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Kinetic and Thermodynamic Considerations for Photocatalyst Design

Frank E. Osterloh

University of California, Department of Chemistry, One Shields Avenue, Davis, CA, 95616, USA

1.1 Introduction

Photochemical processes play a central role on Earth. While natural photosynthesis powers our biosphere and economic growth (through the use of photosynthesis-derived fossil fuels), additional photochemical processes are involved in shaping the "photogeochemistry" of our planet [1]. Light reactions play a role in the creation and function of the ozone ultraviolet (UV) filter in the atmosphere, the degradation of plant materials, man-made chemicals and plastics, and even in the chemical conversion of Earth-abundant minerals.

The potential of photochemical processes for technical applications was first demonstrated by A.E. Becquerel in 1839 when he discovered the photovoltaic effect. Interestingly, it took over a century before this knowledge was applied to practical photovoltaic cells [2]. In 1968, Gerischer's discovery of the dye sensitization effect at illuminated semiconductor surfaces [3] paved the way for Grätzel's construction of the first dye-sensitized photovoltaic cell 1991 [3] and also inspired for the production of hydrogen fuel from illuminated TiO2 photoanodes [4, 5].

Since then, the interest in photochemical reactions for environmental remediation [6-10] and for the production of sustainable fuels has gained steadily [11-17]. In 2018, over 6000 articles were published with the term photocatalytic or photocatalyst in the title. This is about 60 times as many as published on this topic in 1991 when Grätzel's dye-sensitized solar cells made headlines. In contrast, the number of papers published on photosynthesis has been relatively steady in the past three decades, with approximately 1000 publications per year.

In the science community, photochemical reaction systems are typically referred to as "photocatalysts," or as "photosynthetic systems" or sometimes as devices for "artificial photosynthesis." Interestingly, there is no strong differentiation between these terms. For example, the International Union of Pure and Applied Chemistry (IUPAC) defines a "photocatalyst" as a "Catalyst able to produce, upon absorption of light, chemical transformations of the reaction partners. The excited state of the photocatalyst repeatedly interacts with the reaction partners forming reaction intermediates and regenerates itself after each cycle of such interactions." [18] This definition makes no distinction between reactions that deposit photochemical energy in the products and reactions that do not.

According to Nozik [19] and Bard [20], excitonic reactions can be divided into photosynthetic and photocatalytic processes, depending on the thermodynamics of the associated reaction: [21].

"Photoelectrolytic cells . can be classified as photosynthetic or photocatalytic. In the former case, radiant energy provides a Gibbs energy to drive a reaction such as H2O?+?H2?+?½ O2, and electrical or thermal energy may be later recovered by allowing the reverse, spontaneous reaction to proceed. In a photocatalytic cell the photon absorption promotes a reaction with ?G?<?0 so there is no net storage of chemical energy, but the radiant energy speeds up a slow reaction." [22]

As we will show here, this distinction between photocatalytic and photosynthetic devices becomes very significant to the understanding of their function and also to their optimization. An overview of the fundamental processes in photochemical reaction systems is presented in the following sections.

1.2 Mechanistic Aspects of Photochemical Reaction Systems

Photochemical (excitonic) reaction systems generally rely on the creation and transfer of charge carriers to induce the transformation of reagents in the vicinity of the light absorber. Usually, the process begins with the absorption of one or several photons (step 1), as shown in Figure 1.1a. This generates photoelectrons and holes, which subsequently react with reagents (step 2) to produce products. These products may interact with the photocatalyst repeatedly to undergo further transformations or they may react to form the starting materials again.

A very important aspect of a photochemical reaction system is the energy balance of the overall process. Two outcomes are possible, theoretically. In the first one, the products have a greater free energy than the reagents and the Gibbs free energy change for the process is positive, ?G?>?0. An example for this kind of reaction is the photochemical water splitting reaction that produces hydrogen and oxygen. This process has a reaction free energy change of +237?kJ per mol of water, i.e. it is highly endergonic, as intended for a fuel forming reaction.

In the second outcome, the products have a lower combined Gibbs free energy content than the reagents and the overall process is exergonic, ?G?<?0. An example of the second type is the photochemical oxidation of organic matter into carbon dioxide and water, which is highly exergonic, because of the formation of CO2 (?GF = -394.4?kJ?mol-1) and H2O (?GF = -228.6?kJ?mol-1). For example, the Gibbs free energy change for the combustion of propane is -2.074?MJ?mol-1.

Figure 1.1 (a) General photochemical reaction system, including generation of photochemical charge carriers (1), electrochemical forward reactions (2), and backward (3) reactions. (b) Energetics of photochemical reactions. Source: Osterloh [23]. © 2017, American Chemical Society.

The difference in energetics for these processes has an important consequence on the design of the reaction system. If the forward process is endergonic, there is also a need to prevent the reverse thermodynamically favored reaction. This is shown in Figure 1.1b. Because the reaction products are at higher Gibbs free energy than the reagents, they may reform the starting materials, either by direct reaction or with the aid of the "photocatalyst." This limitation does not apply to exergonic processes, which cannot be reversed without additional energy input. Therefore, the ability to prevent the reverse, thermodynamically favored reaction is an important attribute of photochemical reaction systems that promote endergonic reactions.

Thus, in analogy to photoelectrochemical systems (see above), photochemical reaction systems can be classified as either photosynthetic when they promote endergonic (fuel forming) reactions or as photocatalytic when they promote exergonic, thermodynamically favored reactions. The efficiency of a fuel producing device is normally assessed with the energy efficiency of the process, i.e. the amount of photochemical energy stored in the reaction products [24]. For a photocatalytic device, on the other hand, the apparent quantum efficiency and the product selectivity are more suitable for assessing performance.

Because they have differing functions, it is expected that design of photosynthetic and photocatalytic devices will also be different. In this regard, it is useful to analyze a general photochemical process with specific emphasis of the ways for this reaction to become reversed. Let the photochemical reaction system in Figure 1.1a be that of the endergonic process I where an oxidized reagent ROX and a reduced reagent RRED are being converted into a reduced product PRED and an oxidized product POX. For natural photosynthesis, for example, ROX = CO2 and RRED = H2O and PRED = {CHOH} (sugar fragment) and POX = O2.

At a minimum, this conversion must involve steps II-IV, where step II is the absorption of one or several photons to produce one or several electrons and holes with a lifetime sufficient to react in steps III and IV. Step III uses the photoelectron to reduce ROX to PRED and step IV uses the photohole to oxidize RRED to POX.

1. (I) ROX +?RRED??PRED +?POX?G?>?0
2. (II) Cat?+?h???e- +?h+
3. (III) ROX +?e-??PRED
4. (IV) RRED +?h+??POX

After step IV, the photochemical reaction cycle can begin anew with the absorption of more photons.

Once products have been formed in sufficient quantity, the thermodynamically favored backreaction becomes increasingly favorable. It may proceed via reaction paths V-VII. If the products of the reaction are kinetically labile, they may react directly with each other to reform the original reagents, according to step V. This would be possible if the products are free radicals or radical intermediates, for example, superoxide (O2-) or...