In this work, the depth of the interphase in graphene polymer systems is determined by the properties of graphene and interfacial parameters. Furthermore, the actual volume fraction and percolation onset of the nanosheets are characterized by the actual inverse aspect ratio, interphase depth, and tunneling distance. In addition, the dimensions of graphene, along with interfacial/interphase properties and tunneling characteristics, are utilized to develop the power-law equation for the conductivity of graphene-filled composites. Using the derived equations, the interphase depth, percolation onset, and nanocomposite conductivity are graphed against various ranges of the aforementioned factors. Moreover, numerous experimental data points for percolation onset and conductivity are presented to validate the equations. The optimal levels for interphase depth, percolation onset, and conductivity are achieved through high interfacial conductivity and large graphene nanosheets. In addition, increased nanocomposite conductivity can be attained with thinner nanosheets, a larger tunneling distance, and a thicker interphase. The calculations highlight the considerable impacts of interfacial/interphase factors and tunneling distance on the percolation onset. The highest nanocomposite conductivity of 0.008 S/m is acquired by the highest interfacial conduction of 900 S/m and graphene length (D) of 5 μm, while an insulated sample is observed at D < 1.2 μm. Therefore, higher interfacial conduction and larger nanosheets cause the higher nanocomposite conductivity, but the short nanosheets cannot promote the conductivity.

Advanced modeling of conductivity in graphene–polymer nanocomposites: insights into interface and tunneling characteristics
    Abstract
    1 Introduction
    2 Development of equations
    3 Results and discussion
        3.1 Interphase deepness
        3.2 Percolation inception
        3.3 Conductivity
        3.4 Analysis of equations by tested results
    4 Conclusions
    Acknowledgements 
    References

• Yasser Zare(Biomaterials and Tissue Engineering Research Group, Department of Interdisciplinary Technologies, Breast Cancer Research Center, Motamed Cancer Institute, ACECR, Tehran, Iran)
• Muhammad Tajammal Munir(College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)
• Kyong Yop Rhee(Department of Mechanical Engineering (BK21 Four), College of Engineering, Kyung Hee University, Yongin, Republic of Korea)
• Soo‑Jin Park(Department of Chemistry, Inha University, Incheon 22212, Republic of Korea)