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CB/VB edges may be generalized and semi-quantified. Based on these relations, we propose the relative number of reactive charge carriers (CB-e– in t...
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Number of Reactive Charge Carriers — a Hidden Linker between Band Structure and Catalytic Performance in Photocatalysts Jiadong Xiao, Qingzhen Han, Hongbin Cao, Jabor Rabeah, Jin Yang, Zhuang Guo, Linbi Zhou, Yongbing Xie, and Angelika Brückner ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.9b02426 • Publication Date (Web): 16 Aug 2019 Downloaded from pubs.acs.org on August 16, 2019

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Number of Reactive Charge Carriers — a Hidden Linker between Band Structure and Catalytic Performance in Photocatalysts Jiadong Xiao,†,‡,§, Qingzhen Han,† Hongbin Cao,† Jabor Rabeah,*,§ Jin Yang,† Zhuang Guo,†,‡ Linbi Zhou,† Yongbing Xie*,† and Angelika Brückner*,§ † Beijing

Engineering Research Center of Process Pollution Control, Division of Environment Technology and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ University of Chinese Academy of Sciences, Beijing 100049, China § Leibniz-Institute for Catalysis e. V., at the University of Rostock, Albert-Einstein-Straße 29a, D-18059 Rostock, Germany. ABSTRACT: Tailoring the band structure of a photocatalyst without causing significant changes of further properties and deriving unambiguous relation between the number of charge carriers (CB-e? and VB-h+) and their reactivity in a photocatalytic reaction is very challenging but highly important for rational catalyst design. In this work, semiquantitative relations between band structure, number of reactive charge carriers, yield of hydroxyl (•OH) and superoxide (•O2?) radicals and degradation rate of oxalic acid as a model pollutant have been discovered in g-C3N4 photocatalysts by in-situ electron paramagnetic resonance (EPR) coupled with an online spin trapping technique. We demonstrate that it is the number of reactive charge carriers which links the band structure of a photocatalyst with its catalytic performance. An optimum balance between the number and reducing ability of conduction band electrons (CB-e–), which depends on the interplay between band gap and conduction band edge potential, is a key property for highly efficient g-C3N4 photocatalysts. Combination of i) narrowing of the bandgap and upshift of the CB edge at the same time, and ii) using O3 instead of O2 as CB-e? trap would lead to the maximum number of reactive CB-e? and •OH and, hence, to optimal photocatalytic activity. KEYWORDS: g-C3N4 photocatalysis, photocatalytic ozonation, band structure, number of reactive charge carriers, in-situ EPR

INTRODUCTION Hydroxyl radicals (•OH, E0 = 2.80 VNHE1) are the most powerful reactive oxygen species (ROS), able to oxidize unselectively and completely organic pollutants in atmosphere and water.2 Hence, they are often referred to as the best “detergent” of troposphere and wastewater. The yield of •OH produced in-situ is proportional to the oxidation ability of advanced oxidation processes including semiconductor-based photocatalysis, that can sustainably utilize sunlight to generate •OH mainly through O reduction by photoelectrons or H O 2 2 oxidation by holes.3-5 Rational design of photocatalysts beyond the current state of the art for environmental decontamination applications requires a sound knowledge of crucial properties that make a photocatalyst active for •OH production. There is widespread agreement that band structure is a decisive factor which governs the photocatalytic activity (yield of •OH) by affecting the reactions between photoelectrons and the primary oxidant (O2 or O3) as well as between holes and H2O,6-10 but a coherent picture of these complex relationships has, to the best of our knowledge, never been drawn. In many papers, just the impact of the band gap on the catalyst’s ability to absorb light in different spectral regions has been studied by UV-vis diffuse reflectance spectroscopy

(DRS). However, it is the number of charge carriers (CB-e? and VB-h+) and their reactivity against acceptors (O2, O3, H2O, etc.) that govern the yield of active •OH species, and this depends on the specific band structure of a photocatalyst, i.e., on the edge positions of valence band (VB) and conduction band (CB) and the band gap between them. Deriving unambiguous information about these relations would be a driving force for rational catalyst design. To achieve this, one has to master at least two challenges, namely i) knowledgebased tailoring of the band structure of a photocatalyst without causing significant changes of further properties, and ii) (semi)quantification of the number and reactivity of charges transferred from the catalyst surface to surrounding acceptors (O2, O3 or H2O) together with the subsequent generation of short-lived ROS under realistic aqueous conditions. Metal-free graphitic carbon nitride (g-C3N4) with a bandgap of ca. 2.7 eV is a good model photocatalyst for such a study, and various methods for its synthesis have been published.11-14 Its band structure can be tuned without introducing foreign elements in contrast to, e.g., metal oxide semiconductors.15-16 Thus, Liu et al. reported a simple post-calcination method to narrow or broaden the bandgap of g-C3N4 by thermal treatment in argon17 or air,18 respectively. Moreover, we have recently developed a spin-trapping technique using in-situ

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3 increases significantly with rising calcination temperature from 27.3 m2/g for Ar-640 to 236.4 m2/g for Ar-640-Air-570 (Figure S6). (a)

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intralayer amine groups in g-C3N4, as suggested by theoretical calculations of the band structure assuming a monolayer melon sheet to model incompletely condensed g-C3N4. As shown in Figure S11, the loss of NH2/NH groups in the melon sheet (from C24H12N36 to C24H11N35) leads to a decrease of the bandgap from 2.36 to 1.75 eV. In contrast, the bandgap increases with rising calcination temperature in air from 2.42 eV for Ar-640 to 3.02 eV for Ar-640-Air-570 (Figure S9d). This is due to a quantum confinement effect, which shifts the VB and CB edges in opposite directions.25, 27 From the band gap energies derived from UV-vis DRS and the maximum VB energies obtained by XPS, the minimum CB energies were estimated and, thus, the whole picture of relative band structure can be drawn (Figure 4). It is evident that the VB energy remains almost constant while a down- and upshift of the CB edge is caused by thermal treatment in argon and air, respectively. CB minimum

Relative band structure

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Figure 3. Field emission scanning electron microscopy (FESEM) and transmission electron microscopy (FETEM) images of selected g-C3N4: (a) bulk g-C3N4, FESEM; (b) bulk g-C3N4, FETEM; (c) Ar-640, FESEM; (d) Ar-640, FETEM; (e) Ar-640-Air-550, FESEM; (f) Ar-640-Air-550, FETEM. The damage of bulk g-C3N4 structure in the Ar-640-Airtemp samples gives rise to decreasing intensities of the (100) and (002) XRD peaks (Figure S2b). The shift of the (002) XRD peak from 27.5° for Ar-640 to 28.0° for Ar-640-Air-570 (Figure S2b), indicates a decreased interlayer distance between the basic sheets. This agrees with previous observations that the undulated single layers in bulk g-C3N4 are planarized by heating in air, resulting in a slightly denser stacking.18, 24 Almost equal binding energies of C 1s and N 1s core electrons (Table S2) and ATR-IR spectra (Figure 2) before and after calcination in air suggest that the chemical states of both carbon and nitrogen in the exfoliated samples remain unchanged. These results demonstrate that thermal treatment of Ar-640 in air causes oxidative exfoliation of bulk g-C3N4 structure into nanosheets. Band Structure Change of g-C3N4 Caused by Microstructure Variation. The band gap (Eg) and maximum VB energies (versus Fermi level, i.e., EVBM – EF) have been derived from Tauc plots of UV-vis DRS spectra (Figure S9) and VB XPS (Figure S10), respectively, from which the minimum CB energies (ECBM – EF) can be estimated (ECBM – EF = EVBM – EF – Eg). Besides ultraviolet photoelectron spectroscopy (UPS), VB XPS is a standard tool for determining VB edge positions.25-26 Thermal treatment in argon causes a red shift of the absorption edge (Figure S9a) and, consequently, a decrease of the bandgap energy from 2.79 eV for bulk g-C3N4 to 2.42 eV for Ar-640 estimated by a Tauc plot (Figure S9c). This is mainly due to the gradual loss of

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Figure 4. Relative band positions of g-C3N4. Photographs show 50 mg of bulk g-C3N4, Ar-520, Ar-560, Ar-600, Ar-640, Ar-640-Air-490, Ar-640-Air-510, Ar-640-Air-530, Ar-640Air-550 and Ar-640-Air-570 (No. 1-10), respectively. Relation between Photocatalytic Activity and Band Structure. The photocatalytic activity of g-C3N4 materials has been evaluated by degradation rates of oxalic acid (OA) which does almost not react with O3 or with superoxide radicals (•O2?) but is readily decomposed by •OH into CO2 and H2O.19, 28-29 As we have shown previously,19 •O S cannot oxidize OA. 2 This is evident from two facts: i) no OA removal was found when only •O2S was left in Vis/O2/g-C3N4 or Vis/O3/g-C3N4 systems after adding tert-butanol (TBA, a famous •OH scavenger30-31, Figure S12a-b) to quench •OH; ii) Even O3 cannot oxidize OA (Figure S13), though it is a stronger oxidant than •O2S [E0 (O3/•O3S) = +1.03 VNHE, E0 (O2/•O2S) = S16 : VNHE32]. Thus it is straightforward to understand that •O S cannot decompose OA either. A direct •O S quenching 2 2 experiment using p-benzoquinone as a scavenger was not done because p-benzoquinone would decompose to form OA during advanced oxidation processes,33 making it difficult to track the degradation of initial OA. The photocatalytic degradation of OA in the presence of O2 (photocatalytic oxidation, Figure 5a) and 2.1 mol% O3/O2 (photocatalytic ozonation, Figure 5b) follows pseudo-zeroorder kinetics (C/C0 = 1 S k/C0 × time). In agreement with our previous work6, 19, 34-35 and other literature,8-9 the photocatalytic OA removal rate increases by dozens of times already at a very low ozone percentage. This is due to the faster photoelectron transfer and •OH formation in the presence of O3 (O3R•O3SR E3•R•OH) in comparison to that in O2 (O2R•O2SR E2•R 2O2R•OH).19 Note that visible light/O3 causes no OA removal (Figure S13) since ozone

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4 decomposition by photolysis that generates •OH only occurs under UV light well below 300 nm.36 The photocatalytic activity decreases from bulk g-C3N4 to Ar-640 (Figure 5a-b) especially in the presence of O3 (Figure 5b) though the specific surface area (SBET) increases slightly (Figure S6). Ar-640-Air-570 with a notably higher SBET (236.4 m2/g) performed worse than Ar-640-Air-550 (194.8 m2/g). This indicates that the variation of SBET is not a reason for the activity difference, which is in line with our previous result that nanoporous g-C3N4 with higher SBET is unexpectedly not as active as bulk g-C3N4 in photocatalytic ozonation because of the downshift of CB edge.37-38 Similarly, our recent work indicates that the activity improvement by exfoliating bulk gC3N4 into nanosheets arises mainly from the CB upshift which promotes CB-e? capture by O3/O2.19 SBET is of negligible importance here, probably because •OH formation is not adsorption-limited, and OA oxidation by •OH occurs in the liquid phase rather than on the g-C3N4 surface. The latter is supported by two facts: i) OA adsorption on all g-C3N4 samples is negligible (within 30 min) and ii) tert-butyl alcohol (TBA, a liquid-phase •OH scavenger which is scarcely adsorbed on low-polarity carbon surfaces30-31) completely blocks the decomposition of OA (Figure S12a-b). Moreover, the suppression of radiative electron-hole recombination within g-C3N4 itself is also excluded as a major reason, since g-C3N4 with less pronounced radiative charge recombination (reflected by lower photoluminescence intensity, Figure S14) was less active (Figure 5a-b). This means that band structure is most likely the crucial factor that governs photocatalytic activity, as underlined by our previous studies on g-C3N4,6, 26. WO37 and BiVO4.39 This is because band structure of a photocatalyst crucially affects the reaction between charge carriers and acceptors (i.e., affects the charge separation efficiency in the presence of practical reactants), particularly the efficiency of CB-e? capture by O2 or O3.

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Figure 5. Change of OA concentration during (a) Vis/O2/gC3N4 and (b) Vis/O3/g-C3N4 treatment with various g-C3N4 catalysts. OA removal rate constant as a function of the CB edge potential and bandgap of g-C3N4 in (c) Vis/O2/g-C3N4 and (d) Vis/O3/g-C3N4 processes.

To assist the discussion of relations between band structure and photocatalytic activity, the OA removal rate constants are plotted as a function of the CB edge potential (CBEP, i.e., ECBM – EF herein) and the bandgap of g-C3N4 (Figure 5c-d), respectively. The individual impact of the VB edge is not considered here because its shift is negligible (Figure 4) and VB-h+ in g-C3N4 cannot oxidize H2O directly to •OH as evidenced by our in-situ EPR study previously.19 In that work we used DMPO to trap •OH during irradiation of g-C3N4 with visible light under bubbling N2 through the solution (to prevent O2 dissolution and ROS formation upon reduction of O2 by CB-e–). No DMPO-OH adducts could be found under these conditions, which is an experimental evidence that VBh+ in g-C3N4 are unable to oxidize H2O/OHS to •OH, as it was found in numerous previous studies.40-43 This is in accordance with the significantly lower VB edge potential of g-C3N4 compared to the redox potential of the •OH, H+/H2O pair.44 Also, the reaction of VB-h+ with OA is extremely slow. This is evident from Figure S12c, showing an experiment in which sample Ar-640-Air-550 has been irradiated with visible light under continuous bubbling of N2 in the presence of OA and AgNO3. N2 bubbling was done to prevent dissolution of O2 and exclude the formation of ROS derived from O2 while Ag+ was added to trap CB-eS, thus leaving VB-h+ separated. As shown in Figure S12c, negligible OA was removed within 4 hours. Thus, a possible pathway for consumption of VB-h+ could be their reaction with H2O directly to O2 since their redox potential is more positive than that of the O2, H+/H2O pair.45 Unfortunately, the latter reaction is hard to prove experimentally since the feed gas contains O2. The removal rate of OA by visible-light driven oxidation (Vis/O2/g-C3N4) and ozonation (Vis/O3/g-C3N4) increases progressively with the negative shift of the CBEP and the increase of the bandgap (Figure 5c-d). The activity of the most active sample Ar-640-Air-550 in Vis/O2/g-C3N4 is 8.6 times as high as that of the least active one Ar-640 (Figure 5c), while this factor reaches 7.0 under Vis/O3/g-C3N4 (Figure 5d). This indicates that the increasing reducing power of photoelectrons reflected by the negative shift of the CBEP is the main reason for the activity enhancement up to sample Ar-640-Air-550 and compensates the adverse effect of reduced light absorption caused by the widening of the bandgap. For sample Ar-640Air-570 activity declines again in both photocatalytic oxidation and ozonation, indicating that the detrimental effect of large bandgap begins to outweigh the positive effect of negative CBEP. Semi-quantification of Reactive CB-e7 and ROS Formed. To understand the relations between band structure and photocatalytic activity in Figure 5c-d at an electronic and molecular scale, the fate of CB-e?, namely, their birth and further reaction with O3/O2 to generate ROS, was monitored by in-situ EPR on selected samples under realistic aqueous conditions (Figure 6). Full details concerning this method can be found in our previous publication.19 An aqueous suspension of g-C3N4 under visible light and N2 (black line in plots a-d) shows a single Lorentzian line at g = 2.004. This is assigned to CB-e? excited from the VB to the CB of g-C3N4 by visible light.19, 46 In the presence of O2 or O3, this signal drops, since CB-e? are trapped by dissolved O2 or O3, respectively.19 Thus,

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A New Concept to Describe the Relationship between Band Structure and Photocatalytic Activity. The plot of the relative number of reactive CB-e? as a function of the band structure (Figure 6f) shows the same trend as that of the relative number of DMPO-OH (Figure 7d) and of the OA decomposition rate constant (Figure 5c-d) under both Vis/O2/g-C3N4 and Vis/O3/g-C3N4 conditions. This is a clear and direct evidence that it is the band gap (negatively correlated with the integral area of light absorption spectrum in most cases) and CBEP of g-C3N4 (whose VB-h+ cannot oxidize H2O to •OH19) that collectively govern the number of reactive CB-e?, which is itself directly proportional to the yield of •OH (Figure 8a) and to the rate of OA degradation (Figure 8b). This rule is true for both O2 and O3 as photoelectron traps.

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Figure 7. Experimental (black) and fitted EPR spectra (grey) of DMPO spin adducts in Vis/O2/g-C3N4 (a) and Vis/O3/gC3N4 (b). * and + mark the EPR signals of DMPO-OH and DMPO-OOH, respectively; Fitting parameters: g = 2.006; aN = aH\ = 14.9 G for DMPO-OH; aN = 14.2 G, aH\ = 11.4 G and aH]1 = 1.2 G for DMPO-OOH; aN = 7.2 G and a(2×H]) = 4.1 G for DMPOX (5,5-dimethyl-2-pyrrolidone-N-oxyl, 7-line pattern in plot b, bottom trace) formed by oxidation of DMPO

OA removal rate constant

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(cf. Figure S16). (c) Relative numbers (derived from the double integral of the fitted spectrum multiplied by the relative percentage of each component given by EasySpin/Matlab) of DMPO-OOH and DMPO-OH adducts. (d) Relative number of DMPO-OH versus CBEP and bandgap.

Relative no. of DMPO-OH

N2, O2 and O3, respectively (the EPR signal in dark has been subtracted for all); (e) Relative numbers of O2- or O3-trapped CB-e? and residual CB-e? in selected g-C3N4; (f) Relation of the relative number of reactive CB-e? to the CB edge potential and bandgap of g-C3N4 under Vis/O3/g-C3N4 and Vis/O2/gC3N4 conditions. The short-lived •OH radicals, which are reaction products of CB-e? with O3/O2 and the exclusive oxidants for OA degradation (indicated by Figure S12a-b), were further analyzed by in-situ EPR using an online DMPO spin-trapping technique as established previously.19 Figure 7a-b shows the experimental and fitted EPR spectra of trapped ROS under Vis/O2/g-C3N4 and Vis/O3/g-C3N4 conditions, respectively. The relative numbers of DMPO-OH and DMPO-OOH species (the adducts of DMPO with •OH and •O2?, respectively, cf. Figure S16) are plotted in Figure 7c. In agreement with our previous work,19 •O2? (ca. 75% of all DMPO adducts in Vis/O2/g-C3N4) and •OH (ca. 80% of all DMPO adducts in Vis/O3/g-C3N4) proved to be the dominant ROS in Vis/O2/gC3N4 and Vis/O3/g-C3N4 systems, respectively. When switching from oxygen to ozone, a higher total number of trapped ROS is formed. Moreover, the number of DMPO-OH significantly increases along with a drop of the number of DMPO-OOH upon switching from Vis/O2/g-C3N4 to Vis/O3/gC3N4, because O3 is able to form •OH via a robust one-electron reduction pathway (O3R•O3SR E3•R•OH) and can react with •O ? to form •O S that generates further •OH.19 2 3

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Figure 8. (a) Relative number of DMPO-OH adduct and (b) OA removal rate constant as a function of the relative number of reactive CB-e– under Vis/O2/g-C3N4 (red dots and lines) and Vis/O3/g-C3N4 (blue dots and lines) conditions. Thus, bandgap (or the integral area of light absorption spectrum) and CBEP that govern the number and the reducing power of CB-e?, respectively, are two key characteristics of the photocatalyst which have a direct impact on photocatalytic activity (Scheme 1a). The combined effects of band gap and CB/VB edges may be generalized and semi-quantified. Based on these relations, we propose the relative number of reactive charge carriers (CB-e? in the present case, Scheme 1a) as a new concept, which represents what band structure genuinely brings about and, thus, could be useful as an index/tool for exploring how photocatalytic performance changes as a function of the band structure. Reactive charge carriers can be understood as the charges that are separated and directly used for the photocatalytic reaction. Hence, this concept also reflects the charge separation efficiency detected in the presence of reactants and under realistic conditions. It is worth stressing again that the type of photoelectron trap not only affects the number of reactive CB-e? because trapping electrons by O3 is thermodynamically easier than that by O2, but also affects the efficiency of converting CB-e? to •OH by altering the reaction pathway (Scheme 1a).19 Scheme 1. (a) Relationship between band structure and photocatalytic activity and (b) proposal for rational improvement of g-C3N4-based photocatalysts

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8 In-situ EPR study. The in-situ EPR spectroscopic set-up19 is mainly composed of an ozone generator (OZ 500/5, Fischer, Germany), an ozone analyzer (OZOTRON 23, Fischer, Germany), a 300 W Xe-arc lamp (LOT Oriel GmbH, Germany) equipped with a cut-off filter GG420, a Bruker EMX CW-micro X-band EPR spectrometer equipped with an ER4119HS-WI high-sensitivity optical resonator, and a specially designed flat cell (Starna, 0.5 mm inner distance). For monitoring photoelectron transfer, 0.5 mL/min of N2, O2, or O2/O3 (2.1 mol% O3 in O2) were bubbled through a fused silica capillary (0.25 mm inner diameter, Klaus Ziemer GmbH, Germany) into an aqueous g-C3N4 suspension (6 mg gC3N4/300 µL fresh distilled H2O) in the flat cell placed in the EPR cavity. EPR spectra were acquired before and after visible light irradiation for 10 min at 298 K with a microwave power and attenuation of 6.9 mW and 15 dB, respectively, a receiver gain of 1.0 × 104 and a modulation frequency and amplitude of 100 kHz and 5 G, respectively. An online DMPO (5,5-dimethyl-1-pyrroline N-oxide) spintrapping technique was used here to detect reactive oxygen species (full details can be found in our previous work19). Briefly, the reaction of Vis/O2/g-C3N4 or Vis/O2/g-C3N4 was first performed on a suspension of 6 mg g-C3N4/300 µL fresh distilled H2O in the flat cell of the EPR cavity for 10 min. Afterwards, O2 or O3 feeding was stopped and purified DMPO (Enzo Life Sciences GmbH, 50 -L, 600 mM) was added rapidly to the aqueous g-C3N4 suspension via a self-modified syringe. This was done to avoid oxidation of DMPO to DMPOX (5,5-dimethyl-2-pyrrolidone-N-oxyl) by O3. EPR spectra were recorded before and after DMPO addition. g values were calculated using the equation b J \!0 with B0 and b being the resonance field and frequency, respectively. Calibration of the g values was performed using a DPPH standard (g = 2.0036 ± 0.0004). Signal simulation and fitting were carried out using the EasySpin/Matlab toolbox. Computational details. All the calculations presented in this work were carried out using the Cambridge Serial Total Energy Package.59 The exchange-correlation effects were treated within the generalized gradient approximation by using the Perdew-Burke-Ernzerhof function.60 The cutoff energy for the plane wave basis was set to be 310 eV. A monolayer melon sheet C24H12N36 and C24H11N35 were constructed to represent the incompletely condensed g-C3N4 and that with partial loss of intralayer NH2/NH groups, respectively. Structure relaxation was performed within a size-fixed cubic cell with experimental lattice constants of a = 16.7 Å and b = 12.4 Å.20, 23 All atomic positions were relaxed to a force convergence of 0.01 eV/Å, and a 3 × 3 × 1 Monkhorst-Pack scheme k-point mesh was used for the Brillouin zone sampling. The interaction between the valence electrons and the ionic core is described by the ultrasoft pseudopotential.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Elementary analysis, XRD, XPS, nitrogen adsorption-desorption isotherms, TG-DSC-MS, UV-vis DRS, VB XPS and photoluminescence results of g-C3N4; calculation results of g-

C3N4 band structure; •OH trapping experiments by TBA; OA degradation results by O3 and Vis/O3; Ratios of [(CBe?)reactive]rel/[(CB-e?)total]rel; integral areas of light absorption spectra of Ar-640-Air-550 and bulk g-C3N4; DMPO spin trapping mechanism and typical EPR signals of DMPO adducts.

AUTHOR INFORMATION Corresponding Author * Email: [email protected] (A. Brückner). * Email: [email protected] (Y. Xie). * Email: [email protected] (J. Rabeah).

Present Addresses J. X.: Inorganic Chemistry and Catalysis, Debye Institute for Nanomaterials Science, Utrecht University, David de Wiedgebouw, Universiteitsweg 99, 3584 CG Utrecht, The Netherlands.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors appreciate the financial support from Natural Science Foundation of Beijing Municipality (No. 8172043), National Science Fund for Distinguished Young Scholars of China (No. 51425405) and National Key Research and Development Program of China (No. 2017YFC0210304). J. Xiao acknowledges the CAS-DAAD fellowship (Regierungsstipendien VR China – Programme for the Promotion of Outstanding Young Scholars, No. 91637735) for the financial support of doctoral study in Germany.

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