogeneous catalyst systems (Thorne et al., 2016; Upul Wijayantha et al., 2011). Comparatively, the second-order reaction is much less reported for water oxidation. In one such report, Zhao et al. interpreted their observation of second-order water oxidation on hematite as an indication of the coupling of the neighboring metal-oxo species (-Fe^IV = O) in the O-O bond formation (Zhang et al., 2018b). Later, Patzke et al. identified reaction order of ∼2 on bare hematite for surface holes under steady-state oxygen evolution (Li et al., 2019). As far as the third-order water oxidation kinetics, Durrant et al. are the first ones who have observed this relationship (Kafizas et al., 2017; Le Formal et al., 2015). They interpreted the observation as a result of incorporating three holes (or oxidized equivalents) for the rate-limiting intermediate formation (Mesa et al., 2020). Chatman et al. observed a fourth-order spontaneous water oxidation on single crystalline α-Fe₂O₃ facets without photoillumination (Chatman et al., 2015). Francàs et al. derived a fourth-order kinetics on Ni/Fe oxyhydroxide electrocatalysts through spectroelectrochemical study (Francàs et al., 2019). Previous theoretical and experimental studies focus on thermodynamic rate limiting step, whereas the kinetics analyses are scarce due to the elusive intermediates (Zhang et al., 2018a) or scanty transient investigation technologies (Malkani et al., 2020). So far, no report on the fourth-order photocatalytic water oxidation has been published.

Among many possible water oxidation reaction mechanisms (Song et al., 2020; Suen et al., 2017), Figure 1A depicts a simplified scheme on oxygen evolution catalyst, where four intermediates of bare surface site (∗), hydroxyl termination (∗OH), oxygen termination (∗O), and hydroperoxide termination (∗OOH) are proposed to be the catalytic intermediates (or S_n states) (Liao et al., 2012; Nishimoto et al., 2020). A stepwise proton-coupled electron transfer between each state is applied to accommodate the reaction process. Simplistically, we could treat the single reaction loop as a chain of events (from S₁ to S₄) in Figure 1B. For each step, charges could move forward or backward by overcoming an energy barrier between intermediates. Depending on which step is the slowest, fourth-order kinetics is attainable as far as the mathematics and microkinetics are concerned. For a special condition, the RDS in the fourth step is likely to happen from initial intermediate in Figure 1B, where the highest energy barrier (ΔG₄) is drawn limiting the overall reaction rate. By using preequilibrium approximation for the intermediate (S_n) reaction, multiple (e.g., 2–4) charges could be accumulated before proceeding to overcome the RDS, which is proved to running as a high-order (e.g., second, third, or fourth) reaction by the previous numerical calculation (Cao et al., 2021). When the charge is regarded as one of the reactants, the logarithm plots (Figures 1C and 1D) are widely applied in rate-law study to describe how the charges are consumed during the reaction. In Figure 1C, the charge decay is much faster through higher-order reaction than that through a lower order reaction, which are proportional to the power components of charge densities in Figure 1D. Examinations of the possible reaction schematics inspired us to ask a critical question: Can the fourth-order water oxidation kinetics be detected under photocatalytic condition?

Figure 1.

The relationship between reaction order and rate-determining step for water oxidation

Schematics of water oxidation. (A) The serial reaction mechanism for water oxidation at a single active site through four charges transfer mechanism with four intermediates; the reactions can start from any of these intermediates (marked as green scissor); (B) a possible mechanism for a rate-determining step in the fourth step starting from initial intermediates (S₁); the ideal charge decay curve for water oxidation when n^th (n = 1, 2, 3, and 4) reaction takes place; (C) simulated charge decay curves with time; (D) the log-log plot of charge reaction rate under various charge density of panel (C). The parameters for simulation in (C) and (D) were obtained in Tables S1–S4.

This work is motivated to answer this vital question, which can build the link between surface charge accumulation/reaction and RDS in multiple-step redox reactions. The prototypical material is hematite (α-Fe₂O₃), which has an optical bandgap of 2.0–2.2 eV to absorb large portion light. Besides its advantages of low cost, earth abundance, nontoxicity, and stable property, we chose it because water oxidation on n-type hematite under photoelectrochemical conditions was well established (Shen et al., 2016; Sivula et al., 2011). Moreover, the recent reports on high order (second- and third-order) water oxidation kinetics were also made on hematite (Le Formal et al., 2015; Zhang et al., 2018b). making it a desired platform for comparison purposes. The surface photovoltage (SPV) techniques have been previously developed for the investigation of the charge separation and recombination on hematite (Herrmann-Geppert et al., 2013). Moreover, the SPV measured in air, nitrogen, and water by Osterloh et al. showed the signal was strongly affected by the oxidation of surface water (Shelton et al., 2016). Inspired by the laser photolysis study in nature Kok cycle (Kern et al., 2018) and time-resolved Fourier transform infrared spectroscopy (Zhang et al., 2014), we employed a time-resolved surface photovoltage (TRSPV) spectroscopy technique to detect electromagnetic signals directly from the surface charges (Dittrich et al., 2008; Kronik and Shapira, 1999).

Results

The necessary mathematical calculations have been carried out for the rate-law of multiple-step reactions. As shown in Figure 1, the photocatalytic water oxidation is a multiple-step charge transfer reaction. When the water supply is highly excessive than the charge densities Q, the oxidation reaction rate is mainly determined by the charge densities and the surface catalytic sites. Moreover, in a short time period of a single reaction loop (dt), the charges are solely consumed by the elementary reactions, which can be treated as a unique snapshot for serial reactions. For a more special case, when the n^th step charge transfer is the RDS in the multiple-step reactions, the n^th-order reaction rate can be mathematically predicted.

$${\text{S}}_1+Q\rightleftarrows {\text{S}}_2{\text{S}}_2+Q\rightleftarrows {\text{S}}_3\dots {\text{S}}_{\text{n}-1}+Q\rightleftarrows {\text{S}}_{\text{n}}{\text{S}}_{\text{n}}+Q\stackrel{RDS}{\to }{\text{S}}_1$$ (Equation 1)

Fourth-order charge reaction

First, the elemental steps between the intermediates and charges ahead of the RDS (the n^th step) can be simplified by the use of the preequilibrium approximation (Atkins and Paula, 2005) in Equation 1. There are equilibria between the intermediates of S₁, S₂, …, S_n-1, and S_n, due to the faster reversible reactions, which is like a preequilibrium between those intermediates (e.g., K_n-1 is the equilibrium constant between S_n-1 and S_n). Although there are a few transient spectroscopy studies for in situ investigations of some intermediate densities (Kibsgaard and Chorkendorff, 2019; Zandi and Hamann, 2016; Zhang and Frei, 2017), it is difficult to fast analyze all the intermediates consequently at this stage. Here, it is convenient to write the following relationship between the intermediates:

$$\left[{\text{S}}_{\text{n}}\right]=K_{\text{n}-1}\cdot Q\cdot \left[{\text{S}}_{\text{n}-1}\right]$$ (Equation 2)

Analogously, the equations for other intermediates can be obtained (e.g., [S₂] = K₁·[S₁], [S₃] = K₂·[S₂]). Next, for the RDS in the n^th step, the reaction rate is determined by the charge density, elementary rate constant ($k_n^{\prime }$), and intermediate [S_n]:

$$-\frac{\text{d}{Q}_{\text{n}}}{\text{d}t}=k_{\text{n}}^{\prime }\cdot Q\cdot \left[{\text{S}}_{\text{n}}\right]$$ (Equation 3)

The net reaction rate ($R_n^{\prime }$) of each elementary reaction roughly equal to the RDS step:

$$R_1^{\prime }\approx R_2^{\prime }\approx \dots \approx R_{\text{n}-1}^{\text{′}}\approx k_{\text{n}}^{\prime }\cdot \left[{\text{S}}_{\text{n}}\right]\cdot Q$$ (Equation 4)

Therefore, the overall reaction rate of the charges can be summed up with all the elementary steps and written as

$$-\frac{\text{d}Q}{\text{d}t}\approx n\cdot k_{\text{n}}^{\text{′}}\cdot \left[{\text{S}}_{\text{n}}\right]\cdot Q$$ (Equation 5)

where n is the step number for a catalytic loop, representing the total charges in a single turnover. Furtherly, according to Equations 2 and 5, we can translate the overall charge reaction rate by using the initial intermediate density [S₁] equilibrium constants as follows:

$$-\frac{\text{d}Q}{\text{d}t}\approx n\cdot k_{\text{n}}^{\text{′}}\cdot \left(K_{\text{n}-1}\cdot K_{\text{n}-2}\cdot \dots \cdot K_2\cdot K_1\right)\left[{\text{S}}_1\right]\cdot Q^{\text{n}}$$ (Equation 6)

Because all the equilibrium constants, rate constant in the n^th step, and multiple steps can be constants, when the initial intermediate density [S₁] is fixed, the Equation 6 can be simplified as follows:

$$-\frac{\text{d}Q}{\text{d}t}=k_{\text{n}}\cdot Q^{\text{n}}$$ (Equation 7)

where the overall reaction rate constant is set as $k_n\approx n\cdot k_n^{\prime }\cdot \left(K_{\text{n}-1}\cdot K_{\text{n}-2}\cdot \mathrm{...}\cdot K_2\cdot K_1\right)\left[{\text{S}}_1\right]$. Apparently, the Equation 7 depicts a particular and simplified condition when the final n^th step is the RDS of multiple-step reactions, and n^th order reaction kinetics can mathematically exist.

In this work, for the water oxidation reaction in Figures 1A and 1B, if the fourth step is the RDS in oxygen evolution reaction, a fourth-order charge reaction behavior theoretically exists. Furtherly, the serial elemental reactions after the RDS in the multiple-step reactions will not alter the reaction order of the overall process according to the steady-state approximation. That is, a first-, second-, third,- or fourth-order reaction would be possible when the RDS is in the first, second, third, or fourth step of the four-step water oxidation, respectively.

Serial-parallel surface reaction processes

Although a single-order charge reaction model for water oxidation has been achieved in the last section, practically, the charge reactions at the semiconductor surface can be more complex. Generally, the charges are generated after ultrafast photoexcitation, transported to the semiconductor surface through a separation process for further surface reactions. We treated it as a serial process (e.g. can be first-order) (Li et al., 2018). Next, the surface charge reactions at the photoelectrodes are consumed through some competitive processes, such as the surface charge recombination and surface charge transfer reactions (Klahr et al., 2012; Lewerenz and Peter, 2013). The first-order kinetics were very commonly found for surface charge recombination and charge transfer reaction (Lewerenz and Peter, 2013). Due to the surface reaction complexity, it is extremely difficult to completely suppress charge recombination. Furtherly, the surface charge reactions may not be limited to be a single process but containing side reactions.

Based on the serial-parallel reaction model, the surface charges Q_sep are generated through the separation process of the excited ones k_sepQ_exc and consumed by a first-order reaction k₁Q_sep and an n^th order reaction $k_{\text{n}}{Q}_{\text{sep}}^{\text{n}}$, as shown in Equation 8:

$$\frac{\text{d}{Q}_{\text{sep}}}{\text{d}t}=k_{\text{sep}}{Q}_{\text{exc}}-k_1{Q}_{\text{sep}}-k_{\text{n}}{Q}_{\text{sep}}^{\text{n}}$$ (Equation 8)

where the Q_sep is the surface separated charges that can be detected by transient surface photovoltage (Li et al., 2018; Lu et al., 2017), and k_sep, k₁, and k_n are the rate constants for the charge separation, first-order charge recombination, and n^th-order reactions (n ≥ 1), respectively. In the rate-law study, the charge separation process should be fast enough, instead of being the rate-limiting step. According to the charge decay rate of excited charges $Q_{\text{exc}}=Q_{\text{exc,0}}\cdot \exp \left(-k_{\text{sep}}t\right)$, when k_sep and t are sufficiently large, the first separation part k_sepQ_exc in Equation 8 will be negligible in a suitable time window (e.g., t > 5/k_sep). It can be well satisfied for many semiconductors with high crystallinity and slow surface charge reactions. Furtherly, if the surface is dominated by single n^th-order reaction ($k_1{Q}_{\text{sep}}<<k_{\text{n}}{Q}_{\text{sep}}^{\text{n}}$), the Equation 8 can be simplified as

$$-\frac{d{Q}_{\text{sep}}}{dt}\approx k_{\text{n}}{Q}_{\text{sep}}^{\text{n}}$$ (Equation 9)

When the surface is dominated by first-order reaction ($k_1{Q}_{\text{sep}}>>k_{\text{n}}{Q}_{\text{sep}}^{\text{n}}$), the overall reaction rate will approximately be first-order one (k₁Q_sep). The Equation 9 describes an n^th-order reaction behavior even on a complex reaction model. The Equation 9 can also be written in logarithm style as

$$\log \left(-\frac{\text{d}{Q}_{\text{sep}}}{\text{d}t}\right)=\log k_{\text{n}}+n\log Q_{\text{sep}}$$ (Equation 10)

The linear relationship of the reaction rate and the charge density can be shown in log-log plots (Figure 1D). According to Equation 10, when a fourth-order charge reaction exists, one should observe a higher slope (n = 4) in the logarithm plots.

Simulation of surface charge reaction

To investigate how the reaction order (n > 1) and rate constants k_n influence the overall charge decay, some simulations have been carried out based on Equation 8. Figure 2A displays the Q_sep ∼ t curves of first-order and n^th-order parallel surface charge reactions. When the high-order (e.g., n^th) reaction happens, a fast decay of Q_sep can be observed shortly after the initial charge separation. By keeping k_n as a constant (e.g., 5×10⁵ s⁻¹), the curves display different decay trends for the second-, third-, and fourth-order reactions in the early stage (<1 ms). After a prolonged time, the Q_sep~t curve becomes linearly in the log plot, suggesting an exponential decay (e.g., first-order) controls the surface reaction. In Figure 2B, the larger slope could be obtained at higher charge densities (in the top-right), suggesting that the high-order reaction kinetics (e.g., n^th) dominates the surface reactions. Meanwhile, a small slope (e.g., 1) could be observed under a lower charge density region (in the bottom-left).

Figure 2.

Simulated charge reaction plots showing the influence of reaction orders

Charge reaction profile with the first to n^th (n = 1, 2, 3, 4) serial-parallel model (Equation 8): (A) Q_sep ∼ t plot; (B) log(-dQ_sep/dt)∼log(Q_sep) plot. A unit-less charge density is used. Q_exc,0 = 1, k_sep = 2×10⁶⋅s⁻¹, k₁ = 5×10²⋅s⁻¹, and k_n = 5×10⁵⋅s⁻¹ are used.

In Figure 3, the first- and fourth-order reactions are two competitive charge consuming processes, where the differential equation is shown (in Figure 3A). In the time range of 2–6 ms, the logQ_sep ∼ t curves are all linearly, showing that the slopes vary with the k₁ constants, respectively. In the early time range (<1 ms), the decay rate is less influenced. In Figure 3B, the change of rate constant for first-order one (k₁) significantly alters the lower charge density region (bottom-left). The slopes of log-log plot at higher charge density are nearly constant (∼4) in the top-right. In Figure 3C, the increase of fourth-order rate constant (k₄) results in a sharper decrease of charge density in the early stage (<1 ms), and a nearly same exponential decay trend after 2 ms. It is more obvious that the higher-order reaction contributes more to the log-log curves in the top-right of Figure 3D, with a similar slope of 4. In addition, the fast charge separation rate (higher k_sep) is also required; otherwise, the slower charge separation will result in a smaller slope in the higher charge density region (Figure S1), which should be avoided as we have mentioned earlier. In addition, the surface photovoltage is also sensitive to the photogenerated charges densities (see the Figure S2).

Figure 3.

Simulated charge reaction plots in the first to fourth serial-parallel model (Equation 8)

(A) Q_sep ∼ t plot and (B) log(-dQ_sep/dt)∼log(Q_sep) plot, k₁ increases from 50⋅s⁻¹ to 500⋅s⁻¹⋅s⁻¹ and Q_exc,0 = 1, k_sep = 2×10⁶⋅s⁻¹, k₄ = 5×10⁵⋅s⁻¹; (C) Q_sep ∼ t plot; and (D) log(-dQ_sep/dt)∼log(Q_sep) plot, k₄ decreases from 5×10⁵⋅s⁻¹ to 5×10³⋅s⁻¹, and Q_exc,0 = 1, k_sep = 2×10⁶⋅s⁻¹, k₁ = 5×10²⋅s⁻¹.

Based on the simulation results in Figures 2, 3, and S1 and the Equation 10, it is rational to detect the high-order reaction rate for the surface reaction kinetics in the presence of multiple order reactions.

Photoelectrochemical water oxidation on hematite

Because the hematite has been widely studied as photoanode for water oxidation, here, we can briefly characterize the materials and verify photoelectrochemical water oxidation on its surface. The hematite films are characterized as a thickness of ∼80 nm (SEM cross-section in Figure S3) and typical α-Fe₂O₃ crystalline structure (Raman spectrum in Figure S4) (Oh et al., 1998; Zandi et al., 2014). The Mott-Schottky plot of the hematite film (in Figure S5) displayed an n-type semiconductor behavior with a flat band potential (V_fb) at ∼0.33 V versus reversible hydrogen electrode (RHE). The positive flat band potential (>0 V) suggests hydrogen evolution is thermodynamic unfavorable (Figure 4B). However, the energy level of photogenerated holes in valence band (>2 V versus RHE) of hematite is high enough to oxidize water (1.23 V versus RHE) (Sivula et al., 2011). To enable water oxidation, the photogenerated electrons in the conduction band must be extracted through external bias (a potential positive to V_fb) (Sivula et al., 2011) or electron scavenger (Meng et al., 2013). Here, when the hematite is connected to a ground electrode (connection 2 in Figures 4A and 4B), the electron will be extracted by the positive ground potential.

Figure 4.

The photoelectrochemical water splitting on hematite photoanode

(A) The rotating ring disk electrode setup with hematite on disk electrode, while the potential on Pt ring electrode was −0.3 V versus SCE.

(B) Band structures for water oxidation on hematite w and w/o bias.

(C) J-V curves for OER current on hematite disk electrode and ORR current on Pt ring electrode, with chopped UV light.

(D) O₂ detection on Pt ring electrode in 0.1 M KOH with a ground electrode.

(E) O₂ detection on Pt ring electrode in DI water with a ground electrode. 1 corresponds to the connection to potentiostat with bias, whereas 2 corresponds to the ground electrode without bias.

To confirm this prediction and the later observation that TRSPV signals indeed reflect water oxidation kinetics, the control experiments were carried out to prove water oxidation on hematite. We resorted to a rotating ring disk electrode (RRDE) system in Figure 4A, where the trace amount of products (e.g., O₂) would be detected by the ring electrode nearby. As shown in J-V plots with chopped UV light illumination (Figures 4C and S6), the increased anodic current on the hematite disk electrode corresponded to oxygen evolution reaction, where the onset potential was about 0.75 V versus RHE. At the same time, the increase of the cathodic current on the ring electrode upon illumination confirmed that a reduction of oxidized species transported from hematite disk electrode. In Figures 4D and 4E, when the hematite photoelectrode was connected to ground electrode (∼0.74 V versus RHE), the cathodic current increased with chopped light illumination. The surface charges could be consumed in small scale by the surface parallel processes under open-circuit condition, due to the higher energy of holes in the valence band. This proved the water oxidation reaction can occur on hematite under illumination. Another evidence is the reduced products on counter electrode. In Figure S7, the photogenerated electrons on hematite can be transferred to counter electrode, which can reduce Ag⁺ to Ag by using AgNO₃ as electron scavenger (Meng et al., 2013). Thus, it is confirmed that water can be oxidized on hematite surface by the holes in valence band.

Instrument for transient charge analysis

After the water oxidation is proved on hematite, we are highly interested in experimentally verifying the predicted rate law (Equation 10) by the TRSPV technique. As shown in Figure 5, the technique traces the evolution of surface voltage after an ultrafast laser pulse pyrolysis. When an n-type semiconductor is used, the presence of water adsorption at the surface induces a band bending that accumulates photogenerated holes (or positive equivalents) to the surface in Figure 5A (Memming, 2015), which are sensed by a transparent electrode as a positive surface voltage (Chen et al., 2018; Jing et al., 2013). The surface holes in the valence band increase the system energy to overcome the energy barrier in photocatalysis (Figure 5B). With prior knowledge of the capacitor, the surface voltage information can be readily translated into charge densities. Consequently, how the surface charge densities decay as a function of time can be obtained, and hence, the rate laws of the reaction can be determined in Figure 5C (Wright, 2004). To derive the rate-law relationship to chemical reaction mechanisms, the simplified surface charge reactions are displayed in Figure 5D, where the separated charges Q_sep are consumed by parallel reactions. The signal of TRSPV on semiconductor in the presence of water could be strongly related to the oxidation of surface water, which was similar to the SPV analysis on water oxidation under steady illumination (Shelton et al., 2016).

Figure 5.

The scheme of time-resolved surface photovoltage for photocatalytic study on the semiconductor surface in presence of H₂O atmosphere

(A) The photogenerated holes accumulation caused the band edge to shift downward and the photovoltage.

(B) The holes in the valence band increase the system energy to overcome the energy barrier.

(C) The log-log plot of charge reaction rate versus the charge density.

(D) Surface charge reactions show the competitive first-order (k₁) and n^th-order (k_n) processes in the parallel model.

The measured surface voltage is relative to the global ground electrode, which corresponds to the change in reference to the resting state under dark condition. In addition, no electrolytes but adsorbed surface water on semiconductor was employed in our experiments. If the reaction scale is limited, the system could be a miniature analogous to the two-electrode photocatalysis system in Figure 2.

The most important information we seek to collect is how the surface charge density changes as a function of time or charge reaction rate (-dQ/dt). TRSPV is desired for such measurements because it is a pump-probe technique that effectively reports how surface voltage V(t) change as a function of time. By using a parallel-plate capacitor (fluorine-doped tin oxide [FTO] insulating mica with known thickness) as probe, it is ready to translate the measured V(t) to Q(t) and obtain datasets similar to what is shown in Figure 1C. Subsequently, the dependence of the reaction order on the reaction rate of surface charge density can be derived as shown in Figure 1D. Although the details of the simulation are provided (in Figures 2 and 3), we emphasize a few pillars that underpin our derivation. First, every charge that emerges to the surface is a result of a photo-excitation event of photocatalyst, the collective density of which is expressed as Q_exc. What TRSPV probes is the portion that has emerged to the surface Q_sep, whereas the unseparated Q_exc or consumed ones cannot be detected or involve surface reaction.

Second, the sample module was constructed between two electrodes with an insulate mica in between, and the project area A and distance between the two electrodes were fixed during the measurement. As the laser pulse energy was limited at a certain level, the temperature and relative permittivity were less varied; the capacitance of the sample module could be treated as a constant C. According to the equation Q(t) = C·V(t)/A, the time-resolved surface charge density Q(t) can be conveniently obtained. As predicted, plots (in Figures 2 and 3 and Figure S1), the reaction orders, charge separation kinetics, and reaction rate constants change indeed vary the TRSPV curves in different ways. With the suitable semiconductor sample, the TRSPV technique is desirable to record the charge reaction behavior, so that it enables the elucidation of the high-order reaction kinetics.

Water oxidation on hematite at solid/gas interface

The typical TRSPV measurements were carried out in ambient conditions in a sandwich structure (FTO|mica|α-Fe₂O₃/FTO). The hematite photoelectrode was excited by a nanosecond laser pulse (355 nm, 4 ns) to drive the surface water oxidation, which was adsorbed on the surface detected by TG-MS spectrum (in Figure S8). The surface photovoltage is recorded between the front and underlayer FTO electrodes. The initial photogenerated holes density (Q_exc,0) was estimated according to photoelectrochemical performance using the photon flux per laser pulse, incident-photon-to-charge efficiency, and illumination area.

In Figure 6A, the separated charges on the hematite surface were plotted. The positive signal corresponds to the photogenerated holes accumulated at the n-type hematite surface. The surface charges sharply increased to a maximum, which indicated a very fast separation process. After tens of microseconds, the charge quickly decreased until it followed an exponential tendency. Moreover, the decay faster than the exponential trend in the Q_sep~t curve is one important piece of evidence, when higher order (>1) reactions exist. The surface charge kinetics can be investigated with the simplified model in Figure 5D, where only the first- and n^th-order reaction components are included. For the combination with first-second or first to third order reaction model, larger disparity is observed in Figure S9. Next, the rate law between the charge reaction rate (-dQ_sep/dt) and the charge density (Q_sep) is plotted in logarithm style. In Figure 6B, a high slope (∼4.3) of charge decay was displayed in the early stage (<34 μs), and a small slope (∼1) of decay was displayed after prolonged time (>0.61 ms). This suggests both fourth-order and first-order reaction kinetics indeed exist. By using the parallel model of first- to fourth-order reaction kinetics (k₁ = 1.45×10³ s⁻¹ and k₄ = 4×10⁶ (h⁺)³·nm⁻⁶·s⁻¹) as Eq. 8, the simulated curve agrees well with detected TRSPV signal (Figures 6A and 6B). A turnover frequency (TOF) of charge reaction could be as high as 400 nm⁻²·s⁻¹ when the hole density is larger than 0.1 nm⁻², which corresponds to a 100 nm⁻²·s⁻¹ for oxygen evolution. Although the number or structure of active sites has not been identified, the value (100–400 s⁻¹) is comparable to that on nature photocatalyst CaMn₄O₅ (Dismukes et al., 2009).

Figure 6.

Charge reaction kinetics for laser-pumped water oxidation on hematite in presence of H₂O atmosphere

(A) The time-resolved charge density curve (Q_sep ∼ t).

(B) Log-log plot of charge reaction rate versus charge densities.

(C) The charge reaction rates through first- and fourth-order reaction kinetics.

To understand why the apparent reaction order changes with time or charge density, it is necessary to analyze the charge consuming competition. In Figure 6C, the dashed lines represent the reaction rates obeying the fourth-order and first-order reaction kinetics. The fourth-order reaction rate is more sensitive to the charge densities. In an early period (<34 μs), the fourth-order reaction dominates the overall charge reactions, whereas the first-order reaction dominates after prolonged time (>0.61 ms). In the time range of 34 μs–0.61 ms, both charge reaction kinetics are comparable (Figure 6B), which exhibits as a mix-control region. Furtherly, if the first-order reaction contributes more than the fourth-order reaction, the fourth-order reaction may not be observed in log-log plots due to the competing parallel reactions. There was no significant difference on the hematite films prepared by hydrothermal and atomic layer deposition (ALD) techniques (Figure S10), furtherly confirming this possible fourth-order kinetics.

We understand that the surface charges are not solely consumed by chemical reactions but also by some possible physical recombination processes, such as irradiation, trap-assisted Shockley-Hall-Read (SHR) recombination, and the Auger recombination (Neamen, 2012). No matter bulk or surface condition, the majority charge density is much higher than the minority charges in doped semiconductors under the depletion condition. Currently, only first- or second-order processes were reported the band-to-band and SHR recombination (Maity et al., 2018). Even the Auger recombination involves three charge reactions at same site, none of the fourth reaction order has been reported. Herein, the observation of fourth-order process should result from the surface chemical water oxidation process rather than the physical recombination.

As we have shown the surface charge density can alter the photovoltage decay shape (Figure S2), it is possible to investigate the influence of surface charge densities. As we discussed earlier, when the charge separation is fast enough, Equation 8 can be simplified as a parallel reaction model:

$$\frac{\text{d}{Q}_{\text{sep}}}{\text{d}t}=-k_1{Q}_{\text{sep}}-k_{\text{n}}{Q}_{\text{sep}}^{\text{n}}$$ (Equation 11)

Under the boundary condition (Q_sep,0 = Q_exc,0 at t = 0), the solution for a fourth-order reaction in Equation 11 (n = 4) can be written as

$$\frac{Q_{\text{sep}}}{Q_{\text{exc,0}}}=\frac{k_1^{1/3}}{{\left(\left(k_4{Q}_{\text{exc,0}}^3+k_1\right)\exp \left(3k_{1}t\right)-k_4{Q}_{\text{exc,0}}^3\right)}^{1/3}}$$ (Equation 12)

When the first-order process is negligible (k₁ = 0), the relationship for Equation 11 could be written as a single fourth-order surface reaction (Equation 9):

$${\left(\frac{Q_{\text{exc,0}}}{Q_{\text{sep}}}\right)}^3=3k_4{Q}_{\text{exc,0}}^{3}t+1$$ (Equation 13)

We verify the relationship in Equation 13 by varying the charge density in Figure 7. In Figures 7A–7C, the three plots showed a linear relationship between the (Q_exc,0/Q_sep)³ and time (t) in the early stage (<10 μs). For a certain charge density Q_exc,0, the slope corresponds to a constant ($k_4{Q}_{\text{exc,0}}^3$); the slope increases much faster when the charge density increases. In Figure 7D, we found that the slope increment is proportional if the charge density is not too high. It should be noted that higher charge density requires stronger laser illumination, possibly due to surface overheating or poor charge separation. By changing the laser intensity, we have found the reaction kinetics are not induced by the direct absorption of the laser by the water molecules. The linear region in Figure 7D showed a steady rate constant (k₄), which furtherly proved the fourth-order reaction kinetics.

Figure 7.

Method of integration and analysis of results of charge decay under various charge density

For a fourth-order relationship on hematite surface with Q_exc,0 at 1.5, 3.4, and 5.5 for (A), (B), and (C), respectively. (D) The slopes of (Q_exc,0/Q_sep)³∼t against various charge densities. For simplicity, the charge density is normalized to a constant.

Initial intermediate influences the reaction order

Previous numerous calculations suggested the reaction order is strongly related to the RDS in the multiple-step reactions (Cao et al., 2021). According to the DFT calculation, the RDS seldom changes no matter the reaction starts from which intermediate. Thus, for a certain reaction, the switching of the initial intermediate would alter the reaction kinetics. The initiate hematite surface could be covered by a large amount of terminated ∗O below 500 K based on previous density functional theory (DFT) calculation (Bergermayer et al., 2004). Furtherly, when the hematite is treated with deionized water, the O1s spectra in XPS analysis showed that the portion of hydroxyl termination (∗OH) increases (see in Figure S11), which agrees well with the literature reported (Jakub et al., 2019; Yamamoto et al., 2010). By this way, we could monitor the rate law change on a hematite with ∗O or ∗OH dominated surfaces.

In Figure 8A, the log-log plot of the charge reactions on ∗O dominated hematite surface showed similar behavior as that in Figure 6B. Differently, on ∗OH dominated surface, the log-log plot of the charge decay curve (Figure 8B) exhibited a single first-order rate-law feature as the same illumination was applied. Next, the ∗OH domination at the hematite surface can reversibly change back to ∗O-domination after vacuum drying. The fourth-order reaction kinetics can be reproducibly observed on ∗O dominated surface (Figure 8C). Interestingly, in a second hydration treatment to form an ∗OH termination surface, a similar first-order reaction could be observed in Figure 8D. By calculation, the fourth- and first-order reaction rate constants were 2.75×10⁶ (h⁺)³·nm⁻⁶·s⁻¹ and 2.4×10³·s⁻¹ in Figure 8C, which were almost the same as 2.73×10⁶ (h⁺)³·nm⁻⁶·s⁻¹ and 2.2×10³·s⁻¹ in Figure 8A. Next, the first-order reaction rate constants were 1.5×10³ and 0.9×10³·s⁻¹ in Figures 8B and 8D, respectively. Compared with the absolute rate constants, we focus more on the rate-law switching, revealing the fourth-order reaction behavior. Thus, the reaction order switch was reproducible when the surface state periodically changed between initial ∗O and ∗OH intermediates.

Figure 8.

Reversible switch on hematite surface changes the reaction kinetics with different initial intermediates

(A) and (C) hematite sample with ∗O as initial intermediates; (B) and (D) water-treated hematite with ∗OH as initial intermediates. The corresponding RDS at the fourth and first step are shown at the top panel.

Discussion

Considering the catalytic loop in Figure 1A, RDS can be the fourth and first steps starting from ∗O and ∗OH in Figure 8, respectively. Interestingly, either fourth step or first step under the different conditions corresponds to the elementary reaction of ∗OH→∗O. Both rate law results indicate the ∗O formation could be the limiting step in OER on hematite. For the RDS calculation, theoretical DFT calculations of water oxidation have been extensively studied on a single site by the pioneering work of J. Nørskov (Rossmeisl et al., 2007; Seh et al., 2017). Hellman et al. predicted the ∗O formation is the RDS for water oxidation on ∗OH and ∗O terminated hematite surface (001) (Hellman et al., 2015). Zhang et al. found the ∗O formation on (210), (101), and (110) surfaces could be RDS on hematite (Zhang et al., 2016). Recently, Hajiyani et al. proved the ∗O formation is the RDS on ∗OH, FeOH or ∗O terminated hematite (001) (Hajiyani and Pentcheva, 2020). Coincidentally, they reported that the RDS of ∗O formation on ∗OH terminated surface was at the first step; the RDS of ∗O formation on ∗O terminated surface was the fourth step, which is in good agreement with the previous theoretical prediction. Thus, we believe the observed first and fourth-order reaction kinetics should correlate to the OER on hematite.

It is worth noting that the rate-law study provides important kinetic information for any possible reaction mechanism (Naito et al., 2021; Song et al., 2020; Suen et al., 2017). The reaction mechanism in Figure 1A is one of the possible processes, which can build the linkage between rate law and the DFT calculations. However, the water oxidation on metal oxides is not necessarily limited at a single catalytic site; dual-site or multiple-site mechanisms have also been proposed (Mesa et al., 2020; Zhang et al., 2018b). The reaction kinetics could be highly different measured under transient and steady conditions, which may be due to the surface intermediates or other conditions. In Durrant's recent study on hematite photoanode, the oxidation of surface Fe^III-OH to generate Fe^IV = O requires the largest energy change of 1.41 or 1.42 eV (Mesa et al., 2020). The comparable high energy barriers do not meet the preequilibrium assumption or RDS in this study, indicating the reaction is possibly under mixed control during their PEC operating condition. Moreover, Zhang et al. have pointed out that ∗OH formation through an O-O formation mechanism at dual-site on hematite (110) surface will be competing with the ∗O formation at the single site (Zhang et al., 2016). The mix controlling of the multiple-charge transfer reactions will collectively influence the water oxidation reaction. In addition, the higher reaction order does not mean a high active surface, both the active sites and the hole density should be significantly increased to facilitate high current density. Switching the reaction from higher-order to lower-order by surface modification or co-catalyst is significantly important in future mechanism studies.

It is worth noting that the general observed reaction order is the first one, which has been proved by the IMPS (Thorne et al., 2016) and PEIS (Upul Wijayantha et al., 2011) under photoelectrochemical condition (Liu et al., 2019). The observed fourth-order reaction could be due to the 4 holes accumulated before overcoming the RDS, whereas the first-order one could take place without multiple charge accumulation. This also suggested that the detection could be fast enough to capture the transient fourth-order charge decay in short early stage after the light off.

Figure 9 describes the rate-law limitations for the charge reactions. In the serial-parallel reactions with both high and low-order ones, the detected rate-law behavior depends on several factors, including the charge transport (separation), charge density, and the rate constants. Higher charge density facilitates higher order kinetics in the window II, whereas lower density results in lower-order kinetics in the window IV. Moreover, lower reaction kinetics may be found in the window I due to the slower charge transportation. We noticed the serial-parallel reaction model could well explain the mechanism transition with the charge density. In future, more TRSPV measurements can be developed to diagnose the charge reaction kinetics in the medium timescale (ns ∼ s).

Figure 9.

Schematic carton for the analyze reaction kinetics by TRSPV

The scheme shows the limitation of charge separation and mechanism change.

We understand that it is not attainable to list all the possible reaction processes by DFT calculation at this stage. The advantage of this work is to verify the possible RDS through experimental methods. The most exciting breakthrough in this work is bridging the rate-law study and thermodynamic free energy increase of intermediates, which is an important complementary technology for the J-V polarization or Tafel slope study.

Conclusion

In summary, this work shows the reaction kinetics are highly sensitive to the surface intermediates, RDS, and hole density, and thus the rate-law study depicts various mechanisms on heterogeneous photocatalysts. We have developed a time-resolved surface photovoltage method to investigate the charge reaction kinetics. The observation of the fourth-order reaction benefits from the fast voltage response on the surface charges and the suppressed recombination. It is possible that higher catalytic activity could be achieved when the light density or the number of the catalytic sites increase. The time-resolved photolysis is very likely to provide new insights on the multiple-charge transfer reactions, including the oxygen evolution reaction, CO₂ reduction reaction, and N₂ fixation, thereby possessing universal significance.

Limitations of the study

This research focuses on the interesting positive charges accumulation on the hematite, which is hypothesized as a possible fourth-order water oxidation. The oxygen detection was ONLY proved by the rotating ring-disk electrodes in electrolyte rather than on the solid/atmosphere interface. The controlling of surface intermediates could hardly be achieved.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, peptides, and recombinant proteins
FeCl3 (98%)	Sinopharm.com	CAS: 7705-08-0
FeCl3 (97%)	Sigma	CAS: 7705-08-0
NaNO3 (99.5%)	Sinopharm.com	CAS: 7631-99-4
HCl (36-38%)	Sinopharm.com	CAS: 7647-01-0
Ti foil (thickness 0.127 mm)	Sigma-Aldrich	CAS: 7440-32-6
(CH3)3CONa	Sigma-Aldrich	CAS: 865-48-5
Tetrahydrofuran	Sigma	CAS: 109-99-9
NH3·H2O (25-28%)	Sinopharm.com	CAS: 1336-21-6
H2O2 (30% solution)	Sinopharm.com	CAS: 7722-84-1
Argon gas	Suzhou Jinhong gas	1290046-39-7
AgNO3	Sinopharm.com	CAS: 7761-88-8
K4[Fe(CN)6]·3H2O	Alfa Aesar	CAS: 14459-95-1
K3[Fe(CN)6]	Alfa Aesar	CAS: 13746-66-2
D2O	Sinopharm.com	CAS: 7789-20-0
Software and algorithms
Office 365	Microsoft	https://www.microsoft.com
Origin 9	OriginLab	https://www.originlab.com/
MathType 6.9	Wiris	https://www.wiris.com/en/mathtype/

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Xiaogang Yang (xiaogang.yang@gmail.com).

Materials availability

This study did not generate new reagents.

Method details

Hydrothermal and ALD preparation of hematite films

A hydrothermal deposition for hematite (Jang et al., 2015) was carried out as follows: In a solution of 0.15 M FeCl₃ and 1 M NaNO₃, the FeOOH films were deposited on a clean FTO substrate at 100°C for 1-3 h. The samples were quickly annealed in air at 750-800°C for 3-5 min, converting FeOOH into hematite. The ALD of hematite (Lin et al., 2011; Yang et al., 2013) on Pt covered Ti foil was carried out on Savannah system (Cambridge Nanotech). The precusor of iron tert-butoxide (Fe₂(O^tBu)₆) was synthesized based on the reaction 6.3 g (CH₃)₃CONa and 3.2 g FeCl₃ in tetrahydrofuran under 60°C after 5 h. The planear hematite film is prepared through ALD with a loop of 5 s pulse of Fe₂(O^tBu)₆, 15 s exposure, 10 s purge, and 0.05 s pulse of H₂O, 15 s exposure and 10 s purge at 180°C for 500-1000 cycles. Next, the films are annealed in air at 500°C for 30 min.

Photoelectrochemical measurement of O₂ evolution with RRDE and chopped light

The water oxidation product on hematite was proved by RRDE setup (Figure 2A), where oxygen is generated at disk electrode and reduced on ring electrode. The RRDE test was set up on a modulated speed rotator (MSR, Pine research) using a 5-neck flask, Pt disk and Pt ring electrode, a saturated calomel electrode (SCE, 0.241 V vs NHE) connected with an agar gel containing KCl salt bridge as reference electrode, a Pt plate as a counter electrode. The electrolytes were 0.1 M KOH (pH = 13) and deionized water (pH = 7), respectively. A hematite on Pt/Ti foil was cut into round plate (<5.61 mm in diameter). Then the foil was attached to the disk electrode with silver paste, dried in air, so that the edge of the Pt/Ti foil and the residual Pt disk electrode was insulated with a moisture cross-linkable rubber. The potential and current were controlled/collected by an electrochemical potentiostat (AutoLab Nova2.1) with a scan rate of 20 mV/s and a rotating speed of 1600 rpm. The electrolyte was bubbled with Ar to keep the oxygen at a very low level. A UV diode laser (405 nm, 100 mW) was used as the illumination source, which is periodically controlled by an electric relay. The oxidizing species generated from the hematite on disk electrode were detected through the oxygen reduction reaction after transferred to ring electrode at −0.3 V vs SCE.

Electrochemical measurement of reduced product

The other photoelectrochemical and electrochemical measurements were carried out on a potentiostat (CH Instrument, 660E) using a three-electrode configuration: a hematite photoanode, a Pt wire as counter electrode, and a Hg/HgO reference electrode (0.098 V vs. NHE) in 0.1 M KOH (pH = 13). A simulated solar illumination (Perfect light, 100 mW/cm²) with an AM1.5G filter was used as the light source. The polarization curves were recorded using a linear sweep technique under 20 mV/s in J-V plots. The cyclic voltammetry (CV) curves were measured under 1–100 mV/s.

Mott-Schottky plot

The Mott-Schottky plots were obtained based on the space charge capacitance, which was measured in 0.1 M KOH (containing 2 mM K₃Fe(CN)₆/K₄Fe(CN)₆).

SEM morphology characterization

The morphology and surface structures are observed on a scanning electron microscope (FEI, Nova NanoSEM450).

Raman characterization

The Raman spectra were collected on a Renishaw confocal Raman microscope (in Via Reflex) excited with a green laser (532 nm).

Surface binding energy by XPS

The X-ray photoelectronic spectroscopy (XPS) data were investigated using a spectrometer (Thermo Scientific Escalab 250Xi, C1s at 284.5 eV as reference).

TGA-MS of water desorption

The surface water adsorption on hematite nanoparticles was characterized in Ar on a Netzsch thermal gravimetric analyzer (STA 449 F3) coupled with Quadrupole Mass Spectrometer (QMS 403D).

Time-resolved surface photovoltage characterization

The TRSPV signal is measured on a home-made nanosecond laser pulse photocatalysis system in ambient air-condition unless mentioned elsewhere in the main text, where the hematite on FTO substrate (α-Fe₂O₃/FTO) was mounted on the sample holder. The edge part of the hematite was carefully removed by diluted HCl, on which the conductive edge of FTO was connected to the ground. On the top of the sample, it was covered by an insulating mica (∼60 μm) and another FTO plate. The FTO|mica|α-Fe₂O₃/FTO formed a sandwich structure as the parallel-plate capacitor to probe the surface photovoltage. The excitation source was a third harmonic Nd:YAG pulse laser (Quantel BRILEZ/IR-10, 19.2 μJ/pulse, 10 Hz, pulse with of 4 ns) with a wavelength at 355 nm. The illumination area of the hematite sample was about 0.24 cm². The charge density could also be altered by the laser (5-105 μJ/pulse). The voltage signal was collected by an ultra-low-noise voltage pre-amplifier (PerkinElmer, Inc. 5184) and a digital TDS oscilloscope (Tektronix, TDS 3054C, 500 MHz). The data was gathered after the internal trigger from the pulse laser with a pulse of 1-10 Hz to assure the sample surface recover back to the initial state, which was averaged with 256 times acquisition to improve the signal-to-noise level. For the surface water treatment, about 5 μL/cm² deionized (DI) water was dropped and spread on the hematite which facilitates the hematite to form a hydrated surface (∗OH), other conditions for TRSPV were kept same.

Published: December 17, 2021

Data and code availability

All relevant data are available from the lead contact upon reasonable request.

This paper does not report original code.

Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.