Remarkable NanoConfinement Effects on Equilibrated Reactions: Statistical-Mechanics Modeling Focused on Ir Dimerization Beneath Surface Sites in Pd–Ir Nanoparticles
- 120 Downloads
Chemical equilibrium involving a small number of molecules inside a confined nanospace can exhibit considerable deviations from the macroscopic thermodynamic limit due to reduced mixing entropy, as was predicted in several of our works using statistical-mechanics partition-functions and the lattice-gas model (LGM). In particular, significant enhancements of the equilibrium extent and constant are generally anticipated in the case of exothermic reactions. The present work is a substantial extension of this exploration of the so-called “nanoconfinement entropic effect on chemical equilibrium” (NCECE), focusing now on several new issues: (i) general derivation and computations for addition reactions in the non-lattice model (NLM), including endergonic reactions exhibiting significantly weakened NCECE, (ii) comparison with effects predicted for dimerization reactions, for which a novel “inverse NCECE” is obtained for the endergonic range, (iii) a concrete system modeling of Ir dimerization in the core of Pd–Ir cuboctahedral nanoparticles using uniform bond energetics in the LGM versus the NLM. The latter reproduces quite accurately the NCECE effects obtained by the LGM, thus avoiding tedious combinatorial computations, and (iv) Ir dimerization at subsurface sites of the Pd nanoparticles in the framework of the LGM with a more elaborate coordination-dependent bond energetics. It should be noted that the latter subsurface compositional variations can affect catalytic properties of Pd–Ir nanoparticles such as those operating in several applications.
KeywordsPd–Ir catalysts Alloy nanoparticles Sub-surface segregation Nano-confinement Nano-chemical equilibrium Equilibrium constant
We are thankful to Jack Davis for providing DFT data for the Pd and Ir CBEV parametrization.
- 8.Polak M, Rubinovich L (2017) Prediction of enhanced dimerization inside dilute alloy nanoparticles. Int J Nanomater Nanotechnol Nanomed 3(1):023–026Google Scholar
- 9.Hill TL (1994) Thermodynamics of small systems. Dover Publications, New YorkGoogle Scholar
- 10.García-Morales V (2011) Nanothermodynamics. In: Sattler KD (ed) Handbook of nanophysics: principles and methods, vol 1.CRC Press Inc, Boca Raton, FLGoogle Scholar
- 15.Patra S, Pandey AK, Sen D, Ramagiri SV, Bellare JR, Mazumder S, Goswami A (2014) Redox decomposition of silver citrate complex in nanoscale confinement: an unusual mechanism of formation and growth of silver nanoparticles. Langmuir 30(9):2460–2469. https://doi.org/10.1021/la4048787 CrossRefPubMedGoogle Scholar
- 17.Szymanski R, Sosnowski S, Maslanka L (2016) Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A plus B = C in ideally dispersed systems: an apparent violation of the law of mass action. J Chem Phys. https://doi.org/10.1063/1.4944695 CrossRefPubMedGoogle Scholar
- 27.Davis JBA (2014) Private communicationGoogle Scholar
- 30.Zlotea C, Morfin F, Nguyen TS, Nguyen NT, Nelayah J, Ricolleau C, Latroche M, Piccolo L (2014) Nanoalloying bulk-immiscible iridium and palladium inhibits hydride formation and promotes catalytic performances. Nanoscale 6(17):9955–9959. https://doi.org/10.1039/c4nr02836h CrossRefPubMedGoogle Scholar
- 34.Hill TL (1986) An introduction to statistical thermodynamics. Courier Dover Publications, DoverGoogle Scholar
- 40.Stephens IEL, Bondarenko AS, Perez-Alonso FJ, Calle-Vallejo F, Bech L, Johansson TP, Jepsen AK, Frydendal R, Knudsen BP, Rossmeisl J, Chorkendorff I (2011) Tuning the activity of Pt(111) for oxygen electroreduction by subsurface alloying. J Am Chem Soc 133(14):5485–5491. https://doi.org/10.1021/ja111690g CrossRefPubMedGoogle Scholar