Soft magnetic toners: A simple analytic model

Soft magnetic toners, made of magnetic pigments dispersed in a polymer matrix, are modeled. The pigments, roughly spherical in shape, are assumed multidomain and isotropic. The input parameters are the initial intrinsic susceptibility of the pigments, their volume fraction and the particle packing factor of the bulk powder. The analyzis proceeds through 3 steps : (a) microscopic analysis at pigment level, (b) macroscopic analysis at toner particle level, (c) gigascopic analysis at bulk powder level, which usually is the only source of measured data. Demagnetizing fields are taken into account as well as interaction fields which are synthetically modeled to match known limiting cases. A set of analytic formula is derived that, for each of the above levels, relates the apparent initial susceptibility to the input parameters. Applications and experimental verifications are described.