Optimizing photocatalysts and photoreactors for solar fuel synthesis

Optimizing photocatalysts and photoreactors for solar fuel synthesis

Paul Philipp Kant

Paul Philipp Kant

Paul Philipp Kant

Optimizing photocatalysts and photoreactors for solar fuel synthesis

# Optimizing photocatalysts and photoreactors for solar fuel synthesis

by Paul Philipp Kant

Karlsruher Institut für Technologie Institut für Mikroverfahrenstechnik

Optimizing photocatalysts and photoreactors for solar fuel synthesis

Zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften von der KIT-Fakultät für Chemieingenieurwesen und Verfahrenstechnik des Karlsruher Instituts für Technologie (KIT) genehmigte Dissertation

von Paul Philipp Kant, M.Sc.

Tag der mündlichen Prüfung: 10. Juli 2023 Erstgutachter: Prof. Dr.-Ing. habil. Roland Dittmeyer Zweitgutachter: Prof. Dr.-Ing. Clemens Posten

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ISBN 978-3-7315-1323-0 DOI 10.5445/KSP/1000162450

Mein herzlicher Dank gilt all denjenigen, die mich auf meinem Weg begleitet haben, begleiten und begleiten werden.

# **Kurzzusammenfassung**

Heute bekannte Technologien zur Synthese solarer Energieträger weisen eine zu niedrige Energieeffizienz und zu hohe Kosten auf, um ökologisch und ökonomisch sinnvoll eingesetzt werden zu können. Die vorliegende Arbeit analysiert deshalb den Auslegungsprozess eines hocheffizienten fotokatalytischen Prozesses und stellt letztlich einen Versuch dar, Wege hin zu einem hocheffizienten und gleichzeitig kostengünstigen Prozess zur Herstellung von solaren Energieträgern aufzuzeigen.

Die dargestellte Analyse stellt zunächst die herausragende Wichtigkeit der optischen und reaktionstechnischen Eigenschaften der Lichtquelle, des Fotokatalysators und des Fotoreaktors im Auslegungsprozess eines hocheffizienten fotokatalytischen Prozesses dar. In dem Fall, in dem die Sonne als Lichtquelle dient, wie auch bei Prozessen zur Synthese solarer Kraftstoffe, konzentriert sich der Auslegungsprozess selbstverständlich auf das Fotokatalysatorsystem und den Fotoreaktor.

Das erste Ergebnis der vorliegenden Arbeit ist konsequenterweise ein Satz von Methoden zur optischen und reaktionstechnischen Charakterisierung von Fotokatalysatoren und Fotoreaktoren.

Von besonderer Bedeutung ist dabei das vorgestellte Konzept zur Bestimmung von Quantenausbeuten in Fotoreaktionen. Der vorgeschlagene Ansatz ermöglicht dabei eine Variation aller wichtigen Betriebsbedingungen, namentlich die Variation der Temperatur, der Konzentration der Reaktanten, der Wellenlänge und vor allem der lokalen volumetrischen Photonenabsorptionsrate. Die Quantenausbeute ist dabei von herausragender Bedeutung für den Auslegungsprozess eines hocheffizienten fotokatalytischen Prozesses.  Die Quantenausbeute und ihre Abhängigkeit von der Wellenlänge definieren damit ein absolutes Limit für die erreichbare fotokatalytische Effizienz in einem sonnenlichtbasierten fotokatalytischen Prozess.  Die Abhängigkeit der Quantenausbeute von der lokalen volumetrischen Photonenabsorptionsrate ist dabei von besonderer Bedeutung.  Die Auslegung muss darauf abzielen, zur Erreichung einer maximalen fotokatalytischen Effizienz des Gesamtprozesses, Hotspots in der lokalen Photonenabsorptionsrate im Katalysatorbett zu vermeiden.

Die Vermeidung von Hotspots in der lokalen Photonenabsorptionsrate zu vermeiden, ist jedoch nur ein Teilaspekt im Auslegungsprozess eines hocheffizienten Produktionsfotoreaktors. Zusätzlich zu dieser ersten Anforderung, muss ein hocheffizienter Produktionsfotoreaktor eine hohe Transporteffizienz für Photonen von der Fotoreaktorapertur hin zum Fotokatalysator aufweisen. Beides gleichzeitig sicherzustellen, das Ausbleiben von Hotspots in der lokalen Photonenabsorptionsrate und eine hohe Effizienz des Strahlungstransports von der Fotoreaktorapertur ins Reaktionsvolumen, ist eine substanzielle Herausforderung.   Möglich ist das durch eine geschickte Materialauswahl, das Einstellen der optischer Transporteigenschaften derselben und das Design geeigneter Fotoreaktorgeometrien. Die vorliegende Arbeit führt konsequenterweise sowohl ein Satz von Methoden zur Herstellung optischer Komponenten mit präzise eingestellten optischen Transporteigenschaften für den Bau von Fotoreaktorprototypen als auch Methoden zur Herstellung von optisch verdünnten Fotokatalysatoren auf Basis von transluzenten Pulvern aus Silica-basiertem Aerogel ein. Eine optische Verdünnung des Fotokatalysators ist dabei für fast alle Fotokatalysatoren essenziell, da das intensive Absorptions- und Streuverhalten des Fotokatalysators im unverdünnten Zustand in nahezu allen Aufbauten zu extremen Hotspots in der lokalen Photonenabsorptionsrate nahe der beleuchteten Oberfläche führt. Die eingeführte Strategie zur optischen Verdünnung ist dabei geradlinig und leicht auf viele Fotokatalysatorsysteme übertragbar. Die eingeführten Strategien zur Fertigung von Fotoreaktorkomponenten basieren auf additiver Fertigung bzw. 3D Druck, was einen flexiblen Designprozess mit einem hohen Freiheitsgrad in der Geometrie erlaubt. Eine detaillierte Analyse der optischen Transporteigenschaften der gedruckten Komponenten

zeigt jedoch, dass additive Fertigung nur eingeschränkt zur Herstellung optischer Bauteile geeignet ist. Dies ergibt sich aus der typischerweise hohen Oberflächenrauigkeit gedruckter Bauteile und der daraus resultierenden Notwendigkeit einer zeitaufwändigen Nachbearbeitung nach dem Druckprozess. Zum Abschluss wird im Rahmen der vorliegenden Arbeit über die materialbezogenen Aspekte hinaus ein neuartiges Fotoreaktorkonzept eingeführt, das bei korrekter Auslegung sowohl eine homogene Ausleuchtung der Reaktionszone, als auch eine hohe Effizienz des Strahlungstransports von der Reaktorapertur ins Reaktionsvolumen sicherstellt. Zusammengenommen resultieren diese beiden Eigenschaften in einer maximalen fotokatalytischen Effizienz eines sonnenlichtbasierten Gesamtprozesses. Der beschriebene Auslegungsprozess wird dabei durch eine Simulationsumgebung zur Abbildung von Strahlungstransportprozessen in voller räumlicher Auflösung unterstützt. Die Implementierung basiert auf einer Monte Carlo Ray Tracing Methode und ist objektorientiert in MATLAB® geschrieben.  Das sich im Auslegungsprozess ergebende Fotoreaktordesign weist eine ausgeprägte Robustheit gegenüber der Richtung einfallendes Lichtes auf, die sich in sonnenlichtbasierten Prozessen inhärent aus dem Tageslauf der Sonne am Himmel ergibt. Bemerkungswerterweise wird diese Eigenschaft ohne eine mechanische Sonnennachführung erreicht. Dies ergibt eine minimale Systemkomplexität und daraus resultierend niedrige Systemkosten, sowohl in der Herstellung als auch im Betrieb, was in eine Vielzahl von möglichen Anwendungsszenarien mündet. Denkbar sind sowohl Anwendungen auf Hausdächern als auch in Sonnenfarmen.  Dieser Aspekt ermöglicht eine standardisierte, kostengünstige und vor allem skalierbare Produktion des Fotoreaktordesigns.

     Die implementierte Simulationsumgebung zur Abbildung von Strahlungstransport in voller räumlicher Auflösung kann für eine Vielzahl von Herausforderungen im Bereich der Fotoreaktionstechnik eingesetzt werden. Besonders geeignet ist sie zur Unterstützung des Auslegungsprozesses von neuartigen Fotoreaktorkonzepten. Zuletzt sind das entwickelte Fotoreaktorkonzept und die dazugehörige Auslegungsrichtlinie eine Richtschnur für Wege hin zu kostengünstigen fotokatalytischen Prozessen, Prozesse zur Synthese von solaren Energieträgern mit eingenommen.

 Einen langen Weg gilt es hier jedoch noch zu meistern, sowohl auf einer technologischen Ebene als auch auf einer gesellschaftlichen.

# **Short summary**

Solar fuel technologies available today typically exhibit a solar to fuel efficiency too low and a capital and operational cost too high to be ecologically and economically reasonable. The work presented herein, therefore, analyses the design processes of high efficiency photocatalytic processes and lastly attempts to work out ways towards the goal of a high efficiency and low-cost photocatalytic process delivering a solar fuel.

The analysis first addresses the outstanding importance of the optical and reaction engineering properties of (1) the light source, (2) the photocatalyst, and (3) the photoreactor in the design process of a high efficiency photocatalytic process. If the sun represents the light source, as is the case in solar fuel processes, the design process naturally focuses on the photocatalyst and the photoreactor.

Consequently, the first result of the work presented herein is a method toolbox with experimental and simulation-based tools for the determination of optical and reaction engineering properties of photocatalysts and photoreactors.

Of especial relevance is the presented concept for the reliable, and especially precise determination of the quantum yield in photocatalytic reactions as a function of the operating conditions, namely the temperature, the reactants' concentration, the wavelength, and the local volumetric rate of photon absorption. The relevance of the introduced approach emanates from the pivotal role of the quantum yield in high efficiency photoreactor design. The quantum yield represents the efficiency metric on a photocatalyst level by relating the number of production events to the number of photons absorbed by the photocatalyst. The quantum yield and its dependency on the wavelength, therewith, set the ultimate limit for the achievable photocatalytic efficiency in a photocatalytic process driven by sunlight. The ability of the introduced approach to map the quantum yield as function of the operating conditions, consequently, provides the basis for the selection of suitable photocatalysts, and operating conditions in a production process. The dependency of the quantum yield on the local volumetric rate of photon absorption, which translates to the process intensity, thereby, is of outstanding relevance for the

design of high efficiency photoreactors. In the photocatalytic model system developed and characterized in detail in the presented work, the quantum yield systematically decreases with an increasing local volumetric rate of photon absorption, or increasing process intensity, respectively. Such a trend in the quantum yield directly entails the need for a careful optical design of a production photoreactor that avoids photon absorption hot spots in the photocatalyst bed.

Avoiding photon absorption hot spots in the photocatalyst bed is only one requirement in high efficiency photoreactor design. In addition to this first requirement, most importantly, high efficiency photo reactors must ensure a high efficiency of radiation transport from the reactor aperture into the reaction volume. Achieving both at the same time, well defined operating conditions, and a high efficiency of radiation transport, may be a significant challenge. This especially holds for systems in which particulate photocatalysts are employed that tend to scatter light strongly. Addressing this challenge requires the skill to precisely control radiation transport in a photoreactor. This is possible via the selection of suitable materials, the tuning of their optical transport properties, and the design of suitable photoreactor geometries.

The work presented herein, therefore, introduces strategies for the fabrication of optical components for photoreactor prototypes with tuned optical transport properties, and strategies for an optical dilution of photocatalysts via supporting of photocatalysts on translucent silica aerogel powders. The latter is of high relevance in most photocatalyst systems, since they strongly absorb (and scatter) light and therefore tend to develop absorption hot spots close to the illuminated surface if employed without dilution in a photoreactor. The introduced optical dilution strategy is straight forward and applicable to many particulate photocatalysts. The introduced photoreactor component fabrication strategies are based on additive manufacturing, or 3D-printing, respectively, which allows a flexible design process with a high degree of shape freedom. A detailed analysis of optical transport properties of printed optical components, however, reveals that additive manufacturing has a limited suitability for the fabrication of optical components. The latter emanates from the high surface roughness of printed components and the resulting need for time-consuming post-print treatments.

To complete the analysis and method toolbox, beyond the material related aspects, with the present work, a reflective multi-pass photoreactor design concept is presented that, if properly adapted to the employed photocatalyst, can guarantee both a homogeneous illumination of the reaction volume, and

a high efficiency of radiation transport from the reactor aperture into the reaction volume. Together, these two properties result in a maximum photocatalytic efficiency in a solar driven process. The described photoreactor design process, thereby, is supported by a 3D numerical model mapping radiation transport in the photoreactor. The model is Monte Carlo ray tracing-based and implemented in MATLAB®. The implementation is tuned to especially address the tasks of the present work. The resulting photoreactor design exhibits a pronounced tolerance towards different directions of incident light resulting from a moving sun in the sky. Noteworthy, this is achieved without relying on sun tracking. The latter entails a minimal system complexity and system cost, both in fabrication and operation, which allows to imagine a multitude of applications, for instance, on rooftops or in solar farms. The proposed photoreactor design further comprises two different parts only that are manufacturable in polymers via industry established polymer extrusion and injection moulding. This design aspect allows a standardized and as cheap as possible large-scale production of the proposed photoreactor design. Lastly, a detailed simulation-based analysis of the performance of the proposed photoreactor design permits a detailed understanding of achievable limits, prevalent loss mechanisms, and finally the derivation of a simple graphical design guideline. The later facilitates the adaptation and further development of the concept of reflective multi-pass photoreactors in various applications of photocatalysis.

Summarizing, the results of the work presented herein provide substantial support for the further development of low-cost, high efficiency photocatalytic processes. The methods introduced pave the way for detailed reaction engineering analysis of photocatalysts, which is a prerequisite for the selection of suitable photocatalysts and a subsequent photoreactor design process. The strategies introduced for the optical dilution of photocatalysts are simple and straight forward applicable to many photocatalysts. Additive manufacturing is shown to be a suitable tool for the fabrication of photoreactor protypes with some restrictions regarding achievable surface qualities. The implemented radiation transport simulation environment can be used for various task in the field of photochemical engineering, especially in the development and validation of different photoreactor concepts. The proposed high-efficiency and low-cost photoreactor design concept and especially the developed design guideline, lastly, could become one corner stone for a low-cost photocatalytic process to produce solar fuels.

Even though only a small piece in the overall picture, high efficiency photocatalytic processes enabled by sophisticated photochemical engineering

might be one contribution in the endeavour leading towards a sustainable living human population. However, a long way remains to be mastered, both on a technological as well as on a societal level.

# **Bachelor and Master theses**

In the framework of the presented work eight Bachelor and Master theses have been initiated and supervised by the author. Six of those theses addressed aspects of the presented work and are the basis of presented data. Especially, experimental results are based on these theses. The six theses giving the experimental basis for the presented work are:

Momme Rickmers, Interdependencies of radiation transport properties and performance metrics of silica aerogel-supported photocatalyst systems, Master thesis, 2021.

Shengzhi Liang, Experimental & simulative study of light transport in photoreactors, Master thesis, 2021.

Marius Riedinger, Photocatalytic 2 activation with aerogel-supported indiumoxide-based catalysts: catalyst preparation and catalytic characterization, Bachelor thesis, 2021.

Luca Heim, Development of an aerogel-supported /2 catalyst system for photocatalytic water splitting, Bachelor thesis, 2021.

Validierung eines Strahlungstransportmodells für einen Fotoreaktor zur Bestimmung von Quantenausbeuten, Domenik Fischer, 2022.

Bestimmung der Quantenausbeute eines Modellfotokatalysators als Basis für die Auslegung von Fotoreaktoren, Nils Thorben Gensior, 2022.

# **Contents**

**3 Outline of the work** 37

# **1 Introduction**

## **The global challenge faced**

The effects of progressing climate change are no longer abstract concepts [1]. Sea levels observably rise [2], age-old natural habitats disappear [3], once fertile land dries out [4], and disastrous weather extremes are observed more frequently [5]. The impacts of these changes on human life on earth are manifold – health issues [6], migration [7], political tensions [8, 9], just to name a few. Climate change with its multi-faceted nature, thus, represents a substantial threat to human life on earth, and its mitigation becomes an egoistic act of self-preservation for mankind.

The mechanisms governing the processes of climate change are not subject to speculations. There is no serious doubt that greenhouse gases accumulating in the earth's atmosphere drive climate change [1]. There also is no serious doubt that greenhouse gas accumulation is the consequence of human acting, more precisely, human-induced land use change, and the use of fossil energy carriers [1, 10]. It lies in humanities' hands – our hands. The direction that needs to be taken is clear: anthropogenic green house gas emissions must be reduced as fast as possible, but especially before tipping elements in earth's climate system actually do tip [11]. This challenge is a global challenge demanding human cooperation in a global framework. The Paris Agreement of 2015 is a first step in this endeavour [12]. Noteworthy, time is not on mankind's side. According to the Intergovernmental Panel on Climate Change (IPCC), global net green house gas emissions must be cut to zero until latest 2050, if the goals defined in the Paris Agreement shall not fail [13]. Reducing anthropogenic green house gas emissions to net zero in such a short

period of time is a political, societal, and technological challenge. No political framework alone will guarantee success. No behavioural change alone will make technological changes obsolete. But especially no technology alone will permit to continue business as usual. The change desperately needed to mitigate the consequences that climate change imposes on human life on earth pervades societies in nearly all their aspects. Of course, a special focus lies on economy, mainly on the chemistry, the mobility, and the energy sector together being responsible for more than 70 % of accumulated historic anthropogenic green house gas emissions [14].

## **The technological challenges ahead**

Today, roughly 80 % of the annually emitted anthropogenic green house gases result from the use of fossil energy carriers – natural gas, oil, and coal [10]. Renewable energy sources that are greenhouse gas neutral and fossil independent – namely wind, solar, and hydro – are therefore envisioned as the future energy backbone of the world economy. Substantial efforts are undertaken to intensify their exploitation via installation of wind turbines, photovoltaic fields, and hydro power plants delivering renewable electrical energy. Nevertheless, until 2020, renewable electrical energy remained a scarce resource with a share of only 12.6 % in the global primary energy mix [15]. Fortunately, the trend indicates a steady increase of this currently sobering number [16, 15]. However, with an increasing share of renewable electrical energy in the energy mix, transportation and storage of electrical energy becomes a major challenge. Technological development in the field of short and long term electrical energy storage is urgently needed. The most promising options currently in the portfolio are electrochemical energy storage solutions – batteries – and chemical energy storage solutions – namely power-to-x processes that deliver chemical fuels in electrically driven, and carbon dioxide, nitrogen, and water-based fuel synthesis processes. Powerto-x processes are currently the most promising option for large-scale and long-term seasonal energy storage, as well as global energy transportation. Furthermore, they are the only reasonable option for long distance, heavy duty, and air transportation applications [17]. Additionally, carbon dioxidebased power-to-x processes are not only able to deliver an alternative carbon feedstock for non-transportation applications such as in the chemical industry [17] but also an option to serve as a temporary carbon dioxide sink when capturing carbon dioxide from the atmosphere or at least from non-avoidable point sources. Building on existing technologies, some power-to-x processes are close to an economic implementation [18, 19].

Even though being a promising energy storage and transportation technology, power-to-x processes are object to vivid discussions. Core of these debates

is the achievable efficiency in multiple regards – first, with regard to the energy efficiency of the often multi-step processes, and second with regard to the efficiency expressed as carbon dioxide emission reduction potential per amount of electrical energy or financial effort invested. If, for instance, the achievable carbon dioxide emission reduction potential per amount of renewable electrical energy invested was the metric of choice to decide how renewable electrical energy was used, not power-to-x processes but commercial electrical heat pumps replacing fossil fired boilers in residential heating would be the option of choice for timely prioritized implementation [20]. A similar conclusion can be drawn if power-to-x products and direct electrification approaches in residential heating and light transportation scenarios are compared with regard to the financial cost per avoided greenhouse gas emission [17]. These discussions line out that besides the need for electrical energy storage solutions, use conflicts for renewable electrical energy are a substantial challenge in the transition phase from a fossil-based economy towards a sustainable economy independent of fossil energy resources. The discussions thereby highlight on the one hand that the share of renewable electrical energy urgently needs to be increased and on the other hand that more alternative technologies for the replacement of fossil energy carriers are desirable. In best case, these additional options would not depend on the availability of vast amounts of renewable electrical energy. They thereby could appease use conflicts and facilitate the allocation of the scarce resource 'renewable electrical energy' amongst the various envisaged applications. Also, these fossil-fuel alternatives could additionally serve as backup fuels for electricity grid stabilization in case photovoltaic fields, hydro power plants, and wind parks were not able to provide a stable enough supply. One such option are solar fuels.

## **Basics of solar fuel processes**

Instead of renewable electrical energy, processes delivering solar fuels use sunlight to drive photochemical conversions of carbon dioxide and/or water to yield energy carriers [21]. Solar fuel processes are, thereby, quite similar to natural photosynthesis that uses sunlight to convert carbon dioxide and water to carbohydrates. In comparison to power-to-x processes, solar fuel processes can only partially be build from existing technologies and are far less developed. Even the latest benchmark systems only reach a solar to fuel energy efficiency of roughly 1 % (definition see 1.1) [22, 23].

$$\eta\_{STF} = \frac{heating\ value\ of\ produced\ fuel}{energy\ incorporated\ via\ incident\ light} \tag{1.1}$$

To be economically interesting and thereby become a real option in the portfolio of measures in climate change mitigation, the solar-to-fuel energy efficiency of a solar fuel process must lie in the range of 5-10 % [24]. At the same time, having in mind that sunlight collectors for significant production would cover huge areas, the photoreactors employed must be cheap with regard to the cost per covered area. Naturally, this addresses both, the capital and operational expenses. As an illustrative example, to underline the need for low area-specific costs, assuming a 5 % solar-to-fuel energy efficiency, an area only slightly smaller than the German federal state of Saarland (≈2300 km2 ) would be required to produce the kerosene consumed annually by German airports1 .

Inefficient photon usage is a hurdle for all photocatalytic processes, not only solar fuel processes. In a broader context than solar fuels, the efficiency metric employed to assess a photocatalytic process with regard to its efficiency is the photocatalytic efficiency rather than the solar to fuel energy efficiency introduced with equation 1.1. The photocatalytic efficiency relates the number of production events, in case of photoredox reactions the number of transferred electrons, to the number of incident photons in the relevant optical band, definition in accordance to the recommendation by the International Union of Pure and Applied Chemistry (IUPAC) [27], equation (1.2). A photocatalytic efficiency equal to unity, accordingly, would imply that every incident photon was used to contribute to the desired production process.

$$\eta\_{\rho} = \frac{\text{\textquotedblleft of production events in a system}}{\text{\textquotedblleft of incident photons in specified optical band}} \tag{1.2}$$

Improving the photocatalytic efficiency of a photocatalytic process, including solar fuel processes, is governed by the three core elements of any photocatalytic process:

1. The employed photocatalyst absorbing photons and driving the chemical reaction

1 Assuming an average solar global irradiance of 1050 kW h m−2 a −1 [25], a heating value of kerosene equal to 40 MJ kg−1 , and an annual kerosene demand at German airports of 10 Mio. metric tons [26].

If the sun represents the light source, as is the case for solar fuel processes, the engineering of a high efficiency photocatalytic process naturally focuses on the photocatalyst and the photoreactor.

## **Goal of this thesis**

No doubt, the availability of economically and ecologically reasonable solar fuel processes would be an appealing option in climate change mitigation pathways. Synthesized in the global sun belt, they could be traded around the world as fossil energy carriers are traded today. If available in significant amounts, they could support the electrification of the world's economy by providing a backup for electricity grid stabilization and facilitating the allocation of renewable electrical energy. Unfortunately, in 2022, reported solar fuel processes lack in technology readiness to take a significant role. The achieved photocatalytic efficiencies and process costs of the latest benchmark systems are insufficient to be competitive with alternative approaches. The goal of this thesis is, therefore, to examine in detail the challenges of high efficiency photocatalytic process design in the field of solar fuels under the constraint to economize the cost of the proposed photoreaction technology. The work, thereby, firstly analyses the current state of the art and lines out the important engineering challenges. Secondly, it focuses on the appropriate choice and characterization of materials, photocatalysts and photoreactor component materials included. The third part of the work comprises a proposed methodology for high efficiency photoreactor design, and describes and demonstrates a novel low-cost photoreactor design concept that could be a core component of a future commercial solar fuel processes.

# **2 Literature overview**

## **2.1 Photocatalysts**

Photocatalysts employed in solar fuels processes drive a relevant chemical reaction and basically comprise an active material which may be impregnated onto a suitable support material or structure.

### **2.1.1 Target reactions**

Relevant reactions in solar fuel processes yield energy carriers in a broad perspective, including hydrogen [28], carbon monoxide [29], synthesis gas [22], methanol [30, 31], methane [32], but also higher alcohols, or hydrocarbons [33].

Direct photocatalytic reactions of carbon dioxide with water, for instance to yield methane or higher hydrocarbons [32], as pointed out in equation (2.1), include a multitude of reaction steps and are extremely challenging from a kinetic point of view.

$$\mathrm{CO\_2 + 2H\_2O \longrightarrow CH\_4 + 2O\_2} \quad \Delta\_R H^0 \approx 891 \ \mathrm{kJ\,mol^{-1}} \tag{2.1}$$

Remarkably, carbonaceous target products like methane, alcohols, and higher hydrocarbons can also be obtained in thermal reactions of carbon dioxide and hydrogen or carbon monoxide and water. Since the activation of water or carbon dioxide alone is less challenging than reactions of carbon dioxide with water, many works in the field of solar fuels focus on hydrogen or carbon monoxide as target product [21]. Common photocatalytic reactions are, consequently, water splitting, see for instance [23, 34] and refer to equation (2.2), and carbon dioxide splitting, see for instance [34] and refer to equation (2.3).

$$\mathrm{H\_2O} \xrightarrow{\longrightarrow} \mathrm{H\_2} + \frac{1}{2}\,\mathrm{O\_2} \quad \Delta\_R H^0 \approx 285 \text{ kJ mol}^{-1} \tag{2.2}$$

$$\text{CO}\_2 \xrightarrow{\longrightarrow \longrightarrow} \text{CO} + \frac{1}{2}\text{O}\_2 \quad \Delta\_R H^0 \approx 284 \text{ kJ mol}^{-1} \tag{2.3}$$

Still, photocatalytic water and carbon dioxide splitting are challenging reactions that need sophisticated catalyst systems and process designs, see for instance the co-catalyst modified water splitting catalyst system in [35], or the high temperature carbon dioxide activation process in [22]. Less challenging photocatalytic model reactions are methane dry reforming [36], refer to equation (2.4), the reverse water gas shift reaction [37], refer to equation (2.5), or methanol reforming [38], refer to equation (2.6).

$$2\text{ CO}\_2 + \text{CH}\_4 \xrightarrow{\quad} 2\text{ H}\_2 + 2\text{ CO} \quad \Delta\_\text{R}H^0 \approx 247\text{ kJ mol}^{-1} \tag{2.4}$$

$$\mathrm{CO\_2 + H\_2 \longrightarrow CO + H\_2O} \quad \Delta\_R H^0 \approx 41 \text{ kJ} \,\mathrm{mol^{-1}} \tag{2.5}$$

$$\mathrm{CH\_3OH + H\_2O \longrightarrow CO\_2 + 3H\_2} \quad \Delta\_R H^0 \approx 49 \text{ kJ mol}^{-1} \tag{2.6}$$

Noteworthy, these photocatalytic model reactions consume valuable reactants, methane, hydrogen, or methanol and are, therefore, less appealing in the bigger picture of solar fuel processes and climate change mitigation.

#### **2.1.2 Active materials**

An active material suitable for a solar fuel process drives one of the chemical reactions discussed briefly in section 2.1.1. Further, it uses the available photons efficiently to drive the chemical reaction, or with other words, exhibits a high quantum yield in the relevant optical band. The quantum yield is the efficiency metric of the active material and defined by IUPAC as the number of production events, which equals the number of transferred electrons in photoredox reactions, related to the number of photons absorbed by active material at a specific wavelength, equation (2.7) [27]. The 'relevant' optical band is defined by the emission spectrum of the employed light source. It equals the optical band in which the employed light source emits most of its photons.

$$\Phi = \frac{\text{\textquotedblleft of \textquotedblright} production events}{\text{\textquotedblleft of \textquotedblright object\textquotedblright pathons at specific \textquotedblright} \text{\textquotedblleft wavelength}} \tag{2.7}$$

Consequently, an active material suitable for a solar fuels application not only drives a relevant reaction yielding an energy carrier but especially exhibits a high quantum yield in the optical band in which the sun's emission spectrum

**Figure 2.1:** Sunlight reference spectrum for direct illumination and 1.5 air masses (AM1.5D) according to ASTM G173-03 standard [39].

peaks, the ultra violet (UV, < 400 nm) and visible (Vis, 400 < < 800 nm) band, see sunlight reference spectrum in figure 2.1.

A quantum yield different from zero indicates that the considered active material is able to use photons productively in one or another way. Generally speaking, there are two main mechanisms how photons can be used to drive chemical reactions, a thermal and an electrochemical mechanism. In thermal pathways photons are used to generate heat that subsequently drives the chemical reaction. In electrochemical pathways, photons are used to separate and/or excite charge carriers that than provide the energy basis for the desired chemical reaction. Active materials can be grouped depending on which of the two mechanisms is assumed to be the major contributor. A rough grouping scheme comprises solar-driven thermal catalysis, photoelectro catalysis, and photothermal catalysis.

#### **<IP_ADDRESS> Solar-driven thermal catalysis**

In solar-driven thermal catalysis, photons are used to generate heat that subsequently drives the desired chemical reaction [40]. An example for solardriven thermal catalysis are high temperature redox cycles for water and/or carbon dioxide splitting [40], see scheme figure 2.2. In such redox cycles metal

oxides that decompose [41] or are partially reduced [34] at high temperatures are used as active materials. Typically the cycle comprises two steps. In the first step, the metal oxide, for instance Ceria (2) [34], is (partially) reduced at extreme temperature (≈1500 °C), and the side product oxygen is released. Subsequently, the partially reduced metal oxide is used to split the reactants, carbon dioxide and/or water, at slightly lower temperature (≈900 °C). In this second step, the metal oxide is obtained in its initial oxidation state and the products, carbon monoxide, hydrogen, or a mixture of both, are extracted. The purely thermal mechanism in high temperature redox cycles entails a negligible sensitivity of the catalyst activity towards the wavelength of employed photons. Consequently, the whole solar spectrum from UV over Vis to infrared (IR) is of use in solar fuel processes that employ such thermally driven redox cycles [34]. Besides the obviously necessary material stability towards changing temperature and oxidation state, the challenges on the material side lie mostly on the reduceability, the reoxidizability, and the cycle capacity [42]. The material design/selection process aiming for a high overall process efficiency, thereby, is non-trivial and balancing high cycle capacities that allow a low cycle frequency reducing energy losses in the temperature swing itself, and favourable reaction kinetics in the reduction/oxidation step that keep the necessary temperature low and indirectly reduce heat losses induced by excess stripping gas feeds [42, 40].

#### **<IP_ADDRESS> Photoelectro catalysis**

In photoelectro catalysis photons are used to separate charge carriers that subsequently drive the desired chemical reaction. An example for photoelectro catalysis are semiconductor-based active materials [28]. Photon absorption by the semiconductor, thereby, induces excitation of electrons from the valence band (VB) to the conduction band (CB) . Positively charged holes are left behind in the conduction band. Subsequently, if not recombined, electrons and holes migrate to the surface of the active material particle and induce reduction or oxidation reactions, respectively [28, 43]. For an illustration, see scheme figure 2.3.

Whether, or whether not a semiconductor can act as active material for a specific reaction is largely dependent on its electronic band structure [28]. There are two necessary, noteworthy not sufficient, preconditions: Firstly, the available photons must each carry enough energy to excite an electron

**Figure 2.2:** Scheme of a solar-driven high temperature redox cycle comprising a metal oxide 2 as active material. The metal oxide is partially reduced releasing oxygen (2) at extreme temperature and subsequently employed to split water (2) and/or carbon dioxide (2) to yield hydrogen (2) and/or carbon monoxide () at slightly lowered temperature. Presentation adapted from [34].

from the valence band to the conduction band or with other words, the photon energy equal to ℎ must be equal or superior to the band gap energy of the employed semiconductor. Secondly, the band edge potentials, both, the valence, and the conduction band edge potentials, must be positive/negative enough to overcome the redox potential for the desired reaction [28]. For an illustration of these two hurdles, see scheme figure 2.3.

The first precondition, a photon energy bigger than the band gap energy, has decisive consequences for solar fuels applications. The precondition entails that all semiconductor-based active materials can only make use of the fraction of solar irradiation in which each photon carries enough energy to excite an electron from the valence to the conduction band. For many literaturereported, semiconductor-based photocatalysts only photons from the UV band fulfill this criterion, see for instance [44, 45]. This disadvantageous property of many reported photocatalysts limits their attractiveness for solar

**Figure 2.3:** Scheme of a semiconductor-based active material particle (circle) employed for water splitting. Photons are absorbed and excite electrons − from the valence band (VB) to the conduction band (CB). Positively charged holes (ℎ + ) are left behind in the valence band. Electrons and holes subsequently migrate to the surface of the semiconductor particle and drive reduction and oxidation reactions, respectively. Importantly, the band edge potentials (thin solid lines) must be more negative/positive than the redox potentials of the desired reactions (thin dashed lines). For water splitting the band edge potential of the conduction band must be slightly more negative than the redox potential for the reduction of protons to hydrogen (0 eV) and the conduction band edge must be more positive than the redox potential for water oxidation (+1.23 eV). Figure based on [28].

fuel applications drastically, since only roughly 5 % of the solar irradiation on the earth's surface are in the UV band, see sunlight reference spectrum in figure 2.1.

The second named precondition, the band edge potentials, has decisive influence on the applicability of a semiconductor for a specific reaction. In the exemplary case of water splitting, at the first view, there are, for instance, many semiconductors whose band edge positions lie far enough apart that theoretically protons could be reduced and water molecules could be oxidized on one and the same semiconductor particle. The band gap in these potential active materials is wider than the thermodynamically necessary 1.23 eV for water splitting [28]. At the same time many of these potential active materials do not have both, a conduction band edge potential that is negative enough to reduce protons, and a valence band edge potential that is positive enough

to oxidize water molecules. These materials are, therefore, inactive for the water splitting reaction even though their band gap is wide enough [28].

For the sake of the outstanding relevance of the electronic band structure of a semiconductor, many works on photoelectro catalysis explore methods to influence the band gap and the band edge potentials, for instance through semiconductor doping with cations [46] and anions [47], or sensitization through coupling of the semiconductor with small band gap semiconductors [48] or dyes [49].

A very sophisticated way to overcome challenges that arise from unfavourable band edge potentials are Z-scheme active materials systems, see for instance [50, 51, 52]. In these active materials systems two semiconductors are employed. One of the two semiconductors drives the reduction reaction. It has a suitable conduction band edge potential. The second semiconductor drives the oxidation reaction. It has a suitable valence band edge potential. To ensure charge balance, the two semiconductors are coupled in order that electrons from the oxidation semiconductor can be transferred to the reduction semiconductor. The electrical coupling can either be realized via an electron conduction bridge, for instance a metal particle [50], or a redox shuttle mediating between the two semiconductors, for instance iodate/iodine in aqueous solution [51].

Noteworthy, a suitable band structure is not a sufficient condition for a semiconductor to be a promising active material. In order that the semiconductor drives a chemical reaction in consequence of photon absorption, electrons and holes must not recombine but rather must be transported to the active material particle's surface and have a lifetime on the surface long enough for charge carriers to be transferred to the reactants. The more efficient these two transport processes are, and the less significant recombination processes are in consequence, the higher is a potential quantum yield [35]. Typically, recombination and/or transportation of charge carriers to the surface of a semiconductor particle occurs in the time scale of pico- to nanoseconds, and charge transfer from the semiconductor particle to the reactants in the time scale of micro- to milliseconds [43]. Strategies to increase the quantum yield in a photoreaction by influencing the charge carrier dynamics, therefore, can be grouped in strategies that decrease the probability of charge carrier recombination and enhance charge carrier transport in the semiconductor bulk material, and strategies that extend the lifetime of charge carriers on the active material particle's surface.

Typically, a high crystallinity and purity of the semiconductor entails an advantageous mobility of electrons and holes and reduces the density of recombination centers, such as lattice defects, in the bulk material [53, 54, 28]. By designing according materials, recombination is suppressed, and transportation to the semiconductor particle surface is facilitated.

Adding sacrificial agents that act as electron or hole scavengers [28, 55], or engineering of surface defects that act as electron or hole traps [43], extends the lifetime of charge carriers on the particle's surface.

Charge carrier transfer from the semiconductor particle surface to the reactants is the subsequent hurdle that influences achievable reaction rates and quantum yields. The design and appropriate deposition of co-catalysts reducing the over-potential necessary for charge transfer from the semiconductor surface to the reactants is, therefore, another strategy commonly employed to tailor active materials with high quantum yields [28]. An example for this strategy can commonly be found in titania-based photocatalysts employed for water splitting. In these catalyst systems, due to the only slightly negative conduction band edge potential of titania (relative to a standard hydrogen electrode), the reduction reaction of protons to hydrogen often is limiting [28]. Nobel metal co-catalysts reduce the over-potential for hydrogen evolution and, therefore, drastically enhance the photocatalytic hydrogen evolution rate on titania, see for instance [56, 57].

Even though extremely rare in literature, if all three discussed aspects, the electronic band structure of the employed photocatalyst, the charge carrier dynamics, and employed co-catalysts are engineered to perfection, even for challenging photocatalytic reactions like water splitting, quantum yields close to unity are feasible. Examples of such outstanding work are titania nanotubebased photocatalysts with a photodeposited carbon/platinum co-catalyst [45] or aluminum-doped strontium titanate-based photocatalysts (3 : ) with photodeposited rhodium chrome oxide (ℎ/23) and cobalt oxide hydroxide () as co-catalysts [35].

Noteworthy, in addition to the material dominated mechanisms discussed in detail above, the operating conditions may also influence the achievable reaction rates and, especially, quantum yields.

For instance, charge carrier recombination in semiconductors is enhanced at elevated temperatures [53, 54] potentially inducing a decrease of the quantum yield with increasing temperature. The latter is one of the reasons for which most semiconductor-based photocatalysts are operated close to/at room temperature, see for instance [35, 45, 50]. In contrast, product adsorption/desorption and/or consecutive reactions of reaction intermediates towards the reaction products are enhanced as well with increasing temperature and may induce an increase of the quantum yield with increasing

temperature.

As a consequence of their influence on the charge carrier dynamics with their role as electron and hole scavengers, reactant concentrations on the surface of the catalyst, and, thereby, also the reactant concentration in the bulk, influence the reaction kinetics and quantum yields as well.

Last but not least, charge carrier recombination in semiconductors not only depends on the material properties, crystallinity, density of recombination centers like impurities, etc., and the temperature as commented above, but also on the density of photon induced charge carriers, which translates to the intensity of photon absorption, or the light intensity, respectively [53, 54]. Even though not clearly reported in current literature, the dependency on the density of photon induced charge carriers can entail a dependency of the quantum yield on the local volumetric rate of photon absorption, definition in accordance to IUPAC recommendations see equation (2.8) [27].

$$L\_{p,\lambda}^a = \frac{\text{\textquotedblleft of photons absorbed in control volume in given time}}{\text{control volume size} \cdot \text{time interval length}} \tag{2.8}$$

Consequently, quantum yields in semiconductor-based photocatalysis do not only exhibit the obvious dependency on wavelength [35, 45, 58], but also may exhibit a dependency on temperature [59], reactant concentration [55, 57], and local volumetric rate of photon absorption. For an experimental indication for the latter, see for instance [57].

#### **<IP_ADDRESS> Photothermal catalysis**

In photothermal catalysis photons are used for the generation of both, charge carriers, and heat that together drive the desired chemical reaction [60]. Photothermal catalysis, therewith, represents the superposition of solar-driven thermal catalysis and photoelectro catalysis. It attempts to draw a benefit from the best of the two worlds, the ability to make use of the whole solar spectrum in solar-driven thermal catalysis, and the highly specific and potentially efficient reaction pathways achievable via photoelectro catalysis. Many catalyst systems tagged as photothermal catalysts are carbon dioxide hydrogenation catalysts, see for instance [61]. A common model reaction is the reverse water gas shift reaction, equation (2.2). Prominent examples of active materials are black indium oxide [37], silicon nano-wires decorated with non-stoichiometric partially hydroxylated indium oxide [62], or niobium oxide nano-rods decorated with palladium nano-crystals [63]. Importantly, the heating mechanism in these examples is reported to be a localized heating mechanism focusing on the heating of the active sites rather than the bulk material, presumably more efficient and, thereby, less energy intensive than bulk heating. The delineation and experimental proof of a local heating effect, however, is difficult. For a discussion of this issue refer for instance to [63]. The bulk reaction temperatures in reported photothermal catalysis are consequently mild in comparison to reaction temperatures in traditional thermal catalysis for the same reactions. Typical reactor temperatures in photothermal catalysis of the reverse water gas shift reaction are, for instance, in the range from 100 °C to 300 °C [64, 63, 65] with local temperatures estimated to be as high as 570 °C [63] in contrast to reactor temperatures in the range from 500 °C [66] to 900°C [67] in traditional thermal catalysis of the reverse water gas shift reaction.

Material development strategies in photothermal catalysis focus on the search of material systems that show both, semiconducting properties, as well as broad band photon absorption. These demands contradict each other at first sight because of the intrinsic absorption characteristics of semiconductors that only absorb photons that carry enough energy to excite an electron from the valence to the conduction band. Photothermal catalysts are, therefore, exclusively precisely engineered hetero structures combining different materials each contributing to the functionality of the system [63, 37, 62]. Reported black indium oxide, for instance, is a core shell like nano-particle combining a crystalline indium oxide semiconductor in the core with a defect loaded indium oxide shell exhibiting broad band absorption due to induced mid band gap states [37]. Non-stoichiometric, partially hydroxylated indium oxide decorated silicon nano-rods assign the functionalities even clearer. Ultra black silicon nano-rods show broad band absorption, whereas non-stoichiometric, partially hydroxylated indium oxide shows a distinct band gap and semiconducting properties [68].

## **2.1.3 Supports**

In most applications of heterogeneous catalysis, the active material is supported on a support material. The support material may be but is not necessarily inactive towards the chemical reactions occurring. In many cases the interactions between active material and support material are complex and open ways towards catalyst optimization. The primary motivation for supporting active materials on support materials emanate from the objectives

to use the (precious) active material effectively, to tune the selectivity in a reaction, and to reduce deactivation rates to an acceptable extend [69]. Since the desired chemical reactions occur primarily on the surface of the active material, effective use of the active material can be ensured by a fine dispersion of the active material on the (internal) surface of a support material. This results in a large active material surface area with a high density of active centers. Many catalysts exploiting this strategy are (noble-)metal catalysts like described for instance in [70, 71, 72]. Sintering of the finely dispersed active material particles either during the catalyst preparation (in calcination steps), or during catalyst operation, thereby, often deteriorates the activity of the catalyst, see for instance [72]. Choosing suitable support strategies can effectively hinder sintering by a nano-confinement of the active material particles. One example of a successful implementation of such nano-confinement described by Wu at al are noble metal catalysts encapsulated in LTA zeolite voids being stable towards oxidative sintering at temperatures as high as 600 °C [73].

An effective use of the active material is further only guaranteed if proper operating conditions are ensured throughout the whole volume of a porous catalyst particle or pellet [69]. This mainly addresses the reactant concentrations and the temperature. In this view, supporting the active material is a dilution strategy. High local reaction rates, which could entail mass transport hindrances in the catalyst particle and therefrom resulting low catalyst usages, are avoided through the dilution of the active material. The same argumentation holds for heat transport hindrances that could entail undesired hot/cold spots in the catalyst particle in exothermic/endothermic reactions. Supporting active materials on support materials can further have a significant effect on the activity of active centers themselves. Works from Wang et al examining the activity of nickel-based carbon dioxide methanation catalysts reveal, for instance, that nickel catalysts supported in a lanthanum oxide matrix show significantly higher activities than pure nickel catalysts. According to density functional theory calculations, the reason for this might emanate from an increased adsorption strength of carbon dioxide molecules on the active sides on nickel particles in in the vicinity of lanthanum oxide [74].

The pore structure of support materials can have an effect on the selectivity in reactions with a broad product spectrum. One example for such spatial effects induced by the support material's pore structure, reported by Subramanian at al, are cobalt-based Fischer-Tropsch catalysts impregnated on a zeolite-based support [75]. The pore structure and size, thereby, affects the

observed selectivity especially with regard to higher hydrocarbons. Noteworthy, the zeolites employed in the work of Subramanian et al also act as acidic hydro-cracking catalyst, which highlights that support materials can also act as active materials themselves. The differentiation between active material and support material gets further blurred in such cases.

Summarizing, supporting active materials onto support materials can trigger complex mechanics, and can have effects on the activity of active sides, the rate of deactivation processes, the selectivity of reactions and catalyst particle-internal mass and heat transport processes. Obviously, in applications of photocatalysis, in addition to all the material-related and mass and heat transport-related aspects, impregnating the active material on a support material is a way to control radiation transport. With other words, supporting a photocatalytically active material onto a suitable support may be a way to guarantee that there are no limitations on the radiation transport side and the whole employed active material is accessible by photons.

As is the case in traditional thermal catalysis, supports for photocatalytic applications should (1) be stable, meaning they should be able to withstand the operating conditions and the chemical environment, (2) be chemically inert with regard to the target reaction or contribute in a desirable way, (3) provide a large surface area onto which the active material can be deposited, (4) be open porous and have favourable transport properties for the relevant species, and of course, (5) be of low-cost. Lastly, and of utmost importance, supports for photocatalytic applications must be transparent, at least translucent, in the relevant optical band. The latter includes a negligible parasitic absorption of the support. Even though this list of six criteria seems ambitious, there actually are support strategies that do fulfill the requirements. Amongst them are reticulated foams and aerogels.

#### **<IP_ADDRESS> Reticulated foams**

Reticulated foams, example see figure 2.4, are one active material support option in applications of photocatalysis. The foam structure itself, typically, is made from metals [64], or ceramics [76, 77], in a template process. If the material is chosen appropriately, reticulated foams are stable in most chemical environments. With their open porosity but interconnected solid framework, reticulated foams allow deep penetration of light into the reaction volume [76, 77], provide good heat and mass transport properties [78], and have a large surface area for the deposition of active materials. The active material

**Figure 2.4:** Photograph of a reticulated foam made from ceria and employed in a high temperature redox cycle splitting carbon dioxide to carbon monoxide and oxygen. Reprinted with permission from [76]. Copyright 2012 American Chemical Society.

can either be coated onto the inner surface of the foam [64] or, in case the active material was not precious, the foam itself can be made from the active material [76]. Coating of the active material onto the foam can be realized in manifold ways. Examples are direct growth of the active material on the foam surface [64], or simple wash/spin coating with a slurry containing the active material [79].

The crucial light penetration depth is predominantly shaped by the pore density or pore size respectively and lies in the range of millimeters to centimeters [77]. The lower the pore density/the bigger the pores respectively, the higher is the penetration depth and the smaller are gradients in the intensity of photon absorption [77].

#### **<IP_ADDRESS> Aerogels**

Aerogels, exemplary photograph see figure 2.5, are an especially promising active material support option in applications of photocatalysis, see for instance [80, 81]. Aerogels are gas-filled, open porous, interconnected, and mechanically stable networks of nano-scale particles with extreme porosity ranging from 90 % up to 99.99%, see for instance [82]. Aerogels can be made

**Figure 2.5:** Photograph of a silica aerogel monolith employed as active material support showing a slight blue haze emanating from Rayleigh scattering.

based on various materials, for instance silica [83], titania [31], carbon [82], or organic polymers [84]. They have, if the materials are chosen properly, a good thermal stability and are chemically stable in many chemical environments. Specific surface areas of aerogels are huge, typically in the range of several hundred square meters per gram, see for instance [83, 31, 85]. The advantageous huge specific surface area emanates from the high porosity and nano-sized pores, whose size typically lies between 10 nm and 100 nm, see for instance [85, 86]. Due to the small pore size, fluid transport in the gel structure is, depending on the pressure or the mean free path length, respectively, dominated either by diffusion or a superposition of diffusion and viscous flow [85]. Diffusion coefficients are in the range of 10−5 m2 s −1 , which is in the range of gas diffusion coefficients [85]. This is favorable, but sets a limit for the size of aerogel monoliths employed as catalyst supports. The thermal conductivity of aerogels is exceptionally low, see for instance [84]. Aerogel supports, therefore, thermally decouple the active material from the reactor, which may be an advantage in photocatalytic processes in which solar heat (partially) drives the chemical reaction. For examples of corresponding active material systems please refer to section 2.1.2.

As active material support in solar fuel applications, silica aerogels are especially promising due to their high transparency, or low scattering and absorption coefficients, respectively, throughout the UV and Vis band, see

**Figure 2.6:** Scheme depicting a standard silica aerogel synthesis in a sol-gel route starting from the silica precursor tetra methyl ortho silicate (TMOS) dissolved in methanol (3) and ammonia as catalyst ( 3) dissolved in water (2) and comprising the steps of sol formation, gelation, aging, and supercritical drying. The numbers indicate steps in the synthesis in which an active material can be impregnated onto the gel. (1) refers to mixing active material particles into the reacting sol, (2) refers to wet impregnation of an active material precursor into the alcogel, and (3) refers to mixing an aerogel powder with an active material powder. Figure derived from [83].

for instance [87]. Light penetration depths into pure silica aerogels are in the range of centimeters to meters, depending on the wavelength. However, Rayleigh scattering in the nano-sized pores/primary particles induces an increase of the scattering coefficient with decreasing wavelength, resulting in a slight blue haze of silica aerogel monoliths [86], see also figure 2.5, and sets a limit to the application of silica aerogel supports with active materials using deep UV photons.

The synthesis of silica aerogels follows established sol-gel procedures comprising sol formation, gelation, aging, and supercritical drying. For an illustration of a typical synthesis process please refer to figure 2.6. The standard synthesis depicted in figure 2.6 opens up basically three ways for active material impregnation. First, active material particles can be added during the sol formation before gelation, compare for instance [31, 83]. Second, an active material precursor can be impregnated into the alcogel by adding the precursor solution to the reacting sol, or during aging [81]. And third, the already dried aerogel can be ground and mixed with a powder of the active material.

## **2.2 Photoreactors**

A photoreactor provides suitable operating conditions for the employed photocatalyst. It ensures photon absorption, provides a suitable temperature, and governs the reactant supply and product extraction. In a very general perspective, photoreactors comprise a reaction volume shaped by a reactor body and an optical access to the reaction volume, for instance via a window. In applications employing artificial light sources, the light source may be considered as a part of the photoreactor as well. Literature reported photoreactors can be grouped in photoreactors that are intended and designed for research applications and photoreactors that are intended and designed for production scenarios either using sunlight or artificial light sources. The requirements and thereof resulting designs for research and production photoreactors differ significantly.

## **2.2.1 Research photoreactors**

Research photoreactors are the workhorses of the development of high efficiency photocatalytic processes. They are employed for the essential tasks of catalyst screening, reaction kinetic and quantum yield measurements, and mechanistic studies. Photoreactors for mechanistic studies are exclusively tailor-made, addressing the requirements of the respective analysis method, therefore, show a broad design variance, and will not be discussed in detail in this place.

#### **<IP_ADDRESS> Catalyst screening**

Photoreactors for catalyst screening are the most commonly employed research tool in the search for suitable active materials. They often are rather simple systems that are designed to be convenient in use, especially with regard to the catalyst exchange. Well-defined operating conditions, temperature, reactant concentrations, local volumetric rate of photon absorption, and wavelength of the employed light are of course desired but often not feasible within the simple designs employed. For a brief discussion of this challenge, see for instance [61].

In a broad view, the most frequently reported photoreactors for catalyst screening can be grouped in two categories. The first category comprises

**Figure 2.7:** CAD model renderings of three typical photoreactor types employed for photocatalyst screening: two vessel-type reactors (left and centre) and one capillary reactor. In all three depicted photoreactors, photons would be coupled into the reactor from above. The Batch reactor CAD model (left) is derived from design indications in [62] and comprises a two-part reactor body and a quartz glass window that together surround the reaction volume. Reactants and products are fed/extracted over the fluid connector bore. The stirred tank reactor CAD model (centre) is derived from design indications in [35] and comprises a two-part glass vessel with two fluid connectors for purge gas supply and product extraction and a stirring rod. The capillary reactor model is derived from design indications in [63] and comprises a quartz glass capillary with two commercial fluid connectors and a heating block for temperature control.

simple, sometimes stirred vessels, either for batch operation, see for instance [62], or continuous operation, see for instance [35, 57]. The second category comprises glass capillary reactors exclusively for continuous operation, see for instance [88, 63, 31]. For an illustration of exemplary systems representing the two categories, see figure 2.7.

For the sake of simplicity, illumination in both categories is realized in most cases via external light sources. In case of vessel-type reactors, photons are coupled into the reaction volume either through a window, see for instance [62] or, if the vessel is made from glass, through the reactor wall, see for instance [35]. Common light sources are xenon short arc lamps, see for instance [62], halogen lamps, see for instance [55], mercury-vapour lamps, see for instance [57, 38, 56], and light emitting diodes (LEDs), see for instance [89]. Noteworthy, the latter two light source types, mercury-vapour lamps and LEDs, are narrow band light sources, whereas the named thermal light sources, xenon short arc lamps and halogen lamps, are polychromatic light sources with an emission spectrum typically ranging from the UV over the Vis to the IR band. With polychromatic light sources, narrow band pass filters can be used to control the wavelength of photons sent into the reactor, see for instance [38]. With narrow band light sources narrow band pass filters are obsolete, but an exchange of the light source is necessary to modify the wavelength of incident photons. Noteworthy, the number of absorbed photons,

or even the local volumetric rate of photon absorption, is hard to determine with accuracy in such simple vessel-type reactors. For a discussion of this issue, see for instance [61]. With regard to the optical operating conditions most simple vessel-type reactors are, therefore, poorly defined.

Additionally, in batch systems, the reactants are fed previously to the reaction into the reactor, and gas phase/liquid samples are taken after a defined illumination time to test the conversion, see for instance [62]. Inherent to batch reactors is, therefore, a change of the reactant/product concentration during the experiment time. Depending on the achieved conversion, these changes can be significant. With regard to the reactant concentration, batch reactors, therefore, are also poorly defined.

Concluding, most employed screening reactors only give limited insight into the photocatalytic performance of photocatalysts. Due to the poorly defined operating conditions, both on the optical and the reactant concentration side, results obtained in such systems often do not allow meaningful comparisons between works of different working groups. In extreme cases, in which the optical properties differ significantly between photocatalysts, even comparisons between photocatalysts tested in the same photoreactor may not be reasonable. This is because in such systems rather radiation transport than the photocatalytic performance determine the system behaviour, and observations made do not indicate catalytic performance metrics but radiation transport phenomena.

#### **<IP_ADDRESS> Reaction kinetic and quantum yield measurements**

Photoreactors for reaction kinetic and quantum yield measurements are the essential tool in active material and photocatalyst engineering. Reaction kinetics and quantum yields derived with the help of such devices are the fundamental and indispensable basis of the development of high efficiency photoreactors and processes [90, 91]. For a detailed discussion of this need, please refer to section 2.2.2. Photoreactors for reaction kinetic and quantum yield measurements must provide well-defined operating conditions, including temperature, reactant concentration, wavelength of absorbed photons, and the local volumetric rate of photon absorption [90, 91]. A well-defined local volumetric rate of photon absorption is, thereby, of outstanding importance, since only rate law expressions modelling the reaction rate as function of the local volumetric rate of photon absorption are a valid tool for photoreactor design tasks [91]. If considered, the requirement of well-defined operating

conditions results in rather complex photoreactor designs. However, from a fundamental view, it is important to note that well-defined operating conditions represent the necessary precondition for comparable and meaningful measurements [92, 93, 94].

Quantum yield measurements require both experimental access to the number of production events, and experimental or simulative access to the number of photons that are absorbed by the photocatalyst. For clarification, refer to equation (2.7). The number of production events, thereby, is proportional to the product formation rate or the reaction rate, respectively. Measuring the reaction rate or examining the reaction kinetics, respectively, is therefore, an essential part of quantum yield measurements. Any approach suitable for quantum yield measurements, consequently, implies a suitability for reaction kinetic measurements. If the operating conditions are well-defined, reaction kinetics can easily be derived from a measurement of the amount of product molecules at the photoreactor outlet with standard analytical methods, for instance via UV Vis spectroscopy, or liquid/gas chromatography, see for instance [93, 94].

The challenge of quantum yield measurements typically arises from the determination of the number of photons absorbed by the catalyst system. This holds especially for heterogeneously catalysed photoreactions in which scattering complicates the radiation transport problem [27, 35]. For the sake of the complexity of both experimental and simulative approaches that give access to the number of absorbed photons in a photocatalytic experiment, most literature works reporting quantum yields relate the number of production events to the number of incident photons rather than to the number of absorbed photons. These works indirectly assume that the number of absorbed photons equals the number of incident photons. However, the number of incident and absorbed photons can differ significantly, see for instance [94, 95]. According to IUPAC recommendations, quantum yields that are derived under the assumption that the number of absorbed photons equals the number of incident photons should be tagged as apparent quantum yields [27].

The most simplistic photoreactors for apparent quantum yield measurements are vessel-type stirred reactors illuminated from one side, typically from the top [35, 57], scheme see figure 2.7, centre. Either narrow band light sources or the employment of narrow band pass filters is mandatory since the quantum yield is a spectral property defined at a specific wavelength, see equation (2.7). The number of incident photons in these experiments is typically determined either via actinometry, see for instance [57], or with photodiode power

sensors, see for instance [35]. Besides the critical assumption made regarding the number of absorbed photons, the employed vessel-type photoreactors additionally exhibit high gradients in the local volumetric rate of photon absorption that emanate from the unilateral illumination that obviously does not penetrate the whole reaction volume. If the illumination penetrated the whole reaction volume, photons would leave the photoreactor at the side opposite to the illuminated side and the assumption of full photon absorption would be taken ad absurdum. This nonuniform illumination represents an error source if the reaction rate does not scale linearly with the local volumetric rate of photon absorption or with other words if the quantum yield is a function of the local volumetric rate of photon absorption, discussion see for instance [96].

Black-body photoreactors for quantum yield measurements are an advancement compared to the described simplistic vessel-type photoreactors for apparent quantum yield measurements. In these black-body systems, the photocatalyst is placed in a reaction volume that surrounds a cavity, for illustration see 2.8, left. The cavity has an opening, that is very small compared to the inner surface of the cavity. Through the opening photons are coupled into the cavity. Assuming the reaction volume surrounding the cavity was opaque, or with other words, the photocatalyst absorbs/scatters light strong enough in order to avoid any transmittance, indeed any photon sent into the cavity is finally absorbed by the catalyst. Photon losses through the cavity opening are negligible as long as the opening is small in comparison to the cavity's inner surface. Parasitic absorption by the cavity walls is negligible as long as the material is chosen properly with a low absorption coefficient in the relevant optical band. Practical implementations of such black body photoreactors are for instance photoreactors with either a light source or an optical fibre connected to an according cavity immersed in the reaction volume, see for instance [96]. Still these black-body reactors exhibit high gradients in local volumetric rate of photon absorption and, therefore, are only suitable for photocatalysts, in which the quantum yield is independent of the local volumetric rate of photon absorption.

Integrating sphere photoreactors are another advancement in quantum yield measurements, example see for instance [97, 98, 99]. In these setups, a cuvette containing the photocatalyst with reactants, or a flow cell, is placed in an integrating sphere and illuminated through an opening in the integrating sphere surface, illustration see figure 2.8, right. Simplified, the integrating sphere collects all photons that are either transmitted or scattered by the photocatalyst in the cuvette/flow cell. A sensor on the integrating sphere's

**Figure 2.8:** CAD model renderings of two typical photoreactor types employed for quantum yield measurements, one black body type photoreactor (left) and one integrating sphere type photoreactor (right). The black body type photoreactor comprises a cavity that is immersed in the reaction volume. Provided that the reaction volume was opaque, all photons coupled into the cavity, for instance via an optical fibre, are absorbed by the reaction volume regardless of scattering effects in the reaction volume. The CAD model was derived based on details given in [96]. The integrating sphere type photoreactor comprises a flow cell placed in an integrating sphere. The flow cell is illuminated through the light source port in the surface of the integrating sphere. The detector mounted of axis detects the intensity of light that is not absorbed by the photocatalyst in the flow cell and, therewith, gives access to the number of absorbed photons. The CAD model was derived based on details given in [97].

inner surface lastly detects this photon flux. By comparing an integrating sphere measurement of the photocatalyst sample in the sample cell under illumination with a reference measurement without the photocatalyst in place, the number of absorbed photons can be derived experimentally. If the characteristic dimensions and the absorption and scattering coefficients of the reaction volume, or of the photocatalyst respectively, are chosen/tuned properly, the assumption of an approximately uniform distribution of light in the reaction volume or a uniform local volumetric rate of photon absorption is valid. If designed and conducted properly, quantum yield measurements in integrating sphere photoreactors are, therefore, highly reliable. Drawbacks of integrating sphere photoreactors are their complex and expensive design, the sensitivity of integrating spheres and the limited space in standard setups typically comprised in desktop UV Vis spectrometers. The latter limits the

feasibility of complex studies addressing other operating conditions than wavelength and local volumetric rate of photon absorption.

## **2.2.2 Production photoreactors**

Production photoreactors suitable for solar fuel production ensure a high photocatalytic efficiency under the constraint of a low area-specific cost of the resulting system. Achieving both, high photocatalytic efficiency and low-cost at the same time is the crucial prerequisite for a reasonable and commercially feasible implementation of a solar fuel processes. For a brief discussion of this issue see chapter 1.

Maximizing the photocatalytic efficiency of a photocatalytic process is a photoreaction engineering challenge. Presumed a photocatalyst exhibiting a high quantum yield in a relevant optical band was available, and the light source was not variable, the photoreactor optimization task addressing the photocatalytic efficiency focuses on two aspects. First, the photoreactor must provide the operating conditions, temperature, reactant concentrations, local volumetric rate of photon absorption, and to some extent the wavelength of absorbed light, under which the quantum yield peaks. And second, the photoreactor must guide incident photons towards the photocatalyst with minimized photon losses [100]. The latter occur for instance through parasitic absorption by reactor components, mirrors, windows, lenses, etc., or reflective losses through 'misguided' photons missing the reaction volume [94]. For these two reasons, the need of tailored optical operating conditions and the need for efficient radiation transport, high efficiency photoreactor design is based on a precise radiation transport model, or a suitable radiation transport equation, respectively, mapping radiation transport from the photoreactor aperture into the reaction volume [27]. The dependency of high efficiency photoreactor design on a suitable radiation transport model also finds its representation in the general photoreactor design equation, equation (2.9), that returns the achieved photocatalytic efficiency. It relates the number of production events, the wavelength and volume integral of the product of local volumetric rate of photon absorption and quantum yield in the reaction volume ( ), to the number of incident photons, the wavelength and area integral of the spectral photon irradiance (,) in the reactor aperture (). The

photoreactor design equation is, therewith, a reformulation of the definition of the photocatalytic efficiency, equation (1.2).

$$\eta\_p = \frac{\iint L^a\_{p,\lambda} \Phi(T, c\_i, \lambda, L^a\_{p,\lambda}) d\lambda dV}{\iint E\_{p,\lambda} d\lambda dA} \tag{2.9}$$

In order to evaluate the local volumetric rate of photon absorption in the reaction volume, the mentioned radiation transport model is mandatory. Noteworthy, the evaluation of local temperature and concentration fields demand for suitable heat and mass transport models that may indirectly demand for a momentum transport model (fluid dynamic model). The level of complexity in the different aspects, radiation, heat, mass and momentum transport, needed in order to succeed with a photoreactor design task, thereby, largely depends on the sensitivity of the quantum yield towards the respective operating conditions. If the quantum yield is strongly influenced by optical operating conditions, wavelength and local volumetric rate of photon absorption, the implementation of a precise, and most likely complex radiation transport model is necessary. If, on the other hand, temperature and/or reactant concentration only mildly influence the quantum yield, the implementation of complex fluid dynamic, or heat and mass transport models is optional/not advisable. In many photoelectro catalytic systems, the latter is the case [100]. A further complicating design constraint in the design of high efficiency photoreactors for solar applications is a moving light source, or the moving sun, respectively. The employed photoreactor must be able to ensure a high photocatalytic efficiency not only in one irradiation scenario, but throughout the course of the day and year with an according variation of the direction of incident light, which might represent a substantial challenge [94].

Achieving low area-specific cost of a photoreactor employed in a solar fuel process is a multi-faceted challenge. Of course the term 'area-specific cost' addresses capital and operational cost. Achieving low capital costs starts with an appropriate choice of materials. The main reactor body should be made from the cheapest materials possible, for instance polymers, and still should be as lightweight as possible, having in mind, that rather square kilometers than square meters must be covered with 'photoreactor aperture' in order to be able the generate a significant production, see for instance [52, 24]. Expensive materials, for instance the photocatalyst, should be employed as sparingly as possible. The catalyst usage must, therefore, be maximized in most systems [24]. Further, low capital cost can be achieved by a suitable design that is manufacturable with established, low-cost techniques, for instance polymer

injection molding, polymer extrusion, or film blowing. Beyond that, complex and costly components in best case are avoided. This could for instance include sun tracking mechanics that appear to be an elegant mean to address the aforementioned challenge of a varying position of the sun throughout the day and year, but are known for dominating the costs of sunlight harvesting systems, for instance in the field of concentrated photovoltaics [101] or concentrated solar power [102]. Lastly, low capital cost can be achieved by a standardized and modular design that allows easy adaptation to various use cases, and expansion of existing installations.

A modular design, further, is a mean to reduce operational cost. Modules that don't show the desired performance metrics anymore can be exchanged easily without shutting down a whole plant. Further, operational costs can be reduced by a high degree of system integration and automation that both reduce labor intensive works to an absolute minimum necessary. In the perspective of low operational cost, again, simple designs that do not rely on complex and sensitive components, such as sun tracking mechanics, are favorable, if possible.

There is a multitude of different production photoreactors proposed for solar fuels applications. They differ significantly in their design and represent attempts to address the discussed challenge of achieving high photocatalytic efficiency under the constraint of low area-specific cost. As discussed, most designs are, thereby, strongly influenced by the reaction engineering properties of the employed photocatalyst.

#### **<IP_ADDRESS> Highly concentrating systems**

Highly concentrating production photoreactors, example see figure 2.9, are typically designed for either solar-driven thermal or photothermal photocatalysts. Light concentration mainly is employed to achieve the desired reaction temperatures. 'Highly concentrating', thereby, refers to a geometric concentration ratio of at least several hundred to more than two thousand multiples of the solar irradiance, see for instance [22, 40].

Typical systems comprise mirror-based concentrating optics like parabolic troughs, paraboloids and, in a bigger scale heliostat fields that guide incident sunlight into a cavity receiver containing the photocatalyst, see for instance [100, 102, 22]. Noteworthy, even though seemingly exotic at a first glance, concentrating optics reaching such high concentration ratios are well understood, highly efficient and already in large-scale commercial use in concentrated

**Figure 2.9:** Highly concentrating photoreactor at the ETH Zürich employed to operate a solar-driven thermal catalyst system splitting carbon dioxide and water to yield synthesis gas in a high temperature redox cycle. Reprinted with permission from Springer Nature, [22], Copyright 2021.

solar power plants for instance in Quarzazate, Morocco, Almeria, Spain, or Invanpah, California [102]. Sun tracking is mandatory for highly concentrating systems [102]. The law of etendue conservation, equation (2.10), describes a clear thermodynamic limit for the acceptance angle () that concentrating optics in air reaching a certain concentration ratio () may reach at maximum [103]. The higher the concentration ratio, the more precise tracking must be. The high precision of the required tracking optics induces a significant cost penalty for highly concentrating photoreactors [102]. For instance, for solar hydrogen from a high temperature redox cycle implemented in a heliostat field, the cost for the concentrating optics are estimated to contribute roughly 80 % of the final hydrogen cost [40].

$$C \le \frac{1}{\sin^m(\theta)} \quad m = \begin{cases} 1 & \text{for line concentration} \\ 2 & \text{for point concentration} \end{cases} \tag{2.10}$$

In addition to the tracking requirement, highly concentrating systems face a challenge with regard to typical process temperatures. As described in section 2.1.2, typical temperatures needed to drive the thermochemical conversions are in the range of 1000 °C to 1500 °C. Handling such temperatures demands substantial efforts on the engineering side. On the one hand, these temperatures are challenging with regard to available construction materials, for instance the window material of the cavity receiver [22]. On the other side the extreme temperatures impact significantly the achievable efficiencies through (1) radiative heat losses [40], (2) the heat losses that are induced by reactants flowing through the reactor [42], and (3) the heating duty necessary to cycle the reactor temperature [42]. It is also for the extreme temperature and the complex handling of those, that highly concentrating systems are only economically feasible within large-scale applications [102]. Modular designs, adaptable to different use cases, maybe even including small-scale decentral use, are hard to imagine in such high temperature processes.

#### **<IP_ADDRESS> Panel-like systems**

Panel-like photoreactors, example see figure 2.10, are especially suited for ambient temperature photoelectrocatalysts, see for instance [23]. Panel-like, thereby, refers to a thin, slab-like geometry of the photoreactor that allows a modular plant design. Similar panel-like systems are known from photovoltaic applications and, on a side note, kick-started the photovoltaic sector. The most simplistic panel-like production photoreactors are plates, for instance frosted glass plates, coated with the photocatalyst and covered with a transparent window, for instance Pyrex or quartz glass sheets, see [23, 104]. Reactants are either fed into the volume between photocatalyst layer and transparent cover [23] or, in case the photoreactor is a simple inclined plate, flow in a thin film on the catalyst layer [100]. Such straight forward and simple designs theoretically allow mass fabrication of the photoreactor panels and, thereby, production at scale. Further the lack of any concentrating optics induces favorable acceptance characteristics with a broad acceptance angle region that allows an implementation without sun tracking mechanics. This drastically reduces the system cost compared to highly concentrating photoreactors that depend on precise sun tracking. However, the lacking optical design freedom of a simple plate limits reachable photocatalytic efficiencies. Photons either being scattered by or being transmitted through the photocatalyst layer are lost, meaning they are no longer available for production. Additionally, if transmission losses are minimized by increasing the optical thickness of the photocatalyst layer, which is reasonable, gradients

**Figure 2.10:** Panel like production photoreactor with photoelectro chemical photocatalyst splitting water to hydrogen and oxygen. Reprinted with permission from Springer Nature, [23], Copyright 2021.

in the local volumetric rate of photon absorption and a low catalyst usage are indispensable.

Scattering and transmission losses can be reduced with slightly more complex photoreactor panel assemblies. There are, for instance, panel-like photoreactors that are derived from tube bundle reactors, [105]. In these assemblies a bundle of transparent tubes shapes a slab-like reaction volume comprising the tubes and the photocatalyst in the tubes. The tubing walls, thereby, act as light guides, that allow photons to penetrate deep into the the reaction volume. If photons are transmitted or scattered in the photocatalyst in one of the tubes, the likelihood for another absorption chance in one of the neighbouring tubes is rather high [105]. These multiple passages of photons through different or one and the same reaction volumes increase the chance of absorption and consequently the achievable photocatalytic efficiency. Proper dimensioning of the tube wall thickness and tube inner diameter are essential tasks of a successful design of a tube bundle-derived photoreactor panel that ensures a homogeneous local volumetric rate of photon absorption, high catalyst usage, and satisfactory photocatalytic efficiency. On a side note, geometric dimensions of photocatalyst layers that are still partially transparent, or with other words photocatalyst layers that can be illuminated in a way that the local volumetric rate of photon absorption does not possess high gradients, are rather small. Typically they lie more in the range of several dozens of

micro metres to millimeters than in the range of centimeters to meters, even if the active material is supported on a transparent support, see for instance [23].

A significant drawback of tube bundle derived photoreactor panels is the rather intensive construction material use and complicated fluid distribution and collection in tube bundles. If glass is used as construction material, the resulting photoreactors are rather heavy, seen as an area-specific weight. The same holds for photoreactor panels build from frosted glass substrates and transparent glass covers. Due to the outstanding importance of the reactor component cost, see [24], the use of tube-bundle derived photoreactors, or even more general the use of photoreactors made from glass, for large scale solar fuel synthesis is, therefore, questionable.

#### **<IP_ADDRESS> Low-cost systems**

Low-cost production photoreactors are designed with regard to a maximum simplicity and lowest possible cost. Often this entails a penalty with regard to the achievable photocatalytic efficiency. In 2022 such systems only exist as concepts. Low-cost construction materials like polymers, the avoidance of costly components meaning, for instance, no sun tracking, mild process conditions, such as in photoelectro catalysis, and the suitability for mass fabrication are mandatory.

The most popular example of a low-cost photocatalytic production reactor are plastic bags, filled with a photoelectro catalyst and operated at ambient temperature, so called 'baggie' reactors, see for instance [24, 52, 106] and scheme figure 2.11. The envisaged application of 'baggie' reactors is solar hydrogen production via photoelectro catalytic water splitting. The most simplistic scheme of a baggie reactor comprises one plastic bag with a dual function photocatalyst, both reducing protons and oxidizing water. In this scenario, a potentially explosive mixture of hydrogen and oxygen is formed in the plastic bag. To avoid this hazardous characteristic, a further development of the baggie reactor concept foresees the employment of a z-scheme photocatalyst system comprising separate reduction and oxidation catalysts that are operated in two baggie reactors and connected via a diaphragm allowing a redox shuttle to mediate between the two catalyst systems [106]. In this concept, hydrogen and oxygen are obtained in two separate baggies and explosive gas mixtures are avoided. The realization of the two connected baggies remains to be demonstrated, however.

**Figure 2.11:** Scheme of two envisioned low-cost 'baggie' production photoreactors being built from polymer plastic bags, filled with photoelectro catalyst slurry and employed for water splitting. The scheme on top represents a 'baggie' reactor with one photoelectro catalyst both reducing protons to hydrogen and oxidizing water to oxygen. Hydrogen and oxygen are obtained as mixture in one baggie reactor. The bottom scheme comprises two baggie reactors in which separately protons are reduced and water is oxidized. The two bags are connected with a diaphragm that allows a redox shuttle to permeate and mediate between the two photocatalysts. Hydrogen and oxygen are obtained separately in this approach. Reprinted with permission from RSC Publishing, [52], Copyright 2015.

On the radiation transport side, for baggie-like photoreactors the same challenges as for simplistic panel-like photoreactors arise. Scattered and transmitted photons are lost, and, if the catalyst suspension is optically thick to avoid transmission losses, high gradients in the local volumetric rate of photon absorption are indispensable. Consequently, achievable photocatalytic efficiencies are expected to be lower than in more sophisticated reactor concepts including optics [24]. Additionally, handling of explosive mixtures in macroscopic structures entails an impressive explosion hazard, that renders single baggie reactors with a dual function photocatalyst a rather risky concept.

# **3 Outline of the work**

According to the introduced photoreactor design equation, equation 2.9, and as already stated in chapter 1, the development of a high efficiency solar fuel process relies on two core components: (1) a photocatalyst using UV and Vis photons efficiently to drive a relevant chemical reaction of carbon dioxide and/or water and (2) a photoreactor providing optimal operating conditions for the photocatalyst and a high efficiency in radiation transport from the photoreactor aperture to the photocatalyst deposited in the reaction volume. Photocatalysts using photons efficiently to drive chemical reactions of water and carbon dioxide to energy carriers are indeed reported, but complex, precisely engineered material systems. Roughly grouping, there are systems that are operated at medium to extreme temperature, photothermal, and solar-driven thermal catalysts, and systems that are operated at ambient temperature, photoelectro catalysts.

The design of production photoreactors is strongly influenced by the photocatalyst's properties. Decisive is the operating temperature and the therefrom resulting requirements for the optical components. Roughly grouping, there are photoreactor concepts that highly concentrate sunlight and that are designed for extreme process temperatures and panel-like or baggie-like photoreactor concepts without concentrating optics that are designed for ambient temperature operation.

The cost of a solar fuel technology is predominantly shaped by the capital cost of the employed photoreaction technology. Key to a low-cost concept are, therefore, the employment of cheap construction materials for the photoreactor and a design that is manufacturable with low-cost, standard techniques. The employment of technically complex and expensive components, like, for instance, sun tracking mechanics, must be avoided if possible. Costly materials, like, for instance, the photocatalyst, must be used sparingly but especially efficiently. A high catalyst usage is, consquently, mandatory.

To contribute to the endeavour of the development of a high efficiency and low-cost solar fuel process, the present work, consequently, aims to develop and demonstrate a polymer photoreactor concept with a design that allows fabrication via polymer extrusion. The concept shall be panel-like and modular and explicitly excludes the option to employ sun tracking. Even though statically aligned to the sun path, the concept shall ensure a high photocatalytic efficiency for any photocatalyst exhibiting a high quantum yield in the relevant UV Vis band. This explicitly includes heterogeneous photocatalysts that tend to scatter light intensively. Achieving a high photocatalytic efficiency under these conditions, static alignment to the sun path and scattering photocatalysts, demand a design concept that combines the features of highly concentrating photoreactor concepts comprising light concentration and trapping in cavities with the broad acceptance characteristics of simple panel-like or baggie-like photoreactors. All together the envisioned characteristics not only favour an economic implementation in solar farms but also allow to imagine small-scale, decentral applications that may represent a way to establish new technologies in the energy market [107].

The use of polymers as construction material limits the suitability of the envisioned photoreactors to low temperature photocatalysts. Such photocatalysts are photoelectro catalysts. Besides the overarching aim to contribute to the endeavour of the development of a high efficiency and low-cost solar fuel process via the design of suitable photoreactors, the second aim of the present work is, therefore, the development of a model photoelectro catalyst system that can be employed to demonstrate the functionality of the envisioned photoreactor concept. Besides the active material development the efforts in the field of photoelectro catalyst system development shall explicitly include suitable active material support strategies that can be employed to control radiation transport on the photocatalyst level. The latter is necessary to avoid radiation transport hindrances in the catalyst bed and, thereby, opens ways towards a high catalyst usage.

The photoreactor design equation, equation 2.9, also highlights, that two skills are key to success in the development of a high efficiency solar fuel process: (1) the ability to determine quantum yields in photoreactions as a function of the operating conditions, including temperature, reactant concentration, wavelength and especially the local volumetric rate of photon absorption, and (2) the ability to model radiation, heat, mass, and momentum transport in a photoreactor.

The third aim of the present work is, consequently, the development of a method for the precise determination of quantum yields in gas, liquid and multi-phase photoreactions. The focus shall be the precise knowledge and definition of the local volumetric rate of photon absorption in the experiments. To the best of the author's knowledge, this operating condition, the local

**Figure 3.1:** Scheme of the overall challenge of the design of a low cost high efficiency photocatalytic process using carbon dioxide, water, and sunlight to deliver a solar fuel. The Scheme depicts the main development tasks and methods (text boxes) together with their dependencies (grey arrows).

volumetric rate of photon absorption, translating to the process intensity, is only sparingly examined as a parameter influencing the quantum yield in photoreactions. This is even though the local volumetric rate of photon absorption is considered as the most suitable variable to express the influence of 'light intensity' in photoreaction kinetics [91]. Besides its importance for photoreactor design, the envisaged method, therewith, also allows interesting scientific insights into the nature of quantum yields in photoreactions.

And lastly, since the quantum yield is expected to be only slightly sensitive towards temperature and reactant concentration in photoelectro catalyst systems, the fourth aim of the present work is the development of a precise radiation transport model for photoreactors (that can be combined with heat,

mass and momentum transport models). The envisioned radiation transport model shall be able to map radiation transport in multi-component systems with high accuracy but at a reasonable computational cost. The latter opens the way towards numerical design optimizations. Of course, mapping radiation transport with a radiation transport model is only reasonable with the knowledge of optical transport properties, like refractive indices, absorption and scattering coefficients, reflectivity and reflection characteristics, etc.. The determination of these transport properties is, consequently, a supplementary topic of the present work.

Summarizing, the present work addresses the overall challenge of high efficiency low-cost photoreactor design illustrated in figure 3.1 and discusses the following topics in detail (in order as described in the following):

# **4 Radiation transport modelling**

The radiation transport model developed for the tasks in the present work shall be able to map radiation transport in three dimensions in multi-component systems. More concretely, this means that the radiation transport model shall be able to map radiation transport in photoreactor assemblies comprising transparent components like windows or lenses, translucent (turbid) components like particulate catalyst beds, and opaque components like mirror optics or reactor component walls.

A restriction made before all considerations, is that the mapped components do not show gradients in their optical properties. A transparent window for example would have a constant refractive index and absorption coefficient throughout its whole volume. As will be lined out, this assumption facilitates the considerations and implementation significantly.

## **4.1 Physical basis**

In theory, Maxwell's equations entirely describe the propagation of light in any system [108]. Applying Maxwell's equations on a radiation transport problem would allow to assess any imaginable radiation transport performance metric in any imaginable detail level, including, for instance, the local volumetric rate of photon absorption in a photocatalyst placed in the reaction volume of a photoreactor. The resulting complexity and computational effort, however, render this approach in most cases impractical [109]. A simplification is needed in order to deal complex macroscopic multi-component systems, systems like photoreactors, with acceptable computational effort. Geometric optics represent such a simplification [108, 109]. The following, very brief introduction into geometric optics is based on the text books referenced in [108, 109].

#### **4.1.1 Geometric optics**

Geometric optics are applicable if the characteristic dimensions of both the objects in which light travels and the objects with which light interacts are way bigger than the wavelength of the mapped light [109]. In this special case Fermat's principle is applicable and light can be mapped as propagating rays [109].

If the refractive index is constant along a ray path, compare the fundamental assumption made in the introduction of this chapter, light rays are propagating in straight lines [109, 108]. The optical path length of light traveling from point A to B in a medium with constant refractive index, therefore, equals the geometric distance between A and B [109].

If rays cross phase boundaries with a change in refractive index, the propagation direction of the rays is altered [109, 108]. Thereby, the incident ray vector, the refracted ray vector and the phase boundary surface normal vector in the intersection point of ray and phase boundary are coplanar [109]. Figure 4.1 depicts an exemplary path of a ray crossing a phase boundary with a change in the refractive index from 0 (originating medium) to 1. Its change in propagation direction can be derived from Fermat's principle and results in Snell's law, equation (4.1) [109, 108]. The change in direction, thereby, depends on the incident angle (relative to the phase boundary surface normal in the ray phase boundary intersection point) and the change in refractive index from 0 (originating medium) to 1. The direction change is expressed in form of a refraction angle (relative to the phase boundary surface normal vector in the intersection point of ray and phase boundary), equation (4.1). In case 0 > 1, total reflection will occur if the incident angle is above the critical angle , equation (4.2) [109, 108].

$$n\_0 \sin \alpha = n\_1 \sin \beta \tag{4.1}$$

$$\alpha\_{crit} = \arcsin \frac{n\_1}{n\_0} \tag{4.2}$$

On any phase boundary with a change in refractive index, in addition to refraction, partial specular reflection will occur [109, 108]. Specular reflection of rays on phase boundaries can be mapped as a special case of refraction, in which the refractive index changes its sign [109]. Incident and reflection angle equal each other. Incident ray, reflected ray, and the phase boundary surface normal vector are again coplanar. The reflectivity of the phase boundary, being the ratio between reflected ray intensity and incident ray intensity,

**Figure 4.1:** Exemplary path of a ray (yellow arrows) propagating over a phase boundary (horizontal solid line) with a change in refractive index from 0 (originating medium) to 1. The incident angle is defined as angle between the incident ray vector ® and the phase boundary normal vector ® in the intersection point of ray and phase boundary ®. The reflection angle ′ is defined equally between the reflected ray vector ® and ®. The refraction angle is defined as the angle between the refracted ray vector ® and −® (® pointing into the entering medium).

depends on the incident angle and the refractive indices of the two media being in contact at the phase boundary and can be calculated for natural light with the Fresnel equations given with equations (4.3) [109, 108].

$$R = \begin{cases} \frac{1}{2} \left[ \frac{\sin^2 \left( \alpha - \beta \right)}{\sin^2 \left( \alpha + \beta \right)} + \frac{\tan^2 \left( \alpha - \beta \right)}{\tan^2 \left( \alpha + \beta \right)} \right] & \alpha \in (0, \pi] \\\ \left( \frac{n\_1 - n\_0}{n\_1 + n\_0} \right)^2 & \alpha = 0 \end{cases} \tag{4.3}$$

#### **4.1.2 Volume and surface interaction**

The introduced basic principles of geometric optics provide the basis for a model describing light propagating in multi component systems in which each component is transparent and homogeneous with regard to its refractive index. Briefly summarizing, ray paths in such systems are sequences of straight lines whose connecting points lie on phase boundaries. Further modelling is needed in order to map volume absorption, volume scattering, the superposition of both, and the interaction of rays on opaque surfaces. Rays traveling through an absorbing medium with constant refractive index and constant absorption coefficient experience an attenuation which can be described with a Lambert-Beer law approach, equation (4.4) [108, 110]. Thereby refers to the energy transported by the ray, corresponds to the ray path length and corresponds to the absorption coefficient.

$$
\partial \mathcal{I} = -\sigma\_a I \partial \mathcal{L} \tag{4.4}
$$

Additionally, the Lambert Beer type approach can be extended to include scattering. The introduced absorption coefficient is replaced by the extinction coefficient being the sum of absorption and scattering coefficient ( = + ). Noteworthy, in this case of simultaneously occurring absorption and scattering the ray attenuation calculated with the Lambert Beer type approach does no longer equal the absorption intensity because the fraction of scattered light (/) propagates through the medium with altered direction. In order to map the influence of scattering onto the radiation transport problem, the scattering characteristics of the scattering events must be defined. The scattering characteristics describe the intensity distribution of scattered rays around the scattering centre (volume element, that scatters light). Generally these scattering characteristics are complex and depend on the nature (material, size, and shape) of the scattering centers (or particles/pores respectively) [108]. The most simplistic assumption that can be made regarding this scattering characteristic is isotropic scattering into the whole sphere around the scattering centre.

The interaction of rays with opaque surfaces can be modelled with a reflection law correlating the intensity of the reflected ray to the intensity of the incident ray via the reflectivity of the opaque surface, which, thereby, is equally defined as the reflectivity of phase boundaries introduced earlier, equation (4.5), [108].

$$I\_R = RI\_{inc} \tag{4.5}$$

In order to map the influence of reflection events onto the radiation transport problem, in addition to the reflection law, equation (4.5), the reflection characteristics must be defined. The reflection characteristics describe the intensity distribution of reflected rays above the reflecting surface. Generally, these characteristics are complex and depend on the nature of the reflecting surface

(material and surface structure, or more precisely the pore structure of the near surface volume). The most simplistic models that can be applied are ideal specular reflection, which is mapped in analogy to partial reflection of rays on phase boundaries, see subsection 4.1.1, and ideal diffuse reflection which can be mapped with Lambert's cosine law, equation (4.6), [111]. In Lambert's cosine law is the polar angle of the reflected ray, which is defined relative to the surface normal in the intersection point of ray and surface, and the intensity of rays in direction of the surface normal, which can be shown to equal the incident ray intensity divided by . For Lambertian reflection, the intensity distribution with regard to the azimuth angle is homogeneous, or with other words, for one fix polar angle, the intensity does not vary for different azimuth angles.

$$I(\chi) = \cos(\chi) I\_{\text{max}} = \cos(\chi) \frac{I\_{\text{inc}}}{\pi} \tag{4.6}$$

In practice, the reflection characteristics of opaque surfaces are commonly approximated as a superposition of specular and ideal diffuse reflection with a defined specular share. Noteworthy, this represents a drastic simplification. Its validity must be assessed on a case to case basis.

## **4.2 Monte Carlo ray tracing**

Monte Carlo ray tracing is a collective term for Monte Carlo integration techniques for radiation transport problems. The origins of Monte Carlo ray tracing go back to lighting problems in computer graphics. First publications on Monte Carlo ray tracing go back to the sixties of the last century, see for instance [112]. From a very general perspective, Monte Carlo ray tracing techniques are implementations of the geometric optics simplification introduced briefly above. Basically, rays, generated in a source, are traced through a simulation domain comprising one or multiple objects that interact with the ray. On their way through the simulation domain the ray-object interactions are modeled according to the assumed physical models. Typically, the modelled interaction comprises interaction at phase boundaries, namely refraction, reflection and absorption, and interaction in volumes, namely absorption and scattering. For an illustration of a general ray tracing procedure see figure 4.2.

Depending on the level of detail of the interaction models implemented

**Figure 4.2:** Graphical representation of the ray tracing procedure implemented in this work in an exemplary simulation domain comprising a translucent banana and an opaque apple. The initial ray is generated in a 'light source' (point highlighted in green) and gets assigned an initial ray foot point ® 0 and an initial ray direction vector ®0. The ray is then traced in its initial direction until it hits an object comprised in the simulation domain. In the ray object intersection ® 1 the ray object interaction is modelled. In the exemplary presentation the ray is refracted and enters

the translucent banana volume and gets assigned a new ray foot point ® 1 and a new ray direction vector ®1. The ray is then traced through the banana volume. On its way through the banana the physical interaction, absorption and/or scattering, is modelled according to the underlying absorption/scattering models. In the exemplary case, the ray is scattered in ® 2 and gets assigned a new ray foot point and a new ray direction vector ®2. This procedure is repeated until the ray either misses any object in the simulation domain or is absorbed. In the exemplary presentation the ray leaves the translucent banana in ® 3 and gets finally absorbed on the surface

of the opaque apple, the ray end point ® (point highlighted in red).

and depending on the ray tracing technique applied, ray tracing delivers photorealistic image renderings, or in the case of an engineering problem, realistic approximations to the solution of the radiation transport problem to be solved. However, ray tracing techniques are computationally rather costly techniques. In order to map the lighting situation/the radiation transport problem properly, not one but a 'large' number of rays must be traced through the simulation domain over various interactions. The precise number of rays needed depends on the individual case setup and target metric and must be determined on a case to case basis in ray studies. For examples of such ray studies, refer to chapters 6, 7, and 8.

## **4.3 Implementation**

In computer graphics applications of ray tracing the direction of ray tracing typically goes from the view point (eye) into the simulation domain. This facilitates the efficient solution of the rendering equation or efficient generation of images, respectively. The Monte Carlo ray tracing implementation developed for the present work of course does not aim for the efficient generation of images. The aim is to map radiation transport from the light source(s) into the simulation domain with a special focus on absorption phenomena. The question of interest in almost all applications of ray tracing in the present work is: Where in the simulation domain photons are 'deposited' or absorbed? Therefore, the ray tracing direction in the implementation of the present work is the from a physicist's point of view more intuitive direction from the light source(s) into the simulation domain.

### **4.3.1 General procedure**

The general procedure realized with the implementation is graphically summarized in figure 4.2 and depicted in more detail in the flow chart in figure 4.3. The initial step of each ray tracing iteration is the generation of a ray with a pseudo-random location on the light source surface and a pseudo random direction. Thereby, the pseudo-random location and direction are chosen in a way that a large number of rays generated from the light source surface precisely map the assumed shape and emission characteristics of the light source. Subsequently, the closest intersection of the ray with the objects in the simulation domain is determined. Since the refractive index is assumed to be constant in all objects/the environment around the objects, this intersection search is a 'simple' geometric problem equal to the search of an intersection of a straight line with the surfaces of the objects in the simulation domain (compare section 4.1.1). With the closest intersection of the ray found, first, the ray volume interaction on the newly defined ray path segment is modelled. This modelling checks if an absorption or scattering event occurred on the ray path segment, and, if yes, where on the ray path segment it occurred. These two decisions are derived in a way that a large number of rays passing through the mapped volume precisely map the assumed ray attenuation model. With the determined position of the interaction, the type of interaction, absorption or scattering, is determined. If absorption occurred,

**Figure 4.3:** Flow chart of the implemented Monte Carlo ray tracing procedure mapping radiation transport from the radiation source(s) into the simulation domain by tracing a number of 0 rays through the simulation domain. The procedure comprises ray generation in the source, search for ray object intersections, modelling of volume absorption and scattering, and modelling of phase boundary interactions. Flow chart derived in accordance to DIN66001 [113]. Decision diamonds are 'Yes' in vertical direction and 'No' in horizontal direction.

the ray iteration is stopped and a new ray iteration is started in the light source. If instead scattering occurred, a new ray is derived that has its foot point in the derived scattering position on the ray path segment and a new, pseudo-random direction. Thereby, the pseudo-random scattering direction is chosen in a way that a large number of rays scattered in the same scattering centre precisely map the assumed scattering characteristics. If no volume interaction at all occurs, the interaction of the ray in the phase boundary is modelled according to the phase boundary type, either phase boundaries between two translucent objects or phase boundaries between a transparent and an opaque object, and according to the assumed interaction models. If the phase boundary interaction results in an absorption event, the ray iteration is stopped and a new ray iteration is started in the light source. In case of refraction or reflection, a new pseudo-random ray direction vector is assigned to a new ray with its foot point on the phase boundary intersection. Thereby, again, the pseudo-random direction is derived in a way, that a large number of rays interacting on the phase boundary map the assumed reflection characteristics (or refraction characteristics, respectively). From this point onward the procedure is repeated until either the ray is absorbed, the ray misses any of the objects in the simulation domain, or a maximum number of ray iterations is achieved. The last of the named interrupt criteria is necessary to avoid 'lock-in' situations in which rays are caught in infinite reflection scenarios, for instance, in opposite mirrors or internal total reflection scenarios in non absorbing/scattering objects. Such 'lock-ins' would entail an infinite run time. A complete ray tracing simulation with the implementation developed in the present work traces a predefined number of rays and primarily returns the derived ray paths. Additionally, during the solution process the ray end points of absorbed rays together with the properties of the absorbed rays (wavelength and number of absorbed photons/quantity of absorbed energy) are saved. The latter facilitates the evaluation with respect to the local volumetric rate of photon absorption. Noteworthy, the implementation also allows to chose the option to not save any ray paths which reduces the main memory occupancy during the solution process. In many cases this is recommendable since the individual ray paths are of secondary/no interest.

#### **4.3.2 Interaction models**

Objects in the simulation domain in ray tracing implementation in the present work can be assigned two interaction models. One interaction model represents an opaque object with a reflecting surface with a defined reflectivity. Of course the reflectivity can also equal zero which represents a perfect black absorber. Applications of such black objects may be probing surfaces in the simulation domain probing a radiation flux in a certain position/orientation etc., see for instance section 4.3.6. The reflection characteristics can be chosen to be ideally specular, ideally diffuse or a superposition of both with a defined specular share, detail see section 4.1.2. The second interaction model represents a translucent object with a defined refractive index and absorption and scattering coefficient. Ray attenuation in the volume is modelled with a Lambert Beer type approach. Scattering is assumed to be isotropic, for details see section 4.1.2. Scattering and/or absorption coefficients can be set to zero in order to model perfectly transparent objects. Interactions at phase boundaries between two translucent objects or between translucent objects and the environment are modelled according to Snell's law and Fresnel equations, details see section 4.1.1. For the evaluation of the Fresnel equations, light is assumed to be naturally polarized. The environment in the simulation domain is assumed to be homogeneous with respect to its user-defined refractive index and assumed to be non-scattering and non-absorbing.

## **4.3.3 Light source models**

Light sources in the ray tracing implementation in the present work can be mapped as surfaces that either emit ideally diffuse light (Lambertian emission characteristics) or collimated light with a preferential direction and a defined divergence angle. One simulation case can comprise an arbitrary number of light sources of different shape and with different emission characteristics. Each light source will generate the same number of rays during the simulation. The total emission power of the light sources, however, can be assigned individually.

## **4.3.4 Implemented acceleration techniques**

As mentioned, Monte Carlo ray tracing methods are a computationally rather costly methods. Monte Carlo ray tracing implementations, therefore, heavily depend on acceleration techniques that speed up the solution process.

#### **<IP_ADDRESS> Bounding volume acceleration**

The run time determining step in any Monte Carlo ray tracing implementation is the search for ray object surface intersections. Acceleration techniques for this step in particular are, in consequence, mandatory.

In the Monte Carlo ray tracing implementation in the present work, the surface of objects is described with discrete surface elements. In principle ray object intersections can be found by testing every surface element of every object comprised in the simulation domain for a ray intersection, see figure 4.4, left, for illustration. There is no mistaking that this approach is computationally extremely costly, especially for complex simulation domains with many objects and complex shapes. More precisely, the computational effort for this direct search approach is proportional to the number of surface elements in the simulation domain, see dashed line figure 4.5. The implementation in the present work, therefore, comprises a bounding volume acceleration approach that reduces the number of ray surface element intersection tests that are necessary to find an intersection. The idea behind bounding volume acceleration is to run the intersection search on a sorted data set. The surface elements are thereby sorted into a defined set of bounding volumes subdividing the space in the simulation domain. The search strategy in ray object intersection search accelerated with bounding volumes does now no longer test all surface elements for a ray intersection, but only those who are in a bounding volume that has a ray intersection. This precondition of a ray intersection of the bounding volume is the necessary precondition that a surface element in the bounding volume may have a ray intersection. In order that a bounding volume search strategy represents an acceleration technique, the surface of the bounding volumes must be easy to test for ray intersections. More precisely, the intersection test conducted with the bounding volume surface must be computationally less expensive than testing all surface elements in the bounding volume for an intersection. The bounding volume shape must, therefore, be primitive.

In addition to the sorting of surface elements into bounding volumes, bounding volumes can be nested in hierarchies, so bounding volumes can be built around bounding volumes in order to reduce the necessary number of intersection tests of rays with bounding volumes. For illustration of a hierarchical bounding volume search strategy with two hierarchy levels, see figure 4.4, right.

The implementation in the present work comprises a bounding volume search

**Figure 4.4:** Representation of the implemented strategy of bounding volume acceleration in ray object intersection search. In the left scenario all surface elements of banana and apple are tested against a ray intersection. In contrast in the right scenario, bounding volumes are employed to reduce the number of necessary tests to find the closest intersection. The bounding volumes are organised in two levels (red and green bounding volumes). All surface elements are sorted into the second level bounding volumes (depicted in green, for the sake of clarity not all second level bounding volumes are depicted). The surface elements in each second level bounding volume are only tested, if there is a ray intersection with the surface of the second level bounding volume that surrounds them. The second level bounding volumes are only considered in the search if the first level bounding volume surrounding them has a ray intersection. Consequently, less tests for ray surface element tests are necessary in order to find the ray object intersection (compare blue fractions of the banana and apple surface in left and right presentation).

strategy with bounding volumes nested in two hierarchies. Bounding volumes are simple boxes defined around the sorted group of surface elements or the sorted group of higher level bounding volumes, respectively. The number of bounding volumes in one hierarchy level is set depending on the number of surface elements, see equation (4.7). Under the assumption that every surface element has the same likelihood for an intersection, the number of bounding volumes per level calculated with equation (4.7) represents an optimum with a minimum number of ray surface element intersection tests expected.

$$N\_{bV} = \left(\frac{N\_{elements}}{4}\right)^{\frac{1}{3}}\tag{4.7}$$

Sorting of surface elements into bounding volumes is executed previously to the ray tracing procedure. Briefly summarizing the search strategy during the solution process comprises the following three steps: (1) search for intersections of the current ray with first level bounding volumes (depicted in red in figure 4.4, right). (2) If there are intersections of the ray with one of the first level bounding volumes, continue the search in the second step with a search for ray intersections with second level bounding volumes (depicted in green