A Theoretical Formula for the Validity Limits of the Dipole Approximation for a Dielectric Mixture

Abstract:

A newly criterion for the validity limits of the dipole approximation for a dielectric mixture was presented, based on the comparison between the dipole approximation and the numerical solutions by the finite-element method (FEM). In terms of this criterion and the dipole-enhanced model, a simple theoretical formula for the validity limits was derived. This formula includes three variables: the dielectric mismatch, the volume fraction of particles and the precision. Its calculated results have a good agreement with the limits determined by the empirical method in the range of our interest, which indicates the theoretical formula is creditable. Using this formula, we can approximate the precision of the dipole approximation for an arbitrary dielectric mixture. And we found that the dipole approximation is acceptable with the precision equal to 30% when the dielectric mismatch is less than 2.3 (ε_i / ε_e 2.3) for the almost touching spheres.

• Periodical: Advanced Materials Research (Volume 906)
• Pages: 72-80
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.906.72
• Online since: April 2014
• Authors: Chang He Yang*, Ding Long Cao, Lin Song Guo
• Keywords: Dielectric Mixture, Dipole Approximation, Dipole-Enhanced Model, Finite Element Method (FEM), Validity Limits

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