Analytical Model for Determination of Size-Distribution of Colloidal Silver Nanoparticles from Surface Plasmon Resonance Wavelength and Dielectric Functions

In this work it is shown that the size of silver nanoparticles in a colloidal solution can be determined only from the wavelength of the surface plasmon resonance and material and medium dielectric functions. The size dependence of dielectric functions of silver nanoparticles becomes noticeable in nanoparticles which are smaller than 30 nm in size, which is in accordance with Mie scattering theory applicability. The novelty of this work is in the development of an analytical model for the determination of the size of silver nanoparticles derived from applying shift functions to the UV-Vis spectra, resulting in well-known characteristic diameters of log-normal size distribution function. The purpose of these shift functions is the reconstruction of experimental UV–Vis spectra from simulated ones based on the Beer–Lambert law and log-normal distribution function in order to find the mode diameters of colloidal silver nanoparticles. The introduction of Lagrangian analogue of extinction cross section explains the redshift constant characteristic for given nanoparticle material and the size distribution of nanoparticles. Therefore, the size determination of colloidal silver nanoparticles is possible only through UV–Vis spectroscopy.