Abstract
By molecular dynamics simulations and free energy calculations based on Monte Carlo method, the detailed balance between Pt cluster isomers was investigated. For clusters of n ≤ 50, stationary equilibrium is achieved in 100 ns in the canonical ensemble, while longer time is needed for n > 50. Then, a statistical mechanical model was built to evaluate unimolecular isomerization rate and simplify the prediction of isomer formation probability. This model is simpler than transition state theory and can be easily applied on ab initio calculations to predict the lifetime of nanostructures.
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References
Baletto F, Mottet C, Ferrando R (2000) Reentrant morphology transition in the growth of free silver nanoclusters. Phys Rev Lett 84:5544–5547
Baletto F, Mottet C, Ferrando R (2001) Microscopic mechanisms of the growth of metastable silver icosahedra. Phys Rev B 63:155408
Baletto F, Doye JPK, Ferrando R (2002) Evidence of kinetic trapping in clusters of C60 molecules. Phys Rev Lett 88:075503
Baletto F, Mottet C, Ferrando R (2003) Growth of three-shell onion like bimetallic nanoparticles. Phys Rev Lett 90:135504
Brenner DW (1990) Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys Rev B 42:9458–9471
Bulou H, Scheurer F, Goyhenex C, Speisser V, Romeo M, Carrière B, Moreau N, Repain V, Chacon C, Girard Y, Lagoute J, Rousset S, Otero E, Ohresser P (2013) Thermodynamics versus kinetics in a morphology transition of nanoparticles. Phys Rev B 87:155404
Cleri F, Rosato V (1993) Tight-binding potentials for transition metals and alloys. Phys Rev B 48:22–33
Cui C, Gan L, Heggen M, Rudi S, Strasser P (2013) Compositional segregation in shaped Pt alloy nanoparticles and their structural behaviour during electrocatalysis. Nat Mater 12:765–771
Henkelman G, Uberuaga BP, Jónsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113:9901–9904
Henriksen NE, Hansen FY (2008) Theories of molecular reaction dynamics. Oxford University Press, New York
Mills G, Jónsson H (1994) Quantum and thermal effects in H2 dissociative adsorption: evaluation of free energy barriers in multidimensional quantum systems. Phys Rev Lett 72:1124–1127
Mills G, Jónsson H, Schenter GK (1995) Reversible work transition state theory: application to dissociative adsorption of hydrogen. Surf Sci 324:305–337
Riley ME, Coltrin ME, Diestler DJ (1988) A velocity reset method of simulating thermal motion and damping in gas–solid collisions. J Chem Phys 88:5934–5942
Sebetci A, Güvenc ZB (2003) Energetics and structures of small clusters: Pt N , N = 2–21. Surf Sci 525:66–84
Sebetci A, Güvenc ZB, Kökten H (2006) Thermodynamics of small platinum clusters. Comput Mater Sci 35:192–197
Slanina Z, Zhao X, Uhlík F, Lee S-L, Adamowicz L (2004) Computing enthalpy–entropy interplay for isomeric fullerenes. Int J Quantum Chem 99:640–653
Stamenkovic VR, Mun BS, Arenz M, Mayrhofer KJJ, Lucas CA, Wang G, Ross PN, Markovic M (2007) Trends in electrocatalysis on extended and nanoscale Pt-bimetallic alloy surfaces. Nat Mater 6:241–247
Venables JA (2000) Introduction to surface and thin film processes. Cambridge University Press, New York
Wang C, van der Vliet D, More KL, Zaluzec NJ, Peng S, Sun S, Daimon H, Wang G, Greeley J, Pearson J, Paulikas AP, Karapetrov G, Strmcnik D, Markovic NM, Stamenkovic VR (2010) Multimetallic Au/FePt3 nanoparticles as highly durable electrocatalyst. Nano Lett 11:919–926
Xiao L, Wang L (2004) Structures of platinum clusters: planar or spherical? J Phys Chem A 108:8605–8614
Yin C, Ning X-J, Zhuang J, Xie Y-Q, Gong X-F, Ye X–X, Ming C, Jin Y-F (2009) Shape prediction of two-dimensional adatom islands on crystal surfaces during homoepitaxial growth. Appl Phys Lett 94:183107
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This work was supported by the National Natural Science Foundation of China under Grant No. 11304239, and the Fundamental Research Funds for the Central Universities.
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Lin, ZZ. Theoretical investigation of thermodynamic balance between cluster isomers and statistical model for predicting isomerization rate. J Nanopart Res 16, 2201 (2014). https://doi.org/10.1007/s11051-013-2201-5
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DOI: https://doi.org/10.1007/s11051-013-2201-5