Development of a volume fraction scaling function for demagnetization factors in effective media theories of magnetic composites

Three effective medium theories (Maxwell-Garnett, MGT; Bruggeman, BEMT; Coherent Model Approximation, CMA) are often applied to predict dielectric or magnetic susceptibility of polymer-magnetic particle composites. Measured composite susceptibility data for multi-crystalline magnetic particulate aspect ratios near unity and bulk low frequency susceptibilities ranging from 10s to 1000s were used to evaluate EMT model accuracies. Composite volume fractions varied from 5 to 100%. Each theory was evaluated against measured data with emphasis placed on CMA and BEMT. BEMT was selected for incorporation of a scaling function relating demagnetization factors with particulate fraction. The scaled model is ScEMT. Percolation theory and micromagnetic computations were applied as guides in choice of scaling function numerical parameters. Experimental support of scale model physics was taken from measurements of magnetic sphere clustering in two dimensions. Scaling function parameters were determined by a numerical fit to one set of NiZnCuFerrite particle composites. The parameters of the scaling function were held constant and then applied to predict magnetic parameters in others. Those composites incorporated: Fe, Fe-Ni, Ni.34 Zn.65 ferrites; Mn.53 Zn.41 ferrites; NiMn.02 ferrites and Fe3O4. Scaled effective model, ScEMT, and measurement were in good agreement. When combined with Snoek’s law, the combined model improved predictions of resonant frequency in composites and relaxation frequency predictions are in progress. Overall, ScEMT shows improved accuracy for calculating low frequency susceptibility and also composite resonant frequency.