Abstract
The conventional theory of organic coatings assumes that the volume density of pigment particles is uniform throughout the sample. The coating is then described in terms of the pigment volume concentration Π, which equals the volume of pigment divided by the volume of pigment and polymer. Voids form in the coating when the pigment particles are randomly dense-packed, which implies that Π exceeds the critical pigment volume concentration (Φc or that Λ=Π/Φc > 1. Due to fluctuations in the local density of pigment however, some regions in the coating may become randomly dense-packed even below Φc. Hence, voids may form in the densely-packed islands even when Λ<1. Our model for void formation contains two fitting parameters: No is the smallest number of pigment particles in a densely-packed cluster that may contain a void; Cq is the coarseness of the polymer space-filling in the volume of the sample not occupied by pigment. When Cq=0 and Π > 1, the polymer completely fills the interstitial volume and the void concentration vanishes. But when Cq > 0, voids may form in the densely-packed regions of the coating even below Φc. The coarseness parameter Cq, depends on the sample preparation, on the properties of the pigment and polymer, and on the pigment volume concentration Π. For any nonzero Cq we conclude that optical measurements will systematically underestimate Φc. On the other hand, since the density of polymer is less than half the density of pigment, the peak in the mass density p(Π) of the coating will overestimate Φc. Unless Cq is abnormally large, the void percolation threshold value Φv is larger than Φc and is a decreasing function of the coarseness Cq. The predictions of this simple model are in good agreement with experiment, and are relevant to the general class of random concentrated composites which include organic coatings, ceramic polymer slips, composite solid polymer electrodes and some forms of battery separators.
Original language | English |
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Pages (from-to) | 387-403 |
Number of pages | 17 |
Journal | Progress in Organic Coatings |
Volume | 21 |
Issue number | 4 |
DOIs | |
State | Published - Mar 15 1993 |
Externally published | Yes |
Funding
administered by ASEND in North Dakota and from the donors of the Petrolem Research Fund, administered by the American Chemical Society. One of the authors (RSF) would like to acknowledge support from the EPSCOR (Experimental Program to Stimulate Cooperative Research) program,
Funders | Funder number |
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Petrolem Research Fund | |
Russell Sage Foundation | |
American Chemical Society | |
Office of Experimental Program to Stimulate Competitive Research |