Aggregation/agglomeration dependent percolation threshold of spherical nanoparticles in electrically conductive polymer nanocomposites

Abstract This study evaluated the percolation threshold in polymer nanocomposites and its dependence on the aggregation/agglomeration phenomenon. The main objective of the investigation was to propose a particular method that besides revealing the impact of different involved parameters on the percolation threshold could also provide useful information regarding the system characteristics. In line with that, a specific geometrical structure was employed to represent the clusters and assess the variation of the percolation threshold and characteristics of the polymer/particle interphase region. The findings were applied in an improved form of the percolation theory to perform validation against the related experimental data. Improvement was conducted by involving the impact of the newly estimated percolation threshold, aggregations/agglomerations, interphase region, and so forth. Also, specific theories were employed to define the electrical conductivity of the nanoparticle clusters and interphase region. The results showed that the percolation threshold is directly affected by the content of the nanoparticles and the characteristics of the aggregates/agglomerates. Besides, it was revealed that parameters, such as the size of nanoparticles, physical characteristics of the polymer matrix and interphase region, dispersion quality, etc. may substantially affect the percolation threshold and subsequently other physical properties of the system, such as electrical conductivity. Highlights A structural approach toward understanding the percolation phenomenon. Defining the particular dependence of percolation threshold on dispersion quality. Estimating the content of aggregates/agglomerates using percolation theory. Improving the percolation theory to predict the electrical conductivity. Applying the scaling theory to define the electrical conductivity of the interphase.