Retrieval Of Size Distribution And Concentration Of Au-Ag Alloy Nanospheres And Nanospheroids Based On Spectral Extinction Method

Au-Ag alloy nanoparticles have been widely used in the fields of medicine,materials,environment,and energy due to their special localized surface plasmon resonance properties.The optical properties of Au-Ag alloy nanoparticles are closely related to the manipulation of localized surface plasmon resonance,which is strongly dependent on particle size and concentration.Thus,it is very important to effectively regulate the particle size and concentration of Au-Ag alloy nanoparticles,which will determine the properties and applications of alloy nanoparticles.In this paper,the particle size distribution and concentration of Au-Ag alloy nanoparticles(nanospheres and nanospheroids)were inverted based on the spectral extinction method with Mie theory,Tmatrix,and non-negative Tikhonov regularization.Variation of extinction properties of monodisperse Au-Ag alloy nanospheres with particle size and wavelength were analyzed based on Mie theory.The results show that there is correspondence between the resonance wavelength of the extinction spectrum and the particle size in the visible spectral range.Therefore,resonance wavelength method,dual-wavelength extinction method,and improved dual-wavelength extinction method were proposed to invert the particle size and concentration.It was found that if the extinction spectrum of the particles is measured,the particle size and concentration can be retrieved by using the fitting equations.The particle size distribution and concentration of the polydisperse Au-Ag alloy nanospheres were further determined by using the spectral extinction method,and the inversion problem was solved by the non-negative Tikhonov regularization method.Two cases were taken to discuss the inversion results.Without adding random noise to the extinction spectrum,the effects of wavelength range,mean particle size,and standard deviation of particle size on the inversion results were quantitatively investigated.In the case of adding random noise to the extinction spectrum,when the random noise increases from 0.5% to 1.0%,the relative errors of the inversion results are all less than 6%,which indicates that the inversion results obtained by the inversion algorithm have good stability.Based on the spectral extinction method,extending from Au-Ag alloy nanospheres to Au-Ag alloy nanospheroids,the two-dimensional particle size distribution(aspect ratio distribution and length distribution)and concentration of Au-Ag alloy nanospheroids can be inverted simultaneously by using the T-matrix method and non-negative Tikhonov regularization method.The database of extinction cross section was established to improve the timeliness of the inversion algorithm.The effects of two-dimensional particle size steps and wavelength range on the inversion results were quantitatively analyzed,and the relative errors of aspect ratio,length,and extinction spectrum obtained from the inversion are all less than 1%.In order to verify the feasibility and accuracy of the inversion algorithm,the measurement error in the experiment was finally considered.After adding 0.1% random noise to the extinction spectrum,the inversion error of the standard deviation of particle size becomes larger,but within an acceptable range.The use of the spectral extinction method provides an attractive alternative method for microscopic imaging analysis.