Determination of Translational and Rotational Diffusivities of Anisotropic Nanoparticles by Heterodyne Polarized and Depolarized Dynamic Light Scattering

This work presents the determination
of translational
diffusivities DT and rotational diffusivities DR of gold nanorods and silver nanocubes using
polarized
and depolarized dynamic light scattering. In combination with a heterodyne
detection scheme, the signal-to-noise ratio of the analyzed correlation
functions is significantly improved, which reduces the uncertainties
in the determined mean lifetimes of the fluctuations studied and,
thus, in the diffusivities. The heterodyne detection scheme also simplifies
the data evaluation when homodyne conditions cannot be realized. For
nanorods with aspect ratios ranging from 3.6 to 4.8, DT and DR were determined with
average expanded uncertainties of (6 and 8) %. DT and DR increase with increasing
temperature. In contrast, no concentration dependence of the diffusivities
could be found for particle concentrations close to infinite dilution.
Based on their values and a model in the literature, the length and
width of the nanorods could be determined to be in agreement with
the values from electron microscopy with deviations of (12 and 16)
%. In this work, it was also demonstrated that dynamic light scattering
is applicable for the determination of DT and DR for nanocubes with small anisotropy,
with expanded uncertainties of (1.4 and 12) %. Due to the small anisotropic
contribution to the scattered light, DR could only be obtained by depolarized dynamic light scattering.
The experimental DR values are smaller
than those calculated theoretically by the Stokes–Einstein–Debye
relation, which, however, considers the nanocubes as equivalent spheres.

本研究采用偏振与退偏振动态光散射（dynamic light scattering, DLS）技术，测定了金纳米棒与银纳米立方体的平动扩散系数（translational diffusivities，简称$D_T$）与转动扩散系数（rotational diffusivities，简称$D_R$）。结合外差探测（heterodyne detection scheme）方案，所分析的关联函数的信噪比得到显著提升，有效降低了所研究涨落信号平均寿命的测定不确定度，进而减小了扩散系数的测定误差。当无法实现零差探测（homodyne conditions）条件时，外差探测方案亦可简化数据评估流程。

针对长径比介于3.6至4.8之间的金纳米棒，其平动扩散系数与转动扩散系数的平均扩展不确定度分别为6%与8%。扩散系数随温度升高而增大；与之相反，当粒子浓度趋近无限稀释状态时，未观测到扩散系数表现出浓度依赖性。

基于上述扩散系数数值与现有文献中的理论模型，可推算得到金纳米棒的长度与宽度，其结果与电子显微镜（electron microscopy）观测值吻合良好，相对偏差分别为12%与16%。本研究同时证实，动态光散射技术可用于测定各向异性较弱的银纳米立方体的平动与转动扩散系数，其扩展不确定度分别为1.4%与12%。

由于散射光的各向异性贡献较弱，仅能通过退偏振动态光散射技术获取转动扩散系数。实验测得的转动扩散系数数值小于基于斯托克斯-爱因斯坦-德拜（Stokes–Einstein–Debye）关系式的理论计算值，而该理论模型将纳米立方体等效为均质球体。