多分散Au-Ag合金纳米球的光谱消光法反演

贵金属纳米颗粒具有局域表面等离子体共振特性而引起了广泛的关注，其中Au-Ag合金纳米颗粒具有良好的结构稳定性、光热性能以及潜在的抗癌功效而得到普遍研究。在众多应用中的特性与其粒径和浓度密切相关，然而目前常用的电子显微镜观察法和动态光散射法不能同时获得粒径和浓度信息，因此采取有效手段测量颗粒粒径和浓度信息至关重要。基于光谱消光法，利用非负的Tikhonov正则化方法解决反演问题，并根据Mie理论计算消光矩阵。针对噪声问题，采取两种情况研究多分散Au-Ag合金纳米球粒径分布与浓度的反演问题。未添加噪声情况下，颗粒系Ⅰ的反演相对误差小于颗粒系Ⅱ，在波长范围300～500 nm之间的反演相对误差最小，对应平均粒径、粒径标准差和颗粒数浓度的反演相对误差分别为0%，-0.03%和0%。添加随机噪声情况下，将0.5%和1.0%的随机噪声添加进颗粒系Ⅰ中的消光谱，经过数据比较发现在波长范围200～600 nm之间的反演相对误差最小。当添加0.5%的随机噪声时，粒径分布、粒径标准差和颗粒数浓度的变化范围分别为79.76～80.15 nm, 5.60～6.61 nm和0.995 8×1010～1.005 9×1010个·cm-3；当添加1.0%的随机噪声时，粒径分布、粒径标准差和颗粒数浓度的变化范围分别为78.87～80.27 nm, 5.36～9.00 nm和0.992 4×1010～1.027 7×1010个·cm-3。反演结果随着随机噪声的增大，变化范围也明显增大即反演相对误差增大，并且每次添加相同随机噪声后的反演结果不同。为了减少随机噪声导致的不稳定性，对100次反演结果进行平均得到平均粒径、粒径标准差和颗粒数浓度。当随机噪声从0.5%增大至1.0%时，其反演结果的相对误差均增大，但是反演得到的粒径分布、粒径标准差和颗粒数浓度相对误差均小于6%，这说明通过反演算法得到的反演结果具有较好的稳定性。研究表明，光谱消光法为反演多分散Au-Ag合金纳米球粒径分布与浓度提供了一种简单、快速的表征手段，也对研究非球形纳米颗粒有启示作用。

Retrieval of Polydisperse Au-Ag Alloy Nanospheres by Spectral Extinction Method

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.