## Abstract

Efficient simulation methods are presented for determining the standard Gibbs free energy changes for the reactions, M + M _{n-1} ↔ M _{n} (R1), involved in the formation of atomic clusters and nanoparticles (also called particles) in the vapor phase. The standard Gibbs free energy of formation (Δ _{f}G°) of a particle is obtained from these Gibbs free energy changes (ΔG°) by a recursion relationship using the experimental Δ _{f}G° of the monomer. In the present study, this method has been applied to reactions involving Al _{n} particles with n = 2-60. This method has been validated for n = 2, where the experimental thermodynamic properties of Al _{2} have been recompiled using the latest available experimental or highly accurate theoretical data. For n = 2-4, two completely different approaches, a Monte Carlo configuration integral (MCCI) integration of partition functions and a Monte Carlo direct simulation of the equilibrium constants (MCEC), employing four wellvalidated potential energy functions have been used to calculate ΔG° of R1. Excellent agreement is observed for these two methods. Although different potential energy functions give different stage-1 results for n ≤ 10, three high-level correction (HLC) terms, namely, a correction for the potential energy difference of the global minima, another for the electronic excitation contribution, and a third based on calculating isomericrovibrational contribution, have been applied to mitigate deficiencies in the potential energy functions. For n - 2, good agreement has been found between the corrected simulation results and experimental data. For larger n, the more efficient MCEC method has been used. Finally, accurate ΔG° of R1 and thus Δ _{f}G° of A1 _{n} particles with n = 2-60 have been determined. This is the first example of the determination of nanoparticle free energies of formation.

Original language | English (US) |
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Pages (from-to) | 16227-16242 |

Number of pages | 16 |

Journal | Journal of Physical Chemistry C |

Volume | 111 |

Issue number | 44 |

DOIs | |

State | Published - Nov 8 2007 |

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