Photocatalytic Water Splitting: Quantitative Approaches toward

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Photocatalytic water splitting: Quantitative approaches toward photocatalysis by design Kazuhiro Takanabe ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b02662 • Publication Date (Web): 11 Oct 2017 Downloaded from http://pubs.acs.org on October 11, 2017

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Photocatalytic water splitting: Quantitative approaches toward photocatalysis by design Kazuhiro Takanabe* King Abdullah University of Science and Technology (KAUST), KAUST Catalysis Center (KCC) and Physical Sciences and Engineering Division (PSE), 4700 KAUST, Thuwal, 239556900, Saudi Arabia.

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ABSTRACT. A widely used term, “photocatalysis”, generally addresses photocatalytic (energetically down-hill) and photosynthetic (energetically up-hill) reactions and refers to the use of photonic energy as a driving force for chemical transformations, i.e., electron reorganization to form/break chemical bonds. Although there are many such important reactions, this contribution focuses on the fundamental aspects of photocatalytic water splitting into hydrogen and oxygen by using light from the solar spectrum, which is one of the most investigated photosynthetic reactions. Photocatalytic water splitting using solar energy is considered to be artificial photosynthesis that produces a solar fuel because the reaction mimics nature’s photosynthesis not only in its redox reaction type but also in its thermodynamics (water splitting: 1.23 eV vs. glucose formation: 1.24 eV). To achieve efficient photocatalytic water splitting, all of the parameters, though involved at different timescales and spatial resolutions, should be optimized because the overall efficiency is obtained as the multiplication of all these fundamental efficiencies. The purpose of this review article is to provide the guidelines of a concept, “photocatalysis by design”, which is the opposite of “black box screening”; this concept refers to making quantitative descriptions of the associated physical and chemical properties to determine which events/parameters have the most impact on improving the overall photocatalytic performance, in contrast to arbitrarily ranking different photocatalyst materials. First, the properties that can be quantitatively measured or calculated are identified. Second, the quantities of these identified properties are determined by performing adequate measurements and/or calculations. Third, the obtained values of these properties are integrated into equations so that the kinetic/energetic bottlenecks of specific properties/processes can be determined, and the properties can then be altered to further improve the process. Accumulation of knowledge ranging in fields from solid-state physics to electrochemistry and the use of a multidisciplinary


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approach to conduct measurements and modeling in a quantitative manner are required to fully understand and improve the efficiency of photocatalysis.

KEYWORDS. Photocatalysis, water splitting, electrocatalysis, hydrogen evolution, oxygen evolution, band alignment, chemical potential, Fermi level

Introduction General strategy for improved photosynthetic reactions: A photocatalyst is a substance that absorbs photons and generates excited states, which then cause in photophysical and photochemical processes as they return to their original ground states.1 Photocatalyst materials can consist of additional catalytic components, often called cocatalysts, that catalyze electrochemical redox reactions.2 Such an electrocatalyst is often essential to the photocatalyst (photon absorber) because its surface is not typically designed to catalyze redox reactions unless the reaction is an outer-sphere electrochemical reversible reaction. The timescale of electrocatalysis during the photocatalytic process is sufficiently longer than the timescales of photophysical or photochemical processes;3 in many photocatalytic reactions, the photocatalysis can thus be considered to be electrocatalysis where electrocatalyst components induce the redox reactions driven by the potential shifts caused by the photocatalyst (photon absorber). Photocatalysis eventually builds an electromotive force (emf), a difference in chemical potentials or Fermi levels, to enable electrocatalysis.1 This emf transient charging at electrocatalytic sites is indeed required for water-splitting photocatalysts because both the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) require multiple electron transfer reactions at the active species and thus relative slow process compared to prior photophysical processes.


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One may consider the difference between a photocatalyst (photon absorber and electrocatalyst) and a device that consists of a photovoltaic and an electrolyzer (PV + E). Making hydrogen by PV + E technology is still more expensive than using natural gas reforming.4,5 A large number of elementary events are common; however, the photocatalyst may induce charge separation utilizing an electrocatalyst-semiconductor interface or a solid-liquid junction directly,1 potentially skipping the p-n junctions in solid-solid structures. This is the major driving force of cost reduction in photocatalytic system compared to PV + E system. Photocatalytic materials also do not require the wiring of a PV (but instead require the collection of produced gases). On the other hand, in a PV + E configuration, separating the functions of photovoltaic current generation (PV) and electrocatalysis (E) is easily optimizable for these two separate components, and PV + E systems are therefore expected to produce higher efficiencies than photocatalyst systems.6 To combine these systems, PV material can be immersed into aqueous solution,7-9 which allows the material to avoid a detrimental temperature increase (because of the water) and the resultant efficiency loss. There is a significant chance, however, that the PV material corrodes because the water itself is corrosive and even worse at extreme pH values; additionally, fewer photons are expected to be absorbed when the PV is in water because, besides photon loss due to reflection by the water, absorption coefficient of water is non-zero especially beyond 600 nm.10 Lewis recently reviewed the future possibilities for solar energy conversion technology in industry and academia.5 Practical use of either of these systems requires future efforts: PV + E prices must be decreased by engineering or some technical advancement that produces a reasonable device and system, and the photocatalytic efficiency of photocatalysts must be improved without forgetting a final, scaled-up reactor design. Recently, immobilization of photocatalyst powder in sheets for use in overall water splitting was demonstrated,11 but the


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overall efficiency of this catalyst remains low, predominantly because of inefficient charge separation by the photocatalyst materials. Collective efforts are needed to address these complex issues in clearly desired solar energy conversion technology. As recently emphasized by Osterloh,12 photosynthetic reactions (∆G > 0) require detailed photon management and charge separation, in contrast to photocatalytic reactions (∆G < 0), whose performance is most sensitive to surface area. Basing the selection of materials for photon absorption (photocatalyst) solely on their bandgap and electrocatalyst, often called cocatalyst, is not enough to result in photocatalytic efficiency. We will review that defect density, carrier concentrations, and interfaces (metal, semiconductor, electrolyte, etc.) strongly influence efficiency, even when the same materials are used. This fact is widely known, yet there is no consensus as to how to evaluate these properties and consequences. In addition to the use of disparate reporting protocols,13-23 this discrepancy is the reason why every research article reports different efficiencies even when same composition of photocatalyst is used. For instance, there are multiple methods to prepare photocatalyst materials,24 but they result in different photocatalytic performances because unquantifiable or difficult-to-measure properties vary.25 Photocatalysis research is becoming largely arbitrary because of an infinite number of variables, e.g., different precursors, synthesis protocols, annealing, pre/post-treatment, and addition of small quantities of dopants/impurities/additives (often unconsciously); it is very difficult to reproducibly make photocatalysts. In a specific operation, one may want to concretely determine how overall efficiency is improved by a particular “quantity”.25 There are excellent review articles concerning photocatalyst and photoelectrochemical reactions: many focus on various materials and techniques of characterization.26-45 This review is specifically targeted to developing a guideline as to what fundamental key parameters improve photocatalytic


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efficiencies, regardless of the photocatalyst material. It is time to integrate advanced modeling into the design of photocatalyst materials. Without these efforts, photocatalytic research remains abstract, unestablished and unquantifiable. Consolidation of chemical potentials and Fermi levels: The basic concept of photocatalysis relies on the same protocol as all types of catalysis research: a description of chemical potentials of electrons, or Fermi levels. A strong connection between solid-state chemistry and physical chemistry, or photophysics and electrocatalysis, is the accurate description of chemical potentials of electrons in various substances (metals, semiconductors, redox ions in the solution, etc.) at thermodynamic equilibrium or under steady-state illumination. The concepts of the chemical potentials of electrons in metals to semiconductor is well described in an excellent book by Sato.46 Each elementary step/event in “catalysis” including photocatalysis, in terms of thermodynamics and kinetics, becomes quantitatively describable if we have tools to appraise the chemical potentials of electrons, especially reactive ones, in molecules, nanoparticles, and solids (catalyst materials) and in both reactants and products during (photo)catalysis. Work functions of metals, Nernstian redox potentials of molecules/ions, and Fermi levels or flatband potentials of semiconductors are useful statistical measures of energy equilibrium and flow, although overlapping reactive energy states in solids and interfaces makes determining the value of these potentials difficult. Recent advances in solid-state physics and chemistry establishes reasonable theories that can measure (estimate) or calculate such energy levels and their densities of state. This estimate, consisting of a large number of quantifiable parameters,25 can ideally be used to predict overall photocatalytic efficiency, even without experiments. It is thus possible to determine which parameter is most influential in improving overall efficiency. This strategy is


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one step forward to “photocatalysis by design”; the designing systems to reach a target by altering specific parameters rather than randomly screening materials. Successful photocatalysis requires that charged-up electrocatalysts are maintained at the potentials where steady-state redox reactions occur. A scheme can be derived, on a scale of the chemical potential of electrons (and holes), that visualizes the ideal energy transfer (and loss) that occurs during sequential photocatalytic processes. Figure 1 describes an example of the use of a single semiconductor powder as a photocatalyst that is decorated with HER and OER electrocatalysts on the surface, in an attempt to achieve overall water splitting. The process is initiated with photon absorption, as depicted in the middle of Figure 1. Upon light absorption, an excited hole and electron are generated in the valence band and conduction band, respectively, on the femtosecond time scale.47 After rapid relaxation to the edges of their respective bands in femto- to picoseconds, an exciton (electron-hole pair) is separated into free carriers and the semiconductor-catalyst interface guides the electron and hole to the HER and OER catalysts, respectively, generally in nano- to microseconds.47 Substantial losses of potentials are expected at the interface (“interfacial loss”) and may originate from entropic contributions of electrons48-50 and interfacial potential barriers that are generated by inadequate alignment. Successful electron/hole transfer to the electrocatalyst shifts the potentials either negatively or positively at transient time on the millisecond to second time scales, and then maintain steady-state potentials that are allowed to drive steady-state electrochemical redox reactions to produce H2 and O2.47 The solution properties may influence the overall performance by limiting the mass transfer of the reactant ions. How can we draw this type of scheme for every photocatalyst? What properties are involved that determine such potentials at each event? Can we identify the bottleneck that


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limits the overall efficiency? In the next section, the selected key parameters as well as photocatalysis events that occur at different time scales are identified. List of properties involved in photocatalytic water splitting: The primary effort of this review focuses on discussing the fundamental parameters that are involved in photocatalytic water splitting and their quantitative measurement using powdered semiconductor material (the concept can be applied to other photocatalysis as well). Photocatalysis for water splitting indeed involves a complex series of photophysical and electrocatalytic processes.25 The processes involved in photocatalytic reactions are divided into the following six components: 1. Photon absorption 2. Exciton separation 3. Carrier diffusion 4. Carrier transport 5. Catalytic efficiency 6. Mass transfer of reactants and products Events 3 and 4 can occur simultaneously and coherently, but are separated here for convenience. Figure 2 shows this six-gear concept, which represents the photocatalytic watersplitting process sequentially occurring at different time scales.25 Photon absorption initiates nonequilibrium photophysical and photochemical processes. The photon absorption generates an exciton, i.e., excitation of an electron in the valence band (VB) or the highest occupied molecular orbital (HOMO) to the conduction band (CB) or the lowest unoccupied molecular orbital (LUMO).47 The probability to occupy such states are predominantly determined by the electronic structure (local displacement of atoms) of the semiconductor. This femtosecond process is followed by relaxation of the electron and the hole to the bottom of the CB and the top of the


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VB, respectively, on a similar time scale.47 Next, the exciton (electron-hole pair) needs to be separated after overcoming the exciton binding energy determined by the electronic structure; this structure should guide the excited electron and hole (polaron) to move independently, being influenced by their effective masses. The combination of carrier diffusion and transport effectively utilizes the introduced interfaces, i.e., potential differences, and successful charge transfer typically in microseconds to the electrocatalysts decorated on the surface needs to occur. Because the kinetics of electrocatalysis are unfortunately sluggish compared to the prior events, such electrocatalytically active species will be charged either negatively or positively and drive electrocatalytic redox reactions on a time scale typically longer than microseconds.47 The key is that most of the semiconductor and electrocatalytic properties and measures of efficiency at each stage are listed separately and are quantitatively measurable by using various characterization and kinetics measurements. Once a material is synthesized, these properties and efficiencies are quantified so that the bottleneck of the process is identified, leading to improved overall efficiency. Previous reports describe the associated equations and measurement protocols in more detail.25 This contribution aims to emphasize the most influential key components in determining overall photocatalytic efficiency.

Quantification of key properties relevant to photocatalytic water splitting Generation rate: When solar energy conversion is the primary concern, analysis of the solar spectrum provides useful information regarding theoretical maximum efficiency. The solar-tohydrogen (STH) conversion efficiency is defined by the H2-energy generated divided by the entire solar irradiance. Using the NREL standard spectrum of AM 1.5G,51 integration of UV photons accounts for a maximum of 3.3% STH efficiency. Including light from the UV to the


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visible (to 600 nm) results in a maximum theoretical STH efficiency of 17.8%, while up to 800 nm results in >35% (using a single semiconductor). Analysis of the solar spectrum reveals that development of a visible-light-responsive photocatalyst material is essential to achieving substantial solar energy conversion.52 A representative scheme for various visible light responsive materials is shown in Figure 3, which is taken from the review paper by Sivula and van de Krol.45 The bandgap of the materials is minimum thermodynamic requirement for highefficiency photocatalysis; however, the shape of conduction and valence bands are unique to each electronic structure, and densities of state typically become very weak at band edges (bands are not rectangular as described below). It is obvious that if no photons are absorbed, no photocatalysis occurs. The initial step of photocatalysis is unambiguously the absorption of a photon and exciton generation by the photon absorber. Once the photocatalyst material is chosen for investigation, it is crucial to identify its electronic structure (displacements of the atoms or a crystal structure), which in turn determines the densities of the relevant energy states. Commonly, photon flux of incident light, I0, commonly lead to the following relationships: I 0 = A% + T + RS + S + Rd

(1)

where A% is absorptance, the ratio of the absorbed to incident electric field, and T, Rs, S, Rd are lights that are transmitted, specularly reflected, forward-scattered and back-scattered, respectively.53 Most importantly, the absorption coefficient, α(λ), how far photons of a particular wavelength can penetrate before it is absorbed by the material, can be measured or calculated as a function of wavelength.25,27 It also determines important absorption properties such as the bandgap, band positions (flatband potentials), and the direct/indirect nature of light absorption. The absorption spectra indicate the consequences of bandgap excitation, d-d transitions, phonon


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absorptions, and excitations associated with defect states.53 To practically measure absorption coefficients, the single crystal thin-film configuration of semiconductors provides a more precise description because contribution of scattering is minimized and the film thickness is welldefined.54 From transmittance, T, and reflectance, R,55 values, we obtain α for the film thickness, d, when Re−α d 100. From this number, it is clear that management of surface states is critical to controlling the photocatalytic


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activity of powder materials.83 If surface sites are insulated or deactivated to the point at which their concentration is 100 times less than that of complete exposure, the surface and bulk atoms of the same system become comparable. This idea is visualized in Figure 5, and it is consistent with the common observation that having “high crystallinity” and a minimal number of defects enhances photocatalytic efficiency, in contrast to a simple increase in surface area.84 In summary, the minority carrier lifetime is prolonged with a more intrinsic semiconductor (fewer dopants) in the bulk, and surface modification at the interface is crucial for photocatalysts, which is further interacted with the following parameters. Carrier diffusion and transport: The important parameters to consider when selecting photocatalyst materials are, at this point, predominantly the electronic structure, which determines the absorption coefficient, and the charge carrier concentration, which influences carrier lifetime and diffusion length. The next event that occurs during the photocatalytic process is excited carrier transport. Charge separation is a primary concern for photosynthetic reaction and solid liquid interface should be effectively utilized.12 The generated free charge carriers must travel through the bulk of semiconductor to the surface redox sites.85 Such phenomena can be described in terms of electron flow, i.e., current. There are two driving forces for electron (n) and hole (p) movement: diffusion driven by concentration gradient and drift driven by potential gradient:67 J = J diffusion + J drift

(8)

J n = eDn ∇ n + ne µ n E

(9)

J p = −eDp∇p + peµp E

(10)

where e is the elementary charge, D is the diffusion coefficient, ∇ p and ∇ n are the gradients of electrons or holes, µ is the mobility of the charge carrier, p denotes hole concentration, n denotes


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electron concentration, and E is electric field. The diffusion contribution is associated with the diffusion coefficient and mobility of intrinsic semiconductors:61

D=

k BT µ e

(11)

where kB is the Boltzmann constant. The mobility in a specific direction can be further described by

µ=e

τc

(12)

m*

where τc is the collision time of the charge carrier and m* is the effective mass. The criterion for good mobility under ambient condition is considered to be m* < 0.5me (e for electron).61 As mentioned previously, the electronic structure predominantly determines the effective masses and thus the mobility and diffusion coefficient. Practically, the resistivity, charge carrier concentration and resultant mobility of the semiconductors can be measured by using the van der Pauw technique with Hall measurements,86,87 although this method is better when using a highquality semiconductor slab. If there is no potential gradient, free carriers are transferred via diffusion, which is a very inefficient form of carrier transport. The minority carrier diffusion length can be as short as a few nm, but only when the carrier lifetime is on the order of picoseconds. Therefore, movement of free charge carriers must be adequately guided by potential gradients, generating drift current. Such gradients can be made by effective utilization of metalsemiconductor,

semiconductor-electrolyte,

and

semiconductor-semiconductor

interfaces

including surface modifications.85 The decoration of the surfaces of semiconductors causes several effects: the reduction of surface recombination; the introduction of potential gradient; and modification with catalytic components.


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At the metal-semiconductor interface, the key parameters that control the energy level are the work function of the metal and the Fermi level of the semiconductor,46 which may result in a Schottky barrier or ohmic contact, depending on their relative positions and the carrier concentrations. For details, please refer to, e.g., the work of Tung.88 In the literature,89 barrier heights at semiconductor-metal interface were correlated with electronegativity of metal and nature of semiconductor, either ionic (Si, Ge, etc.) or covalent (oxides, like TiO2, SrTiO3, etc.). Figure 6 shows representative interesting trends of barrier heights, ϕBn0, for various metals and semiconductors. An index, “S”, the slope of Figure 6A, gives sensitivity of electronegativity of metal, XM, to the barrier heights. Relatively small S for ionic semiconductors shows that barrier heights are insensitive to electronegativity (or workfunction) of metals, whereas large S for covalent semiconductors indicate they are more sensitive to the difference between Fermi level of semiconductor and metal workfunction. Ohmic contacts have been reported for various combinations of semiconductor and metals and metal alloys.89 Such smooth contacts may improve efficiency by bridging excited electrons to electrocatalysts. Practically, Ti is commonly used as a contact layer for p-Si,91 and Ti and Ta are used for some covalent materials, such as SrTiO392 and LaTiO2N.93 For an unique case, the Cu2O photocathode achieved high photocathodic current when successive deposition of ZnO:Al and TiO2 before Pt catalyst deposition.94 Powder semiconductor seem to be more challenging to achieve this type of decoration in nanoscale, so the establishing technique that allow to develop the smooth contact may lead to high efficiency. At the semiconductor-electrolyte interface,95,96 the Fermi level of the semiconductor and the reduction potential of the solution play a crucial role in determining potential gradient. A successful application of the solid-electrolyte interfaces is the dye-sensitized solar cell, where


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TiO2 collects excited electrons to its conduction band from the dyes anchored to its surface.97 A key to avoid charge recombination is a band bending of TiO2, guiding the injected electrons to its back contact.74 Similarly, photocatalyst surface will experience the band bending when immersed in water. Solving the Poisson equation to x-direction (eq. 13) leads to description of band bending, and this space charge layer should be utilized to achieve effective charge separation.67 d 2Φ x eN =− D 2 dx ε 0ε r

(13)

where Φx is the potential as a function of x, ND is the majority carrier density, ε0 is the static permittivity in vacuum, εr is the static relative permittivity or dielectric constant of the semiconductor. The key parameters in determining the space charge layer are the carrier concentration and the dielectric constant of the semiconductor. The electrolyte is strongly influenced by the surface state and potential-determining ions at the surface.98 In water, the isoelectric point of the semiconductor provides a useful indication of whether the surface is negatively or positively charged.99 Semiconductor-semiconductor interfaces can form p-n junctions, but the details regarding this process are described elsewhere.67 The consequence of potential gradients at interfaces account for the photovoltage: the origin of emf of the electrocatalysts, determining primary efficiency of the photocatalytic system. It is emphasized that the bandgap is not equivalent with the photovoltage; substantial potential losses are expected at surfaces and other interfaces. The Si bandgap of 1.1 eV typically gives an opencircuit voltage or photovoltage gain of only 0.7 eV (~40 % loss) in photovoltaic system.100 Therefore, reporting the bandgap is not likely to be sufficient in further understanding photocatalytic processes and material properties. At the same time, band alignment of various materials is a good start to discuss: however, the Fermi level equilibration between two materials


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(p-n or n-n junctions with type I and II alignments, etc.) does not result in smooth interface, which is strongly influenced by lattice match, impurities, degree of atom diffusion in mutual phases at interface (related to annealing). At this moment, there seems only empirical choices to achieve least-barrier interface for most cases, but in the case of simplified bulk semiconductor, there is a theory to predict the electronic structure, which certainly helps the guideline for material design.101-106 Simplified two-dimensional numerical modeling, a widely known calculation in solar cell community, is able to describe potential gradients inside the semiconductor using classical semiconductor device equations.39,107 These simulations can provide reasonable estimates of quantum efficiency and STH efficiency as a function of wavelength. The quantification of several parameters, i.e., absorption coefficient, band positions, dielectric constant, carrier concentrations, effective masses, mobility, and lifetime, has been discussed thus far. The beauty of this modeling is that the sensitivity of the fundamental parameters can be investigated and the properties that are most influential in determining the overall photocatalytic efficiencies can be identified, i.e., modeling brings us one step closer to “photocatalysis by design”. The overpotentials that are required for HER and OER on the surface are input variables (future work is required to make them outputs of the modeling) in this approach,107 and the diffusion-drift current equation can be solved using generation and recombination rates when the system is under steady-state illumination. In this way, the influence of the metal dispersion on the photocatalytic performance can also be evaluated.99 For many of the equations that are involved in the estimation of photovoltaic currents, the readers are referred to previous studies.25,107 A scheme in Figure 7 shows how the potential gradient close to HER electrocatalyst on an ntype semiconductor under steady-state illumination may look in the bulk of the semiconductor


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when carrier concentrations, carrier lifetimes and carrier mobilities are varied.107 The semiconductor surface was decorated with HER catalyst particle that collects excited electrons, assuming ohmic contact at the interface. The photocatalyst surface was designed to oxidize water, where Schottky contact with electrolyte was assumed. On the photocatalyst surface (left side of Figure 7A), it was assumed that substantial potential gradient exists between HER catalyst and semiconductor bare surface to achieve overall water splitting (1.53 eV). In Figure 7B, excited electrons should flow from right (semiconductor bulk) to left (surface) and downwards, following the slope generated at the semiconductor-electrolyte interface. At high carrier concentrations, a substantial energy barrier (peak), related to the so-called pinch-off effect,88 was observed close to the surface, even if ohmic contact was assumed. On the other hand, lower carrier concentrations result in gradual slopes that guide the excited electron to the left side of the HER catalyst. This observation coincides with finding resultant larger AQE and STH efficiencies at lower carrier concentrations. This type of modeling certainly helps determining the properties that should be targeted to improve overall performance; e.g., the carrier lifetime should be greater than hundreds of picoseconds, etc. Similar simulations suggest that using defective materials, such as dispersions (in particle size and density) of metal nanoparticles, on semiconductor absorbers does not significantly influence efficiency, although a metal catalyst is essential in achieving effective charge separation.107 This result suggests that even though photocatalytic efficiency remains the same, the turnover frequency (TOF; e.g., rate per surface metal site) varies with different electrocatalyst dispersions.23 This variation is because, in this case, charge separation efficiency determines overall efficiency, and electrocatalysts only consume carriers as they arrive. The potential, determined as a consequence of charge separation, is different for each particle, and the current


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(rate) per particle is also thus different; i.e., photocatalysts are electrocatalysts, so the rate (current) is based on the potential.23 A smaller particle, or greater surface area, does not necessarily result in the best overall STH efficiency, and moreover, a high TOF does not always lead to high photocatalytic efficiency of the entire system. On contrary, it is expected that high exciton binding energy materials may only require high dispersion of catalyst to create more number/density of interfaces. As a result, the modeling provides guidance whether photocatalyst properties should be altered or the identity or dispersion of the electrocatalyst should be improved, which is another step forward to “photocatalysis by design”. As seen above, a quantitative description of such optoelectronic properties can be used to estimate theoretical photocatalytic efficiency in ideal semiconductor situations. It gives, at minimum, a good estimate whether the improvement of a semiconductor (including its interface) or an electrocatalyst should be investigated and even which specific parameters should be altered, such as minority carrier concentrations or the catalyst dispersion on the surface.23 It also may allow researchers to consider the potential loss associated at the interfaces. There are measurement techniques that can be used to estimate the potential drop at the (oxy)hydroxide layer on semiconductor surfaces.108-112 It is already effective to simply isolate bare photocatalyst surface from the water electrolyte, e.g., by using some oxide (e.g., SiO2, Al2O3, or TiO2), thus avoiding the surface state and the photocorrosion that is prevalent in some semiconductor compounds.91,94,113-115 However, precisely describing the potential at the interface is still under development. For example, the classic model fails to describe realistic porous ion-permeable electrocatalysts (i.e., oxyhydroxide cocatalysts for water oxidation). Classical semiconductor equations are applicable to bulk materials (the smallest particle size in the COMSOL model used above was 100 nm).107 The smaller particles have a higher specific surface area, a shorter travel


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distance to the surface for their charge carriers, a lower degree of band bending, and, possibly, a wider band gap because of quantum size effects.83 Substantial efforts on efficient interfacial development have been made, especially in photoelectrochemistry applications, and one may refer to a recent excellent review by Li and co-workers on this topic.116 Nevertheless, diffusion and drift remain fundamental principles that describe carrier transport from the bulk to the surface. Simple simulations, as described above, already predict a substantial loss in the potential gradient at the surface. Successfully incorporating anisotropy in electronic structures of crystals by a simple manner (simpler than conventional fabrication of a p-n junction) is the way to make photocatalysts more efficient and cheaper.83 Other directions may include preventing electrolyte junctions from inducing surface recombination as well as improving the majority carrier pathway, e.g., by using a metal-insulator-semiconductor-type junction or a carefully embedded buried-junction active-site that is electronically isolated from environmental effects.117,118 Paradoxically, an approach to insulating a semiconductor from solution is by actually minimizing the beneficial possible utilization of band bending at solid-liquid interfaces. Unlike photoelectrochemical measurement, photocatalysis using powder photon absorber cannot apply external electric field: i.e., the electrons and holes must find their own way to lead to electrocatalysts. A breakthrough to boost the photoconversion efficiency resides in unique establishment of the interface bridging photon absorber and electrocatalyst. Electrocatalytic activity: The climax of the water-splitting reaction finishes with the successful consumption of the photogenerated charge carriers by electrochemical redox reactions. The mismatch between the time scales of charge transfer and electrocatalysis causes accumulation of electrons/holes at their respective redox-active species at the surface, resulting in potential shifts (transient charge up) on metal or metal (oxy)hydroxide particles or, in some cases, the


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photocatalyst surface itself, as a catalyst component.REF Measurements of such potential shifts were reported for metal particles by using probe molecules under illumination.119-123 and for metal (hydr)oxides using electrochemical techniques.109-112 At given potentials, the catalysts should electrocatalyze HER and OER, respectively; the performances of these reactions can be separately measured by using electrochemical techniques that can determine the exact values of applied potentials.1 Electrocatalysis is another unique interface event:124 The reaction proceeds on the catalyst surface atoms together with electrolyte within a double-layer region where at least three-water-equivalent ions/molecules are involved in covalent and non-covalent nature. This requires consideration of not only inner Helmholtz layer but outer Helmholtz layer to describe, e.g., transition states, which means that counter “supporting ions” play significant role in electrocatalytic kinetics.125 It is tremendously difficult, if not possible, to precisely describe the chemical potentials at double-layer region,126 but various efforts are ongoing as electrocatalysis is indeed a core technology to convert renewable energy resources to useful chemical forms.5 Electrocatalytic water splitting itself is a field of study in which many efforts are currently ongoing. Electrocatalytic activity can be ranked using the quantitative values of the exchange current of a given catalyst, i0, and the transfer coefficient, α, which are described by the Tafel equation when the reverse reaction is neglected (Eq. 11);1 however, the terms of these extracted values are still ambiguous due to the lack of a method that can precisely determine active surface areas.

α nF ( Ecat − E 0 ) i0 r= exp , nF RT

(14)

where n is the number of electrons involved in the reaction, F is the Faraday constant, Ecat and E0 are the Fermi level of the catalyst and the redox potential in solution, respectively, R is the universal gas constant, and T is the absolute temperature. The overpotential is defined as the


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difference between Ecat and E0, an additional voltage required (relative to the thermodynamic potential) to drive the respective redox reaction. Microkinetic Tafel analysis for water redox chemistries has been reviewed elsewhere.127 Key aspects of the fundamental study of HERs and OERs include finding descriptors of electrocatalytic activity. Based on Sabatier’s principle, metal-hydrogen bond strengths characterize the HER exchange current density.127,128 Generally, the OER catalyst is also characterized by using the metal-oxygen bond strength as a descriptor, because a linear relationship exists among metal-oxygen, metal-hydroxide and metaloxyhydroxide bond strengths, all of which may be involved in the rate-determining steps.129-131 When acidic conditions are chosen, the development of a non-noble metal electrodes with acid tolerance is required. The recent development of metal phosphide materials is of significant interest because they contain only abundant transition metals, such as Ni, Fe, and Co.132-134 For OERs, mixed oxyhydroxides,135 such as nickel-iron,136,137 perovskites,138 and spinels139 have also been reported as low overpotential electrocatalysts in alkaline conditions that do not use noble metals. One must remember that for industrial applications, catalyst durability is often more important than catalytic performance.9 “Self-healing” capability, i.e., dissolution-redeposit process of the electrocatalyst during electro- and photocatalysis is a compelling method to achieve long-term durability.140-144 Additionally, the temperature of the solution in a practical photoreactor may be substantially higher than room temperature because the photoreactor may absorb infrared irradiation; this factor should be considered in experiments regarding activation energy. Ironically, high activation energies lead to a highly sensitive current increase with temperature changes, resulting in excellent performance under certain relevant water-splitting conditions (e.g., 10 mA cm−2 at mild pH for Ni vs. NiFe OER catalysts)144 or enthalpy-entropy compensations (e.g., in the case of HER at mild pH for Pt, Ni, NiCu, etc.).145


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One of the unique features of photocatalysis is that the photon absorber materials are not stable under extreme pH conditions (acidic or alkaline), which is the regime in which commercial electrolyzers are operated.146 Interestingly, pure water without any supporting electrolyte can be used in overall water splitting with a powder semiconductor photocatalyst147,148 because of the very short distance between the HER (cathode) and the OER (anode), which should occur on the same surface with minimum solution resistance. Electrochemistry is a powerful tool to quantitatively evaluate reactions under near-neutral (or mild) pH conditions.146 The impact of pH on these reactions will be discussed in greater detail later. In short, one must first identify the “reactants” of respective redox reactions: pH change will cause “reactant switching” at a given current level, which is associated with the diffusion contribution.149 In general, hydronium ions (protons) are more easily reduced than water molecules,149 and hydroxyl ions are more readily oxidized than water molecules.146 One critical note is that the “water-splitting” reaction rather paradoxically does not prefer water molecules to be its reactant.146,149 This preference results from the fact that water molecules contain very strong O-H bonds (as is also obvious from the fact that H2O is one of the most thermodynamically stable compounds). To facilitate the water molecule dissociation, anisotropic sites on the surface are effective for heterolytic dissociation of water molecules. For example, in alkaline conditions, Markovic and co-workers reported that islands of nickel or cobalt species on noble metal surfaces (such as Pt) further enhance both HERs and OERs.150 Knowledge obtained by electrocatalytic studies should be successfully transferred to the photocatalytic studies. In any case, electrocatalysis should catch up with current flow from the electrons and holes that are generated in the semiconductor underneath. It is obvious that small potential shifts should trigger the corresponding current flow, and excellent electrocatalysts are


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thus preferred as efficient photocatalysis.52 An excellent example is rough CoOx modification on n-Si photoanode, where almost full utilization of the generated photovoltage was achieved for OER by CoOx under illumination.151 If there is difference in “ranking” electrocatalyst materials during photocatalysis and pure electrocatalysis, it arises from different degrees of potential shifts at the catalyst/semiconductor interfaces, causing the electrocatalysts to not experience the same potentials due to, e.g., different degree of Schottky contact and barrier height, as discussed above, Figure 6.52 On contrary approach, if the kinetics of electrocatalysts for HER and OER require substantial overpotentials (e.g., overvoltage of ~2.0 V), the required bandgap to maximize theoretical STH efficiency essentially becomes larger; the best scenario as large as ~2.4 eV, thus never reaching 10% STH benchmarking efficiency.153 Excellent activity of electrocatalysts that are optically transparent is desired. To achieve efficient overall water splitting in a membrane-less configuration, as Gerischer stated in his early work,85 the suppression of the back reactions of H2 and O2 to form H2O must be suppressed. Noble metals, in particular, are generally excellent HER catalysts but also typically catalyze the back reaction either thermally or electrocatalytically (oxygen reduction reaction).154,155 Successful suppression with nanometer-scale decorations on such electrocatalyst surfaces (core@shell structure) have been reported and use chromium,156,157 molybdenum,158 titanium,159 and lanthanoids,160 as shells. The amorphous structure of very small hydrated clusters makes the materials function as a selective membrane that is not permeable to dissolved gases (including O2), thus preventing back reactions.156,158 There is a possibility to utilize this functionality to protect the surface from poisoning because this membrane function also insulates various redox-active species.157 Development of shell materials that make the OER catalyst selective is also ongoing.


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It is interesting to note that overall photocatalytic efficiency may be further improved by having better HER or OER electrocatalysts under all conditions. Based on this charge-up theory, enhancements in the rate of reduction or oxidation improve the overall efficiency of water splitting, which is determined by the photon flux and the efficiency of carrier transport from the photocatalyst to the redox catalysts because accelerated electron or hole processes affect the potential, which in turn perturbs the rates of the process on the opposite side.161 Because electron and hole transport are parallel reactions, the overall photocatalysis process does not have a single rate-determining step unlike the case of half-reaction electrocatalysis).44,161 In other words, further improvement for electron consumption (HER) or hole consumption (OER) should improve overall efficiencies. Fast consumption of electrons will cause hole accumulation on the OER side, further enhancing the overall rate, or vice versa.162,163 It is also effective to analyze the sensitivity of HER or OER performance to overall photocatalysis performance, which can be evaluated using photocatalysis with isotope effects44 or effectively comparing electrocatalytic reactions under dark conditions.164 Mass transfer (ion diffusion): After decades of studying photocatalysis for water splitting, the efficiency of this process has been tremendously improved.165 The primary focus of photosynthetic reactions is still based on managing photons in the bulk and on the surfaces of photon absorber materials, as mentioned previously. The research in this field has therefore been largely oriented by the synthesis of efficient photon absorber materials, including their electrocatalyst decorations. Nevertheless, when reaching commercially viable efficiency is considered, the mass transfer of reactants and ions in addition to solution resistance can no longer be ignored during electrocatalysis or photocatalysis.150 Much research is focused on systems that work at room temperature, and under such conditions, it is often the case that the


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diffusion of ions contributes to the overall efficiency by creating a concentration overpotential; an additional loss originates from the depletion of reactants. This is certainly the case when photocatalytic remediation of low-concentration substances is the target reaction.12 The rigorous and quantitative determination of parameters in such a process is essentially possible using the thermodynamic and kinetic information that can be generated using electrochemistry. At a given current, sources of potentials are classified into kinetic overpotential (dependent on catalyst), concentration overpotential (independent of catalyst), and solution resistance. The contributions of the concentration overpotential and solution resistance can be quantitatively obtained by using the physical properties of the solution. Detailed quantification and methodology was reviewed in previous literature. Mass transport phenomena in electrochemistry are described by the Nernst-Planck equation with terms for (in this order) diffusion, migration and convection (for species i in the x-direction):1 J i ( x ) = − Di

∂ai ( x ) zi F ∂φ ( x ) − Di ai − ai v ( x ) ∂x RT ∂x

(15)

where J is the flux, D is the diffusion coefficient, z is the charge number and v is the velocity of the forces in the solution.1 The Stokes-Einstein model gives the diffusion coefficient as D=

kT 3π d µ

(16)

where k is the Boltzmann constant, d is the effective diameter of the ion in the hydrated form (Stokes diameter) and µ is the viscosity of the solution.166 Therefore, the parameters governing mass transport flux are the effective size of the species, viscosity of the solution, and activity (or fugacity) of the species. Moreover, solubility of dissolved gases, another quantifiable parameter, is greatly influenced by the identity and molarity of the supporting electrolyte, which correlates with reverse reaction of products going back to water, or hydrogen oxidation reaction (HOR) and


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oxygen reduction reaction (ORR).167 These physical properties can be obtained separately, often from a database,168 and the contribution of mass transport is thus quantifiable. Under relevant reaction conditions, the benchmark STH efficiency of 10% corresponds to a hydrogen production rate of ~154 µmol H2 cm−2 h−1 and a corresponding current of ~8.3 mA cm−2 (assuming that a single semiconductor (or tandem semiconductors) is achieving the overall water splitting). Under static conditions (no convection) at 25 °C, even hydronium (proton) and hydroxide ions can face diffusion-limiting currents, causing “reactant switching”: pH values of ~1.6 or lower (for hydronium ion) and ~12.3 or higher (for hydroxide ion) are necessary in unbuffered conditions. Outside this range of pH (unbuffered, near-neutral pH), reactant switching between H+ (HER) and OH− (OER) to H2O must occur, causing additional kinetic overpotential.150 Obviously, this activity of the reactants, together with minimized solution resistance, is one reason why extreme pH conditions are chosen for the electrolysis of water. In addition, the HER causes an increase in the pH, and the OER causes a decrease in the pH, so the complete isolation of ions in a two-compartment cell will lead to a high concentration overpotential (shifting the thermodynamic potential by 59 mV pH−1), which causes additional loss of overall efficiency. The use of an ion-exchangeable membrane is mandatory to separate H2 and O2 while minimizing these concentration overpotentials.169 Nafion or an alkaline membrane typically works in media with extreme pH,170 although some membranes that may be used as neutral pH values have been recently developed.171 One of the most significant benefits of coproducing an H2/O2 mixture is avoiding the use of membranes and minimizing solution resistance and the pH gradient, i.e., the concentration overpotential.169 However, this process occurs at the expense of producing an explosive gas mixture (H2 and O2).169


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Near-neutral pH conditions makes it possible to use many materials for stable photocatalytic water splitting. Under neutral pH conditions, buffering ions are commonly used to maintain local pH values by utilizing their buffering action.172 In addition to the role of the supporting electrolyte in minimizing solution resistance (iR drop), the buffer ions significantly influence electrocatalysis. The buffer’s counter anion is a carrier for H+ and thus plays a role in transporting the H+ reactant to cathode or abstracting the H+ products from the anode.173-175 At relevant current densities and under ambient conditions, the diffusion of buffer ions may therefore result in substantial concentration overpotentials. For example, using an excellent catalyst, such as Pt, for HER in NaH2PO4, the optimum buffer concentrations for the HER appear to be as high as 1.5-2.0 M at 25 °C.174 It has also been recently determined that some OER catalysts also suffer from concentration overpotentials, or mass-transfer limitation of buffering ions, which can be seen because the rotating-disk electrode current depends on its rotation rate.174 This fact is often neglected in the photocatalysis and photoelectrochemistry community. Another interesting consideration of the activity of the reactants is the use of water vapor as a reactant (liquid water vs. water vapor). Using vapor-phase water has advantages such as the ability to easily control its supply and the use of simple reactor designs, e.g., a fixed bed for powder systems.175 However, using water vapor as a reactant encounters considerable difficulties due to an additional term for the adsorption of water vapor at low partial pressures, which may strongly decrease the overall efficiency. In contrast, using liquid-phase water (close to unity) or the associated ions (H+ or OH−) as reactants can result in high activities, effectively utilizing the electric field applied at the double-layer region. In static photoelectrochemical water splitting, high efficiency (currents) of photoelectrodes leads to additional efficiency loss due to the generated gas bubbles blocking the surface. It was


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reported that hydrophilic surface is preferred to detach the generated bubbles, which was also confirmed by the fact that introduction of surfactant was thus effective to remove gas bubbles. Contact angle at gas-surface interface is known to be correlated, but the details can be found elsewhere. For photocatalyst powder systems, the gas bubble problems seem absent in the literature, yet probably because of low efficiency of the powder suspension system. Since the photocatalytic performance is being improved, one must consider the final form of photocatalyst samples, whether they should be immobilized in which substrates, and types of convective flow of liquids. Associated with this, the temperature of the reactant water may be considered, which impact not only catalytic rates but also the mass transport which also has activation energy with Arrhenius relation. Discussion and perspectives This contribution identified a number of quantifiable parameters associated with the complex processes that occur during photocatalytic water splitting. The processes are sequentially and often coherently connected in the following order and operate at different time scales as the following six-gear concept as shown in Figure 2. These parameters and relevant useful information are summarized in Table 1. Strategy should be adequately planned to investigate photocatalytic materials and reactions. In photoelectrochemical water splitting study, there are some suggested guidelines in the literature,176 which are also useful for investigating photocatalytic water splitting as many phenomena function in common principles. Most of the constants and the quantifiable variables are listed in Table 2. By identifying these “quantities”, one may predict efficiencies using various established equations and thus help directing the researches. For further details regarding the equations, the readers are referred to previous reviews for semiconductor study,25,107,177 and electrochemistry study,173 and literature cited


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therein. One may want to check the absorption coefficient (Gear 1), especially close to band edges, the exciton binding energy (Gear 2) and carrier lifetime (Gear 3). Next is to describe carrier diffusion (Gear 3) and transport (Gear 4). In simple cases, simulation can currently estimate maximum photocatalytic quantum efficiencies based on the quantified values of bulk semiconductor parameters. This will be the first assessment whether the bulk semiconductor properties should be ever suitable for efficient photocatalysis. The guidance obtained is whether the material itself should be altered, the synthesis protocol should be improved (crystallinity), or electrocatalyst decoration should be improved in terms of dispersion and loading, etc. In a typical example, Si is widely available already in a commercial scale, and, upon purchasing, many parameters mentioned in the first part (Gears 1-4) are effectively quantified. Si wafers are commercially available with known dopant concentration and conductivity/resistivity. A µm-order diffusion length is accordingly obtainable, so the strategy is to focus on the further improvement in optical enhancement and surface charge separation with dispersed catalyst decoration. A deconvolution of such properties (including Gear 4-6) for 3D structure p-Si photocathode was well reported by Esposito and co-workers.178 On contrary, for another example, non-oxide materials, such as Ta3N5 used as a visible-light-responsive photocatalyst, have many parameters unknown and remain uncertainties to the semiconductor properties. Such quantities of the parameters were summarized in the literature for Ta3N5.179 This type of (oxy)nitride materials is synthesized at each laboratory usually via nitridation of oxide precursors in NH3 flow at high temperatures. Non-stoichiometry due to remaining oxygen as well as anion vacancy associated with Ta5+ reduction to Ta3+ in the bulk structure is also recognized.180 From the literature, despite the efforts for the surface alteration and catalyst decoration essential to enhance photocatalytic performance, there remain a lot to do to improve bulk properties and


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improve carrier lifetimes.107 Diffusion lengths can be as short as a few nm when carrier trapping of Ta3N5 happens in a picosecond-order181,182 (although a part of carriers that have longer lifetimes was also reported for Ta3N5).183,184 It is still important that the synthesis protocol should be improved for prolong carrier lifetime and resultant diffusion lengths; e.g., flux-assisted protocols for improved crystallinity. It is also time to thoroughly discuss the actual reaction conditions with practical reactor design for photocatalysis (pressure, temperature, activity, etc.),185-189 because they will affect the photovoltage, electrocatalytic kinetics, and the diffusion of ions, etc. As a result, the performance/durability ranking of photocatalytic/electrocatalytic materials may be different from investigations at room temperature under low pressures. Accordingly, the era has come for solar fuel production study to seriously consider the practical photoreactor design together with reaction conditions.186 At a photoreactor in large scale application under solar irradiation, temperature may substantially rise by design, which may be beneficial because many photocatalytic systems are reported to have positive activation energy,11 and kinetic isotope effects from D2O experiments;189,190 i.e., surface electrocatalysis may be sluggish enough to influence overall efficiency. It is desired to maintain small density and high dispersion of the catalysts on the photon absorber not to absorb photons by the catalysts themselves. Such small quantities of the catalysts, especially when the efficiency is improved, prefers high temperature to catch up the electrocatalysis. Choice of materials should also be conducted based on durability and robustness of the photocatalyst materials under the operational reaction conditions. This contribution may serve as a set of guidelines to help identify the kinetic bottleneck with “quantities” that limit the overall efficiency of photocatalysis and to help intentionally improve specific properties: steps forward toward “photocatalysis by design” concept. Finally, the


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concepts shown here are not limited to this reaction and may be applied to, e.g., photocatalytic CO2 reduction or even environmental remediation. To jump to a commercial level of photocatalytic efficiency, consolidated efforts to achieve commercial solar energy conversion processes based on an understanding at the microscopic and macroscopic levels should be made.

AUTHOR INFORMATION Corresponding Author * Kazuhiro Takanabe, email: [email protected] ACKNOWLEDGMENT The research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST). The author appreciates Dr. Angel T. Garcia-Esparza for thorough discussion on simulation data related to Figure 7. REFERENCES (1) Electrochemical methods, 2nd Ed.; Bard, A. J.; Faulkner L. R., Eds.; John Wiley & Sons, Inc.: Danvers, 2001; pp 736-768. (2) Kraeutler, B.; Bard, A. J. J. Am. Chem. Soc. 1978, 100, 2239-2240. (3) Calvo, E. J. In Electrode kinetics: principles and methodology, Bamford, C. H.; Tipper, C. F. H.; Compton R. G., Eds.; Elsevier: Amsterdam, 1986; Vol. 26, pp. 1-74. (4) Shaner, M. R.; Atwater, H. A.; Lewis, N. S.; McFarland, E. W. Energy Environ. Sci. 2016, 9, 2354-2371. (5) Lewis, N. S. Science 2016, 351, aad1920. (6) Nakamura, A.; Ota, Y.; Koike, K.; Hidaka, Y.; Nishioka, K.; Sugiyama, M.; Fujii, K Appl. Phys. Express 2015, 8, 107101. (7) Khaselev, O.; Turner, J. A. Science, 1998, 280, 425-427. (8) Nocera, D. G. Acc. Chem. Res. 2012, 45, 767-776.


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(9) Sun, K.; Saadi, F. H., Lichterman, M. F.; Hale, W. G.; Wang, H.-P.; Zhou, X.; Plymale, N. T.; Omelchenko, S. T.; He, J.-H; Papadantonakis, K. M.; Brunschwig, B. S.; Lewis, N. S. Proc. Nat. Am. Sci. 2015, 112, 3612-3617. (10) Kageshima, Y.; Shinagawa, T.; Kuwata, T.; Nakata, J.; Minegishi, T.; Takanabe, K.; Domen, K. Sci. Rep. 2016, 6, 24633. (11) Wang, Q.; Hisatomi, T.; Jia, Q.; Tokudome, H.; Zhong, M.; Wang, C.; Pan, Z; Takata, T.; Nakabayashi, M.; Shibata, N.; Li, Y.; Sharp, I. D.; Kudo, A.; Yamada, T.; Domen, K. Nat. Mater. 2016, 15, 611-615. (12) Osterloh, F. E. ACS Energy Lett. 2017, 2, 445-453. (13) Mills, A.; Wang, J. J. Photochem. Photobio. A 1999, 127, 123-134. (14) Yang, X.; Ohno, T.; Nishijima, K.; Abe, R.; Ohtani, B. Chem. Phys. Lett. 2006, 429, 606610. (15) Ohtani, B. Chem. Lett. 2008, 37, 217-229. (16) Mills, A Appl. Catal. B 2012, 128, 144-149. (17) Kisch, H. Angew. Chem. Int. Ed. 2013, 52, 812-847. (18) Schanze, K. S.; Kamat, P. V.; Buriak, J. M. ACS Appl. Mater. Interfaces. 2014, 6, 1181511816. (19) Buriak, J. M. Chem. Mater. 2014, 26, 2211-2213. (20) Bahnemann, D.; Kisch, H. J. Phys. Chem. Lett. 2015, 6, 1907-1910. (21) Coridan, R. H.; Nielander A. C.; Francis, S. A; McDowell, M. T.; Dix, V.; Chatman, S. M; Lewis, N. S. Energy Environ. Sci. 2015, 8, 2886-2901. (22) Buriak, J. M.; Jones, C. W.; Kamat, P. V.; Schanze, K. S.; Schatz, G. C.; Scholes, G. D.; Weiss, P. S. Chem. Mater., 2016, 28, 3525-3526. (23) Qureshi, M.; Takanabe, K. Chem. Mater. 2017, 29, 158-167. (24) Takanabe, K.; Domen, K. ChemCatChem 2012, 4, 1485-1497. (25) Takanabe, K. Top. Curr. Chem. 2016, 371, 73-103. (26) Nozik, A. J. Ann. Rev. Phys. Chem. 1978, 29, 189-222. (27) Nosaka, Y.; Ishizuka, Y.; Miyama, H. Ber. Bunsenges. Phys. Chem. 1986, 90, 1199-1204. (28) Memming, R. Top. Curr. Chem. 1988, 143, 79-112. (29) Hagfeldt, A.; Grätzel, M. Chem. Rev. 1995, 95, 49-68.


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Figure 1. Schematic image of the photocatalytic water splitting process. The gear with the number indicates the order of the photocatalytic process to be successful for overall water splitting. For detailed description, please refer to the text.


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Figure 2. Parameters associated with photocatalysis. Overall water splitting is only successful for high efficiencies of all six gears depicted in the scheme. The different timescales of the reactions are also displayed.


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Figure 3. Bandgap structure of oxide and oxynitride semiconductors for photoelectrochemical applications. Contribution of metal cation and oxygen anion states to the conduction and valence bands. The bandgap energy (red for n-type, black for p-type) is shown with respect to the reversible hydrogen electrode and the water redox energy levels (assuming Nernstian behavior four the band-edge energies with respect to electrolyte pH). Reprinted, with permission, from ref 45.


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Figure 4. (A) Hole and (B) electron lifetimes in heavily doped n-type and p-type silicon, respectively. Reprinted, with permission, from ref 75.


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Figure 5. Rough estimation of the ratios of the numbers between the active surface sites (assuming ~4 nm−2 hydroxylated surface as maximum)82 to the bulk carrier. The cubic particle of 100 nm diameter is used as an example.


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Figure 6. (A) Barrier height versus electronegativity of metals deposited on Si, GaSe, and SiO2. (B) Index of interface behavior S as a function of the electronegativity difference of the semiconductors. Reprinted, with permission from ref. 89.


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Figure 7. (A) Geometric model schemes using n-type semiconductor with HER catalyst decoration with the boundary conditions and the assumptions used for the simulations. (B) Potential gradients under the HER catalyst (red dotted line in A) at different donor concentration, carrier mobility, and carrier lifetime. The x-direction represents the depth from surface (left) into the bulk (right) of the semiconductor. An ohmic junction was assumed for the HER catalyst in contact with the semiconductor, whereas a Schottky contact was assumed to calculate the electrolyte interface. The potential difference between HER site and OER site is assumed to be 1.53 eV. Reprinted, with permission, from ref 107.


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Table 1 List of events, parameters, variables, relevant theories and useful characterization techniques for photocatalysis investigation Events

Parameters/ variables

Theory

Characterization techniques

1. Photon absorption

Absorptance / Reflectance / Scattering Absorption coefficient Absorption depth Density of state Effective mass Dielectric constant / dielectric loss Refractive index Exciton binding energy

Franck-Condon principle Lambert-Beer’s law Electromagnetic wave propagation Maxwell Curl equations Electrostatic force Mott-Wannier type Frenkel type

X-ray diffraction UV-VIS-NIR spectroscopy Spectroradiometer

Carrier mobility Diffusion coefficient Carrier lifetime Carrier diffusion length Carrier concentrations Charge recombination kinetics Electric field Drift current Depletion layer width Flatband potential / workfunction / redox potential (potential determining ion) Barrier height Fermi level pinning Density of surface states Kinetics of charge transfer and recombination Exchange current density (charge transfer resistance) Charge/electron transfer coefficient Conductivity Tafel slope Activation energy Diffusion coefficient (ion size viscosity activity coefficient) Solution resistance

Recombination models (srh, Auger) Poisson equation Drift and diffusion equations Continuity equations Boltzmann transport equation Semiconductor devices equations Einstein relation Mott-Schottky analysis Schottky/ohmic contact

2. Exciton separation

3. Carrier diffusion

4. Carrier transport

5. Electrochemistry

6. Mass transfer

Other parameters / variables and characterization techniques

Transient absorption spectroscopy Photoemission spectroscopy optical absorption spectroscopy photoconductivity screening potential spectroscopy magneto-optical spectroscopy van der Pauw technique with Hall measurement Time resolved spectroscopy THz and microwave spectroscopies

Conductivity measurement Photoemission spectroscopy (in air) Ultraviolet photoemission spectroscopy Electrochemistry (aqueous non-aqueous) Intensity modulated photocurrent/photovoltage spectroscopy Ambient pressure X-ray photoelectron spectroscopy

Butler-Volmer analysis Tafel equation

Voltammetry, Tafel analysis Impedance spectroscopy

Nernst-Planck-Poisson equation Fick's law Einstein-Smoluchowski equation Cottrell / Koutechy-Levich equation

Koutechy-Levich analysis Viscometer pH meter Conductivity/ impedance Scanning electron microscope Transmission electron microscope X-ray diffraction X-ray photoelectron spectroscopy

Temperature Activity/fugacity (of reactant and products) Photon flux and photon distribution Durability


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Table 2 Major constants and variables involved in photocatalysis Symbol

Unit

Description

e

C

elementary charge

kB

J K−1

Boltzmann constant

h

Js

Planck constant

ε0

F m−1

vacuum permittivity

me

kg

electron mass

R

J mol−1 K−1

gas constant

F

C mol−1

Faraday constant

Constants

Variables Semiconductor equations T

K

εr(s)

temperature relative permittivity (dielectric constant) of semiconductor

n, p

m−3

electron and hole concentration

ni

m−3

intrinsic carrier concentration

n 0, p 0

m−3

quasi-equilibrium carrier density

NC, NV

m−3

effective density of states in the conduction and valence band

µ n, µ p

m2 V−1 s−1

electron and hole mobility

τn, τp

s

electron and hole lifetime

τc

s

collision time

Dn, Dp

m2 s−1

electron and hole diffusion coefficient


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L

m

diffusion length

P0

m2 s−1

photons absorbed from AM 1.5G

α(λ)

m−1

absorption coefficient

λ

m

wavelength of photon

x

m

depth into the bulk of a semiconductor

ρ

m

surface of the semiconductor

r0, rs

m

catalyst and semiconductor particle size (diameter)

χ

eV

semiconductor electron affinity

Eg

eV

band gap

EC

eV

conduction band edge

EV

eV

valence band edge

m *n, m *p A *n, A *p

effective electron and hole mass A m−2 K−2

effective Richardson constant for electrons and holes Electrochemical parameters

n

number of electrons in reaction

ai

thermodynamic activity (of species i)

γ±

activity coefficient

Di

m2 s−1

diffusion coefficient (of species i)

δ

m

diffusion layer thickness

u

m2 s−1 V−1

ion mobility

a

m

Stokes radius

µ

Pa s

viscosity of solution


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ν

m2 s−1

kinematic viscosity of solution relative permittivity (dielectric constant) of solution

εr(l) η

V

overpotential

α j0

transfer coefficient A cm−2

exchange current density

θ

surface coverage

k

(depending on elementary steps)

rate constant

A

(depending on elementary steps)

preexponential factor

Ea

kJ mol−1

activation energy


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TOC


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Photocatalytic Water Splitting: Quantitative Approaches toward

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