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Spatial point statistics for quantifying TiO2 distribution in paint

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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.

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Acknowledgments

The authors are grateful to James Pamplin and Jane Trewolla for assistance in preparation and measurement of paints, to Martin Taylor and Gary Sleeman for the SEM images, and to Imerys Minerals Ltd for permission to publish this work.

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Authors and Affiliations

  1. Tregears House, Little Treviscoe, St Austell, Cornwall, PL26 7QL, UK

    N. J. Elton

  2. Imerys Minerals Ltd, Par Moor Laboratories, Par, St Austell, Cornwall, PL24 2SQ, UK

    A. Legrix

Authors
  1. N. J. Elton
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  2. A. Legrix
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Corresponding author

Correspondence to N. J. Elton.

Appendix: Paint formulations

Appendix: Paint formulations

See Table 2.

Table 2 Formulation for Paint A
Full size table

In Tables 3 and 4, TiO2 was Tioxide RTC-90, binder was an acrylic styrene emulsion, and dispersant was sodium polyacrylate. Paint B was made using a pre-dispersed slurry of TiO2. Paints C1 and C3 were made from dry powder TiO2 and C2 obtained as a 50:50 blend of C1 and C3. Additives include co-dispersants, defoamer, thickener, and biocide.

Table 3 Formulation for Paint B
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Table 4 Formulation for Paint C
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Elton, N.J., Legrix, A. Spatial point statistics for quantifying TiO2 distribution in paint. J Coat Technol Res 11, 443–454 (2014). https://doi.org/10.1007/s11998-013-9564-5

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