Temperature and size-dependent Hamaker constants for metal nanoparticles.

Theoretical values of the Hamaker constant have been calculated for metal nanoparticles using Lifshitz theory. The theory describes the Hamaker constant in terms of the permittivity of the interacting bodies. Metal nanoparticles exhibit an internal size effect that alters the dielectric permittivity of the particle when its size falls below the mean free path of the conducting electrons. This size dependence of the permittivity leads to size-dependence of the Hamaker constant for metal nanoparticles. Additionally, the electron damping and the plasma frequency used to model the permittivity of the particle exhibit temperature-dependence, which lead to temperature dependence of the Hamaker constant. In this work, both the size and temperature dependence for gold, silver, copper, and aluminum nanoparticles is demonstrated. The results of this study might be of interest for studying the colloidal stability of nanoparticles in solution.