Tinting strength of carbon black

Abstract

The tinting strength of carbon black (i.e., its efficiency in decreasing reflectance when mixed with a white pigment) is of practical importance in the paint industry and is also used in quality control of carbon black manufactured for use in rubber. The relative tinting strength of a carbon black is proportional to its specific absorbance, which we calculate by Mie theory from the refractive index of carbon black and the size of the independent structural units; namely, the fused aggregates, which as a first approximation are treated as solid spheres containing the same volume of carbon. This volume depends primarily on the particle size, and to a lesser but significant extent on the “structure” or number of particles per aggregate, which is calculated from the vehicle absorption at the critical pigment volume concentration. The refractive index of carbon black is estimated from various published data as m = 1.84 (1− 0.46 i). The Mie calculations show that the tinting strength is virtually independent of solid-sphere size below a certain value (approximately at a size parameter of α = 0.7); at larger sizes, the tinting strength diminishes gradually, and eventually becomes nearly proportional to 1/α. The calculated behavior is in good agreement with experimental findings. Calculations of the wavelength dependence of tinting strength show that carbon blacks of small solid-sphere size are of brownish tint “tone,” while those of large size are bluish, in agreement with experimental data. The effect of aggregate size distribution is discussed.