Advancement of the Power-Law Model and Its Percolation Exponent for the Electrical Conductivity of a Graphene-Containing System as a Component in the Biosensing of Breast Cancer.

The power-law model for composite conductivity is expanded for graphene-based samples using the effects of interphase, tunnels and net on the effective filler fraction, percolation start and "b" exponent. In fact, filler dimensions, interphase thickness, tunneling distance and net dimension/density express the effective filler fraction, percolation start and "b" exponent. The developed equations are assessed by experimented values from previous works. Additionally, the effects of all parameters on "b" exponent and conductivity are analyzed. The experimented quantities of percolation start and conductivity confirm the predictability of the expressed equations. Thick interphase, large tunneling distance, high aspect ratio and big nets as well as skinny and large graphene nano-sheets produce a low "b" and a high conductivity, because they improve the conduction efficiency of graphene nets in the system. Graphene-filled nanocomposites can be applied in the biosensing of breast cancer cells and thus the developed model can help optimize the performance of biosensors.