- Email: [email protected]
Au as a cocatalyst loaded on solid solution Bi0.5Y0.5VO4 for enhancing photocatalytic CO2 reduction activity
Materials Letters 238 (2019) 74–76
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Au as a cocatalyst loaded on solid solution Bi0.5Y0.5VO4 for enhancing photocatalytic CO2 reduction activity Wei Chen a,b,⇑, Yanhong Wang a, Wenfeng Shangguan c a
Henan Engineering Research Center of Resource & Energy Recovery from Waste, Henan University, Kaifeng 475004, PR China Institute of Functional Polymer Composites, Henan University, Kaifeng 475004, PR China c Research Center for Combustion and Environmental Technology, Shanghai Jiao Tong University, Shanghai 200240, PR China b
a r t i c l e
i n f o
Article history: Received 26 September 2018 Received in revised form 15 November 2018 Accepted 22 November 2018 Available online 3 December 2018 Keywords: Semiconductors CO2 reduction Nanocomposites Au cocatalyst Charge separation
a b s t r a c t Au as a cocatalyst was deposited on the surface of solid solution Bi0.5Y0.5VO4 by a photodeposition method for photocatalytic reduction of CO2. Au particles loaded on the surface of Bi0.5Y0.5VO4 apparently enhanced the photocatalytic activity of CO2 reduction toward CO evolution. The highest rate of CO evolution was obtained over 1.0 wt% Au/Bi0.5Y0.5VO4, reaching 3.5 times of that of bare Bi0.5Y0.5VO4. The improved photocatalytic performance was assigned to the lower overpotential of Au/Bi0.5Y0.5VO4 for CO evolution than that of bare Bi0.5Y0.5VO4 as well as the formation of Schottky barrier, which promotes the separation of photogenerated electron–hole pairs. Ó 2018 Elsevier B.V. All rights reserved.
1. Introduction Photocatalytic conversion of CO2 into hydrocarbon fuels carried out using solar irradiation as primary energy source provides a green way to solve energy crisis and environmental problems [1,2]. Due to very negative potential of CO2 direct reduction, CO2 reduction involving H2O as an electron donor is regard as a feasible way to convert CO2 to fuels or chemical products [3]. To date, although many photocatalysts [4,5] have been used for photocatalytic CO2 reduction, the fast recombination rate of photoinduced charges seriously restricts photocatalytic conversion efficiency and then hinders its widespread application. It is also desirable to develop photocatalysts for CO2 conversion with good charges separation and transfer capability. As reported, the use of proper cocatalyst play indispensable roles in improving the photocatalytic efficiency [6]. The researches of metal–semiconductor hybrid materials revealed that metal cocatalysts can facilitate charge separation by trapping or discharge electrons through forming Schottky barrier between them, thereby favoring the performance of composite systems [7]. In recent years, we found that the solid solution Bi0.5Y0.5VO4, denoted as BYV, possessed high photocatalytic activity for overall water splitting [8,9]. Therefore, it probably is a promising candidate for
⇑ Corresponding author. E-mail address: [email protected] (W. Chen). https://doi.org/10.1016/j.matlet.2018.11.150 0167-577X/Ó 2018 Elsevier B.V. All rights reserved.
the photocatalytic reduction of CO2 if a proper cocatalyst is loaded on its surface. Herein, we prepared BYV by a solid state method and a photodeposition method was utilized for growing Au particles on its surface. Then, the as-synthesized samples were used as photocatalyst for CO2 conversion with H2O as an electron donor. The effect of BYV with different Au loading contents on photocatalytic performance of CO2 reduction were investigated. Also, a potential mechanism for improving photocatalytic performance toward CO over BYV with Au loading was proposed. Details about the preparation, characterization and photocatalytic activity studies of Au/BYV for CO2 reduction can be obtained in the Supporting Information.
2. Results and discussion 2.1. XRD and DRS analysis The XRD measurement for crystal structures of samples was performed and shown in Fig. 1a. From the XRD patterns, we can clearly see that the diffraction peaks of the naked BYV are indexed to pure tetragonal phase (PDF#14-0133). After loading, no change of the peaks position of BYV were observed, indicating that Au loaded on the surface of BYV instead of doping into its lattice. Of note, after Au loading, the diffraction peak at 2h = 38.1° assigned to Au0 (1 1 1) plane occurred, revealing the presence of Au metal on the surface of BYV [10]. In addition, the broadening of the half
W. Chen et al. / Materials Letters 238 (2019) 74–76
75
Fig. 1. XRD (a) and DRS (b) patterns of BYV with different Au loading contents.
band widths (2h = 38.1°) with decreasing of Au loading indicates that the size of Au particles was smaller while the Au loading content reduced [11]. The optical absorption properties of the samples were investigated by the UV–vis DRS (Fig. 1b). From Fig. 1b, an absorption edge of the pristine BYV at ca. 410 nm was observed. In addition, new absorption peaks in the range of 500–570 nm should be attributed to the surface plasmonic absorption of Au particles on BYV [12,13].
on BYV. The elemental mappings shown in Fig. 2d also indicate that the existence of Bi, Y, V, O and Au in the obtained sample. The uniform distribution of Bi, Y, V, O elements in BYV suggests the formation of BYV solid solution. From the HR-TEM image, the lattice spacing of cocatalyst was observed to be 0.232 nm, matching well with the spacing of (1 1 1) plane of Au0 with cubic structure [15]. The finding is also consistent with XPS analysis. 2.3. Photocatalytic activity
2.2. XPS and TEM analysis To confirm the surface element composition of as-prepared samples and valence state of Au species, the XPS measurement of Au (1.0 wt%) loaded BYV was carried out. In the XPS survey spectra (Fig. 2a), it can be seen that Bi, Y, V, O and Au binding energy peaks were detected. From the HR-XPS spectra of Au cocatalyst (Fig. 2b), the binding energies of Au 4f7/2 and 4f5/2 were found to be 83.6 and 87.2 eV, respectively, corresponding to metallic Au (Au0) [14,15]. This observation confirms that metallic Au were successfully supported onto the BYV surface. The morphology, size and distribution of Au cocatalyst on the surface of BYV was probed by TEM measurement. As shown in Fig. 2c, the Au particles with diameter about 80 nm were coated
Fig. 3a shows the rates of CO evolution on BYV with different Au loading contents along with irradiation time. In this study, CO is the only reduction product and no CH4 is detected. It can be explained that, although the reduction potential of CO2 to CH4 (+0.17 V vs RHE) is more positive than that of CO2 to CO ( 0.11 V), the reduction of CO2 to CH4 which includes 8 protons and 8 electrons possesses high overpotential, which inhibits the occurrence of the reaction [1]. In addition, although loaded BYV photocatalysts have ability to oxidize pure H2O to form O2 [8,9], the yield of O2 is too low to be detected by a TCD detector. From Fig. 3a, for bare BYV, the rate of CO evolution is about 0.07 lmolg 1h 1, suggesting that BYV has the ability to reduce CO2 to CO because of the position of conduction band higher than reduction potential of CO evolution. Of note, the rates of CO evolution have been improved to some extent after Au loading, suggesting that Au particles play an essential role in enhancing the activity toward CO evolution. The amount of Au loaded on BYV has a significant effect on photocatalytic activity and the highest CO evolution rate of 0.25 lmolg 1h 1 is achieved by the 1.0 wt% Au/BYV, which is 3.5 and 1.6 times higher than the rates of pure BYV and 0.5 wt% Au/BYV (0.15 lmolg 1h 1), respectively. BYV with excess cocatalyst loading exhibit almost the same CO evolution rates with BYV probably due to the formation of large particles size and poor dispersion of Au particles on the photocatalyst [16]. 2.4. Photocatalytic mechanism
Fig. 2. XPS survey spectrum of 1.0 wt% Au/BYV (a) and HR-XPS spectra of Au cocatalyst (b); TEM images (c) and EDS mappings (d) of 1.0 wt% Au/BYV.
High photocatalytic activity benefits from the rapid charge separation and lower overpotential of products evolution on the surface of photocatalyst. To uncover the influence of Au cocatalyst on the charges separation, PL emission spectra of the samples was measured. As displayed in Fig. 3b, the emission spectra peak is about 469 nm at the excitation wavelength of 360 nm and the PL intensity for the Au supported BYV substantially decreased, implying that the Au loaded BYV have a better ability to separate electron–hole pairs [16]. The 1.0% Au/BYV exhibits the lowest PL intensity, indicates 1.0% Au/BYV has the best performance for charge separation, thus possessing the highest photocatalytic activity. Excess loading makes against the charge separation and result in the decrease of photocatalytic activity. To investigate
76
W. Chen et al. / Materials Letters 238 (2019) 74–76
Fig. 3. CO evolution rates (a) and PL spectra (b) of BYV with different Au loading contents; LSV curves of BYV and 1.0 wt% Au/BYV samples (c) and the corresponding Tafel plots (d) in 0.1 M KHCO3 aqueous solution with saturated CO2.
the overpotential of CO evolution, the linear sweep voltammetry (LSV) was examined in 0.1 M KHCO3 CO2 saturated aqueous solution (Fig. 3c) and the corresponding Tafel plots are shown in Fig. 3d. It can be seen that the overpotentials of BYV, 1.0% Au/BYV are 0.38 V, 0.28 V, respectively. Clearly, compared with pure BYV, the lower overpotential was gained after Au loading, which are vital for in CO evolution. 3. Conclusions In summary, solid solution Bi0.5Y0.5VO4 photocatalysts with Au loading were synthesized through solid state and photodeposition methods and used for photocatalytic CO2 reduction. Au as a cocatalyst remarkably facilitates the electrons migration from bulk BYV to Au, thus inhibiting the recombination of photogenerated charge carries and enhancing the photocatalytic activity of BYV for CO evolution. Also, Au loading can reduce the overpotential of CO evolution and facilitate the occurrence of CO2 reduction reaction toward CO. Acknowledgements This work was supported by the National Natural Science Foundation of China (51602091), the International Cooperation Project of Department of Science and Technology of Henan Province (162102410011) and Natural Science Foundation of Henan Province (182300410205).
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.matlet.2018.11.150. References [1] X. Chang, T. Wang, J. Gong, Energy Environ. Sci. 9 (2016) 2177–2196. [2] V.H. Nguyen, J.C.S. Wu, Appl. Catal. A: Gen. 550 (2018) 122–141. [3] S. Habisreutinger, L. Schmidt-Mende, J. Stolarczyk, Angew. Chem. Int. Ed. 52 (2013) 2–39. [4] K. Li, B. Peng, T. Peng, ACS Catal. 6 (2016) 7485–7527. [5] W. Xiong, W. Dai, X. Hu, L. Yang, T. Wang, Y. Qin, X. Luo, J. Zou, Mater. Lett. 232 (2018) 36–39. [6] J. Zhang, C.M. Dong, Mater. Horiz. 3 (2016) 608–612. [7] C. Dong, C. Lian, S. Hu, Z. Deng, J. Gong, M. Li, H. Liu, M. Xing, J. Zhang, Nat. Commun. 9 (2018) 1252. [8] W. Fang, Z. Jiang, L. Yu, H. Liu, W. Shangguan, C. Terashima, J. Catal. 352 (2017) 155–159. [9] W. Chen, B. Yang, Q. Yu, L. Mao, Z. Fan, Q. Wang, W. Shanggaun, Appl. Surf. Sci. 355 (2015) 1069–1074. [10] S. Sultana, S. Mansingh, M. Scurrell, K. Parida, Inorg. Chem. 56 (2017) 12297– 12307. [11] G. Cernuto, N. Masciocchi, A. Cervellino, G. Colonna, A. Guagliardi, J. Am. Chem. Soc. 133 (2011) 3114–3119. [12] M. Nguyen, T. Yonezawa, Y. Wang, T. Tokunaga, Mat. Lett. 171 (2016) 75–78. [13] Y. Chang, J. Cuo, C. Chen, Mat. Lett. 209 (2017) 60–63. [14] J. Mao, J. Zhou, Z. Xia, Z. Wang, Z. Xu, W. Xu, P. Yan, K. Liu, X. Guo, Z. Zhang, ACS Catal. 7 (2017) 695–705. [15] C. Xiao, H. Hu, X. Zhang, D. MacFarlane, ACS Sustainable Chem. Eng. 5 (2017) 10858–10863. [16] W. Chen, Y. Wang, S. Liu, L. Gao, L. Mao, Z. Fan, W. Shangguan, Z. Jiang, Appl. Surf. Sci. 445 (2018) 527–534.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Au as a cocatalyst loaded on solid solution Bi0.5Y0.5VO4 for enhancing photocatalytic CO2 reduction activity Wei Chen a,b,⇑, Yanhong Wang a, Wenfeng Shangguan c a
Henan Engineering Research Center of Resource & Energy Recovery from Waste, Henan University, Kaifeng 475004, PR China Institute of Functional Polymer Composites, Henan University, Kaifeng 475004, PR China c Research Center for Combustion and Environmental Technology, Shanghai Jiao Tong University, Shanghai 200240, PR China b
a r t i c l e
i n f o
Article history: Received 26 September 2018 Received in revised form 15 November 2018 Accepted 22 November 2018 Available online 3 December 2018 Keywords: Semiconductors CO2 reduction Nanocomposites Au cocatalyst Charge separation
a b s t r a c t Au as a cocatalyst was deposited on the surface of solid solution Bi0.5Y0.5VO4 by a photodeposition method for photocatalytic reduction of CO2. Au particles loaded on the surface of Bi0.5Y0.5VO4 apparently enhanced the photocatalytic activity of CO2 reduction toward CO evolution. The highest rate of CO evolution was obtained over 1.0 wt% Au/Bi0.5Y0.5VO4, reaching 3.5 times of that of bare Bi0.5Y0.5VO4. The improved photocatalytic performance was assigned to the lower overpotential of Au/Bi0.5Y0.5VO4 for CO evolution than that of bare Bi0.5Y0.5VO4 as well as the formation of Schottky barrier, which promotes the separation of photogenerated electron–hole pairs. Ó 2018 Elsevier B.V. All rights reserved.
1. Introduction Photocatalytic conversion of CO2 into hydrocarbon fuels carried out using solar irradiation as primary energy source provides a green way to solve energy crisis and environmental problems [1,2]. Due to very negative potential of CO2 direct reduction, CO2 reduction involving H2O as an electron donor is regard as a feasible way to convert CO2 to fuels or chemical products [3]. To date, although many photocatalysts [4,5] have been used for photocatalytic CO2 reduction, the fast recombination rate of photoinduced charges seriously restricts photocatalytic conversion efficiency and then hinders its widespread application. It is also desirable to develop photocatalysts for CO2 conversion with good charges separation and transfer capability. As reported, the use of proper cocatalyst play indispensable roles in improving the photocatalytic efficiency [6]. The researches of metal–semiconductor hybrid materials revealed that metal cocatalysts can facilitate charge separation by trapping or discharge electrons through forming Schottky barrier between them, thereby favoring the performance of composite systems [7]. In recent years, we found that the solid solution Bi0.5Y0.5VO4, denoted as BYV, possessed high photocatalytic activity for overall water splitting [8,9]. Therefore, it probably is a promising candidate for
⇑ Corresponding author. E-mail address: [email protected] (W. Chen). https://doi.org/10.1016/j.matlet.2018.11.150 0167-577X/Ó 2018 Elsevier B.V. All rights reserved.
the photocatalytic reduction of CO2 if a proper cocatalyst is loaded on its surface. Herein, we prepared BYV by a solid state method and a photodeposition method was utilized for growing Au particles on its surface. Then, the as-synthesized samples were used as photocatalyst for CO2 conversion with H2O as an electron donor. The effect of BYV with different Au loading contents on photocatalytic performance of CO2 reduction were investigated. Also, a potential mechanism for improving photocatalytic performance toward CO over BYV with Au loading was proposed. Details about the preparation, characterization and photocatalytic activity studies of Au/BYV for CO2 reduction can be obtained in the Supporting Information.
2. Results and discussion 2.1. XRD and DRS analysis The XRD measurement for crystal structures of samples was performed and shown in Fig. 1a. From the XRD patterns, we can clearly see that the diffraction peaks of the naked BYV are indexed to pure tetragonal phase (PDF#14-0133). After loading, no change of the peaks position of BYV were observed, indicating that Au loaded on the surface of BYV instead of doping into its lattice. Of note, after Au loading, the diffraction peak at 2h = 38.1° assigned to Au0 (1 1 1) plane occurred, revealing the presence of Au metal on the surface of BYV [10]. In addition, the broadening of the half
W. Chen et al. / Materials Letters 238 (2019) 74–76
75
Fig. 1. XRD (a) and DRS (b) patterns of BYV with different Au loading contents.
band widths (2h = 38.1°) with decreasing of Au loading indicates that the size of Au particles was smaller while the Au loading content reduced [11]. The optical absorption properties of the samples were investigated by the UV–vis DRS (Fig. 1b). From Fig. 1b, an absorption edge of the pristine BYV at ca. 410 nm was observed. In addition, new absorption peaks in the range of 500–570 nm should be attributed to the surface plasmonic absorption of Au particles on BYV [12,13].
on BYV. The elemental mappings shown in Fig. 2d also indicate that the existence of Bi, Y, V, O and Au in the obtained sample. The uniform distribution of Bi, Y, V, O elements in BYV suggests the formation of BYV solid solution. From the HR-TEM image, the lattice spacing of cocatalyst was observed to be 0.232 nm, matching well with the spacing of (1 1 1) plane of Au0 with cubic structure [15]. The finding is also consistent with XPS analysis. 2.3. Photocatalytic activity
2.2. XPS and TEM analysis To confirm the surface element composition of as-prepared samples and valence state of Au species, the XPS measurement of Au (1.0 wt%) loaded BYV was carried out. In the XPS survey spectra (Fig. 2a), it can be seen that Bi, Y, V, O and Au binding energy peaks were detected. From the HR-XPS spectra of Au cocatalyst (Fig. 2b), the binding energies of Au 4f7/2 and 4f5/2 were found to be 83.6 and 87.2 eV, respectively, corresponding to metallic Au (Au0) [14,15]. This observation confirms that metallic Au were successfully supported onto the BYV surface. The morphology, size and distribution of Au cocatalyst on the surface of BYV was probed by TEM measurement. As shown in Fig. 2c, the Au particles with diameter about 80 nm were coated
Fig. 3a shows the rates of CO evolution on BYV with different Au loading contents along with irradiation time. In this study, CO is the only reduction product and no CH4 is detected. It can be explained that, although the reduction potential of CO2 to CH4 (+0.17 V vs RHE) is more positive than that of CO2 to CO ( 0.11 V), the reduction of CO2 to CH4 which includes 8 protons and 8 electrons possesses high overpotential, which inhibits the occurrence of the reaction [1]. In addition, although loaded BYV photocatalysts have ability to oxidize pure H2O to form O2 [8,9], the yield of O2 is too low to be detected by a TCD detector. From Fig. 3a, for bare BYV, the rate of CO evolution is about 0.07 lmolg 1h 1, suggesting that BYV has the ability to reduce CO2 to CO because of the position of conduction band higher than reduction potential of CO evolution. Of note, the rates of CO evolution have been improved to some extent after Au loading, suggesting that Au particles play an essential role in enhancing the activity toward CO evolution. The amount of Au loaded on BYV has a significant effect on photocatalytic activity and the highest CO evolution rate of 0.25 lmolg 1h 1 is achieved by the 1.0 wt% Au/BYV, which is 3.5 and 1.6 times higher than the rates of pure BYV and 0.5 wt% Au/BYV (0.15 lmolg 1h 1), respectively. BYV with excess cocatalyst loading exhibit almost the same CO evolution rates with BYV probably due to the formation of large particles size and poor dispersion of Au particles on the photocatalyst [16]. 2.4. Photocatalytic mechanism
Fig. 2. XPS survey spectrum of 1.0 wt% Au/BYV (a) and HR-XPS spectra of Au cocatalyst (b); TEM images (c) and EDS mappings (d) of 1.0 wt% Au/BYV.
High photocatalytic activity benefits from the rapid charge separation and lower overpotential of products evolution on the surface of photocatalyst. To uncover the influence of Au cocatalyst on the charges separation, PL emission spectra of the samples was measured. As displayed in Fig. 3b, the emission spectra peak is about 469 nm at the excitation wavelength of 360 nm and the PL intensity for the Au supported BYV substantially decreased, implying that the Au loaded BYV have a better ability to separate electron–hole pairs [16]. The 1.0% Au/BYV exhibits the lowest PL intensity, indicates 1.0% Au/BYV has the best performance for charge separation, thus possessing the highest photocatalytic activity. Excess loading makes against the charge separation and result in the decrease of photocatalytic activity. To investigate
76
W. Chen et al. / Materials Letters 238 (2019) 74–76
Fig. 3. CO evolution rates (a) and PL spectra (b) of BYV with different Au loading contents; LSV curves of BYV and 1.0 wt% Au/BYV samples (c) and the corresponding Tafel plots (d) in 0.1 M KHCO3 aqueous solution with saturated CO2.
the overpotential of CO evolution, the linear sweep voltammetry (LSV) was examined in 0.1 M KHCO3 CO2 saturated aqueous solution (Fig. 3c) and the corresponding Tafel plots are shown in Fig. 3d. It can be seen that the overpotentials of BYV, 1.0% Au/BYV are 0.38 V, 0.28 V, respectively. Clearly, compared with pure BYV, the lower overpotential was gained after Au loading, which are vital for in CO evolution. 3. Conclusions In summary, solid solution Bi0.5Y0.5VO4 photocatalysts with Au loading were synthesized through solid state and photodeposition methods and used for photocatalytic CO2 reduction. Au as a cocatalyst remarkably facilitates the electrons migration from bulk BYV to Au, thus inhibiting the recombination of photogenerated charge carries and enhancing the photocatalytic activity of BYV for CO evolution. Also, Au loading can reduce the overpotential of CO evolution and facilitate the occurrence of CO2 reduction reaction toward CO. Acknowledgements This work was supported by the National Natural Science Foundation of China (51602091), the International Cooperation Project of Department of Science and Technology of Henan Province (162102410011) and Natural Science Foundation of Henan Province (182300410205).
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.matlet.2018.11.150. References [1] X. Chang, T. Wang, J. Gong, Energy Environ. Sci. 9 (2016) 2177–2196. [2] V.H. Nguyen, J.C.S. Wu, Appl. Catal. A: Gen. 550 (2018) 122–141. [3] S. Habisreutinger, L. Schmidt-Mende, J. Stolarczyk, Angew. Chem. Int. Ed. 52 (2013) 2–39. [4] K. Li, B. Peng, T. Peng, ACS Catal. 6 (2016) 7485–7527. [5] W. Xiong, W. Dai, X. Hu, L. Yang, T. Wang, Y. Qin, X. Luo, J. Zou, Mater. Lett. 232 (2018) 36–39. [6] J. Zhang, C.M. Dong, Mater. Horiz. 3 (2016) 608–612. [7] C. Dong, C. Lian, S. Hu, Z. Deng, J. Gong, M. Li, H. Liu, M. Xing, J. Zhang, Nat. Commun. 9 (2018) 1252. [8] W. Fang, Z. Jiang, L. Yu, H. Liu, W. Shangguan, C. Terashima, J. Catal. 352 (2017) 155–159. [9] W. Chen, B. Yang, Q. Yu, L. Mao, Z. Fan, Q. Wang, W. Shanggaun, Appl. Surf. Sci. 355 (2015) 1069–1074. [10] S. Sultana, S. Mansingh, M. Scurrell, K. Parida, Inorg. Chem. 56 (2017) 12297– 12307. [11] G. Cernuto, N. Masciocchi, A. Cervellino, G. Colonna, A. Guagliardi, J. Am. Chem. Soc. 133 (2011) 3114–3119. [12] M. Nguyen, T. Yonezawa, Y. Wang, T. Tokunaga, Mat. Lett. 171 (2016) 75–78. [13] Y. Chang, J. Cuo, C. Chen, Mat. Lett. 209 (2017) 60–63. [14] J. Mao, J. Zhou, Z. Xia, Z. Wang, Z. Xu, W. Xu, P. Yan, K. Liu, X. Guo, Z. Zhang, ACS Catal. 7 (2017) 695–705. [15] C. Xiao, H. Hu, X. Zhang, D. MacFarlane, ACS Sustainable Chem. Eng. 5 (2017) 10858–10863. [16] W. Chen, Y. Wang, S. Liu, L. Gao, L. Mao, Z. Fan, W. Shangguan, Z. Jiang, Appl. Surf. Sci. 445 (2018) 527–534.