Physics-based Computational Method Predicting the Dielectric Properties of Polymer Nanocomposites

The dielectric properties of polymer nanocomposites (PNCs) are crucial in designing electronic packaging, energy storage capacitors, electromagnetic shielding, and biomedical sensors and actuators. The conventional mixing rules-based methods such as the Kerner model, Maxwell–Garnett (MG) model, Maxwell–Wagner-Sillars (MWS) model, Bruggeman model solely rely on the volume fraction (vol%), which is often inadequate to predict the frequency dependency of the effective permittivity of the PNCs, they also do not account for the sizes of the inclusions. A computational model was developed to estimate the dielectric permittivity and the dielectric loss of PNCs using COMSOL multi-physics. Experimental data from previously published references confirmed the validity of the finite element analysis (FEA) based model. Next, the COMSOL model was utilized to quantitatively analyze the complex dielectric constant as a function of the applied frequency, the dielectric properties of the inclusion and the polymer matrix, and the volume fraction of the inclusion. The study was conducted with a polymer matrix of polymethylmethacrylate (PMMA) and five nanoparticles including semiconductor material silicon (Si), inorganic zinc-sulfide (ZnS), metal gold (Au), metal-oxide titanium oxide (TiO 2 ), and dielectric fillers BaTiO 3 (BT). The results show that the frequency-dependent dielectric relaxation behavior, the MWS interfacial polarization, significantly influences the dielectric properties. A 10 vol% inclusion of Si, ZnS, and BT resulted in MWS frequency of 103, 1584, 10 5 Hz. The charge barrier is most substantial in low frequency as it restricts electric field propagation around the inclusion. However, at a significantly high frequency, the charge barrier breaks, lowering the dielectric constant of the composite. In addition to that, a unique behavior was observed in high conductive fillers PNCs (e.g., Au) as the permittivity showed a fillers size dependence even with the same volume fraction. At frequency nearing 10 5 Hz, the Au-PMMA composite showed a higher permittivity with smaller nanoparticles inclusion. This is a significant finding contrary to the existing understandings based on the conventional mixing rules (e.g., MWS, MG, Bruggeman, Kerner model), which does not account for the size of inclusions. The present study has important implications for device engineers and materials manufacturers to choose appropriate materials with desired properties for optoelectronic packaging applications.