Ergodicity and Measurements In Static and Dynamic Light Scattering

arXiv:2508.06427v2 Announce Type: replace Abstract: Static Light Scattering (SLS) and Dynamic Light Scattering (DLS) are very important techniques to study the characteristics of nano-particles in dispersion. The data of SLS is determined by the optical characteristic and the measured values of DLS are determined by optical and hydrodynamic characteristics of different size nano-particles. In general, the nano-particles investigated are considered to be cross-linked soft particles or hyper-branched chains with a three dimensional network structure. Therefore the density of these nano-particles is not homogeneous and the different parts have different optical characteristics. However our experiments reveal that the long time average data of scattered intensity can be perfectly described by homogeneous spherical model. Based on the size distribution obtained using the SLS or TEM technique and the relation between the static and hydrodynamic radii, all the calculated and measured values of $g^{\left( 2\right) }\left( \tau \right) $ investigated are also consistent very well. Since the long time average scattered intensity of non-homogeneous spherical nano-particles can be perfectly described by homogeneous spherical model, the phenomenon of ergodicity happen in our experiments. The results also reveal that the root mean-square radius of gyration $\left\langle R_{g}^{2}\right\rangle ^{1/2}$ obtained using the Zimm plot, Berry plot or Guinier plot is an optical weight size. Due to the different optical average methods of the root mean-square radius of gyration $\left\langle R_{g}^{2}\right\rangle ^{1/2}$ and apparent hydrodynamic radius $R_{app,h}$ and the complex hydrodynamic structures, the dimensionless shape parameter $\rho =\left\langle R_{g}^{2}\right\rangle ^{1/2}/R_{app,h}$ has lost the physical significance to judge the shapes of nano-particles.