Improved aggregation/agglomeration-dependent percolation theory to predict nanoparticle-aided electrical conductivity in polymer nanocomposites: A combination of analytical strategy and artificial neural network

The formation of aggregates/agglomerates in polymer nanocomposites is known as an inevitable phenomenon that may affect many physical/mechanical properties. Accordingly, in this study, the impacts of the size and content of nanoparticle clusters on the electrical conductivity of polymer matrices containing spherical nanoparticles were analytically evaluated. To this end, the well-known percolation theory was improved by involving major system parameters, affected by aggregation/agglomeration, reported to be indicative of how electricity may conduct through (e. g. tunneling effect, percolation threshold, content and equivalent electrical conductivity of nanoparticle domains, etc.). The characteristics of the aggregates/agglomerates were estimated via the combination of a devised strategy, representing the structure of clusters, and the fundamentals of the percolation theory. The average electrical conductivity and density of polymer/particle interphase, formed around nanoparticle domains were calculated using a particularly developed scaling theory. Also, the hypothetical relative location of nanoparticle domains to each other was defined by calculating the average nearest distance between them, benchmarked against the tunneling distance. A two-stage validation procedure was conducted using the data elicited from the literature in order to first, evaluate the model efficiency and secondly, assess its predictive capabilities with the aid of an artificial neural network (error < 7 %).