Conversion of Intensity-Averaged Photon Correlation Spectroscopy Measurements to Number-Averaged Particle Size Distributions. 1. Theoretical Development

• Published in: Langmuir 1999-04, Vol.15 (9), p.3091-3100
• Main Authors: Hanus, Leo H, Ploehn, Harry J
• Format: Article
• Language: English
• Subjects: Chemistry; Colloidal gels. Colloidal sols; Colloidal state and disperse state; Exact sciences and technology; General and physical chemistry
• ISSN: 0743-7463; 1520-5827
• DOI: 10.1021/la980958w

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 Thomas16 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.