Theoretical Development Of a Graphical Analysis Technique To Optimize the Particle Size Distribution Of Pigments in Paints and Coatings

By Richard D. Sudduth

The new analytical expression introduced in this study shows that a plot of the accumulated volume fraction of pigment particles vs. the square root of particle size should be a straight line for the theoretically preferred particle size distribution. This linear theoretical model was also found to be consistent with the experimentally developed linear model proposed by Kaeuffer.

However, Kaeuffer proposed that his straight line went through the origin, but the analytical model developed in this paper has shown that this intercept is not zero. Thus, Kaeuffer’s experimental model is only partially correct. Starting with this new linear model for the theoretically preferred particle size distribution, another simplified analytical expression was also derived to calculate the xth moment average particle size, Dx.

The desired xth moment average particle size was found to depend primarily on the physical property to be predicted. Finally, the simplified calculation of the various D_x particle size averages for this same square root particle size distribution should be useful in predicting the maximum packing fraction, maximum impact, and/or the minimum viscosity for pig-ments in most paint and coating applications.