Pore-Induced Inhomogeneous Interfaces Influencing Dielectric Properties in Low- <i>k</i> Polymer Aerogels

Pore structure plays a pivotal role in regulating the dielectric properties of materials, emerging as a critical strategy for designing microwave communication materials and electronic devices. However, quantifying the pore structure-dielectric property relationship in porous media remains inadequately explored. Herein, a series of low-<i>k</i> polymer phenolic aerogels (PAs) with precisely regulated porosities are employed as a model system to explicitly reveal the dielectric regulation mechanism of pore structure. As porosity decreases from 86 to 22%, the dielectric constant of PAs exhibits a nonlinear rapid increase from 1.3 to 2.5, while dielectric loss (tanδ) rises proportionally from 0.008 to 0.032. It is disclosed that the pore-induced inhomogeneous interfaces, which exhibit a continuous transition from a dense core to a loose shell, could contribute to a lower value of dielectric constant than that of the matrix phase. Accordingly, a three-phase dielectric constant prediction formula that integrates the interfacial phase, bulk polymer, and air is developed. The dielectric constant and the thickness of the interfacial phase are determined according to finite-element simulations. In addition, we identify the interfacial layer-induced interfacial polarization is the dominant loss mechanism in the porous aerogels, and the dielectric loss shows linear scaling with specific surface area and an inverse power-law dependence on particle size. With a particle size below 60 nm, the interface's influence on dielectric properties grows more pronounced. These findings provided a systematic theoretical basis for the inverse design of dielectric properties in porous low-<i>k</i> porous media.