Dimensionless unified modelling of macroscale electric properties of conductive fibre networks in different regimes

The electric properties of conductive fibre networks, which can be representative of carbon nanotube networks, are investigated by means of numerical simulations and a dimensionless unified macroscale model is developed. Fibres are represented as rigid chains of discrete element method particles and we compress systems of fibres in a representative volume element periodic in three dimensions. In the used electric resistor network method, the particles are used as discretisation points to construct a system of linear equations linking the particle conductivities to their local electric potentials and in turn allowing for predictions on the electric macroscale properties of the fibre system. A carried out dimensional analysis suggests suitable scaling laws to unify different macroscale fibre systems in two different regimes - a percolating and a conductive regime. The dimensionless macroscale conductance is found to depend on the percolation threshold and percolation probability. It is moreover found that the critical solid volume fraction for rigid fibres is not only dependent on the fibre aspect ratio, but can also depend on the compression height of the system. Additionally, correlations between transmittance and solid volume fractions are found allowing for possibly simple solid volume fraction estimations in experiments.