Formulas for converting the intensity-averaged particle diameter and polydispersity obtained from quadratic cumulants (QC) analysis of photon correlation spectroscopy (PCS) data to the number-weighted mean and variance of assumed particle size distribution (PSD) forms are derived. The approach of Thomas 16 for log−normal PSDs is used to derive expressions for normal and Schultz−Zimm particle size distributions (PSDs) assuming Rayleigh scattering. Additionally, expressions for the opposite conversion (from the mean and variance of a number-weighted PSD to an intensity-averaged diameter and polydispersity) are derived for normal PSDs using the Guinier approximation of the Rayleigh−Debye−Gans (RDG) form factor for spheres. Heuristics are developed for correcting the PCS-QC-measured polydispersity Q (known to be strongly affected by experimental and data analysis error) to facilitate the application of the conversion formulas. The conversion formulas and corrective heuristics are then used to re-examine previously published comparisons of PCS and transmission electron microscopy (TEM) average particle size measurements. Additionally, the PSDs generated from PCS-QC results using the conversion formulas are compared with the TEM-measured PSD for a Stöber silica suspension. These comparisons show that, despite the assumption of Rayleigh scattering, the intensity to number-weighting conversion formulas applied using the Q corrective heuristics produce reasonably accurate results outside the limits of Rayleigh scattering theory.
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Hanus et al. (1999) studied this question.
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