Modeling the Interface Between Phases in Dense Polymer-Carbon Black Nanoparticle Composites by Dielectric Spectroscopy: Where Are We Now and What are the Opportunities?

The macroscopic properties of polymer nanocomposites (PNC) rely largely on the interphase between the polymer chains and the filler particles. One significant difficulty to solve this issue is to quantitatively model the structure-property correlations due to the interfacial region in these complex materials. While dielectric spectroscopy (DS) measurements are routinely used to characterize the effective permittivity of filled polymers, fitting standard effective medium models and mixing equations to these data remains notoriously difficult to interpret. This is due to the absence of explicit reference to internal length scales characterizing the interfaces in the PNC. As an illustrative example, a two-level homogenization framework is proposed which enables the extraction of useful information on the impact of a thin interphase confined on a nanometer length scale based on broadband DS data. This model leads to new ways of tuning the interphase so as to optimize the material's response to electric field, a situation relevant for electromagnetic shielding. This approach provides guidance on how to observe directly and experimentally the actual properties of the interface between the phases (as opposed to model-based inference). Aside from its secure physical foundation in the theory of effective medium, a significant advantage of this approach is that a genetic algorithm (GA) technique applied to this physics-based model enables the uniqueness of the fit parameters to be considered, as the GA method is robust in terms of finding globally optimum solutions, therefore placing confidence in non-universal values of the percolation exponents. Recent work in physics-informed machine learning indicates that the effective dielectric properties of PNC with many degrees of freedom due to their complex morphology can be described by considering only a few degrees of freedom describing the interface features between the phases in these composites.