Development of the Effective Medium Approximation Applicability Map For Modeling Interface Radiative Properties

Interfacial radiative properties of particulate systems are modeled relying on Effective Medium Approximations (EMAs), which model a heterogeneous system of particles in a host as a homogeneous system. However, EMAs should be handled cautiously, considering their applicability ranges. This study provides a quantitative "safety map" for scientists and engineers, replacing the previous "rule of thumb" that EMAs work as long as particles are smaller than the wavelength. This new map guides the prediction of reliability for applications such as remote sensing, advanced coatings, and atmospheric science. The provided map shows regions where EMA can accurately estimate optical properties of monodisperse, spherical and dielectric particle systems, accounting for the effects of size parameter, volume fraction, and relative refractive index on demarcation. Two distinct approaches are employed for this purpose. The first method is based on the comparison of coherent scattering cross-sections obtained through T-Matrix solutions with the scattering cross-sections of equivalent homogeneous systems estimated with Lorenz-Mie Theory (LMT). In the second method, an effective refractive index is identified by matching the coherent scattering cross-section estimated by the T-Matrix method with the scattering cross-section based on LMT through an inverse analysis. The corresponding reflectance based on the effective refractive index is compared to that based on EMA. It was found that both methods yield consistent results. Two applicability regimes (constant and increasing size parameters) are identified. For small refractive index mismatch, dilute heterogeneous systems can be accurately modeled using the Maxwell Garnett and Bruggeman EMAs when the particle size parameter is below 0.45 which decreases with increasing mismatch. The applicability limit increases beyond a certain volume fraction; however, for large refractive index mismatches it converges and slightly decreases at high volume fractions. The Lewis–Nielsen EMA shows more limited applicability and is mainly valid for dense systems.