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  4. Statistical theory of catalytic hydrogen oxidation processes. Basic equations

Statistical theory of catalytic hydrogen oxidation processes. Basic equations

MMC.
2021;
Volume 8, Number 2
: pp. 267–281
https://doi.org/10.23939/mmc2021.02.267
Received: October 16, 2020
Revised: March 03, 2021
Accepted: March 17, 2021

Mathematical Modeling and Computing, Vol. 8, No. 2, pp. 267–281 (2021)

Authors:
  1. P. P. Kostrobij
  2. B. M. Markovych
  3. I. A. Ryzha
  4. M. V. Tokarchuk
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University; Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine

A 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.

reaction-diffusion processes
non-Markov equations
the method of nonequilibrium statistical operator
  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).
  2. Suchorski Yu.,  Datler M.,  Bespalov I.,  Zeininger J.,  St\"{o}ger-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).
  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).
  4. Gao C., Low J., Long R. et al.  Heterogeneous Single-Atom Photocatalysts: Fundamentals and Applications.  Chem. Rev. 120 (21), 12175–12216 (2020).
  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).
  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).
  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).
  8. Michaelides A., Hu P.  Catalytic water formation on platinum: A first-principles study.  J. Am. Chem. Soc. 123 (18), 4235–4242 (2001).
  9. Völkening S., Bedörftig 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).
  10. Sachs C., Hildebrand M., Völkening 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).
  11. Sachs C., Hildebrand M., Völkening 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).
  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).
  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).
  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).
  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).
  16. Suchorski Y., Rupprechter G.  Heterogeneous surfaces as structure and particle size libraries of model catalysts.  Catalysis Letters. 148, 2947–2956 (2018).
  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).
  18. March N. H.  Chemical Bonds Outside Metal Surfaces.  Plenum Press, New York and London (1986).
  19. Smith J. R. (Ed.)  Theory of Chemisorption.  Springer-Verlag, Berlin, Heidelberg, New York (1980).
  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).
  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).
  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).
  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).
  24. Zhdanov V. P.  Surface restructuring kinetic oscillations and chaos in heterogeneous catalytic reactions.  Phys. Rev. E. 59 (6), 6292–6305 (1999).
  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).
  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).
  27. Nekhamkina O., Digilov R., Sheintuch M.  Modeling of temporally complex breathing patterns during Pd-catalyzed CO oxidation.  J. Chem. Phys. 119 (4), 2322–2332 (2003).
  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).
  29. Maximoff S. N., Head-Gordon M. P.  Chemistry of fast electrons.  Proceedings of the National Academy of Sciences. 106 (28), 11460–11465 (2009).
  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).
  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).
  32. Maximoff S. N., Head-Gordon M.  Origin of fast electrons in catalytic hydrogen oxidation over platinum.  arXiv: Materials Science (2014).
  33. Maximoff S. N.  Role of charge transfer in catalytic hydrogen oxidation over platinum.  arXiv preprint arXiv:1407.2570 (2016).
  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).
  35. Zubarev D. N., Morozov V., Röpke G.  Statistical mechanics of nonequilibrium Processes. Vol. 1, Basic Concepts, Kinetic Theory.  Akad. Verl., Berlin (1996).
  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).
  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).
  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, ІСМР-06-25U (2006), (in Ukrainian).
  39. Mryglod I. M.,  Tokarchuk M. V.  Hydrodynamic Theory of a Magnetic Liquid.  Condens. Matter Phys. 3, 116–133 (1994).
  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).
  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).
  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).
  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).
  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).