Determination of hydrodynamic diameter of small flocs by means of direct movie analysis of Brownian motion

Direct movie analysis of the Brownian motion of single colloidal particles under optical microscope was carried out to determine hydrodynamic diameter. Mean squared displacements of individual particle against time interval of observation were obtained from the trace of Brownian motion. The hydrodynamic diameter is obtained via diffusion coefficient determined on the basis of Einstein relation. The validity of the applied method was statistically confirmed by the comparison of predicted relative error with those obtained from the measurement using uniform polystyrene latex particles of three different diameters. Determination of hydrodynamic diameters with coefficients of variation (CV) less than 6% was achieved when processing 501 frames. Achieved coefficients of variation correspond to those statistically predicted for the Brownian motion. Obtained diameter of doublet was consisted with those reported by other researchers. In the case of flocs composed with primary particle more than three, the value of CV slightly increases up to 7.3%. This increment can be ascribed to deviation of center of mass determined from projected image from true value. However, within this accuracy the hydrodynamic diameters of coagulated flocs being composed of up to six primary particles were determined. The determined hydrodynamic diameters were found to be significantly smaller than the maximum distances in the projection indicating different power law relation against the number of composing particles in flocs.