A Scaled Effective Medium Theory for Calculation of Resonant and Relaxation Frequency in Magnetic Composites

Ricky Lamar Moore

doi:10.11648/j.ajpa.20210901.13

Abstract

Scaled Effective Medium Theory (ScEMT) is applied to predict magnetic resonant and relaxation frequency in polymer-magnetic particle composites with favorable comparison to measured data. A single scaling function is identified that uses magnetic particulate resonant and relaxation frequencies, or magnetization and anisotropy field, volume fraction and DC susceptibility as predicted by ScEMT. Previous publications demonstrated that ScEMT improved the prediction of DC susceptibility as compared to classical models. Maxwell-Garnett (MGT) and Coherent Model Approximation (CMA) serve as theoretical baselines for comparison. However, both require separate scaling functions in their prediction of resonant and relaxation. Measured data are presented that suggest a single scaling function of ScEMT is sufficient to calculate both parameters. The paper emphasizes the application of the models and shows a wide range of particulate chemistries. ScEMT calculates susceptibility, resonant and relaxation frequency that agree with measurement. The paper concludes by predicting dispersive permeability that represents improvement over both CMA and MGT models. Future studies will address formulation of an EMT model (s) that describe mixtures of hard and soft magnetic materials mixed in a polymer composite. EMT for composite dielectric properties will be expanded to address the chaining. Early results of that effort will be reported in a separate paper.

Highlights

Composites formed as mixtures of magnetic and nonmagnetic materials are applied in a wide range of modern RF technologies
Scaled Effective Medium Theory (ScEMT) is most accurate in the prediction of resonant frequency (Equations 8 and 10) and especially for composites using a pigment with large susceptibility values
Coherent Model Approximation (CMA), MGT and ScEMT with various volumetric scales are used in the relaxation frequency study

Summary

Introduction

Composites formed as mixtures of magnetic and nonmagnetic materials are applied in a wide range of modern RF technologies. Composites with desired electromagnetic frequency dispersive parameters have historically been developed by experimentation using an iterative process of formulation-measurement-formulationmeasurement, etc. This procedure introduces a latency in the design process for identifying optimized material formulations and purely empirical approaches can investigate only a limited parameter space. This lag time and additional effort can be reduced and parameter spaces fully investigated by using accurate predictive models of electromagnetic mixture parameters. MGT and CMA use different power laws in particulate volume fraction and susceptibility, to predict resonance and relaxation. The ScEMT scaling of resonant and relaxation frequency uses a single scaling parameter that predicts both frequency parameters of composite with good accuracy

ScEMT Review

Composite Resonant Frequency and Relaxation Time Constants

Findings

Conclusions and Path Forward