Calculating Size-Dependent Hamaker Constants for Gold, Silver, and Copper Nanoparticles in Aqueous Media

Le Tri Dat; Vinh N.T. Pham; Phong Vo Quoc; Vy Nguyen Duy

doi:10.15625/0868-3166/23866

Author affiliations

Authors

Le Tri Dat Faculty of Physics and Engineering Physics, University of Science, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-4395-3173
Vinh N.T. Pham Department of Theoretical Physics, University of Science, Ho Chi Minh City 70000, Vietnam
Phong Vo Quoc University of Science, Ho Chi Minh City 70000, Vietnam
Vy Nguyen Duy Van Lang University, Ho Chi Minh City, Vietnam https://orcid.org/0000-0001-5470-460X

DOI:

https://doi.org/10.15625/0868-3166/23866

Keywords:

Drude model, Hamaker constant, metallic nanoparticle, interaction

Abstract

This study determines the Hamaker constant for van der Waals interactions between metallic nanoparticles in water, incorporating realistic size-dependent dielectric properties. Using Lifshitz theory, the Hamaker constant is evaluated through Matsubara summation and an integral formulation based on the dielectric function at imaginary frequencies. To obtain ε(iξ), we combine experimental optical data with a modified Drude model whose damping rate varies with nanoparticle radius, ensuring accurate low- and high-frequency behavior. From experimental refractive-index data, plasma frequencies and damping constants for gold, silver, and copper are extracted in the low-energy range. The resulting Hamaker constants without size effects are 220.0 zJ (Au–water–Au), 215.4 zJ (Ag–water–Ag), and 207.2 zJ (Cu–water–Cu). Including size corrections reduces the Hamaker constant for smaller particles due to enhanced electron surface scattering. These results are applied to compute van der Waals energies between spherical nanoparticles, showing strong dependence on particle size and separation distance.

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