Modeling cluster voids and pigment distribution to predict properties and CPVC in coatings. Part I: dry coating analysis
Authors: Sudduth R.D. 
Published: November 2008

PurposeThe primary objective of this two part study was to show theoretically how pigment cluster voids and pigment distribution can influence the critical pigment volume concentration (CPVC) and consequently the properties of a dry coating. In Part I of this study a pigment clustering model with an analytical solution has been developed that was a modification of an earlier model by Fishman, Kurtze, and Bierwagen that could only be solved numerically.Design/methodology/approachThe original derivation of the clustering concept developed by Fishman et al. resulted in a mathematical analysis which was only able to be solved numerically and was found to be very tedious to utilize directly. In this study, a new successful derivation utilizing some of the original concepts of Fishman et al. was generated and shown to result in a practical and much more useable analytical analysis of the clustering concept. This new model was then applied directly to quantify the influence of flow agents or surfactants in a coating formulation on the CPVC as described by Asbeck.FindingsIt was found that the largest deviation from 100 per cent pigment dispersion with no pigment clusters occurred just before and just after the ultimate CPVC (UCPVC). A theoretical relationship was also found between the pigment cluster dispersion coefficient, Cq, and CPVC. This result was consistent with the experimental relationship between CPVC and the per cent flow additive as found by Asbeck. The density ratio of overall coating to the pigment density was found to go through a maximum at a global volume fraction of pigment that was slightly greater than the UCPVC as expected for a mechanical property. It was also identified that mechanical failure of most coating formulations should be apparent at either the “Lower Zero Limit” or the “Upper Zero Limit” global volume fraction pigment as defined in this study.Research limitations/implicationsWhile the experimental measurement of the parameters to isolate the clustering concepts introduced in this study may be difficult, it is expected that better quantitative measurement of clustering concepts will eventually prove to be very beneficial to providing improved suspension applications including coatings.Practical implicationsThe theoretical relationship developed in this study between the pigment cluster dispersion coefficient, Cq, and CPVC and the experimental relationship between CPVC and the per cent flow additive found by Asbeck inferred a direct relationship between Cq and the per cent flow additive. Consequently, it was shown that the theoretical pigment cluster model developed in this study could be directly related to the experimental matrix additive composition in a coating formulation. The implication is that the measurement tool introduced in this study can provide better measurement and control of clustering in coatings and other suspension applications.Originality/valueIn this study, a new successful derivation utilizing some of the original concepts of Fishman et al. was generated and shown to result in a practical and much more useable analytical analysis of the clustering concept. This new model was then applied directly to quantify the influence of flow agents or surfactants in a coating formulation on the CPVC as described by Asbeck.