Spatial point statistics for quantifying TiO2 distribution in paint

Abstract

Spatial point statistics such as Clark-Evans R, Ripley’s K, and the neighborhood distribution function (NDF) have been used to study the spatial distribution of TiO2 particles in sections of paint films. Particle coordinates were obtained from electron micrographs. Ripley’s K and the NDF are particularly useful in detecting segregation, randomness, or aggregation at various length scales. Other statistics such as aggregate-size distributions were also calculated. The spatial distribution in well-dispersed paints studied here is essentially random and observed aggregates are explained by the spatial inhomogeneity inherent in the random distributions. The aggregate-size distributions are approximately logarithmic for well-dispersed paints. Mean aggregate size increases with increasing pigment volume concentration (15–30%PVC), even though the spatial distribution remains random, showing that crowding at high PVC is a heterogeneous process. Mean aggregate sizes determined by microscopy correlate well with opacity and other paint properties. Computer simulation shows that spatial point and aggregate-size analysis of points in 2-D slices taken from a 3-D volume underestimate absolute aggregate sizes, but that spatial statistics and aggregate distributions correlate strongly with those obtained from the original 3-D distribution. Therefore, results from analysis of micrographs are expected to translate to the 3-D paint film. As expected, coarse extenders crowd the TiO2 and increase aggregation, but highly anisodiametric particles appear less deleterious than blocky particles.