Li, Zhen Hua and Bhatt, Divesh and Schultz, Nathan E. and Siepmann, J. Ilja and Truhlar, Donald G. (2007) *Free energies of formation of metal clusters and nanoparticles from molecular simulations: Al-n with n=2-60.* JOURNAL OF PHYSICAL CHEMISTRY C, 111 (44). pp. 16227-16242.

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Official URL: http://pubs.acs.org/doi/abs/10.1021/jp073559v

## Abstract

Efficient simulation methods are presented for determining the standard Gibbs free energy changes for the reactions, M + Mn-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 (Delta(f)G degrees) of a particle is obtained from these Gibbs free energy changes (Delta G degrees) by a recursion relationship using the experimental Delta(f)G degrees 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 well-validated potential energy functions have been used to calculate Delta G degrees 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 isomeric-rovibrational 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 Delta G degrees of R1 and thus Delta(f)G degrees of Al-n particles with n = 2-60 have been determined. This is the first example of the determination of nanoparticle free energies of formation.

Item Type: | Article |
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Subjects: | Material Science > Nanochemistry |

ID Code: | 3547 |

Deposited By: | Farnush Anwar |

Deposited On: | 16 Jan 2009 14:33 |

Last Modified: | 16 Jan 2009 14:33 |

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