On the nanoparticle interphase

It has been well documented that the addition of nanoparticles, size less than 100 nm, to various polymer matrices leads to desirable properties, including higher permittivity values and increase in the storage modulus. Often these improvements are related to the nanoparticle-matrix interphase, a region with properties different from both the matrix and filler. Due to the large surface-area-to-volume ratio of nanoparticles, the interphase is much more influential in affecting nanocomposite properties compared with properties of composites containing microparticles. In certain nanocomposites, low filler loadings of high-dielectric nanoparticles can lead to an anomalous reduction in permittivity resulting in a dielectric constant lower than that of the matrix. A simple theoretical model to describe this anomalous reduction in permittivity has yet to be formulated. We propose a three-dimensional theoretical model that assumes hard, spherical nanoparticles, surrounded by interphase layers that may overlap, arranged on a simple-cubic lattice. The volume fractions of the individual phases are calculated analytically in distinct geometrical regimes that arise from different filler loadings. Subsequently, the bulk permittivity of the composite is calculated using three-phase Wiener bounds.