Mutually-dependent kinetics and energetics of photocatalyst/co-catalyst/two-redox liquid junctions

Abstract

Water-splitting by photocatalyst particles has attracted much attention recently for its potential to produce renewable H₂ at scale. However, the correlation between the energetics at photocatalyst/co-catalyst/water interfaces and their interfacial charge-transfer kinetics is still elusive, especially when the energetics are expected to vary spatially along the liquid-junction interface. First, we derived a kinetic model for photocatalyst particles in contact with two-redox potentials, H⁺/H₂ and O₂/H₂O, i.e., a semiconductor/two-redox liquid junction. We adopted the principle of detailed balance proven for one-redox liquid junctions and extended this principle to a locally out-of-equilibrium electrolyte containing multiple redox potentials, the condition typical for photocatalysts. To validate the model, we established a characterization framework to simulate photocatalyst operation by using photoelectrodes. The open-circuit conditions mimicked operating photocatalyst surfaces; and the (quasi-) Fermi levels, probed by ohmic back contacts, indicated charge-separation efficiency. Quantitative data fitting further validated the two-redox kinetic model. These characterizations correlated local energetics with multi-electron charge-transfer kinetics, which exhibit tuneable branching ratios controlled by H₂-and-O₂ gas-mixture compositions and co-catalyst selectivity. Unlike the conventional photoelectrode/electrolyte interfaces, SrTiO₃ model particles decorated with Pt co-catalysts were found to bear liquid-junction interfaces of spatially varying energetics with designated reductive and oxidative sites. It is shown that, uniquely for photocatalysts, the local kinetic-controlled energetics vary spatially across photocatalyst/co-catalyst/water interfaces of individual particles, and affect charge-separation efficiency sensitively. The mutually dependent behaviour between local kinetics and spatially varying energetics were confirmed for two practical photocatalytic systems, Al-doped SrTiO₃ and Ta₃N₅. This study exemplified and elucidated the design principles for developing efficient photocatalysts.

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Broader context

Photocatalytic water-splitting for hydrogen generation is a promising approach for converting solar energy to chemical energy. However, the application of photocatalytic water-splitting is still limited by its low efficiency with 0.4% being its current state-of-the-art. Photocatalytic water-splitting involves coupled photophysical and electrocatalytic processes: light absorption, generation of electron–hole pairs, charge separation and bulk transport, charge transfer across interfaces for catalytic reactions, and mass transfer of reactants and products. To develop efficient photocatalyst particles for commercial applications, it is necessary to fully understand individual steps and their coupled processes. Among these processes, charge separation in bulk and charge transfer across the photocatalyst/water interface have not been well investigated. The driving force and process of charge separation in photocatalysts have been investigated in one of our latest studies. Herein, we are deciphering the charge-transfer process across the photocatalyst/(co-catalyst)/water interface and further integrating it into a dynamic photocatalyst model. Our work revealed that the energetics of photocatalysts during operation was correlated with the kinetics of the charge-transfer process and the kinetic-controlled energetics affect charge separation efficiency sensitively.

1. Introduction

Solar-driven water-splitting by using photocatalyst particles has the potential to produce cost-effective hydrogen (H₂) fuels at scale.^1,2 So far, several visible-light active photocatalysts such as Ta₃N₅ semiconductors have been demonstrated for water splitting.^3–7 For example, the predicted solar-to-hydrogen conversion efficiency limit for Ta₃N₅ is ∼17%,⁸ but the record remains <1% under sunlight indicating a big gap between experiments and theory. One of the biggest hurdles to improve the efficiency of each type of photocatalysts is the insufficient understanding of their charge-separation processes, which are coupled with the charge-transfer processes across the photocatalyst/water interfaces.⁹ Individual photocatalysts of 20–500 nm in diameter, decorated with co-catalysts of <5 nm in diameter and surrounded by water under sunlight, undergo the following processes: light absorption, generation of electron–hole pairs, charge separation and transport to photocatalyst/water interfaces, charge transfer across the interfaces to drive multi-electron catalysis, and mass transfer of reactants (e.g., H₂O, H⁺) and products (e.g., H₂ and O₂).¹⁰ Uniquely, each photocatalyst particle co-evolves H₂ and O₂ at their respective and nearby sites on the same surface of the particles. Subsequent H₂ and O₂ separation ensures a safe solar-fuel production. To reveal photocatalyst design principles, ab initio simulation of mesoscale photocatalysts at an excited state should fully reveal the interdependence of these processes. This simulation is applicable to molecular sensitized and quantum-dot photochemical systems so far, but remains too complex for >10 nm-diameter particles.^11–13

Conventionally, a photocatalyst/co-catalyst/water junction is described by thermodynamic equilibration of the electrochemical potentials between the semiconductor and the liquid, assuming the photocatalyst is in contact with only one redox couple. The photocatalyst/co-catalyst/water junction may be an adaptive junction of variable barrier heights,¹⁴ or a buried junction.¹⁵ However, this description is not sufficiently relevant to photocatalyst particles considering that the two redox couples of H⁺/H₂ and O₂/H₂O co-exist, which drives the local solution environment out of equilibrium. For these reasons, the photocatalysis community need a photocatalyst particle model to explicitly describe the complex photocatalyst/co-catalyst/water junction under non-equilibrium conditions.

Since the model based on thermodynamic equilibration is limited, the Gerischer–Lewis kinetic model for semiconductor/liquid junctions was applied to the model systems. It embodies the forward and backward charge-transfer process, i.e., microscopic reversibility, which underpins the thermodynamic equilibration behaviour at the semiconductor/liquid junctions. This kinetics model is useful because it can be extended to multiple redox charge-transfer pathways simply by invoking the principle of detailed balance. Lewis and co-workers chose a single-crystal SrTiO₃ photoanode system to elucidate the kinetic model: current–potential behaviour is a statistical outcome of all the concurring interfacial charge-transfer events, in both forward and backward directions.^16,17 However, their model used a bare SrTiO₃ photoanode without a well-defined H⁺/H₂ redox and thus not applicable to practical photocatalysts suspended in an out-of-equilibrium solution. Besides, water-oxidation catalysis then was not well characterized, and so were the kinetics for the multi-electron water-oxidation process as well as the reductive processes of H₂ evolution and O₂ reduction. For metal–liquid interfaces, Bard and Faulkner discussed that the poised potential of a metallic electrode in non-equilibrium solutions reflects the potential of zero currents.¹⁸ But this notion has not yet been applied to semiconductor/two-redox liquid junctions with out-of-equilibrium solutions. Furthermore, because efficient photocatalyst particles, by design, always employ co-catalyst nanoparticles, kinetics and energetics at reaction sites are expected to vary spatially. For these reasons, the photocatalysis community need a photocatalyst particle model to explicitly describe the complex photocatalyst/co-catalyst/water junction under non-equilibrium conditions. The liquid-junction energetics at local catalytic sites should be applied with the Gerischer–Lewis semiconductor/two-redox kinetic model.

To develop a semiconductor/two-redox kinetic model for photocatalyst particles, we extended the principle of detailed balance (see the Glossary in ESI†) by explicitly involving the H⁺/H₂ and O₂/H₂O redox couples and acquiring their reported multi-electron catalytic kinetics (to be elaborated in Section 2). “Detailed balance” herein refers to a host of charge-transfer rate processes at local catalytic sites. For each catalytic site distributed spatially across the liquid-junction interface, its microscopic pathways involve both forward and backward charge-transfer directions for all operative acceptor/donor couples. Here, the notations of H⁺/H₂ and H₂O/H₂ will be used interchangeably, the choice of which should depend on local pH. Potentials and energetics are referenced to the reversible hydrogen electrodes (RHE) for a range of operational pH values.

First, single-crystalline SrTiO₃, SrTiO₃/Pt and SrTiO₃/(Cr₂O₃/Pt) photoelectrode systems will be used to step-wise validate the semiconductor/two-redox kinetic model for photocatalysts. The front liquid interface of these model photoelectrodes simulates the photocatalyst/(co-catalyst)/water junctions. We will establish an initial set of experimental methods to simulate and diagnose photocatalysts by systematically controlling their interfacial charge-transfer kinetics. In parallel with measuring the energetics, we vary kinetic branching ratios of charge-transfer rates to both H⁺/H₂ and O₂/H₂O redox couples, and correlated the experimentally controlled kinetics with the measured energetics. We then realized that although the Gerischer–Lewis model accounts for charge-transfer kinetics of multiple redox couples in describing the current–potential behaviour, it so far rather concerns spatially uniform liquid junctions, where co-catalysts only make perturbations to band-bending energetics according to the pinch-off effect; the performance of most photoelectrodes does not concern lateral charge separation along the liquid-junction interface.^17,19 We had shown that photocatalyst particles can be fully depleted with charges when suspended in water. The charge separation is likely dominated by lateral, diffusion-dominated transport of charge carriers.⁹ We therefore suggest a renewed picture: at photocatalysts, separation of electrons and holes is driven by small gradients of electron and hole quasi-Fermi levels. These gradients distribute laterally along the same liquid-junction interface, and the local energetics may change under varying local gas compositions dynamically. Specifically, the charge separation along the lateral dimension of liquid interfaces induces charge accumulation at the respective sites for H₂ and O₂ evolution. The lateral charge separation competes with the bulk or interfacial charge recombination. As the charges accumulate locally, the asymmetry of band bending will be reduced and so is the lateral potential gradient. As a result, the internal electric field makes less contribution to the local charge separation efficiency.

After quantitatively validating the semiconductor/two-redox kinetic model, we then applied it to practical photocatalysts of Al-doped SrTiO₃ and Ta₃N₅, to elucidate their kinetics and energetics during operation. Ta₃N₅ represents an emerging class of visible-light-responsive photocatalysts, which still require guidance for substantial activity improvement.^5,20,21 Al-doped SrTiO₃ (Al:SrTiO₃) was chosen because this photocatalyst exhibits efficient charge separation, despite only active with ultraviolet irradiation.^22–24 What makes photocatalysts interesting is the mutually dependent kinetics and energetics. In these photocatalysts, the kinetic branching ratios of local catalytic pathways should determine the local liquid-junction energetics, which affects the lateral potential gradient and thus the charge-separation efficiency; and in return, the charge-separation efficiency affects local catalytic rates, which determine local kinetics. We used these examples to elucidate how co-catalysts affect water-splitting activity, charge-separation efficiency, and back reactions due to H₂/O₂ recombination.

2. Theory of semiconductor/two-redox junctions

2.1 Semiconductor/two-redox kinetic model in the dark

A kinetic model was used to describe the charge-transfer processes at semiconductor/liquid junctions. The model accounts for the detailed balance of kinetic rates for all the microscopic forward and reverse charge-transfer pathways at a semiconductor/liquid junction. At the original semiconductor/one-redox liquid junction, the rates of forward electron transfer from the conduction band (CB) states to the acceptor species of a redox couple were hypothesized to be proportional to both concentrations of local acceptor species and surface electrons, multiplied with the charge-transfer rate constant as a pre-factor.¹⁷ The forward hole-transfer kinetics can be described similarly: valence band (VB) states accept electrons from the donor species. The net charge carrier fluxes are determined by the offset of electrochemical potentials. Electron or hole forward transfer establishes microscopic reversibility with the respective backward transfer. Under steady-state zero currents, the total forward rates are equal to the total reverse rates. The derivation is outlined in Section S1 and illustrated in Fig. S1 of the ESI.† In this case, thermodynamic equilibration is defined as in the dark and in the absence of a net current flow. The electrochemical potentials of semiconductor and co-catalyst always equilibrate, despite co-catalysts reaching a steady-state potential with a non-equilibrium solution purged with a (H₂ + O₂) gas mixture (see the Glossary in ESI†).

Regarding the semiconductor/two-redox liquid junction, a SrTiO₃/Pt/water model junction was employed. SrTiO₃ was chosen as the model photocatalyst due to its stability and its suitable band edge positions for overall water-splitting. Pt was chosen as a co-catalyst since Pt serves as electron accumulation sites on photocatalysts and is kinetically active for charge transfer to both H⁺/H₂ and O₂/H₂O redox couples.^25,26 In our experiments, n-type SrTiO₃ is chosen because intrinsic single-crystal SrTiO₃ is too resistive. The SrTiO₃/Pt/water junction has the barrier height dominated by the SrTiO₃/water junction with negligible contributions from the local SrTiO₃/Pt barrier, i.e., pinch-off effects, because the size of Pt particles deposited on SrTiO₃ is small (see Section S2 and Fig. S2–S5, ESI†). We also assume that the SrTiO₃/Pt interface exhibits variable barrier heights, i.e., the adaptive junction behaviour but not a buried junction with a fixed barrier height: the potential of Pt particles varies with the surface chemistry of Pt (e.g., by forming a surface hydride/hydroxide/oxyhydroxide surrounding Pt) in a way that can affect local band bending as Pt potentials vary. The assumption of being an adaptive junction will be verified in Section 3.4 by quantitative analysis and in Section 5 by the SrTiO₃:Al-particle study.

In the derivation for the charge-transfer processes at a SrTiO₃/Pt/water junction, the rate constants for both forward and backward electron-transfer pathways had only been deduced for outer-sphere one-electron redox couples. For each pathway in water-splitting photocatalysis, we took the respective multi-step micro-kinetics as reported in the literature,^27–29 and expressed the rate law based on concentrations of surface charges and surface-bound intermediates involved in the rate-determining step. We expressed the rate law regarding the reaction intermediates on Pt surfaces following two assumptions: (i) SrTiO₃/Pt in water forms an adaptive junction as discussed above; (ii) the exchange current densities at SrTiO₃/Pt junctions are much larger than those at Pt/water junctions under operation (see Section S2, ESI†). When SrTiO₃/Pt is brought into contact with water, electrons at the CB edge of SrTiO₃ will transfer to both H⁺/H₂ and O₂/H₂O through the Pt co-catalysts. Each pathway results in a branching ratio which depends on the respective kinetic rate, as illustrated in Fig. 1a and b.¹⁶ Here, “H⁺/H₂” and “O₂/H₂O” represent the respective half-reactions but are not the actual intermediates involved. Intermediates such as O₂/O₂˙⁻, O₂/H₂O₂ or H₂O₂/OH* couples are catalytic site specific and are not expressed in the generic model.

Fig. 1 Charge-transfer process at SrTiO₃/Pt/water junctions and steady-state current–potential (J–E) behaviour of SrTiO₃ photoelectrodes in the dark and under illumination (Pt is not presented in all figures for clear illustration). E_f, E_f,n and E_f,p denote the potentials of the Fermi level, electron quasi-Fermi level, and hole quasi-Fermi level of SrTiO₃, respectively; E₀ is the flat band potential of SrTiO₃; E₁ and E₃ denote the redox potentials of H⁺/H₂, i.e., E(H⁺/H₂), and O₂/H₂O, i.e., E(O₂/H₂O), respectively; E₂ denotes the potential of SrTiO₃ reaching steady-state in the dark; E is the potential of SrTiO₃; J₁ and J₂ denote the net electron current density from SrTiO₃/Pt to H⁺/H₂ and O₂/H₂O, respectively; J₃ is the net hole current density from SrTiO₃ to O₂/H₂O; and, J = J₁ + J₂ + J₃. The solid arrows and dashed arrows represent the major and minor pathways for charge transfer, respectively. This figure was drawn in one dimension for simplicity according to the pinch-off assumption. E_f,n and E_f,p in (c) do not overlap at the same location since they indicate the electron quasi-Fermi level at the Pt sites and the hole quasi-Fermi level at the SrTiO₃ sites, respectively.

The kinetic pathways for electron transfer from the CB to the H⁺/H₂ redox in alkaline electrolytes can be expressed as

Eqn (1) represents a two-electron H₂ evolution half-reaction but is not the rate-determining step. Electron transfer to the H⁺/H₂ redox on SrTiO₃/Pt follows a sequence of a Volmer step followed by either a Heyrovsky step or a Tafel step,³⁰

H₂O + Pt* + e⁻ → H_ad + OH⁻ (Volmer step) (2)

H_ad + H₂O + e⁻ → H₂+ OH⁻ (heterolytic Heyrovsky step) (3)

2H_ad → H₂ (homolytic Tafel step) (4)

where Pt* and H_ad denote the active sites on Pt and the H atom adsorbed on the sites, respectively. Note that the quantitative rate law is co-catalyst specific. For a hydrogen evolution half-cell reaction on Pt in base, the Volmer step, eqn (2), is typically the rate-determining step,³¹ which we assume for the SrTiO₃/Pt system. The forward interfacial electron current density to H⁺/H₂via Pt co-catalysts (assuming SrTiO₃ surfaces not as active as Pt for H₂ evolution) can be expressed as

J_1,forward = −qk₁[Pt*]n_s = −qk₁[Pt*]n_s0 exp[q(E₀ − E)/n₁k_BT] (5)

The backward interfacial electron current density to SrTiO₃ can be expressed as

J_1,backward = qk₁⁻¹[H_ad] = qk₁[Pt*]n_s1 = qk₁[Pt*]n_s0 exp[q(E₀ − E₁)/n₁k_BT] (6)

where [Pt*] and [H_ad] are the concentration of “Pt*” and “H_ad”, respectively; n_s0, n_s1, and n_s are the averaged surface electron concentrations at the respective potentials of E₀, E₁, and E as indicated in Fig. 1; n₁ is the ideality factor for the electron-transfer current density to H⁺/H₂, determined by the liquid-junction J–E behaviour or catalyst Tafel slope. Applying detailed balance, the net interfacial electron current density to H⁺/H₂via Pt can be expressed as

J₁ = −qk₁[Pt*](n_s − n_s1) = −qk₁[Pt*]n_s0{exp[q(E₀ − E)/n₁k_BT] − exp[q(E₀ − E₁)/n₁k_BT]} (7)

The concentration of H₂ and O₂ in the electrolyte will be correlated with [Pt*] indirectly, thereby modulating the net interfacial electron current density, i.e., J₁, to the H⁺/H₂ redox; k₁ is a rate constant independent with H₂, O₂, H_ad, or Pt* concentrations, and is determined by the exchange current density of Pt.

The forward interfacial electron transfer to the O₂/H₂O redox can be expressed by

Eqn (8) represents an overall four-electron O₂ reduction reaction. The rate-determining step of Pt-catalysed O₂ reduction (the forward electron transfer in eqn (8) was reported to be the first electron-transfer step):²⁸

O_2(ad) + H₂O + e⁻ → HOO_ad + OH⁻ (9)

where O_2(ad) and HOO_ad represent O₂ and HOO_ad species adsorbed on Pt reaction sites, respectively. The forward interfacial electron current density to O₂/H₂O via Pt co-catalysts (assuming SrTiO₃ surfaces not active for O₂ reduction) can be expressed as

J_2,forward = −qk₂[O_2(ad)]n_s = −qk₂[O_2(ad)]n_s0 exp[q(E₀ − E)/n₂k_BT] (10)

where k₂ is a rate constant independent of H₂, O₂, or O_2(ad) concentrations; n₂ is the ideality factor for the interfacial current density of electron transfer to O₂/H₂O. In case of ideal liquid junctions, n₁ and n₂ take the value of 1.

The backward electron transfer (i.e. reverse direction of eqn (8)) to the CB of SrTiO₃ involves both the backward reaction of water oxidation and Pt oxidation.²⁹ This backward electron transfer pathway is two steps in series, from liquids to Pt and then from Pt to the CB of SrTiO₃. The second step of Pt to the CB of SrTiO₃ is not considered the rate limiting step (see Section S2, ESI†). The first step of the backward transfer can be via water or hydroxyl oxidation catalyzed by PtO surfaces (according to experimental pH, the half-reactions in base are listed):

Besides, the first step of backward transfer can be via Pt oxidation:The reaction of PtO formation from Pt (eqn (13)) may proceed in two steps:Because little is known about the rate-determining step for eqn (11)–(15), the backward electron transfer of eqn (8) catalysed by Pt particles can, at this stage, be expressed as an empirical rate law:

J_2,backward = q(k_PtOH/Pt⁻¹[Pt] + k_PtO/PtOH⁻¹[PtOH] + k_PtOOH/PtO⁻¹[PtO] + k_Pt/PtOOH⁻¹[PtOOH]) (16)

where [Pt] and [PtOH] are the surface concentrations of metallic Pt and OH-terminated Pt sites, respectively; [PtO] and [PtOOH] are the surface concentrations of Pt=O and Pt–OOH sites, respectively. k_PtOH/Pt⁻¹, k_PtO/PtOH⁻¹, k_PtOOH/PtO⁻¹, and k_Pt/PtOOH⁻¹ are the respective rate constants for eqn (11)–(15). Applying detailed balance, the net interfacial electron current density to O₂/H₂O via Pt co-catalysts (assuming that SrTiO₃ surfaces are not active for O₂ reduction) can be expressed as

J₂ = −qk₂[O_2(ad)]n_s0 exp[q(E₀ − E)/n₂k_BT] + q(k_PtOH/Pt⁻¹[Pt] + k_PtO/PtOH⁻¹[PtOH] + k_PtOOH/PtO⁻¹[PtO] + k_Pt/PtOOH⁻¹[PtOOH]) (17)

The concentrations of H₂ and O₂ in electrolytes are correlated with [O_2(ad)], thereby modulating J₂. We note that the rate laws for J₁ and J₂ may be updated considering concerted proton and electron transfer kinetics.

At steady state in the dark, the net current density across the SrTiO₃/Pt/water junction should be zero:

J₁ + J₂ = 0 (18)

SrTiO₃ used in our experiments is a n-type semiconductor with a free-electron concentration of ∼1 × 10¹⁸ cm⁻³ (see ESI,† Materials and methods). Its hole carrier concentration is negligible in the dark. Therefore, we can assign VB hole-transfer kinetics to be zero in the dark.

These equations imply that J₁ and J₂ can be modulated independently by controlling the partial pressure of H₂ and O₂ in the gas mixture that purges the solution; and if the partial pressure of H₂ and O₂ is fixed, all the rate constants should be held invariable, which determines the potential of SrTiO₃ under steady-state in the dark (E₂). These considerations will be used in Section 3.4 to quantitatively validate the semiconductor/two-redox model.

2.2 Semiconductor/two-redox kinetic model under illumination

Hole transfer occurs via bare SrTiO₃ sites but not via Pt sites. As shown in Fig. S6 (ESI†), the J–E behaviour of SrTiO₃/Pt photoanodes under illumination were indistinguishable during flow of O₂ or H₂. Otherwise, Pt would serve for H₂ oxidation and the J–E behaviour would be different. The oxidation of H₂ on bare SrTiO₃ has never been reported, which is most likely due to poor H₂ adsorption on SrTiO₃. Based on these observations, we can deduce that the hole transfer from SrTiO₃ to H⁺/H₂ is negligible and that hole transfer is mainly through bare SrTiO₃ to O₂/OH⁻, as described byWater oxidation on native reaction sites on SrTiO₃ is initiated by the formation of trapped holes on the surface of SrTiO₃ and the first hole-transfer step was found in many reports to be the rate-determining step,^32,33

OH⁻ + h⁺ → OH_ad (20)

where OH⁻ and OH_ad are the hydroxide ions in the double layer and the surface-bound hydroxyl groups on SrTiO₃, respectively. The photocurrent J₃, which is the net interfacial hole current density to O₂/H₂O, can be expressed as

J₃ = J_3,forward + J_3,backward = qk₃[OH⁻]p_s − qk₃⁻¹[OH_ad] ≈ qk₃[OH⁻]p_s (21)

where J_3,forward and J_3,backward are the hole current density in the forward and backward direction, respectively; J_3,forward and J_3,backward are independent of the partial pressures of H₂ and O₂; k₃ denotes the rate constant of holes transfer from the VB of SrTiO₃; [OH⁻] is the concentration of hydroxide ions in the double layer; p_s is the surface hole concentration corresponding to the local hole quasi-Fermi level, E_f,p. E_f,p has an upper limit because the most oxidative intermediate is surface-bound hydroxyl radicals of the OH˙/OH redox (E(OH˙/OH) = +2.38 V vs. RHE) and the activation barrier of backward hole injection has a lower bound of (2.90 − 2.38) V = 0.52 V. Therefore, it is reasonable to drop the backward term, J_3,backward, which will be a negligibly minute number as compared to the typical photocurrents in light-on measurements.

Under steady-state illumination as shown in Fig. 1c, J₃ balances with J₁ and J₂:

J₁ + J₂ + J₃ = 0 (22)

Based on eqn (7), (17), (21) and (22), E_f,n and E_f,p at the SrTiO₃/liquid interface can be calculated, and the difference of E_f,n and E_f,p is defined as the photocatalysts photovoltage.

2.3 Expected behaviour of a SrTiO₃/Pt/water junction under open-circuit conditions

To verify the proposed kinetic model, the SrTiO₃/Pt/water junction was evaluated using a single-crystal SrTiO₃ photoelectrode. The front liquid contact of the SrTiO₃/Pt model photoelectrode consists of hole accumulation and electron accumulation sites, respectively, for light-driven water oxidation and H₂ evolution. The back contact is an indium layer. This ohmic back contact enables probing of the open-circuit potential (OCP) with negligible perturbation to the charge separation processes at the front SrTiO₃/Pt/water interfaces. At steady-state open circuits where the net current density is zero, the front liquid interface of the SrTiO₃/Pt model photoelectrode can be considered a two-dimensional planar photocatalyst (Fig. 2). In this configuration, the OCP represents an area-averaged Fermi level in the dark and an area-averaged electron quasi-Fermi level under steady-steady illumination for all the Pt sites. Note that the local Fermi level may vary spatially, but the measurement only produces one value due to its statistical nature. Measuring these variations is out of the scope of this study, but it is possible by developing liquid-phase electrochemical scanning probe microscopy in a future study.³⁴

Fig. 2 Spatially-varying band bending energetics at SrTiO₃/Pt/water interface in the dark and under illumination. E_f,n and E_f,p at bare SrTiO₃ surfaces overlap because their active sites trap hole charge to drive water oxidation.

Based on the theoretical analysis in Sections 2.1 and 2.2, we expect the following experimental behaviour for a SrTiO₃/Pt photoelectrode:

Steady-state potential in the dark. In the dark, the electrochemical potentials of SrTiO₃ and Pt equilibrate. Despite the solution not being at equilibrium, the steady-state potential of a SrTiO₃/Pt photoelectrode (E₂, which is measured as OCPs) is determined by the branching ratios of electron-transfer rates to H⁺/H₂ (k₁) vs. to O₂/H₂O (k₂), and [Pt*] and [O_2(ad)] as described in eqn (7), (17) and (18). When the electrolyte is purged with 100% H₂, the reaction sites on Pt are mostly covered by H_ad. Since k₁[Pt*] ≫ k₂[O_2(ad)] in this condition, only J₁ pathway is active. Under a steady-state condition, the OCP of a SrTiO₃/Pt photoelectrode should approach 0 V vs. RHE, E(H⁺/H₂). When the electrolyte is purged with 100% O₂, the reaction sites on Pt are mostly covered by O_2(ad). Since k₂[O_2(ad)] ≫ k₁[Pt*] in this condition, only J₂ pathway is active. Under a steady-state condition, OCP should approach ∼1.06 V vs. RHE. This OCP does not approach 1.23 V vs. RHE, E(O₂/H₂O), because Pt oxidation is involved in the charge transfer (see Section S3, ESI†). When the magnitudes of k₁[Pt*] and k₂[O₂] become comparable (electrolytes purged with a H₂ and O₂ mixture), OCPs should be between 0 and 1.06 V vs. RHE, as the H₂ compositions vary from 0% to 100% in the H₂ and O₂ mixture. These deductions will be confirmed in Sections 3.1–3.3.

Light-intensity threshold. In the dark, E₂ is located between E(H⁺/H₂) and E(O₂/H₂O), as mentioned in the previous paragraph. The electron transfer between SrTiO₃/Pt and H⁺/H₂ is dominated by a backward electron current density from H₂ back to the CB edge of SrTiO₃, i.e., the backward pathway of eqn (1). This backward electron-transfer current density is equal to the forward current density from the CB edge of SrTiO₃ to O₂, whereas the other current densities are negligibly small. In this case, the SrTiO₃/Pt/water interface functions as a shorted H₂/O₂ fuel cell. Under illumination, a sufficiently high photon flux is required to cancel the flux of H₂/O₂ recombination and to achieve net accumulation of H₂ and O₂ products. This threshold photon flux is defined as the light-intensity threshold, which generally exists for a liquid-junction interface that simultaneously exchanges charge with more than one redox couple. To confirm our deduction, the light-intensity thresholds of SrTiO₃/co-catalyst/water junctions were measured with results shown in Fig. S7 and S8 and further discussed in Section S4 (ESI†). The threshold of absorbed photon flux is estimated by the recombination current density when the model photoelectrode is poised at 0 V vs. RHE.

3. Experiments to validate the two-redox kinetic model

3.1 Charge-transfer behaviour at SrTiO₃/water junctions

Single-crystalline n-type SrTiO₃ in a photoelectrode configuration was used to verify the kinetic model. The band edge positions of SrTiO₃ in water were −0.4 V vs. RHE for the CB and 2.9 V vs. RHE for the VB.³ The flat band potential was −0.15 V vs. RHE as explained in Section S5 with Fig. S9 and S10 (ESI†). The potential vs. RHE will be used, because E(H⁺/H₂) and E(O₂/H₂O) will be involved in the discussion. The OCPs of bare SrTiO₃ were measured in a “light-on and light-off” sequence in an aqueous electrolyte (0.5 M Na₂SO₄, pH = 12.5) purged with a (H₂ + O₂) gas mixture of several well-controlled compositions. After every “light-on” or “light-off,” we waited long enough to let the OCP reach steady state, so that the measurement error was reduced to less than 50 mV. The OCPs in the dark were recorded after cutting off the illumination because illumination served to establish a steady state of product/reagent concentrations at the liquid junction. The kinetic branching ratios for the several co-existing electron-transfer pathways were monitored via the OCPs of SrTiO₃ in water. Under steady state, the net current density across SrTiO₃/water junction became zero, as described in eqn (18) (in the dark) or eqn (22) (under illumination).

The OCPs of a SrTiO₃ photoelectrode contacting an electrolyte purged with a (H₂ + O₂) gas mixture is shown in Fig. 3a. This weak dependence on H₂ and O₂ compositions, as discussed in Section S6 (ESI†), indicates a charge-transfer process dominated by surface states. The SrTiO₃/water junction can be approximated as a SrTiO₃/surface-state junction as illustrated in Fig. 4a, which reveals the operation of an inactive photocatalyst.

Fig. 3 Open-circuit potentials (OCPs) of (a) SrTiO₃, (b) SrTiO₃/Pt, and (c) SrTiO₃/(Cr₂O₃/Pt) photoelectrodes in an aqueous electrolyte purged with a (H₂ + O₂) gas mixture. The electrolyte is 0.5 M Na₂SO₄(aq) solution with pH adjusted to 12.5.

Fig. 4 Proposed models for the charge-transfer process at (a) SrTiO₃, (b) SrTiO₃/Pt, and (c) SrTiO₃/(Cr₂O₃/Pt) photoelectrodes that contact water the moment before equilibrium. The potential of SrTiO₃ was set at a flat band condition. The solid and dashed arrows represent the major and minor pathways for electron transfer, respectively. J₀, J₁ and J₂ denote the net electron current density to the surface states, H⁺/H₂ and O₂/H₂O, respectively. For each redox, the forward and reverse pathways were not shown individually but, for simplicity, were shown as an arithmetic sum of the respective forward and reverse current densities.

3.2 Charge-transfer behaviour at SrTiO₃/Pt/water junctions

To develop a semiconductor/water two-redox liquid junction and to reveal the operation of an active photocatalyst as illustrated in Fig. 4b, Pt was electro-deposited on SrTiO₃ (see the Experimental section). Fig. 3b shows the measured OCPs of a SrTiO₃/Pt photoelectrode contacting an electrolyte purged with a (H₂ + O₂) gas. When light was blocked, its OCP reached steady state in less than 100 s, shown in Fig. 3b, a much shorter time than 1000 s for a SrTiO₃ electrode, shown in Fig. 3a. The OCPs in the dark shifted from 0.02 V (at 100% H₂) to 0.90 V vs. RHE (at 100% O₂) with a wider span than those of bare SrTiO₃. The 0.88 V OCP range for SrTiO₃/Pt was comparable to the 1.02 V of FTO/Pt electrodes, as shown in Fig. S11 (ESI†). These results indicate that Pt effectively facilitated the electron exchange with both H⁺/H₂ and O₂/H₂O couples, and overwhelmed the electron transfer to surface states. The OCP in pure O₂ (0.90 V vs. RHE) was still 0.33 V more negative than 1.23 V vs. RHE, e.g. E(O₂/H₂O), because this OCP was showing the mixed potential of Pt oxidation reactions and oxygen reduction reactions (see Section S3, ESI†). The OCP in pure H₂ (0.02 V vs. RHE) was also slightly more positive than the 0 V vs. RHE, e.g. E(H⁺/H₂), possibly due to the concurrent but non-negligible involvement of electron transfer to surface states. To further confirm the effects of H₂ and O₂ compositions on the surface kinetics of SrTiO₃/Pt, the OCPs of SrTiO₃/Pt in electrolytes purged under a flow of (H₂ + N₂) mixture and (O₂ + N₂) mixture were shown in Fig. S12 with the result further discussed in Section S7 (ESI†). In summary, the gas-composition dependence of OCPs of SrTiO₃/Pt in the dark qualitatively verified the proposed kinetic model for semiconductor/two-redox liquid junctions.

3.3 Charge-transfer behaviour at a SrTiO₃/(Cr₂O₃/Pt)/water junction with co-catalyst selectivity

We further verified the kinetic model for semiconductor/two-redox liquid junctions by tuning the electron-transfer branching rates to H⁺/H₂vs. O₂/H₂O couples in water. We experimented with a Cr₂O₃ layer coated on Pt particles to adjust the magnitude of H₂ evolution and O₂ reduction rates, k₁ in eqn (7) and k₂ in eqn (17), respectively. Coating a Cr₂O₃ layer over Pt co-catalyst particles was reported to suppress O₂ reduction to a negligible rate (greatly decreasing k₂ in eqn (17)),³⁵ but only marginally suppress electron transfer to H⁺/H₂ (moderately decreasing k₁ in eqn (7)). The kinetic model with Cr₂O₃ was illustrated in Fig. 4c. The OCPs of SrTiO₃/(Cr₂O₃/Pt) in water were expected to be around E(H⁺/H₂) irrespective of the O₂ concentration in the gas mixture, because the J₂ pathway via Pt was effectively suppressed.

The OCPs of SrTiO₃/(Cr₂O₃/Pt) in water with a (H₂ + O₂) and with a (H₂ + N₂) gas mixture were shown in Fig. 3c and Fig. S13, respectively (ESI†). The OCPs of SrTiO₃/(Cr₂O₃/Pt) in the (H₂ + O₂) gas mixture was near E(H⁺/H₂) for the whole range of 0–100% O₂ compositions. The OCPs measured in the (H₂ + O₂) and the (H₂ + N₂) gas mixture at the same concentration of H₂ were very close. In the (H₂ + O₂) gas mixture, the OCP shifted from 0.03 to 0.12 V vs. RHE with decreasing H₂ concentrations from 100% to 0%. This change only corresponds to the Nernstian potential change under dilution. The results obtained matched well with the expected outcome by imposing the two-redox kinetic model.

3.4 Quantitative validation of the semiconductor/two-redox kinetic model

To quantitatively validate the proposed kinetic model, we fit the kinetic rate law of the forward interfacial electron transfer from SrTiO₃/Pt to O₂/H₂O, as expressed in eqn (10), with experimental data. Taking the logarithm of both sides of eqn (10), the equation can be expressed as:According to eqn (23), the log J_2,forwardvs. (E₀ − E) curve should be linear and the slope is independent of the gas composition. Furthermore, the intercept of the linear curve with the log J_2,forward axis is equal to log(qk₂[O_2(ad)]n_s0), the pre-factor of eqn (10) in a logarithm scale. The pre-factors extrapolated from log fitting are supposed to be consistent with those extrapolated from the detailed balance by using the dark OCPs measured in a series of (O₂ + N₂) mixtures. Here, we assumed that the pre-factors should be identical for the same composition of O₂ in the gas mixture, e.g., irrespective of the balancing gas of H₂ or N₂ in the (H₂ + O₂) or (O₂ + N₂) mixtures.

Experimentally, we measured the total electron current density across the SrTiO₃/Pt/water junction (J) vs. E in the dark (Fig. S14, ESI†), then extracted the J_2,forward component from the total J, and plotted the log J_2,forwardvs. (E₀ − E) curve (Fig. S15, ESI†). The linear region of the log J_2,forwardvs. (E₀ − E) curves were fitted for various gas compositions. The slopes and the intercepts of these log-linear lines were extracted (Fig. S16 and Table S3, ESI†). The process for extracting the J_2,forward component and the pre-factors is elaborated in Section S8 (ESI†).

The slopes of these log-linear lines were found to be independent of gas compositions. However, the slope of ∼160 mV dec⁻¹ is more than twice of the ideal semiconductor/liquid junction exponential behaviour of 59 mV dec⁻¹, that is, the ideality factor n₂ > 2. This departure from the ideal behavior was consistent with our adaptive junction assumption because the catalytic current is limiting J_2,forward. In this case, n₂ is correlated with the Tafel slope of Pt's catalytic behaviour. Furthermore, the pre-factors of qk₂[O_2(ad)]n_s0 extracted from the intercepts of the log-linear plots (Table S3, ESI†) matched well with those independently obtained from dark OCP measurements (Table S5, ESI†), as compared in Fig. S17 (ESI†). To summarize our fitting results, (log J_2,forward − log(qk₂[O_2(ad)]n_s0)) vs. (E₀ − E) was plotted in Fig. 5, where qk₂[O_2(ad)]n_s0 was independently obtained by dark OCP measurements. These log-linear lines overlapped with each other under various gas compositions, which directly validates eqn (23). The agreement above quantitatively validates the kinetic rate law of eqn (10) and further validates the detailed balance principle of our two-redox kinetic model. The kinetic rate law of the forward interfacial electron transfer from SrTiO₃/Pt to H⁺/H₂, i.e., J_1,forward expressed by eqn (5), can be validated using a similar procedure.

Fig. 5 (log J_2,forward − log(qk₂[O_2(ad)]n_s0)) vs. (E₀ − E) under various gas compositions. log(qk₂[O_2(ad)]n_s0) is the pre-factor which was calculated from dark OCP measurements. Error bars arose from the variation of dark OCP measurements.

4. A dynamic model for photocatalyst particles

We recently reported that asymmetric band bending between low barrier-height electron accumulation sites and high barrier-height hole accumulation sites on a photocatalyst drove charge separation.⁹ For a SrTiO₃/Pt/water junction, we consider that an electric field is dropped across the Pt-decorated SrTiO₃ surfaces and native SrTiO₃ surfaces locally, which drives local charge separation. As discussed in Section 2.1, the barrier-height energetics along the Pt-decorated SrTiO₃ surfaces in the dark were expected to vary with the potential of Pt depending on the surface kinetics. This feature was confirmed in Section 3. As discussed in Section 2.2, the barrier-height energetics on the native SrTiO₃ surfaces in the dark did not vary with the local gas compositions. Hence, we introduce a photocatalyst particle model by combining the adaptive liquid junction assumption, kinetic-controlled local energetics (extended Gerischer–Lewis model), and spatially varying barrier heights (asymmetric band bending) for charge separation. This comprehensive photocatalyst particle model was illustrated by a two-dimensional diagram, Fig. 2: Pt-decorated SrTiO₃ surfaces feature kinetics dependent barrier heights; to drive efficient charge separation, Pt-decorated SrTiO₃ surfaces (electron accumulation sites) exhibit a low barrier height and native SrTiO₃ surfaces (hole accumulation sites) exhibit a high barrier height; at the respective local electron- or hole-accumulation site, the current–potential behaviour follows the two-redox kinetic model.

Under illumination, E_f splits into individual E_f,n and E_f,p at the respective photocatalytic sites. The direction of local charge separation is distributed along the particle/liquid interface. E_f,n can be monitored by OCPs, while E_f,p cannot be directly measured by the current electrochemical method. Section S9 (ESI†) discussed the position of E_f,p and the estimation of photovoltages under illumination. It is deduced that the hole quasi-Fermi level was located at (1.23 V vs. RHE + an overpotential). Moreover, the more negative the OCP under identical illumination conditions, the higher the photovoltage and the better the charge separation. In Section 5, the measured OCP under illumination, i.e., the potential of E_f,n, will be used to indicate charge-separation efficiency.

Through OCP measurements of photocatalyst-assembled photoelectrodes, the asymmetry of local barrier heights in the dark and the efficiency of charge separation under illumination at photocatalysts can be readily quantified. If the local kinetics varies (indicated by the OCP in the dark), the kinetics-controlled energetics is expected to adjust the band bending asymmetry and dynamically modulate charge separation efficiency (indicated by OCPs under illumination). This narrative of mutually-dependent kinetics and energetics at a SrTiO₃/Pt/water junction will be applied to diagnose the operation of SrTiO₃:Al and Ta₃N₅ photocatalysts in Section 5.

5. Application of the particle model to particulate SrTiO₃:Al and Ta₃N₅ photocatalysts

We elucidated the mutually-dependent charge-separation and charge-transfer behaviour at the operative photocatalyst/co-catalyst/water interfaces. These findings will be applied to optimizing practical photocatalyst/co-catalyst combinations. SrTiO₃:Al (ultraviolet-light responsive) and Ta₃N₅ (visible-light responsive) absorbers were taken as examples to diagnose photocatalyst activity and to elucidate co-catalyst functionality. The control experiments (see Section S10 with Fig. S18 and S19, ESI†) showed that the Ti back contacts that are ohmic to SrTiO₃:Al particles displayed no redox activity despite their contact with electrolytes; the Ti back contacts were not affecting the OCP measurement of photocatalysts.

The OCPs of Ti/SrTiO₃:Al particle-assembled photoelectrodes in water purged with a (H₂ + O₂) gas mixture were summarized in Fig. 6a, and those with a (H₂ + O₂), a (H₂ + N₂) or a (O₂ + N₂) gas mixture were shown in Fig. S20 (ESI†). The OCP trend in the dark was comparable to that shown in Section 3.1 for single-crystalline SrTiO₃. The OCPs of <0 V vs. RHE under illumination showed that water-splitting on SrTiO₃:Al was possible but realistically limited by the slow electron-transfer kinetics between SrTiO₃:Al and H⁺/H₂ in water. This observation was consistent with the small but non-zero water-splitting activity of particulate SrTiO₃:Al suspensions as quantified by gas chromatography (Fig. S21, ESI†).

Fig. 6 Summary of OCPs in the dark (filled circles) and OCPs under illumination (hollow circles) for (a) Ti/SrTiO₃:Al, (b) Ti/SrTiO₃:Al/Pt and (c) Ti/SrTiO₃:Al/RhCrO_x particle-assembled photoelectrodes in an electrolyte purged with a (H₂ + O₂) gas mixture. E(H⁺/H₂) and E(O₂/H₂O) were calculated based on the Nernst equation. The arrows point to two conditions for the energy diagrams of SrTiO₃:Al/Pt shown in Fig. S23 (ESI†). The electrolyte is 0.5 M Na₂SO₄(aq) solution with pH adjusted to 12.5.

The OCPs of Ti/SrTiO₃:Al/Pt particle-assembled photoelectrodes in water purged with a (H₂ + O₂) gas mixture were summarized in Fig. 6b, and those with a (H₂ + O₂), a (H₂ + N₂) or a (O₂ + N₂) gas mixture were shown in Fig. S22 (ESI†). The trend of this OCP data set measured in the dark was similar with that for single-crystalline SrTiO₃/Pt, indicating the improved electron-transfer kinetics. The OCPs of Ti/SrTiO₃:Al/Pt photoelectrodes under illumination were dependent on the O₂ concentration, as shown in Fig. 6b. The OCPs shifted positively as the O₂ concentration increased. The OCP in 100% O₂ is 150 mV more positive than that in 100% H₂. Moreover, only when the O₂ concentration was lower than 20%, the electron quasi-Fermi level was <0 V vs. RHE, i.e., E(H⁺/H₂).

As illustrated in Fig. S23 (ESI†), the presence of O₂ reduced the band bending in SrTiO₃:Al/Pt, which reduced the electric field between SrTiO₃:Al/Pt and bare SrTiO₃:Al sites, made charge separation less effective, and thus reduced the charge-separation efficiency. The gas-composition dependent OCPs under illumination revealed that the water-splitting activities of particulate SrTiO₃:Al/Pt was determined by the redox selectivity of Pt. Deduction from OCP measurements was consistent with the measured water-splitting activities of particulate SrTiO₃:Al/Pt, where the H₂ evolution rates in H₂ and O₂ environments, respectively, were shown to be 13 μmol h⁻¹ and ∼0 μmol h⁻¹, respectively (see Fig. S24, ESI†). SrTiO₃:Al/Pt photocatalysts switched from inactive to active, when O₂ compositions reduce to <40%.

The trend of OCPs of Ti/SrTiO₃:Al/Pt photoelectrodes in water purged with a (H₂ + O₂) gas mixture also confirms that the SrTiO₃:Al/Pt junction is adaptive. If SrTiO₃:Al/Pt were to form a buried junction, its barrier height at Pt sites would be a constant and high value. As a result, the charge separation efficiency should remain the same. In this case, OCPs under illumination would not vary with H₂ and O₂ gas compositions. This buried-junction assumption contradicts the gas-composition dependent OCPs shown in Fig. 6b.

SrTiO₃:Al/Pt was capable of splitting water but its activity was about two orders of magnitude lower than that of SrTiO₃:Al/RhCrO_x by comparing Fig. S24 and S25 (ESI†). The OCPs of Ti/SrTiO₃:Al/RhCrO_x in water purged with a (H₂ + O₂) gas mixture were summarized in Fig. 6c, and those with a (H₂ + O₂), a (H₂ + N₂) or a (O₂ + N₂) gas mixture were shown in Fig. S26 (ESI†). By comparing the charge-separation and charge-transfer processes of SrTiO₃:Al/RhCrO_x with SrTiO₃:Al/Pt (see Section S11 and Fig. S24–S28, ESI†), it was concluded that the advantages of loading RhCrO_x on SrTiO₃:Al were (1) less charge-carrier recombination at the SrTiO₃:Al/RhCrO_x interfaces, and (2) enough band bending asymmetry for efficient charge separation, across local electron and hole accumulation sites under the full span of gas compositions. For these reasons, the combination of SrTiO₃:Al/RhCrO_x was the most active for photocatalytic water splitting, with the operational band energetics illustrated in Fig. S28 (ESI†).

The OCPs of Ta/Ta₃N₅, and Ta/Ta₃N₅/Pt in water, and Ta/Ta₃N₅/Pt thin-film photoelectrodes in 20 vol% MeOH aqueous solution purged with a (H₂ + O₂) gas mixture were summarized in Fig. 7; the full data set appears in Fig. S29 (ESI†). The trend of OCPs of Ta/Ta₃N₅/Pt in the dark was similar with that of SrTiO₃/Pt in Section 3.2, but the trend of OCPs under illumination was different. It reveals that Ta₃N₅/Pt and SrTiO₃/Pt showed similar charge-transfer kinetics, but Ta₃N₅ were much less efficient for charge separation under illumination. As shown in Fig. 7b, the OCPs of Ta/Ta₃N₅/Pt under illumination and at any gas composition were more positive than E(H⁺/H₂). Moreover, when the O₂ concentration in a (H₂ + O₂) gas mixture was less than 20%, there was almost no difference between OCPs in the dark and under illumination. This meant that most of the photo-generated carriers recombined even though a maximum amount of band-bending asymmetry was achieved for Ta₃N₅ in pure H₂ (see Fig. S23, ESI†). The severe recombination of photo-generated carriers implies that Ta₃N₅ bulk was too defective to split water. To improve the charge separation on Ta₃N₅, we used methanol as a sacrificial electron donor to immediately consume the photo-generated holes from Ta₃N₅, and to reduce recombination. As shown in Fig. 7c, the OCPs of Ta/Ta₃N₅/Pt in the dark and under illumination split regardless of the composition of the gas flow. This result confirmed that the fast and irreversible kinetics of methanol oxidation alleviated severe charge recombination. This point was further supported by the observed non-activity of particulate Ta₃N₅/Pt suspension in pure H₂, and the observed activity in 20 vol% MeOH aqueous solution, as shown in Fig. S30 (ESI†). Our OCP study indicated that improving optoelectronic properties of Ta₃N₅, such as the lifetimes of charge carriers, should be the priority at the current stage.

Fig. 7 Summary of OCPs in the dark (filled circles) and OCPs under illumination (hollow circles) for (a) Ta/Ta₃N₅, and (b) Ta/Ta₃N₅/Pt photoelectrodes in water, and (c) Ta/Ta₃N₅/Pt photoelectrodes in 20 vol% methanol (MeOH) aqueous solution purged with a (H₂ + O₂) gas mixture. E(H⁺/H₂) and E(O₂/H₂O) were calculated based on the Nernst equation.

6. Conclusion

Our study offers quantitative design principles for optimizing the solar-to-fuel conversion efficiency of photocatalyst particles. The correlation between charge-transfer rates and band energetics at the photocatalyst/(co-catalyst)/water junction were described using a semiconductor/two-redox kinetic model. This model considered all the forward and backward charge-transfer pathways with the acceptor and donor species or intermediates at the liquid-junction interface. These interfacial charge-transfer events were accounted for under the principles of detailed balance and microscopic reversibility. The kinetic model was validated experimentally by using single-crystalline SrTiO₃, SrTiO₃/Pt and SrTiO₃/(Cr₂O₃/Pt) model photoelectrodes. The kinetic model further provided in-depth understanding of the dynamic interplay between kinetic-controlled energetics and local charge-separation processes at a photocatalyst/(co-catalyst)/water liquid junction.

Applying the established experimental framework for the SrTiO₃ model photocatalysts, we further elucidated the mutually dependent kinetics and energetics of photocatalyst particles, such as SrTiO₃:Al and Ta₃N₅. The experimental OCP study on SrTiO₃:Al/Pt particle-assembled photoelectrodes revealed the importance of manipulating the surface kinetics for photocatalytic water splitting, especially in the comparison between the SrTiO₃:Al/Pt and SrTiO₃:Al/RhCrO_x combinations: it is necessary to tailor the energetics between photocatalysts and co-catalysts to reduce the interfacial charge recombination. In contrast, Ta₃N₅ was so defective in bulk that at the current stage, studies on this photocatalyst should focus on improving its optoelectronic properties, such as the lifetimes of charge carriers. Our model provides insights into optimizing a photocatalyst/co-catalyst junction by quantitatively identifying the effects of asymmetric band bending on charge separation, which competes with the loss of efficiency due to bulk recombination controlled by semiconductor optoelectronic properties and due to interfacial recombination controlled by photocatalyst/co-catalyst interfacial properties. We recognize the merit of using high turnover-frequency co-catalysts such as Pt, but rather emphasize their other functionalities shown in the photocatalyst/co-catalyst combination, such as passivating surface electronic defects and creating asymmetric barrier heights.

Author contributions

All the authors contributed to the manuscript, and all authors have given approval to the final version of the manuscript.

Conflicts of interest

The authors declare no competing financial interests.

Acknowledgements

The authors would like to thank Dr Min Li at Yale's Materials Characterization Core for his invaluable help with XRD and SEM measurements, Mr Hao Lyu for preparing Al-doped SrTiO₃ particles and Mr Yutaka Sasaki for preparing Ta₃N₅ thin films. The authors also recognize the start-up support from the Tomkat Foundation, and thank Dr Tianshuo Zhao for the helpful discussion. RY acknowledges a fellowship support from the Japan Student Services Organization.

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Footnotes

† Electronic supplementary information (ESI) available: Additional results are provided. See DOI: 10.1039/c9ee02910a

‡ Both authors contributed equally to this manuscript.

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