Size Dependences of Hamaker’s Parameter and Free Energy of Van der Waals Interaction for System of Two Spherical Metal Nanoparticles
N. A. Smirnova$^{1}$, A. V. Korotun$^{1}$, I. M. Titov$^{2}$
$^{1}$Zaporizhzhia Polytechnic National University, 64 Zhukovsky Str., UA-69063 Zaporizhzhya, Ukraine
$^{2}$UAD Systems, 84 Olexandrivska Str., UA-69002 Zaporizhzhya, Ukraine
Received: 09.11.2021; final version - 12.03.2022. Download: PDF
Within the framework of the Drude model for the dielectric function and taking into account the bulk and surface mechanisms of relaxation, expressions are obtained for the size dependences of the Hamaker’s parameter and the Van der Waals free energy of the interaction of spherical metal nanoparticles. As shown, that the discrepancy in the ratios obtained has no consequences, since the values of the parameters at which the ‘ultraviolet catastrophe’ takes place correspond to situations that are not of practical interest. Calculations of the Hamaker’s parameter and free energy are made for gold, copper, platinum, and aluminium nanoparticles of different radii located at different distances from each other in the frequency range of practical interest. As established, that the size effects are most pronounced at relatively small distances between metal particles, while with an increase in the distance between them, a significant weakening of the Van der Waals interaction takes place. As shown, that a significant difference in the effective relaxation rate leads to the fact that the Hamaker’s parameter for particles of different metals reaches a maximum at different particle sizes. As found, that for the nanoparticles of the studied metals, the free energy decreases with increasing radius, however, for all metals except gold, this decrease is insignificant, which is explained by the different contribution of surface scattering to the effective relaxation rate. As proved, that the quantitative and qualitative discrepancies between the results of calculations for nanoparticles of various metals are associated with different volumetric concentrations of conduction electrons (different frequencies of volumetric plasmons) and differences in the values of the volumetric relaxation rate.
Key words: Hamaker’s parameter, Van der Waals interaction, metal nanoparticle, size effects, free energy, relaxation rate.
URL: https://mfint.imp.kiev.ua/en/abstract/v44/i05/0587.html
DOI: https://doi.org/10.15407/mfint.44.05.0587
PACS: 34.20.Cf, 68.35.Np, 68.65.-k, 73.20.Qt, 73.50.Bk
Citation: N. A. Smirnova, A. V. Korotun, and I. M. Titov, Size Dependences of Hamaker’s Parameter and Free Energy of Van der Waals Interaction for System of Two Spherical Metal Nanoparticles, Metallofiz. Noveishie Tekhnol., 44, No. 5: 587—599 (2022) (in Ukrainian)