The Quantitative Measurement of Pigment Dispersion by Fractal and Other Methods

Lacunarity analysis is a method for describing fractal patterns with spatial or textural variations. This method has also been applied to nonfractal and multifractal patterns such as texture, roughness, and porosity. In this paper, an approach is presented for quantitatively describing the nature of particle dispersion in toner by analysis of digitized photomicrographs with fractal dimension and lacunarity analysis. Image analysis of computer synthesized dispersion profiles varying in such properties as mean agglomerate size, agglomerate size distribution, loading, and spatial homogeneity is presented. We find that agglomerate size can be measured by changes in the fractal dimension as determined by modified Richardson plots obtained by a box counting method. Additionally, we find that the spread in the agglomerate size distribution and the spatial homogeneity of the dispersion are correlated with lacunarity as measured by the sliding box algorithm.