Plasmonic nanoparticles can be used to engineer radiation decay of a dipole in close proximity to the surface of the particle. We present a theoretical analysis of the quantum yield of an electric dipole near a silver or gold nanoparticle of several different sizes. Specifically, we detail the calculation and simulation of the normalized quantum yield of an electric dipole coupled with a plasmonic nanoparticle. We find that the local electric field near the electric dipole is enhanced and has its characteristics altered.
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.
Epsilon-near-zero (ENZ) metamaterials are designed to exhibit a near-zero response for the real part of the dielectric permittivity at a given frequency or in a specific frequency range. Typically, this frequency range is relatively small. In this paper, we present an approach to broaden this range by controlling the size of the nanoparticles embedded in a thin film. Noble metal nanoparticles exhibit an external size effect that redshifts the Surface Plasmon Resonance frequency with an increase of the size of the particles. The absorption spectrum of a material can be directly related to its dielectric permittivity via the Kramers-Kronig relations. We use the Kramers-Kronig relations to retrieve the complex effective dielectric permittivity of a composite film, which is designed to exhibit ENZ behavior over a broad frequency range. We synthesize a composite thin film embedded with metal nanoparticles of a broad size distribution. Such a material exhibits a broad SPR, and, in turn, broadband ENZ behavior.
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.
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