Hamaker-Lifshitz constants 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 free-electron Drude model for metals. For bulk metals, the Drude model does is size independent. However, the conducting electrons in small metal nanoparticles exhibit surface scattering, which changes the complex dielectric permittivity function. Additionally, the Drude model can be modified to include temperature dependence. That is, an increase in temperature leads to thermal volume expansion and increased phonon population, which affect the scattering rate of the electrons and the plasma frequency. Both of these terms contribute significantly to the Drude model for the dielectric permittivity of the particles. In this work, we show theoretically that scattering of the free conducting electrons inside noble metal nanoparticles with the size of 1 – 50 nm leads to size-dependent dielectric permittivity and Hamaker-Lifshitz constants. In addition, we calculate numerically the Hamaker-Lifshitz constants for a variety of temperatures. The results of the study might be of interest for understanding colloidal stability of metal nanoparticles.
P. Pinchuk and A. O. Pinchuk, "Size- and temperature-dependent Hamaker constants for heterogeneous systems of interacting nanoparticles," Proc. SPIE 9923, Physical Chemistry of Interfaces and Nanomaterials XV, 99230X (Presented at SPIE Nanoscience + Engineering: August 30, 2016; Published: 26 September 2016); https://doi.org/10.1117/12.2237062.
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