Discussing the Relationship between the Static and Dynamic Light Scattering

Both the static $(SLS)$ and dynamic $(DLS)$ light scattering techniques are used to obtain the size information from the scattered intensity, but the static radius $R_{s}$ and the apparent hydrodynamic radius $R_{h,app}$ are different. In this paper, the relationship between SLS and DLS is discussed using dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) microgels, with a simple assumption that the hydrodynamic radius $R_{h}$ is in proportion to the static radius $R_{s}$, when Rayleigh-Gans-Debye approximation is valid. With the assistance of the simulated data, the apparent hydrodynamic radius $R_{h,app}$ has been discussed. The results show that the apparent hydrodynamic radius is different with the mean hydrodynamic radius of particles and is a composite size obtained from averaging the term $\exp (-q^{2}D\tau)$ in the static size distribution $G(R_{s})$ with the weight $R_{s}^{6}P(q,R_{s})$.