Modeling and Optimization of the Photocatalytic Reduction of

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Modeling and Optimization of the Photocatalytic Reduction of Molecular Oxygen to Hydrogen Peroxide over Titanium Dioxide Bastien Burek, Detlef W. Bahnemann, and Jonathan Zacharias Bloh ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.8b03638 • Publication Date (Web): 19 Nov 2018 Downloaded from http://pubs.acs.org on November 19, 2018

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Modeling and Optimization of the Photocatalytic Reduction of Molecular Oxygen to Hydrogen Peroxide over Titanium Dioxide Bastien O. Burek1,2, Detlef W. Bahnemann2,3, Jonathan Z. Bloh1* 1

DECHEMA-Forschungsinstitut, Theodor-Heuss-Allee 25, 60486 Frankfurt am Main, Germany. E-mail: [email protected]; Web: http://dechema-dfi.de/TC.html 2 Institut für Technische Chemie, Leibniz Universität Hannover, Callinstraße 3, 30167 Hannover, Germany 3 Laboratory “Photoactive Nanocomposite Materials”, Saint-Petersburg State University, Ulyanovskaya str. 1, Peterhof, Saint-Petersburg, 198504, Russia

Abstract This study focuses on understanding the mechanisms for optimization of the photocatalytic hydrogen peroxide production over TiO2 (Aeroxide P25). Via precise control of the reaction parameters (pH, temperature, catalyst amount, oxygen content, sacrificial electron donor and light intensity) it is possible to tune either the apparent quantum yield or the production rate. As a result of the optimization, apparent quantum yields of up to 19.8 % and production rates of up to 83 µM min-1 were obtained. We also observed a light dependent change of the reaction order and an interdependency of the light intensity and catalyst amount and developed a well-fitting kinetic model for it, which might also be applied to other reactions. Furthermore, a previously unreported inactivation of the photocatalyst in case of water oxidation is described. Keywords: photocatalysis, light intensity, titanium dioxide (TiO2), oxygen reduction, peroxide (H2O2), catalyst inactivation

hydrogen

Introduction Hydrogen peroxide (H2O2) is a versatile compound with a broad use in many industrial areas. For example, it is utilized in medicine, waste water treatment, as a ripening agent, in detergents and even as a liquid propellant.1,2 The main use of H2O2 is certainly pulp and paper bleaching3,4 and as a reactant in chemical syntheses.5–7 Especially as an oxidant H2O2 is an interesting compound since it has a high atom efficiency (47.1 wt-% are active oxygen), it has a high oxidation potential over the whole pH range (EO=1.763 V at pH 0, EO=0.878 V at pH 14), and since water is the only by-product it is environmentally friendly.1 Nowadays, industrial H2O2 production is mainly realized via the anthraquinone process which requires two separate high energy demanding reaction steps (hydrogenation and oxidation).8,9 The direct synthesis of H2O2 from gaseous O2 and H2 over metallic catalysts, like Pd and Au nanoparticles or combined catalysts like Pd-Au and Pd-Pt has also been studied intensively to overcome the ecoissues of the anthraquinone system.10 Amongst other methods, the well-known electrosynthesis has also re-emerged as a green method if renewable energy is used for H2O2 generation via oxygen reduction or water oxidation.11–14 Utilizing light as energy source for the photocatalytic generation of H2O2 over semiconductor materials is at least known since Baur and Neuweiler reported its generation over ZnO in 1927.15 As ACS Paragon Plus Environment

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only light, water, molecular oxygen and the catalyst are necessary it can be regarded as an ecofriendly method. It is often applied in the field of waste water treatment where H2O2 is reported to be one of the responsible substances for the degradation of organic pollutants, e.g., various pharmaceuticals and dyes.16,17 Furthermore, it is considered as a promising solar fuel using sunlight for the photocatalytic H2O2 production.18,19 Recently, it also got into focus in processes which require a precise control of the H2O2 concentration via in situ generation thereof, such as epoxidation or H2O2 dependent enzyme reactions.20,21 The mechanism for the production of H2O2 directly from water and oxygen on the surface of an illuminated semiconductor photocatalyst has been described many times.22–29 The simultaneously occurring oxygen reduction and water oxidation can proceed via two consecutive one-electron transfers or one concerted two-electron transfer. The in the absence of additional co-catalysts more probable one-electron reactions follow a path via several radical intermediates which can react in multiple pathways in reversible reactions,30 illustrated in Fig. 1a. The formed H2O2 can also be further photocatalytically reduced to water or re-oxidized to O2. Introducing easily oxidizable (sacrificial) reagents such as alcohols into the system replaces water as the electron donor and, due to their lower oxidation potentials and faster reaction kinetics, strongly inhibits other oxidation processes. In Fig. 1b the photocatalytic oxidation of 2-propanol31 as sacrificial reagent for H2O2 generation is shown exemplary. a

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Figure 1. Schematic view of the possible reaction pathway of photocatalytic hydrogen peroxide generation via reduction of oxygen without (a) and with (b) 2-propanol as sacrificial electron donor in aqueous media.

Kormann et. al.22 reported a kinetic model for the initial phase of the hydrogen peroxide formation reaction based on the described mechanisms. According to it, the rate of H2O2 formation (rF) is zero order (eq. 1) while the degradation process (rD) follows first order kinetics (eq.2), both are linearly dependent on the (absorbed) photon flux ( ). In combination they lead to a steady state concentration, which should be independent of the light intensity. The time-dependent concentration of hydrogen peroxide can be explicitly expressed by eq. 3: (eq. 1) (eq. 2) ACS Paragon Plus Environment

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(eq. 3) In general, TiO2 is often reported to exhibit very low apparent quantum yields (also known as photonic efficiency), many claim TiO2 to be inefficient mainly due to a high electron-hole recombination rate and a high decomposition rate of H2O2 on TiO2, especially on P2532 and are therefore looking for other more efficient catalyst materials such as brookite nanorods,33 reduced graphene oxide,34,35 carbon nitride,36–38 carbon dots,39 N-doped carbon nanohorns,40 oxidized carbon nanotubes41 and Au-BiVO442 or modifications of the TiO2 based system (e.g., fluoride based surface passivation,43 metal nanoparticles like Au44,45 or Au/Ag46 as cocatalysts, Cu2+ as charge transfer mediator47 and various sacrificial electron donors30,34). However, a direct comparison of the different materials under the same conditions is difficult as they have different physical and chemical properties (surface, particle size, dispersibility, optical characteristics, band gap, just to name a few) which may all affect their efficiency. Consequently, each material has different optimal working conditions. Furthermore, different light sources and reactor types are used which makes a comparison even more complicated. In case of cascade processes where the second step dictates some of the conditions (e.g., enzyme coupled reactions18) a comparison under those fixed conditions is necessary. However, to evaluate the materials themselves it is more advisable comparing the results for each respective optimized condition. We show that the efficiency of a photocatalytic process utilizing TiO2 can be optimized via engineering of reaction conditions and understanding the reaction kinetics as well as the correlation between those parameters. Therefore, the H2O2 generation over illuminated TiO2 has been investigated in detail and the influence of the reaction parameters (pH, temperature, catalyst amount, oxygen content, sacrificial electron donor and light intensity) as well as their interdependency is critically discussed.

Experimental section All experiments were performed in a 14 mL cylindrical glass reactor. (cf. Fig. S1) For the illumination two different controllable UV-LED Systems (LEDMOD365.1050.V2, Omicron and M365LP1, Thorlabs) both with peak emission at 365 nm have been used in combination with collimating optics to reach a homogeneous light distribution over the whole illumination window (2 cm circular diameter, 3.14 cm² area). Unless mentioned otherwise, the temperature of the suspension was kept at 25 ± 0.5 °C by circulating water through an outer jacket around the reactor. The magnetically stirred suspensions were pre-saturated via bubbling of O2 which was continued during the reactions with a flow rate of 2 mL min-1. The incident photon flux in the reactor was determined using ferrioxalate actinometry.48 Photocatalytic H2O2 generation TiO2 (0.01-10 g L-1, Evonik Aeroxide P25) was suspended in distilled water or phosphate buffer (0.1 M), respectively, with or without adding 2-propanol (99.5%, Aldrich). To completely disperse TiO2 the suspensions were sonicated with an ultrasonic glass finger (2 x 5 s, 20 % A, UP200St, Hielscher). During the experiments, 300 µL samples were taken from the reaction solution in defined temporal intervals and filtered through a syringe filter (0.2 µm, PVDF, Roth). The H2O2 concentration of the samples was analyzed using the horse radish peroxidase (HRP) catalyzed stoichiometric dimerization of p-hydroxyphenylacetic acid (POHPAA) which yields a fluorescent product.49 POHPAA (4 mg, Alfa Aesar, freshly recrystallized twice from water) and lyophilized powder of HRP (1 mg, ACS Paragon Plus Environment

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163 u/mg, Type II, Sigma) were both dissolved in TRIS buffer (12.5 mL, 1.0 M, pH 8.8, Alfa Aesar) respectively. To a 100 µL sample containing H2O2, 12.5 µL of each solution were added and the fluorescence signal (λex = 315 nm, λem = 406 nm, 25 °C) was determined in a microplate reader (SynergyMx, BioTek) after 30 min. For the experiments with a varying oxygen content, mass flow controllers (F-201CV, Bronkhorst) have been used to mix N2 and O2 in defined compositions. The obtained concentration-time-profiles were analyzed with eq. 3 to obtain the respective formation and decomposition rate constants kF and kD. Ferrioxalate Actinometry Chemical actinometry was performed at 25 °C using 14.0 mL of a freshly prepared (by mixing potassium oxalate and iron(III) chloride and recrystallization from water) 150 mM potassium ferrioxalate solution in 50 mM sulfuric acid. The solutions were irradiated under gentle stirring in a darkened room to avoid interference from other light sources. To determine the amount of Fe(II) formed during a reaction 25 µL samples were diluted with 20 µL of a 0.1 % aqueous 1,10phenanthroline solution, 75 µL of 50 mM sulfuric acid and 50 µL of 1 M acetate buffer. The final volume of the mixture was adjusted to 200 µL with MilliQ water. The absorbance of the ferroin complex (λmax = 510 nm) was measured in a microplate reader (PowerWave HT, BioTek). The photon flux density was subsequently calculated via the generation rates of Fe(II), cf. eq. S1.

Results and Discussion In order to understand and explain the complex interplay of the different reactions parameters that influence the photocatalytic hydrogen peroxide formation and degradation reaction, these were studied under 121 different conditions excluding duplicates, which is by far the largest collection of experimental data on this reaction. For each reaction, formation and degradation rate constants were calculated from the time-concentration profiles according to eq. 3. Also, the incident photon flux density ( ) for the photocatalytic set-ups has been measured using ferrioxalate actinometry,48 and the respective apparent quantum yields ( ) were calculated using eq. 4, taking into account that hydrogen peroxide requires two reduction equivalents: (eq. 4) To optimize a photocatalytic reaction, it is necessary to understand the impact of the reaction conditions on the parameter of interest (e.g., formation rate) and to identify the limiting factors. Therefore, we systematically investigated the impact of different reactions parameters on both the kinetics and the efficiency. The respective results are shown hereafter. Effect of 2-propanol as sacrificial reagent Small alcohols such as 2-propanol are well-known to be oxidized photocatalytically by TiO2 providing two electrons which can be used to reduce molecular oxygen to H2O2. (cf. Fig 1 b) The further oxidation of the emerging aldehydes or ketones to carboxylic acids, shorter chain oxygenates and finally CO2 can provide additional electrons. Since 2-propanol is first oxidized to acetone whose further oxidation proceeds much slower,50 it is a very good model compound as the electrons are mainly provided by the first oxidation step and there is only little influence of further oxidation steps. One issue using an alcohol as sacrificial electron donor is possible autoxidation directly with molecular oxygen or with the photocatalytically generated superoxide radicals which may lead to a ACS Paragon Plus Environment

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deficient electron balance.51 Another factor that needs to be taken into account is the so-called current doubling effect which originates from the strong reducing power of the formed alcohol radicals which can inject an electron into TiO2, effectively doubling the number of reducing equivalents per photon.52

H2O2 formation rate constant kF / µM min-1

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Figure 2. Dependence of the H2O2 generation (kF, ▪) and degradation (kD, ◦) rate constants on the 2-propanol -1 -1 -1 concentration. Reaction conditions: 0.1 M phosphate, pH 7, 0.1 g L TiO2, 25 °C, 365 nm, 219 µE L min , -1 2 mL min O2-bubbling.

Fig. 2 shows the generation and degradation rates in dependence on the 2-propanol concentration. The H2O2 generation rate first rises steadily with increased 2-propanol concentration but then slightly declines after passing through a maximum at 10 vol%. This finding can be explained by a better availability of the alcohol at higher concentrations due to better mass transfer and catalyst surface coverage, while too much alcohol blocks the surface for oxygen adsorption and reduction. The degradation rate gets smaller with a higher alcohol amount due to preferred oxidation of 2-propanol and therefore less oxidation of H2O2. The solubility of O2 in the solution is also a little higher with the alcohol present, which could slightly increase the reaction rate.11 However, as the reaction rate is already quite saturated with respect to the oxygen availability (vide infra), this effect is likely negligible. The higher solubility might become interesting in the case of very high H2O2 generation rates were the diffusion of O2 from the gas phase through the solution to the surface might become a limiting factor. The degradation of the peroxide is suppressed in the presence of the alcohol by about 75%, but this effect is already saturated at 1 vol-%. This is expected as the alcohol is much easier to oxidize than water and therefore better competes with the peroxide in the oxidation reaction. Effect of solution pH The pH of the solution has impacts at different parts of an aqueous photocatalytic system which might explain the complex pH dependence of photocatalytic H2O2 generation and degradation rates shown in Figs. 3 and S37. The degradation rate rises exponentially with the pH, regardless of the presence of 2-propanol. Albeit it is known that the degradation rate rises with the pH,53 it is not possible to separate the photocatalytic degradation of H2O2 from the other degradation mechanisms such as thermal and non-photoinduced catalytic decomposition. While H2O2 is stabilized in acidic


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Figure 3. pH dependence of the H2O2 generation (kF, ▪) and degradation (kD, ◦) rate constants. Conditions: 0.1 M -1 -1 -1 -1 phosphate, 0.1 g L TiO2, 10 vol-% 2-propanol, 25°C, 365 nm, 219 µE L min , 2 mL min O2-bubbling.

The generation rates on the other hand show a completely different behavior. With 2-propanol the formation rate rises between pH 2 and 5 then stagnates until pH 7 and reaches a maximum around pH 8 before it drops again at a higher pH. In case of water oxidation the rate seems to be rather constant between pH 2 and 7, if there are many differences they are too low to be detected, above pH 8, the generation rate rises exponentially, cf. Fig. S37. With a change in pH the dissociation of water and therefore the concentration of protons and hydroxyl ions in solution changes, which are directly involved in the reaction mechanism as intermediate reactants and consequently have an impact on the H2O2 kinetics. (cf. Fig. 1) The reaction mechanism suggests that high proton concentrations accelerate the O2 reduction through facilitation of superoxide protonation while slowing down oxidation processes since hydroxyl radical and alcohol radical generation are accompanied by proton formation. This would indicate that under the conditions employed, the system appears to be more limited by the oxidation processes than the oxygen reduction and hence increasing the pH also increases the overall reaction rate. This might explain the rise of kF between pH 2 and 5. Between pH 5 and 7 TiO2 crosses its isoelectric point (approx. pH 6.3 for P25),54 and at pH 7 the dissociation of water has its minimum. Combined this might explain the invariance of the formation rate in this pH region since the positive effect of the reduced proton concentration on the oxidation rate is counteracted by the change in surface charge. In addition to surface charge effects, the dispersibility is not optimal in this pH region according to the zeta potential54 which might lead to agglomeration and therefore less accessible catalytic surface. At pH 8 there is a maximum of bridging O(H)-groups55 which are directly involved in oxidative surface processes.56 Furthermore, there is less electron-hole-recombination at a higher pH57 and the higher hydroxyl ion concentration also favors H2O2 generation as it improves deprotonation of the alcohol and hydroxyl ions. However, photocatalytic oxidation of alcohols is slower at pH >9 which is related to the strong adsorption of the intermediate products.58 Another aspect one has to keep in mind is the shift of the position of the conduction (CB) and valence band (VB) with the pH (approx. -0,059 V pH-1). At a higher pH the CB becomes more reductive which should enhance reduction of O2 as the O2/O2•- potential stays constant above a pH of approx. 4.8.31


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Light Intensity and catalyst amount Understanding the impact of light intensity in photocatalytic reactions is very important for the application of photocatalysis both in academia and industry. Particularly, if these reactions are intensified by increasing the incident photon flux, this becomes a very critical aspect. The effect of increased light intensity has been studied for a number of different photocatalytic reactions but is not completely understood yet. Many authors state that at low light intensity, the reaction rate increases linearly with the photon flux while at higher intensities, it follows a square root dependence. This non-linearity at high photon fluxes is generally assumed to be a result of increased charge carrier recombination and typically interpret as a (photo)catalyst property.59–62 As recombination is the only considered loss process once photons have been absorbed, any observed non-linearity will naturally be accompanied by increased recombination. However, in this case, recombination is only a symptom of catalyst inefficiency and not its actual cause. Other authors report that at very high light intensities, the reaction may change again to an exponential increase for multi-electron transfer reactions, highlighting that currently there is no clear consensus on the behavior of photocatalysts with increased light intensity and its mechanism.63 The latter will likely have no effect in the present study as here all reactions are interpret as (consecutive) one-electron transfers. Since data on the behavior of hydrogen peroxide generation of illuminated titanium dioxide at high light intensities is not available in the literature, experiments with both light intensity (2.55801 µE L-1 min-1) and catalyst concentration (0.01-10 g L-1) each spanning four orders of magnitude were conducted. Fig. 4 shows exemplary profiles of the light intensity and catalyst concentration effects. At low light intensities, the formation rate rises approximately linearly with the photon flux, this is even more apparent when consulting a log-log plot (cf. Fig. S30 and S35). When the light intensity exceeds a value of about 100-200 µE L-1 min-1, the formation rate starts to deviate from linear behavior and shows diminishing returns. After this point, the reaction order is 0.2-0.8 with respect to the light intensity (cf. Fig. S30 and S35). This agrees well with the reports of a square root dependence (reaction order 0.5) at high light intensity. However, our observation here is that the higher the catalyst concentration is the higher is also the reaction order, there appears to be an interdependence of both parameters that has up to now, never been reported. At the highest studied catalyst concentrations, the reaction order is significantly higher than 0.5 even at extremely high light intensities, this observation cannot be readily explained by the traditional models. irradiance / mW cm-2 60

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Figure 4. Exemplary dependence of kF (▪) and kD (◦) from a) (left) the photon flux density at a fixed catalyst -1 amount of 2 g L , cf. Fig. S13-22 for the related concentration-time curves and b) (right) from the catalyst -1 -1 amount at a fixed light intensity of 3437 µE L min , cf. Fig. S21 for the related concentration-time curves. Both


ACS Catalysis

-1

data sets were obtained at 0.1 M phosphate, 25°C, 365 nm, 2 mL min O2-bubbling, pH 7, 10 vol-% 2-propanol. Also shown is the calculated fit for the formation rate according to the developed model (eq. 14) as a solid black line.

Fig. 5 shows the dependence of the apparent quantum yield ( , calculated according to eq. 4) on the incident photon flux. As a consequence of the linear behavior the quantum yield is nearly constant at low light intensities. However, mimicking the behavior of the formation rate it rapidly decreases at a higher photon flux, with the inflection point at about 200 µE L-1 min-1. Liu et. al. already described a comparable behavior for the quantum yield.64 This behavior is observed irrespectively of the presence of a sacrificial electron donor with the only difference being a constant multiplier on the quantum yield which is always higher by a factor of about 7 when 2-propanol is added.

10

apparent quantum yield / %

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1

0.1

with 2-propanol without 2-propanol

0.01 1

10

100

1000

10000

photon flux density / µE L-1 min-1

Figure 5. Light Intensity dependence of the apparent quantum yield without (◦) and with (▪) 10 vol-% 2-1 -1 propanol. Conditions: 0.1 g L TiO2, 0.1 M phosphate, 25°C, 365 nm, 2 mL min O2-bubbling (▪) pH 7, 10 vol-% 2-propanol, (◦) pH 4 and no alcohol.

At a fixed light intensity, the formation rate rises with the catalyst amount until it reaches a saturation, cf. Fig. 4. The initial increase of kF can simply be explained by increased light absorption with increased photocatalyst concentration. At a concentration of 0.03 g L-1, all of the light (>99 %) is already absorbed but the reaction rate at higher light intensities continues to increase far beyond this point which may not appear logical at first glance. Also, the photocatalyst concentration required for saturation gradually increases with the light intensity. Both of these observations are usually not accounted for in the present kinetic models. The decomposition rate constant seems to be independent of both the catalyst amount and light intensity (cf. Fig. 4) when 2-propanol is present. Without a sacrificial electron donor the decomposition rate slightly increases with both parameters, but to a lesser extent than the formation rate (cf. Figs. S34 and S38). This indicates that the decomposition rate is strongly influenced by other factors such as thermal decomposition and the photocatalytic contribution is difficult to directly determine. As a consequence of the relative invariance of the decomposition rate constant, the steady state concentration also changes with both light intensity and catalyst amount. This is contradictory to the simple model proposed by Kormann et. al.22 which predicts the steady state concentration to be invariant of the light intensity. In order to explain these new observations, we developed a new kinetic model based on only three primary reactions to simulate the behavior. The first reaction ( , eq. 5) is the excitation of the ACS Paragon Plus Environment

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ACS Catalysis

photocatalyst, which requires a photon and a reactive site ( ) that is not already excited. Here, charge carrier creation and subsequent trapping on reactive surface sites are simplified as a single process that is modulated by the intrinsic quantum yield of the photocatalyst ( ) and the absorbed photon flux ( ). (eq. 5) The second reaction ( , eq. 6) is the recombination or relaxation of those excited states ( ) which depends linearly on their density (with respect to the total number of reactive sites ). This rate does not include recombination of charge carriers before they are trapped, as that is already included in . The total rate of charge carrier recombination is approximately second order with respect to the light intensity (cf. SI, chapter 4.2) as is commonly assumed in similar models. (eq. 6) The third reaction ( , eq. 7) is the charge transfer from the excited reactive state to an adsorbed substrate ( ) to form the product ( ), which is dependent on both the number of excited reactive states (surface trapped charge carriers) and the surface coverage with the target molecule ( ), similar to a Langmuir-Hinshelwood approach. Note that here, we only consider the half-reaction (oxidation or reduction) which is rate limiting as the corresponding other reaction often proceeds with several orders of magnitude higher rate and therefore has only little impact on the overall reaction rate. (eq. 7) Assuming quasi-stationarity, these three reactions can be distilled into a local reaction rate, which can be simplified by defining (eq. 9) as the maximum attainable reaction rate per catalyst mass, depending on the intrinsic reaction rate constant (per reactive site , or more practical per catalyst mass ) the current substrate concentration and resulting surface coverage as well as the photocatalyst concentration. The rate is dependent on both the photocatalyst concentration and the local light intensity. In both parameters, the equation shows a saturation-curve-like behavior where an increase in one parameter increases the saturation point of the other one. Similar rate equations have also been formulated by other authors, who are however usually not considering light intensity and catalyst concentration as interdependent.61,65–70 (eq. 8) (eq. 9) (eq. 10) Also, in most of those cases the reaction rates are calculated as a function of the average light intensity without taking its very inhomogeneous distribution into account. This is a valid approach only if the reaction rate scales linearly with the light intensity! If the reaction rate has a non-linear response to the light intensity, as in the present and many other cases, the global reaction rate can only be calculated by integrating over the whole reactor volume, taking the local volumetric rate of photon absorption (LVPRA, in this case) into account. Since this can be quite a challenging and ACS Paragon Plus Environment

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time-consuming endeavor, particularly for complex reactor and light source geometries, it is unfortunately only done in few cases.62,66,71,72 Currently, there exists no easily applicable model for heterogeneous photocatalytic reactions which takes the LVRPA into account. Fortunately, the system employed herein features a collimated light source and rotational symmetry and therefore only shows a variation of light intensity in one dimension ( ). If reflection is neglected, the light intensity can therefore simply be calculated according to the Lambert-Beer-law (and its derivative), using the average photon flux density ( ), the length of the reaction vessel ( ) and the extinction coefficient and concentration of the photocatalyst ( =16.4 mol g cm-1, ), eq. 11. This allows to easily calculate the local reaction rate ( ), eq. 12, by combining eqns. 10 and 11, which is further simplified by defining α as the optical density per catalyst mass. Consequently, the global reaction rate ( ) for the given system is obtained by integration of the local reaction rate over the reactor length, eq. 14. This global reaction rate is typically the only observable one and in this case equals the hydrogen peroxide formation rate constant kF. (eq. 11) (eq. 12) (eq. 13)

(eq. 14) For most cases, the equation can be further simplified (which may even be necessary for computation with large values of α) into eq. 15. (eq. 15) This rate equation only has 3 parameters ( , and ), all of which have direct physical meaning, one constant ( , dependent only on the setup geometry and the photocatalyst material used) and the variables and . The rate equation was subsequently applied to the observed data points (non-linear optimization, Levenberg-Marquardt algorithm with least squares), the resulting plot is shown in Fig. 6. The aforementioned model fits the observed behavior quite well and also allows to extract the parameters maximum reaction rate constant ( =1358 µmol g-1 min-1), recombination rate constant ( =653 µM min-1) and intrinsic quantum yield ( =2.623%, note that this is only half the value of the apparent quantum yields used in the first part of the manuscript since it does not account for the requirement of two reduction equivalents for one molecule of H2O2).


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ACS Catalysis

Figure 6. Interdependence of the measured H2O2 formation rate constant kF on the amount of catalyst and the photon flux density shown as black and dark grey dots. Also shown is the calculated best fit to the proposed model (eq. 14) as a surface plot, the vertical lines attached to the data points show their respective difference to the calculation. Data points that are black mean they are on or above the surface plot, dark grey data points signify they are below the surface.

According to this calculation, the maximum attainable local reaction rate (at infinite light intensity) is 1358 µmol g-1 min-1, which is governed by the intrinsic reaction kinetics of the photocatalyst ( ) and its surface coverage with oxygen (or the electron donor if that becomes the limiting factor). Consequently, it can only be further increased by using a (co)catalyst with better kinetics for the reaction or by increasing the oxygen availability (e.g., higher pressure, solvent with better oxygen solubility). Note that a higher catalyst concentration will also increase this parameter, however, this cannot be done indefinitely due to solubility/dispersibility limits. At low light intensities, the local reaction rate is linearly dependent on the light intensity, according to eq. 16. Here, it is evident that at lower catalyst concentrations, this rate may be diminished by increased charge carrier recombination. (eq. 16) The global reaction rate only increases linearly with the light intensity (constant quantum yield) as long as the local reaction rate at the beginning of the reactor ( , cf. eq. 13) can still reach the maximum attainable rate. This is the case as long as eq. 17 is fulfilled. (eq. 17)


ACS Catalysis

Using the calculated parameters for the present system this is the case when µE L-1 min-1 (at 1 g L-1 catalyst concentration), which fits very well with the observation that the reaction rate increases linearly with the light intensity up to a photon flux density of about 100-200 µE L-1 min-1, cf. Fig. S30. The mentioned maximum reaction rates are 2-3 orders of magnitude higher than the average observed reaction rates, so one could conclude that the reaction kinetics cannot be a limiting factor. However, since the local light intensity at the very beginning of the reactor is in this case (eq. 11 with ) higher than the average light intensity, the local reaction rate actually approaches this limiting case. As seen in Fig. 7, the maximum theoretically obtainable reaction rate, eq. 16, is actually higher than the maximum rate given by the reaction kinetics at the very beginning of the illumination zone. Consequently, there is a significant loss of quantum efficiency due to kinetic constraints which is the origin of the non-linear response of the reaction rate with the light intensity.

500

Local reaction rate R(z) / µM/min

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

400

Rate without limitations Calculated rate Kinetically limited rate

300

Loss of efficiency due to kinetic constraints

200

100

0 0.0

0.2

0.4

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Reactor depth z / cm

Figure 7. The maximum attainable reaction rate ( ), the non-limited local reaction rate (eq. 16 with eq. 11) and the actual local reaction rate (eq. 13) in dependence of the depth into the reactor (z) for an exemplary -1 -1 -1 case of =0.1 g L and =5802 µE L min .

Therefore, the non-linearity at higher light intensities is primarily a consequence of the inhomogeneous light distribution and not an immutable material property as often assumed. If homogeneous light distribution could be achieved, for instance by means of delocalized internal illumination, this would eliminate the from eq. 17, allowing (in this case) up to 151 times higher global reaction rates without losing quantum yield.73 However, reaction setups featuring strong gradients in the light distribution will likely never be able to achieve both good quantum yields and high productivity at the same time due to kinetic constraints in the hot spots. It should be noted that in the current version of the model, the neglection of scattering may lead to an overestimation of the absorbed photon flux as light scattered out of the reactor is incorrectly counted as absorbed. Consequently, the quantum yield is underestimated and should be interpret as a lower limit,74 since particularly back-scattering from the front-window can be quite significant.71 This error can be minimized by reactor design (e.g. using reflectors) or by determining the amount of scattered-out light and correcting the incident photon flux by it.75


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Effect of dissolved oxygen

0.05 2.0 0.04 1.5 0.03

1.0 0.02

0.5

0.01

0.0

0.00 0

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80


The dependence of the generation and degradation rates of the O2 content in the bubbling gas is shown in Fig. 8. As long as the availability of oxygen on the surface of TiO2 is a limiting factor, the generation rate is dependent of the oxygen content. When the oxygen availability is not limiting anymore, a higher oxygen content does not further increase the generation rate. This saturation point appears to be reached at about 50 % in our case. Comparing these results with a study of photocatalytic H2O2 production with ZnO22 where saturation was already reached at about 20 %, one can conclude that the point of saturation is dependent on the magnitude of the generation rate, similar effects have also been found for phenol degradation.60 If the generation rate is lower, a lower gradient between liquid and gas phase oxygen is required to maintain saturation at the catalyst surface and therefore less oxygen content in the atmosphere is required. Furthermore, this coincides with reports of a faster decay of dissolved oxygen with a higher reaction rate during photocatalytic experiments in a closed system.76 It is important to both guarantee a sufficiently high dissolved oxygen content and also to keep it that way with a high oxygen transfer rate into the solution. Simply bubbling air into the solution through a tube might not suffice in all cases, particularly if high light intensities are employed.

H2O2 formation rate constant kF / µM min-1

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100

O2 content in the gas phase / %

Figure 8. Dependence of the H2O2 formation (kF, ▪) and degradation (kD, ◦) rate constants on the amount of -1 oxygen in the bubbling gas. Conditions: 0.1 M phosphate, pH 7, 0.1 g L TiO2, 10 vol-% 2-propanol, 25°C, -1 -1 -1 365 nm, 219 µE L min , 10 mL min gas-bubbling. Also displayed is the calculated formation rate according to the model (eq. 14 with eq. 18) as a solid black line.

The developed model can directly be applied to this case as the reaction rate already features an adsorption term ( ). Using a Langmuirian adsorption term (with oxygen pressure in the gas phase and adsorption constant ), the oxygen adsorption can be directly incorporated into the term of the model, eq. 18 (here we approximate the dissolved oxygen content as proportional to the gas phase oxygen pressure). (eq. 18) Applying the model (eq. 14) with this modification (eq. 18) yields a very good fit, cf. Fig. 8, with an adsorption constant of 2.582 atm-1. The calculated reaction rate levels off far earlier than the adsorption isotherm since at high oxygen content, is less limiting and therefore yields diminishing returns. Consequently, the oxygen content needed for saturation is strongly dependent on the


ACS Catalysis

reaction rate and light intensity, in line with the abovementioned observation that other authors claim that less oxygen is required for saturation (at also lower light intensity).22 Effect of temperature Photocatalytic processes are often described to proceed efficiently at ambient temperature with only negligible temperature processes due to low activation energies. Nonetheless, in the case of H2O2 generation two effects of temperature can be observed. In the presence of 2-propanol the generation of H2O2 rises exponentially with the temperature while in the case of water oxidation the generation is approximately constant in the investigated range of 5 – 60°C. (cf. Figs. 9 and S36) From the respective Arrhenius plot (cf. Fig. S33) a pseudo activation energy of 19.7 kJ mol-1 can be calculated for the H2O2 generation with 2-propanol. However, an attempt to integrate the temperature dependence into the model by defining an Arrhenius dependence, eq. 19, yields only an acceptable fit (cf. Fig. 9) for the lower temperatures ( ≤40°C) with an activation energy ( ) of 31.6 kJ mol-1 and a pre-exponential factor ( ) of 5.9· 1010 µM min-1. (eq. 19)

6

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0.04 0.03

2 0.02 1 0.01 0

0.00 0

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35

40

45

50

55

60


The fact that this approach yields a different value for the activation energy and also the apparent non-exponential behavior of the calculated reaction rate with higher temperature is a consequence of the non-linear response of the reaction rate on . The under-estimation of the model in this case indicates that other parameters such as recombination rate, adsorption and intrinsic quantum yield also have a temperature dependence that is not considered by this simple approach. Nonetheless, this illustrates that our model can also be extended to account for temperature effects at least for moderate values of up to about 40 °C.


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65

Temperature / °C

Figure 9. Temperature dependence of the H2O2 generation (kF, ▪) and degradation (kD, ◦) rate constants. -1 -1 -1 -1 Conditions: 0.1 M phosphate, pH 7, 0.1 g L TiO2, 10 vol-% 2-propanol, 365 nm, 204 µE L min , 2 mL min O2bubbling. Also displayed is the calculated formation rate according to the model (eq. 14 with eq. 19) as a solid black line.

The degradation rate of H2O2 increases exponentially with a higher temperature, regardless of the presence of an alcohol. This could possibly be due to both, thermal dissociation and a faster photocatalytic degradation. A higher temperature improves mass transport and adsorption kinetics which explains the faster oxidation of 2-propanol and simultaneously higher oxygen reduction rates as well as the faster degradation of H2O2. As water is present in excess and adsorbs very well on TiO2, ACS Paragon Plus Environment

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ACS Catalysis

the increased mass transfer has only a negligible effect on the oxidation of water (at least in case of the low reaction rates observed here). Even though the oxygen solubility is lower at higher temperatures11 which should lead to lower photocatalytic H2O2 generation rates53, this effect appears to be overcompensated by the improved kinetics of the charge transfer. Usually photocatalytic processes are described to have a negligible temperature dependence, at least in the region of room temperature.77 The reason that in the present case, the temperature has quite a noticeable effect might be due to the fact that under the employed conditions, the intrinsic reaction rate ( ) is one of the limiting factors for the overall reaction. For other reactions with better intrinsic kinetics or lower light intensities whose reaction rate is mostly governed by the absorbed photon flux, temperature likely has no significant effect. Optimized reaction conditions Using all the information gathered on the effects of the different reaction parameters, optimized conditions to achieve a maximum in formation rate and quantum yield could be predicted. As already shown by other authors it is not possible to optimize for both a high generation rate and a high apparent quantum yield at the same time since the generation rate strictly increases with a higher photon flux while the apparent quantum yield drops due to increased recombination (cf. Fig. 5). Therefore, two different optimized conditions can be defined. These were subsequently verified by conducting respective experiments, their results are shown in Table 1. Table 1. Kinetic constants and apparent quantum yields for the respective optimized conditions. Reaction -1 conditions: 365 nm illumination, pH 8, 0.1 M phosphate, 60°C, 2 mL min O2-bubbling. For optimization of kF: -1 -1 5 g L TiO2, for optimization of ξ: 0.1 g L TiO2. (cf. Figs. S5-8 for the corresponding concentration-time profiles)

without 2-propanol 10 vol-% 2-propanol

photon flux density [µE L-1 min-1]

kF [µM min-1]

kD [min-1]

ξ [%]

c(H2O2)SS [µM]

2.4

0.03

0.02

2.4

3.1

5802

9.3

2.7

0.3

1.5

2.4

0.25

0.01

19.8

16.6

5802

82.9

0.2

2.9

423.2

With this approach, apparent quantum yields of up to 19.8 and 2.4 % could be achieved, with and without the presence of 2-propanol, respectively, which exceed the best reported values for pure TiO2 by far. Likewise, formation rates of up to 82.9 or 9.3 µM min-1 were achieved with the highest employed light intensities. Even though certainly lower, the apparent quantum yield in this case was still acceptable with 2.9 % and 0.3 %, respectively. In order to put these values into perspective, they are compared to other reports of photocatalytic hydrogen peroxide formation. Many of those reports do not give values for the quantum yields and miss either the incident photon flux or the peroxide formation rate so it cannot be readily calculated either, so a comparison with those is unfortunately not readily possible.30,46,78 On unmodified TiO2, quantum yields of 1 % were reported without the use of a sacrificial reagent, which is less than half the value reported herein.22 Higher values were reported when sacrificial reagents were present, for ACS Paragon Plus Environment

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instance 2 % with acetate22 and 3.5 % with isopropanol34, which are comparable to the numbers reported herein for high light intensity but 5-10 times lower than under the optimized conditions. Those could only be matched by using other catalyst material such as carbon nitride (up to 26 %)36,37 or modifying them with expensive co-catalysts. For instance Ag/TiO2 achieved up to 7% apparent quantum yield34, while Au/TiO2 was reported with 13-22 %.44,53 Consequently, through careful optimization of the reaction conditions, quantum yields comparable to be best reported catalysts to date could be achieved just with ordinary TiO2 without using any expensive noble metals. It is very likely that a similar optimization will lead to even higher numbers on the improved catalysts, which is a matter of ongoing research. Long-term effects The stabilizing effects of phosphate and 2-propanol in photocatalytic H2O2 production are well known,34,78 both of them effect a lower degradation rate and at the same time higher formation rates (cf. Fig. S46). Consequently, the steady state concentration of H2O2 reached with a sacrificial electron donor are much higher and are also stable for at least 24 hours. Nonetheless, as the reaction rates are dependent of the concentration of the sacrificial electron donor, there might also occur changes in the steady state concentration because of the consumption of the donor over the time. However, a different behavior is observed in the case of water oxidation, in the absence of an alcohol and independent of the presence of phosphate. Here, an unexpected drop of the H2O2 concentration occurs after longer reaction times (>5 hours). Adding H2O2 to the reaction suspension after deactivation of the catalyst shows that the catalyst can still degrade H2O2 (cf. Fig. S40), so it is not entirely deactivated. As the degradation rate seems to be unaffected we suspect that the change in the observed concentration is a result of a decreased formation rate. Therefore, to describe the concentration-time profile shown in Fig. 10 we applied an empiric function derived from the standard kinetic model but extended the formation rate by an exponential decay component (with the parameters and , eq. 20.). From integration of eqns. 2 and 20 results the explicit eq. 21 which is used to fit the data with good precision. (eq. 20) (eq. 21) A heterogeneous photocatalyst like TiO2 is often described to remain unaltered during a reaction, sometimes slow inactivation is described. Our finding of an unexpected sudden deactivation of the oxidation ability of TiO2 has up to this point not been mentioned or discussed in the literature, albeit careful study of published data reveals that at least the onset of this effect is often apparent.22,34 Recently a comparable effect of sudden catalyst deactivation has been observed during hydrogen evolution with Pt-loaded P25.79


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c(H2O2) / µM

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ACS Catalysis

25 20 15 10 5 0 0

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time / min

Figure 10. Concentration-time profile for photocatalytic H2O2 formation through oxidation of H2O and -1 simultaneous reduction of O2. The fit is done according to eq. 20. Reaction conditions: 0.05 g L TiO2, 25°C, -1 -1 -1 203.8 µE L min , 365 nm 0.1 M phosphate, pH3, 2 mL min O2-bubbling. The shaded area corresponds to the 95 % confidence interval.

Curiously, the reaction system can be reactivated by adding or replacing part of the solution by fresh water or buffer which somehow immediately heals the catalyst (cf. Figs. S41 and S42). The light intensity also affects the catalyst deactivation. At higher light intensities, the inactivation occurs earlier which indicates a relation to UV induced surface defects, cf. Fig. S43. The inactivation is also more pronounced at lower solution pH (cf. Fig. S44) which coincides with the observation of surface roughening during water oxidation especially at a pH

Modeling and Optimization of the Photocatalytic Reduction of

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