Size-dependent Hamaker constants for silver and gold nanoparticles

Hamaker-Lifshitz constants are material specific constants that are used to calculate van der Waals interaction forces between small particles in solution. Typically, these constants are size-independent and material specific. According to the Lifshitz theory, the Hamaker-Lifshitz constants can be calculated by taking integrals that include the dielectric permittivity, as a function of frequency, of the interacting particles and the medium around particles. The dielectric permittivity of interacting metal nanoparticles can be calculated using the Drude model, which is based on the assumption of motion of free conducting electrons. For bulk metals, the Drude model does not predict any sizedependence of the dielectric permittivity. However, the conducting electrons in small noble metal nanoparticles (R ~ 10nm) exhibit surface scattering, which changes the complex permittivity function. In this work, we show theoretically that scattering of the free conducting electrons inside silver and gold nanoparticles with the size of 1 – 50 nm leads to size-dependent dielectric permittivity and Hamaker-Lifshitz constants. We calculate numerically the Hamaker-Lifshitz constants for silver and gold nanoparticles with different diameters. The results of the study might be of interests for understanding colloidal stability of metal nanoparticles.