Estimation of the Kubelka—Munk scattering coefficient from single particle scattering parameters

Computer colour matching of paints is based on the determination of the Kubelka—Munk absorption (K) and scattering coefficients (S) of pigments. K and S are sensitive to particle size in the range of sizes employed in paint technology. The K—M theory does not provide any guidelines for the correction of the values of K and S with a change in particle size. On the other hand the Mie theory linear scattering coefficient can be calculated from a knowledge of size and refractive index of the pigment. A number of relations correlating the K—M scattering coefficient and the linear scattering coefficient have been proposed in the literature. Attempts are made to estimate the K—M scattering coefficient using a relation suggested by Mudgett and Richards and to make a comparison with experimental values. The Mie theory equations being complex, simplified equations applicable to pigment sizes for the calculation of Mie theory parameters are proposed. The viability of the simplified equations has been established by comparing the results with those obtained using the full Mie equations.The K—M scattering coefficient for titanium dioxide pigments has been determined from reflectance measurements. The particle size of titanium dioxide has been determined by a light scattering method. The K—M scattering coefficient calculated from the linear scattering coefficient obtained using the simplified expressions agrees with experimental results. This suggests a method for the correction of the values of K and S with changes in pigment particle size.