1. School of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830054, China
2. Key Laboratory for Luminescence Minerals and Optical Functional Materials of Xinjiang, Urumqi 830054, China
Abstract：Noble metal nanoparticles have attracted much attention because of their local surface plasmon resonance properties, among which Au-Ag alloy nanoparticles have widespread investigated for their good structural stability, photothermal properties, and potential anticancer efficacy. The properties in many applications are closely related to particle size and concentration. However, the currently used electron microscopy observation method, and dynamic light scattering method cannot obtain both particle size and concentration information, so it is very important to take effective means to measure particle size and concentration. Based on the spectral extinction method, the inversion problem is solved using a non-negative Tikhonov regularization method and the extinction matrix is calculated using the Mie theory. For the noise problem, two cases are adopted to study the inversion of the particle size distribution and concentration of polydisperse Au-Ag alloy nanospheres. In the case of without noise, the inversion error of particle systems Ⅰ is smaller than that of particle systems Ⅱ, and the inversion error is the smallest in the wavelength range of 300～500 nm, where the inversion errors of the mean particle size, the standard deviation of particle size, and the particle number concentration are 0%, -0.03%, and 0%, respectively. In the case of adding random noise, 0.5% and 1.0% random noises were added to the extinction spectrum of particle systems Ⅰ. The inversion error was the smallest in the wavelength range of 200～600 nm. When 0.5% random noise was added, the ranges of particle size distribution, the standard deviation of particle size, and particle number concentration were 79.76～80.15 nm, 5.60～6.61 nm, and 0.995 8×1010～1.005 9×1010 particle·cm-3, respectively; when 1.0% random noise was added, the ranges of particle size distribution, the standard deviation of particle size, and particle number concentration were 78.87～80.27 nm, 5.36～9.00 nm, and 0.992 4×1010～1.027 7×1010 particle·cm-3, respectively. It was found that with the increase of random noise, the variation range of the inversion result also increased significantly (i. e., the relative error of the inversion increases). The mean particle size, the standard deviation of particle size, and the particle number concentration were averaged after 100 random noise sequences were added. When the random noise increases from 0.5% to 1.0%, the relative errors of the inversion results increase, but the relative errors of the particle size distribution, the standard deviation of particle size, and the particle number concentration are less than 6%. It indicates that the inversion results obtained by the algorithm have good stability. This investigation shows that the spectral extinction method provides a simple and rapid characterization means for the inversion of particle size distribution and concentration of polydisperse Au-Ag alloy nanospheres, and also has enlightenment for the investigation of non-spherical nanoparticles.
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