The effects of density fluctuations in organic coatings

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Abstract
It is usually assumed that the pigment and polymer concentrations are homogeneously distributed in an organic coating. This would imply that voids only appear when the pigment volume concentration (PVC) p exceeds the critical pigment volume concentration (CPVC) pc. However, a great deal of experimental work suggests that voids actually appear even below the CPVC. In this article, we present a phenomenological theory for the effects of density fluctuations on the formation of voids both below and above the CPVC. If the distribution of the local PVC p(x) is Gaussian, then our theory contains two phenomenological parameters: a coarseness parameter Cp which is proportional to the width of the Gaussian distribution, and the diameter d0 of the smallest densely packed cluster of pigment particles. When Cp=0, the homogeneous model of void formation is recovered; but for any nonzero coarseness, voids will appear even below the CPVC. In agreement with earlier work, we find that optical measurements will underestimate pc. While bulk properties like the void density depend only on the coarseness parameter Cp, microscopic properties like the distribution of void diameters dv(x) in the coating also depend on the diameter d0. Above the void percolation threshold pv of an organic coating, chains of voids span the sample. If the coarseness parameter of the Gaussian model is larger than about 0.2, then pv will drop below pc. As in our earlier work, we find that the peak in the mass density overestimates the CPVC. By formulating a simple theory for the Young’s modulus of the coating, we show that the Young’s modulus also peaks above pc for any nonzero Cp, in agreement with recent experiments.