Conversion of intensity-averaged photon correlation spectroscopy measurements to number-averaged particle size distributions. 1. Theoretical development

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 Stober 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.