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### Characterizing the Mechanical Properties of Coatings as Influenced by CPVC and Zero Limit Considerations

#### Abstract

Recently four different theoretical relationships have been discovered between the CPVC and the “Zero Limit” global pigment volume concentration that can be applied to the mechanical properties of coatings. Consequently, the primary mechanical property addressed in this study was tensile strength using a recently published model. Fortunately this new tensile strength model included the “Zero Limit” packing fraction in characterizing the maximum in tensile strength as a function of the volume fraction of pigment and the consequential increase in voids in the composite. An indication of the significance and capabilities of this tensile strength model were addressed in the successful fitting of two sets of tensile strength data. Using this new tensile strength model it was found that the location of the tensile strength maximum can be varied independent of the magnitude of the “Zero Limit” Global Pigment Volume Fraction. This new tensile strength model was also extended using the relationship identified in an earlier publication by Pierce et al (23) who found experimentally a direct relationship between the CPVC, the maximum density of the composite and the maximum tensile strength as a function of the volume concentration of pigment. Using Cluster theory from a previous publication, this study was able to show theoretically that the maximum density of a particulate composite should occur at approximately the same location as the CPVC. Surprisingly it was found that the relationship between the Upper Cluster Zero Limit and the CPVC appeared to give the best fit of Pierce’s tensile strength data. The expectations were that the Lower Zero Limit should have given a better fit to the data since this condition yielded an equal probability between the available void volume and the available matrix volume.