Size-dependent strain and surface energies of gold nanoclusters

Ali, Saif Mohsin; Myasnichenko, V.S.; Neyts, Erik C.

doi:10.1039/c5cp06153a

Cited by 73 publications

(64 citation statements)

References 83 publications

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“…Nanoparticles may even exhibit a quasi-liquid or glassy structure, states having no equivalents in the bulk [14]. Recent calculations of the surface energy of gold as function of the particle size by Ali et al [51] have predicted an increase of the surface energy with decreasing particle size. However, these authors used the coordinates of the surface atoms to calculate the surface of the particle.…”

Section: Reviewmentioning

confidence: 99%

Surface energy of nanoparticles – influence of particle size and structure

Vollath¹,

Fischer²,

Holec³

2018

Beilstein J. Nanotechnol.

172

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The surface energy, particularly for nanoparticles, is one of the most important quantities in understanding the thermodynamics of particles. Therefore, it is astonishing that there is still great uncertainty about its value. The uncertainty increases if one questions its dependence on particle size. Different approaches, such as classical thermodynamics calculations, molecular dynamics simulations, and ab initio calculations, exist to predict this quantity. Generally, considerations based on classical thermodynamics lead to the prediction of decreasing values of the surface energy with decreasing particle size. This phenomenon is caused by the reduced number of next neighbors of surface atoms with decreasing particle size, a phenomenon that is partly compensated by the reduction of the binding energy between the atoms with decreasing particle size. Furthermore, this compensating effect may be expected by the formation of a disordered or quasi-liquid layer at the surface. The atomistic approach, based either on molecular dynamics simulations or ab initio calculations, generally leads to values with an opposite tendency. However, it is shown that this result is based on an insufficient definition of the particle size. A more realistic definition of the particle size is possible only by a detailed analysis of the electronic structure obtained from initio calculations. Except for minor variations caused by changes in the structure, only a minor dependence of the surface energy on the particle size is found. The main conclusion of this work is that surface energy values for the equivalent bulk materials should be used if detailed data for nanoparticles are not available.

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Section: Reviewmentioning

confidence: 99%

Surface energy of nanoparticles – influence of particle size and structure

Vollath¹,

Fischer²,

Holec³

2018

Beilstein J. Nanotechnol.

172

View full text Add to dashboard Cite

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“…These figures have in common the leftmost curve, which is taken as a reference. It corresponds to uncharged NPs with the density of bulk Au V M = 0.01695 nm 3 , 5,7,41 the interfacial free energy γ ∞ = 0.980 J/m 2 as determined from recent MD simulations of Au NPs 45 (equivalent to γ n A n ≈ an 2/3 with a = 1.8765 eV, see Supporting Information), the dodecanethiol binding area A L = 0.1764 nm 2 as determined from experimental data 5,7,10 (see Supporting Information), a binding energy per ligand E n = 1.60 eV estimated from experimental observations (see Supporting Information), and a temperature of 120°C commonly used for DR with boiling solvent or silicon oil baths. 22,41 In other words, the reference curve includes no fitting parameter but only values estimated from recent publications.…”

Section: ■ Theorymentioning

confidence: 99%

Understanding Digestive Ripening of Ligand-Stabilized, Charged Metal Nanoparticles

Manzanares

Peljo

2017

J. Phys. Chem. C

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Most syntheses of thiolate-protected metal nanoparticles (NPs) include a thermochemical step in which the as-prepared, polydisperse NPs are transformed to a narrower size distribution in a poorly understood process known as digestive ripening (DR). Previous theoretical approaches considered either surface and electrostatic contributions or surface and ligand-binding contributions. We show that the three contributions are needed to obtain theoretical predictions in agreement with experimental observations. Although statistical thermodynamics does not clarify mechanistic details, it certainly provides valuable insights on the DR process. Remarkably, a relatively simple theory with no fitting parameters satisfactorily explains the roles of the metal:ligand ratio, the NP charge, the relative permittivity of the solvent, the ripening temperature, the binding energy, and the ligand chain length.

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“…Recently, most of the studies concern under-coordinated atoms [1][2][3][4][5][6][7], in particular those located at the edges and corners of nanoparticles, whose atomic scales is approximately N ¼ 4pK 3 =3 when the diameter K of the particles is in the range from 10 to 1 nm [8][9][10][11][12][13][14]. Indeed, experimental studies have reported an increase in chemical reaction rates with the relative number of these under-coordinated atomic sites [15][16][17].…”

Section: Introductionmentioning

confidence: 96%