Statistical theory of catalytic hydrogen oxidation processes. Basic equations

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dc.citation.epage281
dc.citation.issue2
dc.citation.spage267
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationІнститут фізики конденсованих систем НАН України
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.affiliationInstitute for Condensed Matter Physics of NAS of Ukraine
dc.contributor.authorКостробій, П. П.
dc.contributor.authorМаркович, Б. М.
dc.contributor.authorРижа, І. А.
dc.contributor.authorТокарчук, Михайло Васильович
dc.contributor.authorKostrobij, P. P.
dc.contributor.authorMarkovych, B. M.
dc.contributor.authorRyzha, I. A.
dc.contributor.authorTokarchuk, M. V.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-10-24T07:21:46Z
dc.date.available2023-10-24T07:21:46Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractЗапропоновано статистичний опис процесів каталітичної оксидації водню з врахуванням реакційно-дифузійних процесів для магнітоактивних іонів, атомів адсорбованих на поверхні металу. Отримано основні немарковські рівняння переносу для параметри скороченого опису реакційно-дифузійнійних процесів для магнітоактивних іонів, атомів адсорбованих на поверхні металу у методі нерівноважного статистичного оператора Зубарєва. Розглянуто також слабонерівноважні реакційно-дифузійні процеси
dc.description.abstractA statistical description for the processes of catalytic hydrogen oxidation is proposed taking into account the reaction–diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface. The basic non-Markov transfer equations are obtained for the abbreviated description parameters of reaction-diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface in the method of nonequilibrium statistical Zubarev operator. Weakly nonequilibrium reaction-diffusion processes are also considered.
dc.format.extent267-281
dc.format.pages15
dc.identifier.citationStatistical theory of catalytic hydrogen oxidation processes. Basic equations / P. P. Kostrobij, B. M. Markovych, I. A. Ryzha, M. V. Tokarchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 2. — P. 267–281.
dc.identifier.citationenStatistical theory of catalytic hydrogen oxidation processes. Basic equations / P. P. Kostrobij, B. M. Markovych, I. A. Ryzha, M. V. Tokarchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 2. — P. 267–281.
dc.identifier.doidoi.org/10.23939/mmc2021.02.267
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60382
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 2 (8), 2021
dc.relation.references[1] Yartys V. A., Lototskyy M. V., Akiba E. et al. Magnesium based materials for hydrogen based energy storage: Past, present and future. International Journal of Hydrogen Energy. 44 (15), 7809–7859 (2019).
dc.relation.references[2] Suchorski Yu., Datler M., Bespalov I., Zeininger J., St¨oger-Pollach M., Bernardi J., Gronbech H., Rupprechter G. Surface-Structure Libraries: Multifrequential Oscillations in Catalytic Hydrogen Oxidation on Rhodium. J. Phys. Chem. C. 123 (7), 4217–4227 (2019).
dc.relation.references[3] Cao L., Liu W., Luo Q. et al. Atomically dispersed iron hydroxide anchored on Pt for preferential oxidation of CO in H2. Nature. 565, 631–635 (2019).
dc.relation.references[4] Gao C., Low J., Long R. et al. Heterogeneous Single-Atom Photocatalysts: Fundamentals and Applications. Chem. Rev. 120 (21), 12175–12216 (2020).
dc.relation.references[5] Qiao B., Wang A., Yang X. et al. Single-atom catalysis of CO oxidation using Pt1/FeOx. Nature Chemistry. 3 (8), 634–641 (2011).
dc.relation.references[6] Yakovkin I. N., Chernyi V. I., Naumovetz A. G. Effect of Li on the adsorption of CO and O on Pt. Journal of Physics D: Applied Physics. 32 (7), 841–844 (1999).
dc.relation.references[7] Allian A. D., Takanabe K., Fujdala K. L. et al. Chemisorption of CO and Mechanism of CO Oxidation on Supported Platinum Nanoclusters. J. Am. Chem. Soc. 133 (12), 4498–4517 (2011).
dc.relation.references[8] Michaelides A., Hu P. Catalytic water formation on platinum: A first-principles study. J. Am. Chem. Soc. 123 (18), 4235–4242 (2001).
dc.relation.references[9] V¨olkening S., Bed¨orftig K., Jacobi K., Wintterlin J., Ertl G. Dual-path mechanism for catalytic oxidation of hydrogen on platinum surfaces. Phys. Rev. Lett. 83 (13), 2672–2675 (1999).
dc.relation.references[10] Sachs C., Hildebrand M., V¨olkening S., Wintterlin J., Ertl G. Spatiotemporal self-organization in a surface reaction: From the atomic to the mesoscopic scale. Science. 293 (5535), 1635–1638 (2001).
dc.relation.references[11] Sachs C., Hildebrand M., V¨olkening S., Wintterlin J., Ertl G. Reaction fronts in the oxidation of hydrogen on Pt(111): Scanning tunneling microscopy experiments and reaction-diffusion modeling. J. Chem. Phys. 116, 5759–5773 (2002).
dc.relation.references[12] Mitsui T., Rose M. K., Fomin E., Ogletree D. F., Salmeron M. A scanning tunneling microscopy study of the reaction between hydrogen and oxygen to form water on Pd(111). J. Chem. Phys. 117, 5855–5858 (2002).
dc.relation.references[13] Wilke S., Natoli V., Cohen M. H. Theoretical investigation of water formation on Rh and Pt Surfaces. J. Chem. Phys. 112, 9986–9995 (2000).
dc.relation.references[14] Schaak A., Shaikhutdinov S., Imbihl R. H/D-isotope effects in chemical wave propagation on surfaces: The O2+H2 and NO+H2 reactions on Rh(110) and Rh(111). Surface Science. 421 (1–2), 191–203 (1999).
dc.relation.references[15] Monine M. I., Schaak A., Rubinstein B. Y., Imbihl R., Pismen L. M. Dynamics of subsurface oxygen formation in catalytic water formation on a Rh(1 1 1) surface – Experiment and simulation. Catalysis Today. 70 (4), 321–330 (2001).
dc.relation.references[16] Suchorski Y., Rupprechter G. Heterogeneous surfaces as structure and particle size libraries of model catalysts. Catalysis Letters. 148, 2947–2956 (2018).
dc.relation.references[17] Africh C., Lin H., Corso M., Esch F., Rosei R., Hofer W. A., Comelli G. Water Production Reaction on Rh(110). J. Am. Chem. Soc. 127 (32), 11454–11459 (2005).
dc.relation.references[18] March N. H. Chemical Bonds Outside Metal Surfaces. Plenum Press, New York and London (1986).
dc.relation.references[19] Smith J. R. (Ed.) Theory of Chemisorption. Springer-Verlag, Berlin, Heidelberg, New York (1980).
dc.relation.references[20] Suhl H., Smith J. H., Kumar P. Role of Spin Fluctuations in the Desorption of Hydrogen from Paramagnetic Metals. Phys. Rev. Lett. 25 (20), 1442–1445 (1970).
dc.relation.references[21] Yucel S. Theory of ortho-para conversion in hydrogen adsorbed on metal and paramagnetic surfaces at low temperatures. Phys. Rev. B. 39 (5), 3104–3115 (1989).
dc.relation.references[22] Kato H. S., Okuyama H., Yoshnobu J., Kawai M. Estimation of direct and indirect interactions between CO molecules on Pd(1 1 0). Surface Science. 513 (2), 239–248 (2002).
dc.relation.references[23] Ziff R. M., Gulari E., Barshad Y. Kinetic phase transitions in an irreversible surface reaction model. Phys. Rev. Lett. 56 (24), 2553–2556 (1986).
dc.relation.references[24] Zhdanov V. P. Surface restructuring kinetic oscillations and chaos in heterogeneous catalytic reactions. Phys. Rev. E. 59 (6), 6292–6305 (1999).
dc.relation.references[25] Cisternas J., Keverkidis I., Li X. CO oxidation on thin Pt crystals: Temperature slaving and derivation of lumped models. J. Chem. Phys. 118 (7), 3312–3328 (2003).
dc.relation.references[26] Kostrobii P. P., Tokarchuk M. V., Alekseyev V. I. Time evolution modelling of the surface cover for catalytic synthesis of ammonia. Preprint of the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, ICMP-03-28U (2003), (in Ukrainian).
dc.relation.references[27] Nekhamkina O., Digilov R., Sheintuch M. Modeling of temporally complex breathing patterns during Pdcatalyzed CO oxidation. J. Chem. Phys. 119 (4), 2322–2332 (2003).
dc.relation.references[28] Pavlenko N., Kostrobij P. P., Suchorski Yu., Imbihl R. Alkali metal effect on catalytic CO oxidation on a transition metal surface: a lattice-gas model. Surface Science. 489 (1–3), 29–36 (2001).
dc.relation.references[29] Maximoff S. N., Head-Gordon M. P. Chemistry of fast electrons. Proceedings of the National Academy of Sciences. 106 (28), 11460–11465 (2009).
dc.relation.references[30] Hervier A., Renzas J. R., Park J. Y., Somorjai G. A. Hydrogen oxidation-driven hot electron flow detected by catalytic nanodiodes. Nano letters. 9 (11), 3930–3933 (2009).
dc.relation.references[31] Hervier A. Charge Transfer and Support Effects in Heterogeneous Catalysis. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Chemistry in the Graduate Division of the University of California, Berkeley (2011).
dc.relation.references[32] Maximoff S. N., Head-Gordon M. Origin of fast electrons in catalytic hydrogen oxidation over platinum. arXiv: Materials Science (2014).
dc.relation.references[33] Maximoff S. N. Role of charge transfer in catalytic hydrogen oxidation over platinum. arXiv preprint arXiv:1407.2570 (2016).
dc.relation.references[34] Park J. Y., Baker L. R., Somorjai G. A. Role of hot electrons and metal–oxide interfaces in surface chemistry and catalytic reactions. Chemical reviews. 115 (8), 2781–2817 (2015).
dc.relation.references[35] Zubarev D. N., Morozov V., R¨opke G. Statistical mechanics of nonequilibrium Processes. Vol. 1, Basic Concepts, Kinetic Theory. Akad. Verl., Berlin (1996).
dc.relation.references[36] Kostrobii P. P., Rudavskii Yu. K., Ignatyuk V. V., Tokarchuk M. V. Chemical reactions on adsorbinq surface kinetic level of description. Conden. Matter Phys. 6 (3), 409–423 (2003).
dc.relation.references[37] Rudavskii Yu., Kostrobii P., Tokarchuk M., Batsevych O. Statistical theory of diffusion processes for magnetoactive particles adsorbed on the metal surface. Visnyk Natsionalnoho universytetu “Lvivska politekhnika”. 540, 77–84 (2005), (in Ukrainian).
dc.relation.references[38] Rudavskii Yu. K., Kostrobii P. P., Tokarchuk M. V., Batsevych O. F. Equations of reaction-diffusion processes for magnetoactive particles near the metal surface. Preprint of the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, IСМР-06-25U (2006), (in Ukrainian).
dc.relation.references[39] Mryglod I. M., Tokarchuk M. V. Hydrodynamic Theory of a Magnetic Liquid. Condens. Matter Phys. 3, 116–133 (1994).
dc.relation.references[40] Mryglod I. M., Tokarchuk M. V., Folk R. On the hydrodynamic theory of a magnetic liquid. I. General description. Physica A. 220 (3–4), 325–348 (1995).
dc.relation.references[41] Mryglod I. M., Tokarchuk M. V. Statistical hydrodynamics of magnetic fluids. I. The nonequilibrium statistical operator method. Theoretical and Mathematical Physics. 115, 479–495 (1998).
dc.relation.references[42] Tokarchuk M. V., Kostrobii P. P., Humenyuk Y. A. Generalized transport equations of diffusion-reaction processes. The nonequilibrium statistical operator method. Journal of Physical Studies. 5 (2), 111–120 (2001).
dc.relation.references[43] Kostrobii P. P., Tokarchuk M. V., Humenyuk Y. A. Nonequilibrium statistical operator method: Generalized transport equations of diffusion-reaction processes. Europ. Phys. Journal B – Condensed Matter and Complex Systems. 36 (4), 555–565 (2003).
dc.relation.references[44] Kostrobij P. P., Tokarchuk M. V., Markovych B. M., Ihnatiuk V. V., Hnativ B. V. Reaktsiino–dyfuziini protsesy v systemakh “metal–gaz”. Lviv, Lviv Polytechnic National University (2009), (in Ukrainian).
dc.relation.referencesen[1] Yartys V. A., Lototskyy M. V., Akiba E. et al. Magnesium based materials for hydrogen based energy storage: Past, present and future. International Journal of Hydrogen Energy. 44 (15), 7809–7859 (2019).
dc.relation.referencesen[2] Suchorski Yu., Datler M., Bespalov I., Zeininger J., St¨oger-Pollach M., Bernardi J., Gronbech H., Rupprechter G. Surface-Structure Libraries: Multifrequential Oscillations in Catalytic Hydrogen Oxidation on Rhodium. J. Phys. Chem. P. 123 (7), 4217–4227 (2019).
dc.relation.referencesen[3] Cao L., Liu W., Luo Q. et al. Atomically dispersed iron hydroxide anchored on Pt for preferential oxidation of CO in H2. Nature. 565, 631–635 (2019).
dc.relation.referencesen[4] Gao C., Low J., Long R. et al. Heterogeneous Single-Atom Photocatalysts: Fundamentals and Applications. Chem. Rev. 120 (21), 12175–12216 (2020).
dc.relation.referencesen[5] Qiao B., Wang A., Yang X. et al. Single-atom catalysis of CO oxidation using Pt1/FeOx. Nature Chemistry. 3 (8), 634–641 (2011).
dc.relation.referencesen[6] Yakovkin I. N., Chernyi V. I., Naumovetz A. G. Effect of Li on the adsorption of CO and O on Pt. Journal of Physics D: Applied Physics. 32 (7), 841–844 (1999).
dc.relation.referencesen[7] Allian A. D., Takanabe K., Fujdala K. L. et al. Chemisorption of CO and Mechanism of CO Oxidation on Supported Platinum Nanoclusters. J. Am. Chem. Soc. 133 (12), 4498–4517 (2011).
dc.relation.referencesen[8] Michaelides A., Hu P. Catalytic water formation on platinum: A first-principles study. J. Am. Chem. Soc. 123 (18), 4235–4242 (2001).
dc.relation.referencesen[9] V¨olkening S., Bed¨orftig K., Jacobi K., Wintterlin J., Ertl G. Dual-path mechanism for catalytic oxidation of hydrogen on platinum surfaces. Phys. Rev. Lett. 83 (13), 2672–2675 (1999).
dc.relation.referencesen[10] Sachs C., Hildebrand M., V¨olkening S., Wintterlin J., Ertl G. Spatiotemporal self-organization in a surface reaction: From the atomic to the mesoscopic scale. Science. 293 (5535), 1635–1638 (2001).
dc.relation.referencesen[11] Sachs C., Hildebrand M., V¨olkening S., Wintterlin J., Ertl G. Reaction fronts in the oxidation of hydrogen on Pt(111): Scanning tunneling microscopy experiments and reaction-diffusion modeling. J. Chem. Phys. 116, 5759–5773 (2002).
dc.relation.referencesen[12] Mitsui T., Rose M. K., Fomin E., Ogletree D. F., Salmeron M. A scanning tunneling microscopy study of the reaction between hydrogen and oxygen to form water on Pd(111). J. Chem. Phys. 117, 5855–5858 (2002).
dc.relation.referencesen[13] Wilke S., Natoli V., Cohen M. H. Theoretical investigation of water formation on Rh and Pt Surfaces. J. Chem. Phys. 112, 9986–9995 (2000).
dc.relation.referencesen[14] Schaak A., Shaikhutdinov S., Imbihl R. H/D-isotope effects in chemical wave propagation on surfaces: The O2+H2 and NO+H2 reactions on Rh(110) and Rh(111). Surface Science. 421 (1–2), 191–203 (1999).
dc.relation.referencesen[15] Monine M. I., Schaak A., Rubinstein B. Y., Imbihl R., Pismen L. M. Dynamics of subsurface oxygen formation in catalytic water formation on a Rh(1 1 1) surface – Experiment and simulation. Catalysis Today. 70 (4), 321–330 (2001).
dc.relation.referencesen[16] Suchorski Y., Rupprechter G. Heterogeneous surfaces as structure and particle size libraries of model catalysts. Catalysis Letters. 148, 2947–2956 (2018).
dc.relation.referencesen[17] Africh C., Lin H., Corso M., Esch F., Rosei R., Hofer W. A., Comelli G. Water Production Reaction on Rh(110). J. Am. Chem. Soc. 127 (32), 11454–11459 (2005).
dc.relation.referencesen[18] March N. H. Chemical Bonds Outside Metal Surfaces. Plenum Press, New York and London (1986).
dc.relation.referencesen[19] Smith J. R. (Ed.) Theory of Chemisorption. Springer-Verlag, Berlin, Heidelberg, New York (1980).
dc.relation.referencesen[20] Suhl H., Smith J. H., Kumar P. Role of Spin Fluctuations in the Desorption of Hydrogen from Paramagnetic Metals. Phys. Rev. Lett. 25 (20), 1442–1445 (1970).
dc.relation.referencesen[21] Yucel S. Theory of ortho-para conversion in hydrogen adsorbed on metal and paramagnetic surfaces at low temperatures. Phys. Rev. B. 39 (5), 3104–3115 (1989).
dc.relation.referencesen[22] Kato H. S., Okuyama H., Yoshnobu J., Kawai M. Estimation of direct and indirect interactions between CO molecules on Pd(1 1 0). Surface Science. 513 (2), 239–248 (2002).
dc.relation.referencesen[23] Ziff R. M., Gulari E., Barshad Y. Kinetic phase transitions in an irreversible surface reaction model. Phys. Rev. Lett. 56 (24), 2553–2556 (1986).
dc.relation.referencesen[24] Zhdanov V. P. Surface restructuring kinetic oscillations and chaos in heterogeneous catalytic reactions. Phys. Rev. E. 59 (6), 6292–6305 (1999).
dc.relation.referencesen[25] Cisternas J., Keverkidis I., Li X. CO oxidation on thin Pt crystals: Temperature slaving and derivation of lumped models. J. Chem. Phys. 118 (7), 3312–3328 (2003).
dc.relation.referencesen[26] Kostrobii P. P., Tokarchuk M. V., Alekseyev V. I. Time evolution modelling of the surface cover for catalytic synthesis of ammonia. Preprint of the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, ICMP-03-28U (2003), (in Ukrainian).
dc.relation.referencesen[27] Nekhamkina O., Digilov R., Sheintuch M. Modeling of temporally complex breathing patterns during Pdcatalyzed CO oxidation. J. Chem. Phys. 119 (4), 2322–2332 (2003).
dc.relation.referencesen[28] Pavlenko N., Kostrobij P. P., Suchorski Yu., Imbihl R. Alkali metal effect on catalytic CO oxidation on a transition metal surface: a lattice-gas model. Surface Science. 489 (1–3), 29–36 (2001).
dc.relation.referencesen[29] Maximoff S. N., Head-Gordon M. P. Chemistry of fast electrons. Proceedings of the National Academy of Sciences. 106 (28), 11460–11465 (2009).
dc.relation.referencesen[30] Hervier A., Renzas J. R., Park J. Y., Somorjai G. A. Hydrogen oxidation-driven hot electron flow detected by catalytic nanodiodes. Nano letters. 9 (11), 3930–3933 (2009).
dc.relation.referencesen[31] Hervier A. Charge Transfer and Support Effects in Heterogeneous Catalysis. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Chemistry in the Graduate Division of the University of California, Berkeley (2011).
dc.relation.referencesen[32] Maximoff S. N., Head-Gordon M. Origin of fast electrons in catalytic hydrogen oxidation over platinum. arXiv: Materials Science (2014).
dc.relation.referencesen[33] Maximoff S. N. Role of charge transfer in catalytic hydrogen oxidation over platinum. arXiv preprint arXiv:1407.2570 (2016).
dc.relation.referencesen[34] Park J. Y., Baker L. R., Somorjai G. A. Role of hot electrons and metal–oxide interfaces in surface chemistry and catalytic reactions. Chemical reviews. 115 (8), 2781–2817 (2015).
dc.relation.referencesen[35] Zubarev D. N., Morozov V., R¨opke G. Statistical mechanics of nonequilibrium Processes. Vol. 1, Basic Concepts, Kinetic Theory. Akad. Verl., Berlin (1996).
dc.relation.referencesen[36] Kostrobii P. P., Rudavskii Yu. K., Ignatyuk V. V., Tokarchuk M. V. Chemical reactions on adsorbinq surface kinetic level of description. Conden. Matter Phys. 6 (3), 409–423 (2003).
dc.relation.referencesen[37] Rudavskii Yu., Kostrobii P., Tokarchuk M., Batsevych O. Statistical theory of diffusion processes for magnetoactive particles adsorbed on the metal surface. Visnyk Natsionalnoho universytetu "Lvivska politekhnika". 540, 77–84 (2005), (in Ukrainian).
dc.relation.referencesen[38] Rudavskii Yu. K., Kostrobii P. P., Tokarchuk M. V., Batsevych O. F. Equations of reaction-diffusion processes for magnetoactive particles near the metal surface. Preprint of the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, ISMR-06-25U (2006), (in Ukrainian).
dc.relation.referencesen[39] Mryglod I. M., Tokarchuk M. V. Hydrodynamic Theory of a Magnetic Liquid. Condens. Matter Phys. 3, 116–133 (1994).
dc.relation.referencesen[40] Mryglod I. M., Tokarchuk M. V., Folk R. On the hydrodynamic theory of a magnetic liquid. I. General description. Physica A. 220 (3–4), 325–348 (1995).
dc.relation.referencesen[41] Mryglod I. M., Tokarchuk M. V. Statistical hydrodynamics of magnetic fluids. I. The nonequilibrium statistical operator method. Theoretical and Mathematical Physics. 115, 479–495 (1998).
dc.relation.referencesen[42] Tokarchuk M. V., Kostrobii P. P., Humenyuk Y. A. Generalized transport equations of diffusion-reaction processes. The nonequilibrium statistical operator method. Journal of Physical Studies. 5 (2), 111–120 (2001).
dc.relation.referencesen[43] Kostrobii P. P., Tokarchuk M. V., Humenyuk Y. A. Nonequilibrium statistical operator method: Generalized transport equations of diffusion-reaction processes. Europ. Phys. Journal B – Condensed Matter and Complex Systems. 36 (4), 555–565 (2003).
dc.relation.referencesen[44] Kostrobij P. P., Tokarchuk M. V., Markovych B. M., Ihnatiuk V. V., Hnativ B. V. Reaktsiino–dyfuziini protsesy v systemakh "metal–gaz". Lviv, Lviv Polytechnic National University (2009), (in Ukrainian).
dc.rights.holder© Національний університет “Львівська політехніка”, 2021
dc.subjectреакційно-дифузійні процеси
dc.subjectнемарковські рівняння
dc.subjectметод нерівноважного статистичного оператора
dc.subjectreaction-diffusion processes
dc.subjectnon-Markov equations
dc.subjectthe method of nonequilibrium statistical operator
dc.titleStatistical theory of catalytic hydrogen oxidation processes. Basic equations
dc.title.alternativeСтатистичний підхід до теоретичного опису процесів каталітичної оксидації водню. Основні рівняння
dc.typeArticle

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Mathematical Modeling And Computing. – 2021. – Vol. 8, No. 2