Different Particle Sizes Obtained from Static and Dynamic Laser Light Scattering

Detailed investigation of static and dynamic laser light scattering has been attempted in this work both theoretically and experimentally based on dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) microgels. When Rayleigh-Gans-Debye approximation is valid, a new radius $R_{s}$, referred to as a static radius, can be obtained from the static light scattering $(SLS)$. If the absolute magnitude of the scattered intensity and some constants that are related to the instrument and samples are known, the average molar mass for large particles can be measured. The size information obtained from SLS is purely related to the optical properties of particles, i.e., to $R_{s}$ and its distribution $G(R_{s})$. The size information obtained from dynamic light scattering $(DLS)$ is more complicated, the size distribution of which is a composite distribution that is not only related to the optical properties of particles, but also related to the hydrodynamic properties and the scattering vector. Strictly speaking, an apparent hydrodynamic radius $R_{h,app}$ 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 $R_{s}^{6}P(q,R_{s})$ that is also a function of both $R_{s}$ and the scattering vector $q$.