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5 article(s) from Vollath, Dieter

Criteria ruling particle agglomeration

Dieter Vollath

Beilstein J. Nanotechnol. 2021, 12, 1093–1100, doi:10.3762/bjnano.12.81

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Figure 1: Flow chart of the algorithm to calculate the agglomeration of an ensemble in the direction of a max...

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Figure 2: Plot of the distribution function after 4.7 × 10⁶ collisions of a starting ensemble consisting of 10...

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Figure 3: Number of particles as function of the particle volume and the number of collisions. This simulatio...

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Figure 4: Entropy S* as function of the number of collisions. For this example, the starting ensemble consist...

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Figure 5: Distribution function of particle sizes according to Kätelhön and co-workers [18]. Figure 5a displays the result...

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Figure 6: Entropy and enthalpy of agglomerated ensembles as function of the number of collisions. This simula...

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Figure 7: Comparison of the different possible contributions to the free enthalpy as function of the number o...

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Full Research Paper

Published 29 Sep 2021

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Agglomerates of nanoparticles

Dieter Vollath

Beilstein J. Nanotechnol. 2020, 11, 854–857, doi:10.3762/bjnano.11.70

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Figure 1: Course of the probability for different sizes of agglomerates. The calculations were performed for ...

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Figure 2: Reduced entropy S/k as a function of the number of particles in an ensemble. The linear dependency ...

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Figure 3: Number of particles in the largest agglomerate as a function of the particle number in the ensemble....

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Letter

Published 02 Jun 2020

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Energy distribution in an ensemble of nanoparticles and its consequences

Dieter Vollath

Beilstein J. Nanotechnol. 2019, 10, 1452–1457, doi:10.3762/bjnano.10.143

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Figure 1: Free enthalpy for a 2 nm gold particle in solid and liquid phase. Additionally, this graph shows th...

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Figure 2: Probability for the transformation of (a) 2 nm and (b) 5 nm diameter gold particles in the vicinity...

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Figure 3: Experimental data for the magnetic noise power of cobalt measured at a frequency of 100 Hz accordin...

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Figure 4: Size distribution of cobalt particles, determined from the transition to superparamagnetic state [5]. ...

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Figure 5: The transformation temperature in lead from normal to superconducting as a function of the particle...

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Figure 6: Real part of the magnetic susceptibility χ’ of lead as function of the temperature in the vicinity ...

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Figure 7: Particle size distribution of lead particles calculated by evaluation of the magnetic susceptibilit...

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Full Research Paper

Published 19 Jul 2019

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Surface energy of nanoparticles – influence of particle size and structure

Dieter Vollath,
Franz Dieter Fischer and
David Holec

Beilstein J. Nanotechnol. 2018, 9, 2265–2276, doi:10.3762/bjnano.9.211

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Figure 1: Melting temperature of gold nanoparticles according to Castro et al. [11] and Cluskey et al. [13]. One real...

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Figure 2: Visualization of the setting for the estimation the number of next neighbors (coordination number) ...

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Figure 3: Relative coordination number q of an atom at the surface of a spherical particle as function of the...

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Figure 4: Graph of Equation 6. Also in this case, a lower limit for the particle diameter exists (α = β = 1).

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Figure 5: Surface energy for gold nanoparticles as function of the particle diameter according to Gang et al. ...

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Figure 6: Landau’s order parameter M for tin particles of different particle diameters as function of the rad...

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Figure 7: Difference of the surface energy between the solid and the liquid state at the melting temperature ...

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Figure 8: Radial profiles of the density for a fcc metal cluster consisting of 3302 atoms versus the particle...

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Figure 9: Thickness of the liquid and the quasi-liquid transition layer close to the surface of a 18 nm gold ...

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Figure 10: Translational order parameter for gold particles of different particle diameter as function of the ...

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Figure 11: Melting temperature of lead according to Coombes [16]. This figure shows two ranges of melting temperat...

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Figure 12: Surface energy of gold as function of the particle size according to Ali et al. [51]. The graphs show t...

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Figure 13: Results of molecular dynamic calculations of the surface energy of gold [54]. (a) All the results, wher...

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Figure 14: High-resolution electron micrograph of a zirconia, ZrO₂, and an alumina, Al₂O₃ nanoparticles. (a) A...

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Figure 15: Surface energy of the three modifications of titania at a temperature of 300 K as function of the p...

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Figure 16: Surface energy of silver particles as function of the particle diameter [49]. This graph shows the orig...

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Figure 17: Surface energy of aluminum particles as function of the particle diameter [58]. This graph shows both t...

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Figure 18: Binding energy of the atoms in the outmost layer of an Au₅₅ cluster [14]. Additionally, for each coordi...

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Review

Published 23 Aug 2018

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Au₅₅, a stable glassy cluster: results of ab initio calculations

Dieter Vollath,
David Holec and
Franz Dieter Fischer

Beilstein J. Nanotechnol. 2017, 8, 2221–2229, doi:10.3762/bjnano.8.222

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Figure 1: Histograms of the coordination numbers for the two starting configurations crystalline and random. ...

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Figure 2: Radial distribution function of gold atoms in the amorphous cluster determined by averaging the num...

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Figure 3: Energy release during relaxation of a random ensemble forming a cluster as function of the relaxati...

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Figure 4: Development of the maximum and the average coordination number of the originally crystalline cluste...

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Figure 5: Total energy of the originally crystalline Au₅₅ cluster as a function of the temperature, relative ...

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Figure 6: Energy necessary to remove one atom from an Au₅₅ cluster, which is equivalent to the enthalpy of su...

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Figure 7: Surface area per Au₅₅ cluster in the glassy phase as a function of the “cut-off” charge density.

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Figure 8: Dependency of the radius of the glassy Au₅₅ cluster on the “cut-off” charge density. The calculated...

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Full Research Paper

Published 25 Oct 2017

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Criteria ruling particle agglomeration

Agglomerates of nanoparticles

Energy distribution in an ensemble of nanoparticles and its consequences

Surface energy of nanoparticles – influence of particle size and structure

Au55, a stable glassy cluster: results of ab initio calculations

Au₅₅, a stable glassy cluster: results of ab initio calculations