Skip to main content

Advertisement

SpringerLink
Log in

Catalytic Thermodynamics of Nanocluster Adsorbates from Informational Statistical Mechanics

  • Published:
Catalysis Letters Aims and scope Submit manuscript

Abstract

This letter presents a new approach for studying the catalytic thermodynamics of cuboctahedral nanoclusters, using informational statistical mechanics. The Morse potential determines bond energies between cluster atoms in a coordination type calculation. Applied density functional theory calculations demonstrate adatom effects on the thermodynamic quantities, which are derived from a Hamiltonian. Calculations of the entropy, free energy, and total energy show linear behavior, as the coverage of oxygen on platinum, and hydrogen on palladium, increases from bridge sites on the surface. The data exhibits size effects for the measured thermodynamic properties with cluster diameters between 2 and 5 nm. Entropy and enthalpy calculations of Pt–O2 compare well with previous theoretical data for Pt(111)–O2, and trends for Pd–H are similar to experimental measurements on Pd–H2 nanoclusters. These techniques are applicable to a wide variety of cluster–adsorbate interactions, encouraging further research.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Maruyama K, Nori F, Vedral V (2009) Rev Mod Phys 81:1–23

    Article  Google Scholar 

  2. Berut A, Arakelyan A, Petrosyan A et al (2012) Nature 483:187–189

    Article  CAS  Google Scholar 

  3. Toyabe S, Shoichi S, Takahiro U et al (2010) Nat Phys 6:988–992

    Article  CAS  Google Scholar 

  4. Koski J, Maisi V, Sagawa T, Pekola JP (2014) Phys Rev Lett 113:030601

    Article  CAS  Google Scholar 

  5. Parrondo JMR, Horowitz JM, Sagawa T (2015) Nat Phys 11(2):131–139

    Article  CAS  Google Scholar 

  6. Goold J, Huber M, Riera A, Rio L, Skrzypczyk P (2016) J Phys A 49(14):143001

    Article  Google Scholar 

  7. Horodecki M, Oppenheim J (2013) Nat Commun 4:2059

    Article  Google Scholar 

  8. Shannon CE (1948) Bell Syst Tech J 27:379–423

    Article  Google Scholar 

  9. Jaynes ET (1957) Phys Rev 106(4):620–630

    Article  Google Scholar 

  10. Jaynes ET (1957) Phys Rev 108(2):171–190

    Article  Google Scholar 

  11. Estrada E, Hatano N (2007) Chem Phys Lett 439:247–251

    Article  CAS  Google Scholar 

  12. Morse PM (1929) Phys Rev 34:57–64

    Article  CAS  Google Scholar 

  13. Girifalco LA, Weizer VG (1959) Phys Rev 114(3):687–690

    Article  CAS  Google Scholar 

  14. Bassett DW, Webber PR (1978) Surf Sci 70:520–531

    Article  CAS  Google Scholar 

  15. Rogan J, Varas A, Valdivia JA, Kiwi M (2013) J Comput Chem 34:2548–2556

    Article  CAS  Google Scholar 

  16. Parodi D, Ferrando R (2007) Phys Lett A 367:215–219

    Article  CAS  Google Scholar 

  17. Calvo F, Yurtsever E (2013) Comput Theor Chem 1021:7–15

    Article  CAS  Google Scholar 

  18. Wen Z, Zhu YF, Jiang Q (2014) Mater Chem Phys 145:51–55

    Article  CAS  Google Scholar 

  19. Johnson RA (1973) J Phys F 3:295–321

    Article  CAS  Google Scholar 

  20. Kang Y, Pyo JB, Ye X, Diaz RE, Gordon TR, Stach EA, Murray CB (2013) ACS Nano 7(1):645–653

    Article  CAS  Google Scholar 

  21. Syrenova S, Wadell C, Nugroho FAA et al (2015) Nat Mater 14(12):1236–1244

    Article  CAS  Google Scholar 

  22. Manchester FD, San-Martin A, Pitre JM (1994) J Phase Equilib 15:62–83

    Article  CAS  Google Scholar 

  23. Behm RJ, Christmann K, Ertl G (1980) Surf Sci 99:320–340

    Article  CAS  Google Scholar 

  24. Conrad H, Ertl G, Latta EE (1974) Surf Sci 41:435–446

    Article  Google Scholar 

  25. Wilke S, Hennig D, Lober R, Methfessel M, Scheffler M (1994) Surf Sci 307–309:76–81

    Article  Google Scholar 

  26. Paul JF, Sautet P (1996) Phys Rev B 53:8015–8027

    Article  CAS  Google Scholar 

  27. Niu W, Zhang L, Xu G (2010) ACS Nano 4(4):1987–1996

    Article  CAS  Google Scholar 

  28. Larsson EM, Langhammer C, Zoric I, Kasemo B (2009) Science 326:1091–1094

    Article  CAS  Google Scholar 

  29. Mikheykin AS, Dmitriev VP, Chagovets SV, Kuriganova AB, Smirnova NV, Leontyev IN (2012) Appl Phys Lett 101:173111

    Article  Google Scholar 

  30. Kittel C (2005) Introduction to solid state physics, 8th edn. Wiley, Hoboken, NJ

    Google Scholar 

  31. Martienssen W, Warlimont H (2005) Springer handbook of condensed matter and materials data. Springer, Berlin

    Book  Google Scholar 

  32. Jiang Q, Lu HM (2008) Surf Sci Rep 63:427–454

    Article  CAS  Google Scholar 

  33. Shandiz MA (2008) J Phys 20:325237

    Google Scholar 

  34. Roduner E (2006) Chem Soc Rev 35:583–592

    Article  CAS  Google Scholar 

  35. Shustorovich E (1984) J Am Chem Soc, 106:6479–6481

    Article  CAS  Google Scholar 

  36. Wettergren K, Hellman A, Calvalca F, Zhdanov VP, Langhammer C (2015) Nano Lett 15:574–580

    Article  CAS  Google Scholar 

  37. Calle-Vallejo F, Martinez JI, Garcia-Lastra JM, Sautet P, Loffreda D (2014) Angew Chem Int Ed 53:8316–8319

    Article  CAS  Google Scholar 

  38. Calle-Vallejo F, Tymoczko J, Colic V, Vu QH, Pohl MD, Morganstern K, Loffreda D, Sautet P, Schuhmann W, Bandarenka AS (2015) Science 350:185–189

    Article  CAS  Google Scholar 

  39. Weinberg WH (1973) J Vac Sci Technol 10(1):89–94

    Article  CAS  Google Scholar 

  40. Han J, Hu W, Deng H (2009) Surf Interface Anal 41:590–594

    Article  CAS  Google Scholar 

  41. Lu HM, Jiang Q (2004) J Phys Chem B 108:5617–5619

    Article  CAS  Google Scholar 

  42. Gland JL (1980) Surf Sci 93:487–514

    Article  CAS  Google Scholar 

  43. Li L, Larsen AH, Romero NA et al (2013) J Phys Chem Lett 4:222–226

    Article  CAS  Google Scholar 

  44. Sohrab SH (2014) Int J Mech 8:73–84

    Google Scholar 

  45. Langhammer C, Larsson EM, Kasemo B, Zoric I (2010) Nano Lett 10:3529–3538

    Article  CAS  Google Scholar 

  46. Li Y, Qi W, Huang B, Wang M (2012) J Phys Chem C 116:26013–26018

    Article  CAS  Google Scholar 

  47. Vayssilov GN, Lykhach Y, Migani A et al (2011) Nat Mater 10:310–315

    Article  CAS  Google Scholar 

  48. Jaeger NI, Jourdan AL, Schulz-Ekloff G (1991) J Chem Soc Faraday Trans 87(8):1251–1257

    Article  CAS  Google Scholar 

  49. Kneringer G, Netzer FP (1975) Surf Sci 49:125–142

    Article  CAS  Google Scholar 

  50. Ono LK, Yuan B, Heinrich H, Cuenya BR (2010) J Phys Chem C 114:22119–22133

    Article  CAS  Google Scholar 

  51. Ono LK, Croy JR, Heinrich H, Cuenya BR (2011) J Phys Chem C 115:16856–16866

    Article  CAS  Google Scholar 

  52. Pursell CJ, Hartshorn H, Ward T, Chandler BD, Boccuzzi F (2011) J Phys Chem C 115:23880–23892

    Article  CAS  Google Scholar 

  53. Pursell CJ, Chandler BD, Manzoli M, Boccuzzi F (2012) J Phys Chem C 116:11117–11125

    Article  CAS  Google Scholar 

  54. Karp EM, Campbell CT, Studt F, Abild-Pederson F, Norskov JK (2012) J Phys Chem C 116:25772–25776

    Article  CAS  Google Scholar 

  55. Wadell C, Pingel T, Olsson E et al (2014) Chem Phys Lett 603:75–81

    Article  CAS  Google Scholar 

  56. Sachs C, Pundt A, Kirchheim R et al (2001) Phys Rev B 64:075408

    Article  Google Scholar 

  57. Wadell C (2015) Ph.D. Thesis, Chalmers University Technology, Sweden

  58. Bardhan R, Hedges LO, Pint CL et al (2013) Nat Mater 12:905–912

    Article  CAS  Google Scholar 

  59. Lasser R, Klatt KH (1983) Phys Rev B 28:748–758

    Article  Google Scholar 

  60. Bockris JO’M, Abdu R (1998) J Electoanal Chem 448:189–204

    Article  CAS  Google Scholar 

  61. Fiorin V, Borthwick D, King DA (2009) Surf Sci 603:1360–1364

    Article  CAS  Google Scholar 

  62. Griessen R, Strohfeldt N, Giessen H (2016) Nat Mater 15:311–317

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We made use of the MATLAB file, Cluster Generator, which can be found in Mathworks File Exchange Central. We thank G.L. Gürtler and E.I. Altman for reviewing the manuscript.

Author information

Authors and Affiliations

  1. Mesalands Community College, 911 South 10th Street, Tucumcari, NM, 88401, USA

    Forrest H. Kaatz

  2. Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Heverlee, Belgium

    Adhemar Bultheel

Authors
  1. Forrest H. Kaatz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adhemar Bultheel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Forrest H. Kaatz.

Ethics declarations

Conflict of interest

Both authors, F.H. Kaatz and A. Bultheel, declare that there is no conflict of interest, financial or otherwise.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaatz, F.H., Bultheel, A. Catalytic Thermodynamics of Nanocluster Adsorbates from Informational Statistical Mechanics. Catal Lett 148, 1451–1461 (2018). https://doi.org/10.1007/s10562-018-2338-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10562-018-2338-z

Keywords

Search

Navigation