Detection of small polydispersities by photon correlation spectroscopy

Abstract

We consider dilute suspensions of homogeneous polydisperse spherical particles for which the Rayleigh–Gans–Debye (RGD) approximation is valid. For two model particle size distributions we calculate the dependence on scattering vector Q of the average scattered intensity I(Q) and the effective diffusion coefficient De(Q) obtained from the first cumulant measured by photon-correlation spectroscopy. If the mean particle radius R̄ is large enough (≳170 nm) that the intensity form factor P(QR̄) shows at least one minimum in the accessible range of Q, we find that De(Q) exhibits a characteristic variation with Q which is very sensitive to the sample polydispersity. Under favorable conditions it should be possible to measure polydispersities (standard deviation/mean size) as small as 0.01. These theoretical considerations are supported, at least qualitatively, by experiment. We also discuss briefly the effect of relaxing the RGD approximation and the implications of this work for the more common PCS probes of polydispersity such as Laplace transformation of the light scattering correlation function.