A theoretical treatment of graphene nanocomposites with percolation threshold, tunneling-assisted conductivity and microcapacitor effect in AC and DC electrical settings

Small quantities of graphene fillers in the polymeric matrix allow us to obtain a novel class of lightweight nanocomposites with outstanding electrical properties. The availability of appropriate simulation models taking into account the morphological and physical features of such an interesting material is very important for design and optimizations of high performance devices and systems. In this study, a continuum model is developed to determine the effective AC and DC electrical properties of graphene nanocomposites. The proposed theory consists of three major components, embodying the most fundamental characteristics of the graphene nanocomposites, i.e. percolation threshold, interface effects, and additional contribution of electron hoping and microcapacitor structures to interfacial properties. (i) The development starts from the effective medium theory for a nanocomposite with perfect interface, in which the corresponding formula is expressed in terms of complex conductivity moduli for the dielectric constituent phases. (ii) For the study of interface effects, we further introduce a diminishing layer of interphase with interfacial conductivity and permittivity, to form a thinly coated graphene inclusion that is subsequently embedded in the matrix. (iii) In the last step, a phenomenological model is developed to represent the electron tunneling activity and formation of microcapacitors in the context of our continuum theory. In this way, these phenomena are taken as two statistical processes that depend on the volume concentration of graphene fillers, and can be well described by Cauchy's probability function. The outcome of proposed methodology is a widely useful model that involves only limited number of input parameters. The validity and applicability of developed model is verified through consideration of several experimental data for real nanocomposites. It is demonstrated that the proposed model can successfully capture the quantitative behavior of various data sets in AC and DC electrical settings.